# Tables of Sextics Containing a Cubic Subfield

## Cases where S contains one prime

 S S4×C2 A4×C2 S4- S4+ A4 D6 S3 C6 Total {2} 0 {3} 1 1 2 txt gp {5} 0 {7} 1 1 txt gp {11} 0 {13} 1 1 txt gp {17} 0 {19} 1 1 txt gp {23} 1 1 txt gp {29} 0 {31} 1 1 2 txt gp {37} 1 1 txt gp {41} 0 {43} 1 1 txt gp {47} 0 {53} 0 {59} 1 1 1 3 txt gp {61} 1 1 txt gp {67} 1 1 txt gp {71} 0 {73} 1 1 txt gp {79} 1 1 txt gp {83} 1 1 txt gp {89} 0 {97} 1 1 txt gp {101} 0 {103} 1 1 txt gp {107} 1 1 1 3 txt gp {109} 1 1 txt gp {113} 0 {127} 1 1 txt gp {131} 0 {137} 0 {139} 1 1 1 1 4 txt gp {149} 0 {151} 1 1 txt gp {157} 1 1 txt gp {163} 1 1 1 3 txt gp {167} 0 {173} 0 {179} 0 {181} 1 1 txt gp {191} 0 {193} 1 1 txt gp {197} 0 {199} 1 1 2 txt gp {211} 1 1 2 txt gp {223} 1 1 txt gp {227} 0 {229} 3 3 1 1 8 txt gp

## Cases where S contains two primes

 S S4×C2 A4×C2 S4- S4+ A4 D6 S3 C6 Total {2,3} 132 7 22 22 1 48 8 7 247 txt gp {2,5} 18 3 3 6 1 31 txt gp {3,5} 2 1 1 10 5 3 22 txt gp {2,7} 7 1 7 15 txt gp {3,7} 2 1 1 10 5 12 31 txt gp {5,7} 2 1 3 6 txt gp {2,11} 36 6 6 12 2 62 txt gp {3,11} 6 3 3 12 6 3 33 txt gp {5,11} 0 {7,11} 3 3 txt gp {2,13} 60 7 10 10 1 12 2 7 109 txt gp {3,13} 2 1 1 16 8 12 40 txt gp {5,13} 3 1 3 7 txt gp {7,13} 3 1 12 16 txt gp {11,13} 2 1 1 2 1 3 10 txt gp {2,17} 0 {3,17} 4 3 2 2 1 10 5 3 30 txt gp {5,17} 0 {7,17} 2 1 3 6 txt gp {11,17} 2 1 1 4 2 10 txt gp {13,17} 3 3 txt gp {2,19} 78 7 13 13 1 18 3 7 140 txt gp {3,19} 4 3 2 2 1 10 5 12 39 txt gp {5,19} 3 3 txt gp {7,19} 3 1 2 1 12 19 txt gp {11,19} 3 1 3 7 txt gp {13,19} 2 1 1 2 1 12 19 txt gp {17,19} 3 3 txt gp {2,23} 54 9 9 18 3 93 txt gp {3,23} 6 3 3 12 6 3 33 txt gp {5,23} 2 1 1 2 1 7 txt gp {7,23} 2 1 1 2 1 3 10 txt gp {11,23} 2 1 1 2 1 7 txt gp {13,23} 2 1 3 6 txt gp {17,23} 2 1 1 2 1 7 txt gp {19,23} 2 1 1 2 1 3 10 txt gp {2,29} 102 17 17 18 3 157 txt gp {3,29} 8 4 4 12 6 3 37 txt gp {5,29} 0 {7,29} 3 1 3 7 txt gp {11,29} 2 1 1 2 1 7 txt gp {13,29} 3 3 txt gp {17,29} 0 {19,29} 2 1 1 2 1 3 10 txt gp {23,29} 2 1 3 txt gp {2,31} 18 35 3 3 5 6 1 7 78 txt gp {3,31} 4 2 2 12 6 12 38 txt gp {5,31} 2 1 3 6 txt gp {7,31} 2 1 12 15 txt gp {11,31} 4 2 2 4 2 3 17 txt gp {13,31} 2 3 1 1 1 2 1 12 23 txt gp {17,31} 4 2 2 4 2 3 17 txt gp {19,31} 3 1 2 1 12 19 txt gp {23,31} 2 3 1 1 1 4 2 3 17 txt gp {29,31} 2 3 1 1 1 2 1 3 14 txt gp {2,37} 60 7 10 10 1 12 2 7 109 txt gp {3,37} 2 3 1 1 1 16 8 12 44 txt gp {5,37} 3 3 txt gp {7,37} 2 1 12 15 txt gp {11,37} 3 1 2 1 3 10 txt gp {13,37} 12 12 txt gp {17,37} 3 3 txt gp {19,37} 6 2 12 20 txt gp {23,37} 2 3 1 1 1 2 1 3 14 txt gp {29,37} 3 1 3 7 txt gp {31,37} 8 6 4 4 2 4 2 12 42 txt gp {2,41} 0 {3,41} 10 5 5 10 5 3 38 txt gp {5,41} 0 {7,41} 3 1 2 1 3 10 txt gp {11,41} 6 3 3 4 2 18 txt gp {13,41} 2 1 1 2 1 3 10 txt gp {17,41} 8 4 4 4 2 22 txt