# Tables of Sextics Containing a Quadratic Subfield

## Cases where S contains one prime

 S C32 D4 C32 C4 C32 C22 C32 C2 D6 S3 C6 Total {2} 0 {3} 1 1 1 3 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 1 3 txt gp {37} 1 1 txt gp {41} 0 {43} 1 1 txt gp {47} 0 {53} 0 {59} 1 1 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 txt gp {109} 1 1 txt gp {113} 0 {127} 1 1 txt gp {131} 0 {137} 0 {139} 1 1 1 3 txt gp {149} 2 2 txt gp {151} 1 1 txt gp {157} 1 1 txt gp {163} 1 1 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 1 3 txt gp {211} 1 1 1 3 txt gp {223} 1 1 txt gp {227} 0 {229} 1 1 1 3 txt gp

## Cases where S contains two primes

 S C32 D4 C32 C4 C32 C22 C32 C2 D6 S3 C6 Total {2,3} 50 4 22 8 48 8 7 147 txt gp {2,5} 6 1 7 txt gp {3,5} 2 4 5 10 5 3 29 txt gp {2,7} 2 2 7 11 txt gp {3,7} 2 4 20 10 5 12 53 txt gp {5,7} 1 2 1 3 7 txt gp {2,11} 2 1 12 2 17 txt gp {3,11} 2 9 6 12 6 3 38 txt gp {5,11} 2 2 txt gp {7,11} 3 3 txt gp {2,13} 1 2 12 2 7 24 txt gp {3,13} 4 4 16 32 16 8 12 92 txt gp {5,13} 3 3 txt gp {7,13} 12 12 txt gp {11,13} 1 2 1 3 7 txt gp {2,17} 12 12 txt gp {3,17} 2 4 5 10 5 3 29 txt gp {5,17} 0 {7,17} 1 2 1 3 7 txt gp {11,17} 1 4 2 7 txt gp {13,17} 2 3 5 txt gp {2,19} 3 3 18 3 7 34 txt gp {3,19} 2 4 20 10 5 12 53 txt gp {5,19} 3 3 txt gp {7,19} 4 2 1 12 19 txt gp {11,19} 3 3 txt gp {13,19} 4 2 1 12 19 txt gp {17,19} 3 3 txt gp {2,23} 4 3 18 3 28 txt gp {3,23} 8 9 6 12 6 3 44 txt gp {5,23} 2 1 3 txt gp {7,23} 1 2 1 3 7 txt gp {11,23} 2 1 3 txt gp {13,23} 2 1 2 1 3 9 txt gp {17,23} 2 1 3 txt gp {19,23} 1 2 1 3 7 txt gp {2,29} 2 3 18 3 26 txt gp {3,29} 2 9 6 12 6 3 38 txt gp {5,29} 2 4 6 txt gp {7,29} 2 3 5 txt gp {11,29} 2 1 3 txt gp {13,29} 8 3 11 txt gp {17,29} 2 2 txt gp {19,29} 1 2 1 3 7 txt gp {23,29} 2 2 1 5 txt gp {2,31} 2 1 6 1 7 17 txt gp {3,31} 2 9 24 12 6 12 65 txt gp {5,31} 2 1 2 1 3 9 txt gp {7,31} 4 2 1 12 19 txt gp {11,31} 1 2 4 2 3 12 txt gp {13,31} 4 2 1 12 19 txt gp {17,31} 1 2 4 2 3 12 txt gp {19,31} 4 2 1 12 19 txt gp {23,31} 1 2 4 2 3 12 txt gp {29,31} 1 2 1 3 7 txt gp {2,37} 4 2 1 2 12 2 7 30 txt gp {3,37} 28 2 16 32 16 8 12 114 txt gp {5,37} 3 3 txt gp {7,37} 2 4 2 1 12 21 txt gp {11,37} 2 2 1 2 1 3 11 txt gp {13,37} 12 12 txt gp {17,37} 2 3 5 txt gp {19,37} 12 12 txt gp {23,37} 1 2 1 3 7 txt gp {29,37} 4 3 7 txt gp {31,37} 1 8 4 2 12 27 txt gp {2,41} 8 2 10 txt gp {3,41} 2 4 5 10 5 3 29 txt gp {5,41} 4 4 txt gp {7,41} 1 2 1 3 7 txt gp {11,41} 1 4 2 7 txt gp {13,41} 1 2 1 3 7 txt gp {17,41} 1 4 2 7 txt gp {19,41} 1 2 1 3 7 txt gp {23,41} 2 2 1 5 txt gp {29,41} 2 1 3 txt gp {31,41} 1 2 1 3 7 txt gp {37,41} 4 2 3 9 txt gp {2,43} 2 1 2 12 2 7 26 txt gp {3,43} 2 4 20 10 5 12 53 txt gp {5,43} 1 2 1 3 7 txt gp {7,43} 4 2 1 12 19 txt gp {11,43} 2 1 2 1 3 9 txt gp {13,43} 2 4 2 1 12 21 txt gp {17,43} 1 2 1 3 7 txt gp {19,43} 4 2 1 12 19 txt gp {23,43} 1 2 1 3 7 txt gp {29,43} 1 2 1 3 7 txt gp {31,43} 1 8 4 2 12 27 txt gp {37,43} 12 12 txt gp {41,43} 2 1 2 1 3 9 txt gp {2,47} 6 2 1 12 2 23 txt gp {3,47} 8 9 6 12 6 3 44 txt gp {5,47} 1 4 2 7 txt gp {7,47} 2 1 2 4 2 3 14 txt gp {11,47} 2 1 3 txt gp {13,47} 3 3 txt gp {17,47} 0 {19,47} 3 3 txt gp {23,47} 1 4 2 7 txt gp {29,47} 1 4 2 7 txt gp {31,47} 2 1 2 1 3 9 txt gp {37,47} 2 1 2 1 3 9 txt gp {41,47} 1 4 2 7 txt gp {43,47} 1 2 1 3 7 txt gp {2,53} 2 4 3 18 3 30 txt gp {3,53} 2 4 5 10 5 3 29 txt gp {5,53} 0 {7,53} 1 2 1 3 7 txt gp {11,53} 2 2 txt gp {13,53} 2 2 3 7 txt gp {17,53} 2 2 txt gp {19,53} 1 2 4 2 3 12 txt gp {23,53} 3 6 3 12 txt gp {29,53} 2 2 4 txt gp {31,53} 4 8 4 3 19 txt gp {37,53} 8 3 11 txt gp {41,53} 0 {43,53} 2 1 2 1 3 9 txt gp {47,53} 4 2 1 7 txt gp {2,59} 2 6 24 4 36 txt gp {3,59} 8 9 6 12 6 3 44 txt gp {5,59} 2 2 1 5 txt gp {7,59} 4 5 10 5 3 27 txt gp {11,59} 2 1 3 txt gp {13,59} 1 2 1 3 7 txt gp {17,59} 2 2 1 5 txt gp {19,59} 1 2 4 2 3 12 txt gp {23,59} 1 4 2 7 txt gp {29,59} 4 2 1 7 txt gp {31,59} 1 2 4 2 3 12 txt gp {37,59} 1 2 4 2 3 12 txt gp {41,59} 2 2 1 5 txt gp {43,59} 8 1 2 1 3 15 txt gp {47,59} 2 1 3 txt gp {53,59} 2 2 1 4 2 11 txt gp {2,61} 1 2 12 2 