gp {19,41} 6 3 3 2 1 3 18 txt gp {23,41} 2 1 3 txt gp {29,41} 2 1 1 2 1 7 txt gp {31,41} 2 1 3 6 txt gp {37,41} 3 3 txt gp {2,43} 36 35 6 6 5 12 2 7 109 txt gp {3,43} 6 3 3 10 5 12 39 txt gp {5,43} 2 1 1 2 1 3 10 txt gp {7,43} 3 1 2 1 12 19 txt gp {11,43} 6 3 3 3 1 2 1 3 22 txt gp {13,43} 2 1 1 2 1 12 19 txt gp {17,43} 6 3 3 2 1 3 18 txt gp {19,43} 2 1 12 15 txt gp {23,43} 2 1 1 2 1 3 10 txt gp {29,43} 2 1 3 6 txt gp {31,43} 2 3 1 1 1 4 2 12 26 txt gp {37,43} 3 1 12 16 txt gp {41,43} 2 3 1 1 1 2 1 3 14 txt gp {2,47} 36 6 6 12 2 62 txt gp {3,47} 10 5 5 12 6 3 41 txt gp {5,47} 6 3 3 4 2 18 txt gp {7,47} 2 1 1 4 2 3 13 txt gp {11,47} 2 1 3 txt gp {13,47} 3 1 3 7 txt gp {17,47} 0 {19,47} 3 3 txt gp {23,47} 4 2 6 txt gp {29,47} 4 2 2 4 2 14 txt gp {31,47} 6 3 3 3 1 2 1 3 22 txt gp {37,47} 3 1 2 1 3 10 txt gp {41,47} 2 1 1 4 2 10 txt gp {43,47} 6 3 3 3 1 2 1 3 22 txt gp {2,53} 126 21 21 18 3 189 txt gp {3,53} 2 3 1 1 1 10 5 3 26 txt gp {5,53} 0 {7,53} 6 3 3 2 1 3 18 txt gp {11,53} 0 {13,53} 3 1 3 7 txt gp {17,53} 0 {19,53} 2 1 1 4 2 3 13 txt gp {23,53} 10 5 5 6 3 29 txt gp {29,53} 0 {31,53} 2 1 1 8 4 3 19 txt gp {37,53} 3 3 txt gp {41,53} 0 {43,53} 6 3 3 2 1 3 18 txt gp {47,53} 2 1 1 2 1 7 txt gp {2,59} 144 24 24 24 4 220 txt gp {3,59} 4 2 2 12 6 3 29 txt gp {5,59} 2 1 1 2 1 7 txt gp {7,59} 4 2 2 10 5 3 26 txt gp {11,59} 2 1 1 2 1 7 txt gp {13,59} 2 1 1 2 1 3 10 txt gp {17,59} 6 3 3 2 1 15 txt gp {19,59} 4 2 2 4 2 3 17 txt gp {23,59} 8 4 4 4 2 22 txt gp {29,59} 2 1 1 2 1 7 txt gp {31,59} 6 3 3 4 2 3 21 txt gp {37,59} 8 4 4 4 2 3 25 txt gp {41,59} 2 1 1 2 1 7 txt gp {43,59} 6 3 3 3 1 2 1 3 22 txt gp {47,59} 2 1 1 2 1 7 txt gp {53,59} 4 2 2 4 2 14 txt gp {2,61} 60 7 10 10 1 12 2 7 109 txt gp {3,61} 4 3 2 2 1 16 8 12 48 txt gp {5,61} 3 3 txt gp {7,61} 12 12 txt gp {11,61} 2 3 1 1 1 2 1 3 14 txt gp {13,61} 6 3 3 2 1 12 27 txt gp {17,61} 3 3 txt gp {19,61} 2 1 1 2 1 12 19 txt gp {23,61} 4 3 2 2 1 4 2 3 21 txt gp {29,61} 3 3 txt gp {31,61} 2 3 1 1 1 2 1 12 23 txt gp {37,61} 3 1 12 16 txt gp {41,61} 3 1 3 7 txt gp {43,61} 12 12 txt gp {47,61} 8 4 4 4 2 3 25 txt gp {53,61} 6 3 3 3 1 2 1 3 22 txt gp {59,61} 4 2 2 4 2 3 17 txt gp {2,67} 36 7 6 6 1 12 2 7 77 txt gp {3,67} 12 3 6 6 1 10 5 12 55 txt gp {5,67} 4 3 2 2 1 4 2 3 21 txt gp {7,67} 6 3 3 4 2 12 30 txt gp {11,67} 2 1 1 4 2 3 13 txt gp {13,67} 12 12 txt gp {17,67} 3 3 txt gp {19,67} 2 1 1 2 1 12 19 txt gp {23,67} 2 1 1 2 1 3 10 txt gp {29,67} 3 3 txt gp {31,67} 6 3 3 3 1 2 1 12 31 txt gp {37,67} 8 4 4 4 2 12 34 txt gp {41,67} 4 2 2 4 2 3 17 txt gp {43,67} 6 6 3 3 2 2 1 12 35 txt gp {47,67} 3 3 txt gp {53,67} 6 3 3 3 1 2 1 3 22 txt gp {59,67} 2 3 1 1 1 2 1 3 14 txt gp {61,67} 2 1 1 2 1 12 19 txt gp {2,71} 150 25 25 18 3 221 txt gp {3,71} 6 3 3 3 1 12 6 3 37 txt gp {5,71} 0 {7,71} 3 1 3 7 txt gp {11,71} 2 1 1 2 1 7 txt gp {13,71} 3 3 txt gp {17,71} 2 1 1 4 2 10 txt gp {19,71} 2 1 1 4 2 3 13 txt gp {23,71} 2 1 1 4 2 10 txt gp {29,71} 0 {31,71} 2 1 3 6 txt gp {37,71} 2 1 1 4 2 3 13 txt gp {41,71} 4 2 2 6 3 17 txt gp {43,71} 4 2 2 4 2 3 17 txt gp {47,71} 2 1 1 2 1 7 txt gp {53,71} 8 4 4 6 3 25 txt gp {59,71} 6 3 3 4 2 18 txt gp {61,71} 2 1 1 2 1 3 10 txt gp {67,71} 3 3 txt gp {2,73} 36 7 6 6 1 12 2 7 77 txt gp {3,73} 12 6 6 6 2 16 8 12 68 txt gp {5,73} 2 1 1 2 1 3 10 txt gp {7,73} 3 1 12 16 txt gp {11,73} 3 3 txt gp {13,73} 6 2 12 20 txt gp {17,73} 3 1 3 7 txt gp {19,73} 2 1 12 15 txt gp {23,73} 2 1 3 6 txt gp {29,73} 3 3 txt gp {31,73} 2 1 1 2 1 12 19 txt gp {37,73} 6 3 3 3 1 2 1 12 31 txt gp {41,73} 6 3 3 2 1 3 18 txt gp {43,73} 3 1 12 16 txt gp {47,73} 6 3 3 2 1 3 18 txt gp {53,73} 3 3 txt gp {59,73} 8 4 4 4 2 3 25 txt gp {61,73} 12 12 txt gp {67,73} 2 1 12 15 txt gp {71,73} 2 1 3 6 txt gp {2,79} 132 7 22 22 1 12 2 7 205 txt gp {3,79} 4 3 2 2 1 10 5 12 39 txt gp {5,79} 3 3 txt gp {7,79} 2 1 1 2 1 12 19 txt gp {11,79} 3 3 txt gp {13,79} 2 3 1 1 1 4 2 12 26 txt gp {17,79} 3 1 2 1 3 10 txt gp {19,79} 2 1 12 15 txt gp {23,79} 2 1 1 2 1 3 10 txt gp {29,79} 4 2 2 4 2 3 17 txt gp {31,79} 2 1 1 4 2 12 22 txt gp {37,79} 2 1 1 2 1 12 19 txt gp {41,79} 2 3 1 1 1 2 1 3 14 txt gp {43,79} 2 1 1 2 1 12 19 txt gp {47,79} 4 2 3 9 txt gp {53,79} 2 1 1 2 1 3 10 txt gp {59,79} 2 1 1 4 2 3 13 txt gp {61,79} 2 6 1 1 2 2 1 12 27 txt gp {67,79} 2 3 1 1 1 2 1 12 23 txt gp {71,79} 3 1 4 2 3 13 txt gp {73,79} 4 3 2 2 1 6 3 12 33 txt gp {2,83} 60 10 10 12 2 94 txt gp {3,83} 8 4 4 12 6 3 37 txt gp {5,83} 8 4 4 8 4 28 txt gp {7,83} 3 1 4 2 3 13 txt gp {11,83} 2 1 1 4 2 10 txt gp {13,83} 2 3 1 1 1 2 1 3 14 txt gp {17,83} 2 1 3 txt gp {19,83} 2 3 1 1 1 2 1 3 14 txt gp {23,83} 8 4 4 10 5 31 txt gp {29,83} 2 1 3 txt gp {31,83} 2 1 1 4 2 3 13 txt gp {37,83} 2 1 3 6 txt gp {41,83} 6 3 3 2 1 15 txt gp {43,83} 8 4 4 4 2 3 25 txt gp {47,83} 2 1 1 2 1 7 txt gp {53,83} 4 2 2 4 2 14 txt gp {59,83} 2 1 1 4 2 10 txt gp {61,83} 12 6 6 10 5 3 42 txt gp {67,83} 2 1 1 2 1 3 10 txt gp {71,83} 2 1 1 2 1 7 txt gp {73,83} 2 3 1 1 1 2 1 3 14 txt gp {79,83} 8 4 4 4 2 3 25 txt gp {2,89} 42 7 7 6 1 63 txt gp {3,89} 4 3 2 2 1 10 5 3 30 txt gp {5,89} 0 {7,89} 2 1 3 6 txt gp {11,89} 0 {13,89} 3 3 txt gp {17,89} 0 {19,89} 8 4 4 4 2 3 25 txt gp {23,89} 4 2 2 4 2 14 txt gp {29,89} 6 3 3 2 1 15 txt gp {31,89} 4 3 2 2 1 4 2 3 21 txt gp {37,89} 2 1 1 2 1 3 10 txt gp {41,89} 0 {43,89} 2 1 3 6 txt gp {47,89} 0 {53,89} 0 {59,89} 2 1 1 2 1 7 txt gp {61,89} 6 3 3 3 1 2 1 3 22 txt gp {67,89} 6 3 3 3 1 2 1 3 22 txt gp {71,89} 0 {73,89} 3 3 txt gp {79,89} 2 3 1 1 1 2 1 3 14 txt gp {83,89} 8 4 4 10 5 31 txt gp {2,97} 36 7 6 6 1 12 2 7 77 txt gp {3,97} 18 9 9 16 8 12 72 txt gp {5,97} 3 3 txt gp {7,97} 2 6 1 1 2 2 1 12 27 txt gp {11,97} 4 2 2 4 2 3 17 txt gp {13,97} 12 12 txt gp {17,97} 3 3 txt gp {19,97} 2 3 1 1 1 2 1 12 23 txt gp {23,97} 4 2 2 4 2 3 17 txt gp {29,97} 2 1 1 2 1 3 10 txt gp {31,97} 2 3 1 1 1 10 5 12 35 txt gp {37,97} 3 1 12 16 txt gp {41,97} 3 3 txt gp {43,97} 6 3 3 3 1 2 1 12 31 txt gp {47,97} 4 3 2 2 1 4 2 3 21 txt gp {53,97} 3 3 txt gp {59,97} 12 6 6 4 2 3 33 txt gp {61,97} 12 12 txt gp {67,97} 3 1 12 16 txt gp {71,97} 2 1 1 2 1 3 10 txt gp {73,97} 3 1 12 16 txt gp {79,97} 6 2 2 1 12 23 txt gp {83,97} 2 1 1 2 1 3 10 txt gp {89,97} 3 1 3 7 txt gp {2,101} 126 21 21 18 3 189 txt gp {3,101} 8 4 4 10 5 3 34 txt gp {5,101} 0 {7,101} 2 1 1 4 2 3 13 txt gp {11,101} 2 1 1 2 1 7 txt gp {13,101} 3 3 txt gp {17,101} 0 {19,101} 3 3 txt gp {23,101} 6 3 3 2 1 15 txt gp {29,101} 0 {31,101} 3 1 2 1 3 10 txt gp {37,101} 3 1 3 7 txt gp {41,101} 0 {43,101} 6 3 3 2 1 3 18 txt gp {47,101} 0 {53,101} 6 3 3 2 1 15 txt gp {59,101} 8 4 4 4 2 22 txt gp {61,101} 6 3 3 2 1 3 18 txt gp {67,101} 6 3 3 2 1 3 18 txt gp {71,101} 0 {73,101} 6 3 3 2 1 3 18 txt gp {79,101} 3 1 3 7 txt gp {83,101} 2 1 1 2 1 7 txt gp {89,101} 2 1 1 2 1 7 txt gp {97,101} 2 1 1 2 1 3 10 txt gp {2,103} 42 7 7 7 1 6 1 7 78 txt gp {3,103} 4 3 2 2 1 10 5 12 39 txt gp {5,103} 6 3 3 4 2 3 21 txt gp {7,103} 2 1 12 15 txt gp {11,103} 2 1 1 4 2 3 13 txt gp {13,103} 6 2 2 1 12 23 txt gp {17,103} 2 1 1 2 1 3 10 txt gp {19,103} 8 6 4 4 2 4 2 12 42 txt gp {23,103} 2 3 1 1 1 2 1 3 14 txt gp {29,103} 2 1 1 2 1 3 10 txt gp {31,103} 6 2 2 1 12 23 txt gp {37,103} 6 2 12 20 txt gp {41,103} 3 3 txt gp {43,103} 2 1 1 2 1 12 19 txt gp {47,103} 8 4 4 6 3 3 28 txt gp {53,103} 2 1 3 6 txt gp {59,103} 2 1 1 2 1 3 10 txt gp {61,103} 8 6 4 4 2 4 2 12 42 txt gp {67,103} 12 6 6 4 2 12 42 txt gp {71,103} 4 2 2 4 2 3 17 txt gp {73,103} 9 3 12 24 txt gp {79,103} 3 1 2 1 12 19 txt gp {83,103} 2 1 1 2 1 3 10 txt gp {89,103} 2 3 1 1 1 4 2 3 17 txt gp {97,103} 2 1 12 15 txt gp {101,103} 6 3 3 4 2 3 21 txt gp {2,107} 126 21 21 18 3 189 txt gp {3,107} 12 3 6 6 1 18 9 3 58 txt gp {5,107} 4 2 2 4 2 14 txt gp {7,107} 6 3 3 2 1 3 18 txt gp {11,107} 2 1 1 4 2 10 txt gp {13,107} 2 1 1 2 1 3 10 txt gp {17,107} 2 1 1 2 1 7 txt gp {19,107} 4 3 2 2 1 4 2 3 21 txt gp {23,107} 4 2 2 4 2 14 txt gp {29,107} 6 3 3 2 1 15 txt gp {31,107} 2 1 1 4 2 3 13 txt gp {37,107} 2 1 1 2 1 3 10 txt gp {41,107} 2 1 1 2 1 7 txt gp {43,107} 6 3 3 3 1 2 1 3 22 txt gp {47,107} 8 4 4 4 2 22 txt gp {53,107} 2 1 1 2 1 7 txt gp {59,107} 14 7 7 10 5 43 txt gp {61,107} 2 1 1 2 1 3 10 txt gp {67,107} 2 3 1 1 1 2 1 3 14 txt gp {71,107} 2 1 1 2 1 7 txt gp {73,107} 10 5 5 6 3 3 32 txt gp {79,107} 6 3 3 10 5 3 30 txt gp {83,107} 8 4 4 4 2 22 txt gp {89,107} 8 4 4 4 2 22 txt gp {97,107} 4 2 2 4 2 3 17 txt gp {101,107} 4 2 2 4 2 14 txt gp {103,107} 2 1 1 2 1 3 10 txt gp {2,109} 60 35 10 10 5 12 2 7 141 txt gp {3,109} 8 3 4 4 1 18 9 12 59 txt gp {5,109} 3 3 txt gp {7,109} 3 1 2 1 12 19 txt gp {11,109} 6 3 3 2 1 3 18 txt gp {13,109} 3 1 12 16 txt gp {17,109} 3 1 3 7 txt gp {19,109} 2 3 1 1 1 2 1 12 23 txt gp {23,109} 2 3 1 1 1 2 1 3 14 txt gp {29,109} 3 3 txt gp {31,109} 3 1 2 1 12 19 txt gp {37,109} 12 12 txt gp {41,109} 3 1 3 7 txt gp {43,109} 2 3 1 1 1 2 1 12 23 txt gp {47,109} 3 3 txt gp {53,109} 2 1 1 2 1 3 10 txt gp {59,109} 8 4 4 4 2 3 25 txt gp {61,109} 12 12 txt gp {67,109} 2 3 1 1 1 2 1 12 23 txt gp {71,109} 3 1 2 1 3 10 txt gp {73,109} 3 1 12 16 txt gp {79,109} 12 12 txt gp {83,109} 2 1 3 6 txt gp {89,109} 3 3 txt gp {97,109} 3 1 12 16 txt gp {101,109} 6 3 3 3 1 2 1 3 22 txt gp {103,109} 12 12 txt gp {107,109} 2 3 1 1 1 2 1 3 14 txt gp {2,113} 0 {3,113} 10 5 5 12 6 3 41 txt gp {5,113} 2 1 1 2 1 7 txt gp {7,113} 3 1 3 7 txt gp {11,113} 0 {13,113} 3 3 txt gp {17,113} 2 1 1 2 1 7 txt gp {19,113} 2 3 1 1 1 2 1 3 14 txt gp {23,113} 4 2 2 10 5 23 txt gp {29,113} 2 1 1 2 1 7 txt gp {31,113} 2 1 3 6 txt gp {37,113} 3 3 txt gp {41,113} 0 {43,113} 6 3 3 3 1 4 2 3 25 txt gp {47,113} 2 1 1 4 2 10 txt gp {53,113} 0 {59,113} 6 3 3 2 1 15 txt gp {61,113} 3 1 3 7 txt gp {67,113} 4 2 2 4 2 3 17 txt gp {71,113} 2 1 1 2 1 7 txt gp {73,113} 2 1 1 2 1 3 10 txt gp {79,113} 2 1 3 6 txt gp {83,113} 2 1 1 4 2 10 txt gp {89,113} 2 1 1 2 1 7 txt gp {97,113} 2 1 1 2 1 3 10 txt gp {101,113} 0 {103,113} 6 3 3 3 1 2 1 3 22 txt gp {107,113} 6 3 3 2 1 15 txt gp {109,113} 6 3 3 3 1 2 1 3 22 txt gp {2,127} 90 35 15 15 5 6 1 7 174 txt gp {3,127} 8 6 4 4 2 10 5 12 51 txt gp {5,127} 2 3 1 1 1 2 1 3 14 txt gp {7,127} 3 1 2 1 12 19 txt gp {11,127} 3 3 txt gp {13,127} 2 1 12 15 txt gp {17,127} 4 2 2 4 2 3 17 txt gp {19,127} 3 1 2 1 12 19 txt gp {23,127} 4 2 3 9 txt gp {29,127} 2 1 3 6 txt gp {31,127} 2 3 1 1 1 4 2 12 26 txt gp {37,127} 2 3 1 1 1 4 2 12 26 txt gp {41,127} 3 3 txt gp {43,127} 2 3 1 1 1 2 1 12 23 txt gp {47,127} 3 1 3 7 txt gp {53,127} 2 1 1 2 1 3 10 txt gp {59,127} 2 1 1 4 2 3 13 txt gp {61,127} 2 3 1 1 1 4 2 12 26 txt gp {67,127} 2 1 1 2 1 12 19 txt gp {71,127} 3 3 txt gp {73,127} 2 3 1 1 1 4 2 12 26 txt gp {79,127} 2 1 12 15 txt gp {83,127} 4 2 3 9 txt gp {89,127} 3 1 2 1 3 10 txt gp {97,127} 2 3 1 1 1 2 1 12 23 txt gp {101,127} 2 1 1 4 2 3 13 txt gp {103,127} 3 1 2 1 12 19 txt gp {107,127} 8 3 4 4 1 4 2 3 29 txt gp {109,127} 12 12 txt gp {113,127} 4 2 2 4 2 3 17 txt gp {2,131} 78 13 13 18 3 125 txt gp {3,131} 8 4 4 12 6 3 37 txt gp {5,131} 2 1 1 2 1 7 txt gp {7,131} 2 1 1 4 2 3 13 txt gp {11,131} 6 3 3 2 1 15 txt gp {13,131} 3 1 2 1 3 10 txt gp {17,131} 6 3 3 4 2 18 txt gp {19,131} 3 3 txt gp {23,131} 2 1 1 4 2 10 txt gp {29,131} 2 1 3 txt gp {31,131} 6 3 3 2 1 3 18 txt gp {37,131} 6 3 3 2 1 3 18 txt gp {41,131} 6 3 3 2 1 15 txt gp {43,131} 2 3 1 1 1 4 2 3 17 txt gp {47,131} 2 1 1 2 1 7 txt gp {53,131} 2 1 1 2 1 7 txt gp {59,131} 4 2 2 8 4 20 txt gp {61,131} 3 1 2 1 3 10 txt gp {67,131} 3 1 3 7 txt gp {71,131} 16 8 8 4 2 38 txt gp {73,131} 6 3 3 2 1 3 18 txt gp {79,131} 3 1 3 7 txt gp {83,131} 6 3 3 4 2 18 txt gp {89,131} 0 {97,131} 3 1 3 7 txt gp {101,131} 2 1 1 2 1 7 txt gp {103,131} 3 3 txt gp {107,131} 6 3 3 2 1 15 txt gp {109,131} 4 2 2 4 2 3 17 txt gp {113,131} 0 {127,131} 3 1 3 7 txt gp {2,137} 42 7 7 6 1 63 txt gp {3,137} 8 4 4 12 6 3 37 txt gp {5,137} 0 {7,137} 2 1 1 2 1 3 10 txt gp {11,137} 0 {13,137} 6 3 3 2 1 3 18 txt gp {17,137} 0 {19,137} 3 3 txt gp {23,137} 2 1 1 8 4 16 txt gp {29,137} 8 4 4 4 2 22 txt gp {31,137} 6 3 3 8 4 3 27 txt gp {37,137} 3 1 3 7 txt gp {41,137} 6 3 3 2 1 15 txt gp {43,137} 2 3 1 1 1 2 1 3 14 txt gp {47,137} 2 1 3 txt gp {53,137} 2 1 1 2 1 7 txt gp {59,137} 2 1 1 2 1 7 txt gp {61,137} 3 3 txt gp {67,137} 3 1 2 1 3 10 txt gp {71,137} 2 1 1 4 2 10 txt gp {73,137} 3 1 3 7 txt gp {79,137} 2 3 1 1 1 2 1 3 14 txt gp {83,137} 4 2 2 4 2 14 txt gp {89,137} 0 {97,137} 3 3 txt gp {101,137} 0 {103,137} 2 3 1 1 1 2 1 3 14 txt gp {107,137} 6 3 3 2 1 15 txt gp {109,137} 2 1 1 2 1 3 10 txt gp {113,137} 0 {127,137} 8 3 4 4 1 10 5 3 38 txt gp {131,137} 2 1 1 2 1 7 txt gp {2,139} 84 7 14 14 1 12 2 7 141 txt gp {3,139} 6 3 3 12 6 12 42 txt gp {5,139} 6 3 3 6 3 3 24 txt gp {7,139} 2 3 1 1 1 2 1 12 23 txt gp {11,139} 2 1 1 2 1 3 10 txt gp {13,139} 4 2 2 4 2 12 26 txt gp {17,139} 6 3 3 2 1 3 18 txt gp {19,139} 6 3 3 4 2 12 30 txt gp {23,139} 10 3 5 5 1 10 5 3 42 txt gp {29,139} 4 2 2 4 2 3 17 txt gp {31,139} 8 3 4 4 1 10 5 12 47 txt gp {37,139} 14 3 7 7 1 10 5 12 59 txt gp {41,139} 12 6 6 4 2 3 33 txt gp {43,139} 8 4 4 4 2 12 34 txt gp {47,139} 6 3 3 2 1 3 18 txt gp {53,139} 2 1 1 2 1 3 10 txt gp {59,139} 8 3 4 4 1 4 2 3 29 txt gp {61,139} 6 3 3 2 1 12 27 txt gp {67,139} 2 3 1 1 1 2 1 12 23 txt gp {71,139} 8 4 4 4 2 3 25 txt gp {73,139} 2 6 1 1 2 2 1 12 27 txt gp {79,139} 8 3 4 4 1 8 4 12 44 txt gp {83,139} 4 2 2 4 2 3 17 txt gp {89,139} 2 1 1 2 1 3 10 txt gp {97,139} 2 3 1 1 1 2 1 12 23 txt gp {101,139} 12 6 6 10 5 3 42 txt gp {103,139} 4 3 2 2 1 4 2 12 30 txt gp {107,139} 12 6 6 4 2 3 33 txt gp {109,139} 2 1 1 2 1 12 19 txt gp {113,139} 2 1 1 2 1 3 10 txt gp {127,139} 2 1 1 2 1 12 19 txt gp {131,139} 2 3 1 1 1 2 1 3 14 txt gp {137,139} 4 2 2 4 2 3 17 txt gp {2,149} 60 10 10 12 2 94 txt gp {3,149} 4 2 2 10 5 3 26 txt gp {5,149} 0 {7,149} 3 3 txt gp {11,149} 2 1 1 2 1 7 txt gp {13,149} 6 3 3 2 1 3 18 txt gp {17,149} 0 {19,149} 2 1 1 2 1 3 10 txt gp {23,149} 6 3 3 10 5 27 txt gp {29,149} 0 {31,149} 8 4 4 4 2 3 25 txt gp {37,149} 3 1 3 7 txt gp {41,149} 2 1 1 2 1 7 txt gp {43,149} 2 1 3 6 txt gp {47,149} 0 {53,149} 0 {59,149} 12 6 6 10 5 39 txt gp {61,149} 2 3 1 1 1 2 1 3 14 txt gp {67,149} 2 3 1 1 1 2 1 3 14 txt gp {71,149} 2 1 3 txt gp {73,149} 6 3 3 3 1 2 1 3 22 txt gp {79,149} 2 1 1 4 2 3 13 txt gp {83,149} 4 2 2 4 2 14 txt gp {89,149} 0 {97,149} 3 1 3 7 txt gp {101,149} 2 1 1 2 1 7 txt gp {103,149} 3 3 txt gp {107,149} 4 2 2 4 2 14 txt gp {109,149} 3 3 txt gp {113,149} 0 {127,149} 14 7 7 2 1 3 34 txt gp {131,149} 8 4 4 4 2 22 txt gp {137,149} 16 8 8 4 2 38 txt gp {139,149} 8 3 4 4 1 4 2 3 29 txt gp {2,151} 42 7 7 7 1 6 1 7 78 txt gp {3,151} 4 3 2 2 1 10 5 12 39 txt gp {5,151} 4 2 2 4 2 3 17 txt gp {7,151} 2 1 12 15 txt gp {11,151} 3 3 txt gp {13,151} 6 3 3 3 1 2 1 12 31 txt gp {17,151} 3 3 txt gp {19,151} 2 6 1 1 2 2 1 12 27 txt gp {23,151} 4 2 2 10 5 3 26 txt gp {29,151} 2 3 1 1 1 2 1 3 14 txt gp {31,151} 4 6 2 2 2 4 2 12 34 txt gp {37,151} 3 1 2 1 12 19 txt gp {41,151} 3 1 2 1 3 10 txt gp {43,151} 3 1 2 1 12 19 txt gp {47,151} 3 3 txt gp {53,151} 3 1 2 1 3 10 txt gp {59,151} 12 3 6 6 1 4 2 3 37 txt gp {61,151} 2 3 1 1 1 2 1 12 23 txt gp {67,151} 2 3 1 1 1 2 1 12 23 txt gp {71,151} 10 5 5 6 3 3 32 txt gp {73,151} 2 3 1 1 1 2 1 12 23 txt gp {79,151} 3 1 2 1 12 19 txt gp {83,151} 3 1 4 2 3 13 txt gp {89,151} 4 2 2 4 2 3 17 txt gp {97,151} 6 3 3 2 1 12 27 txt gp {101,151} 3 1 2 1 3 10 txt gp {103,151} 2 1 12 15 txt gp {107,151} 2 3 1 1 1 4 2 3 17 txt gp {109,151} 12 12 txt gp {113,151} 2 1 1 2 1 3 10 txt gp {127,151} 6 2 2 1 12 23 txt gp {131,151} 20 3 10 10 1 4 2 3 53 txt gp {137,151} 3 3 txt gp {139,151} 2 1 1 4 2 12 22 txt gp {149,151} 4 2 2 4 2 3 17 txt gp

## Cases where S contains three primes

 S S4×C2 A4×C2 S4- S4+ A4 D6 S3 C6 Total {2,3,5} 2002 15 143 143 1 434 31 15 2784 txt gp {2,3,7} 2100 120 150 150 8 420 30 60 3038 txt gp {2,5,7} 532 15 38 38 1 84 6 15 729 txt gp {3,5,7} 66 7 11 11 1 120 20 28 264 txt gp {2,3,11} 2394 15 171 171 1 490 35 15 3292 txt gp {2,5,11} 630 45 45 98 7 825 txt gp {3,5,11} 90 15 15 138 23 7 288 txt gp {2,7,11} 602 15 43 43 1 70 5 15 794 txt gp {3,7,11} 102 7 17 17 1 114 19 28 305 txt gp {5,7,11} 6 1 1 12 2 7 29 txt gp {2,3,13} 2100 120 150 150 8 420 30 60 3038 txt gp {2,5,13} 532 75 38 38 5 84 6 15 793 txt gp {3,5,13} 72 7 12 12 1 120 20 28 272 txt gp {2,7,13} 700 180 50 50 12 84 6 60 1142 txt gp {3,7,13} 78 21 13 13 3 114 19 91 352 txt gp {5,7,13} 12 14 2 2 2 12 2 28 74 txt gp {2,11,13} 1050 15 75 75 1 126 9 15 1366 txt gp {3,11,13} 120 7 20 20 1 132 22 28 350 txt gp {5,11,13} 30 7 5 5 1 18 3 7 76 txt gp {7,11,13} 30 14 5 5 2 18 3 28 105 txt gp {2,3,17} 2590 75 185 185 5 490 35 15 3580 txt gp {2,5,17} 644 46 46 84 6 826 txt gp {3,5,17} 108 7 18 18 1 132 22 7 313 txt gp {2,7,17} 546 15 39 39 1 70 5 15 730 txt gp {3,7,17} 90 7 15 15 1 120 20 28 296 txt gp {5,7,17} 12 2 2 24 4 7 51 txt gp {2,11,17} 714 51 51 126 9 951 txt gp {3,11,17} 126 7 21 21 1 126 21 7 330 txt gp {5,11,17} 36 6 6 18 3 69 txt gp {7,11,17} 66 11 11 30 5 7 130 txt gp {2,13,17} 238 15 17 17 1 42 3 15 348 txt gp {3,13,17} 108 7 18 18 1 192 32 28 404 txt gp {5,13,17} 6 7 1 1 1 6 1 7 30 txt gp {7,13,17} 30 14 5 5 2 18 3 28 105 txt gp {11,13,17} 24 4 4 24 4 7 67 txt gp {2,3,19} 2324 180 166 166 12 476 34 60 3418 txt gp {2,5,19} 672 15 48 48 1 112 8 15 919 txt gp {3,5,19} 108 14 18 18 2 132 22 28 342 txt gp {2,7,19} 518 180 37 37 12 98 7 60 949 txt gp {3,7,19} 102 28 17 17 4 138 23 91 420 txt gp {5,7,19} 24 14 4 4 2 18 3 28 97 txt gp {2,11,19} 1092 75 78 78 5 140 10 15 1493 txt gp {3,11,19} 96 14 16 16 2 108 18 28 298 txt gp {5,11,19} 7 1 7 15 txt gp {7,11,19} 35 5 6 1 28 75 txt gp {2,13,19} 798 120 57 57 8 98 7 60 1205 txt gp {3,13,19} 138 21 23 23 3 120 20 91 439 txt gp {5,13,19} 42 7 7 7 1 18 3 28 113 txt gp {7,13,19} 30 21 5 5 3 18 3 91 176 txt gp {11,13,19} 42 7 7 7 1 18 3 28 113 txt gp {2,17,19} 546 15 39 39 1 70 5 15 730 txt gp {3,17,19} 114 35 19 19 5 132 22 28 374 txt gp {5,17,19} 66 11 11 30 5 7 130 txt gp {7,17,19} 24 14 4 4 2 12 2 28 90 txt gp {11,17,19} 18 7 3 3 1 18 3 7 60 txt gp {13,17,19} 12 7 2 2 1 12 2 28 66 txt gp {2,3,23} 2590 15 185 185 1 518 37 15 3546 txt gp {2,5,23} 826 59 59 126 9 1079 txt gp {3,5,23} 90 15 15 126 21 7 274 txt gp {2,7,23} 294 15 21 21 1 42 3 15 412 txt gp {3,7,23} 120 7 20 20 1 108 18 28 322 txt gp {5,7,23} 30 5 5 24 4 7 75 txt gp {2,11,23} 1064 76 76 112 8 1336 txt gp {3,11,23} 174 29 29 168 28 7 435 txt gp {5,11,23} 30 5 5 36 6 82 txt gp {7,11,23} 18 3 3 6 1 7 38 txt gp {2,13,23} 826 15 59 59 1 126 9 15 1110 txt gp {3,13,23} 156 7 26 26 1 216 36 28 496 txt gp {5,13,23} 30 7 5 5 1 30 5 7 90 txt gp {7,13,23} 12 14 2 2 2 12 2 28 74 txt gp {11,13,23} 12 2 2 30 5 7 58 txt gp {2,17,23} 868 62 62 84 6 1082 txt gp {3,17,23} 120 7 20 20 1 126 21 7 322 txt gp {5,17,23} 60 10 10 42 7 129 txt gp {7,17,23} 30 5 5 24 4 7 75 txt gp {11,17,23} 54 9 9 42 7 121 txt gp {13,17,23} 48 8 8 42 7 7 120 txt gp {2,19,23} 1792 15 128 128 1 168 12 15 2259 txt gp {3,19,23} 102 14 17 17 2 108 18 28 306 txt gp {5,19,23} 30 5 5 18 3 7 68 txt gp {7,19,23} 36 14 6 6 2 18 3 28 113 txt gp {11,19,23} 36 7 6 6 1 12 2 7 77 txt gp {13,19,23} 30 7 5 5 1 18 3 28 97 txt gp {17,19,23} 42 7 7 18 3 7 84 txt gp

## Cases where S contains four primes

 S S4×C2 A4×C2 S4- S4+ A4 D6 S3 C6 Total {2,3,5,7} 26820 372 894 894 12 3120 104 124 32340 txt gp {2,3,5,11} 28650 31 955 955 1 3150 105 31 33878 txt gp {2,3,7,11} 29922 372 998 998 12 3300 110 124 35836 txt gp {2,5,7,11} 8310 31 277 277 1 690 23 31 9640 txt gp {3,5,7,11} 1540 75 110 110 5 980 70 60 2950 txt gp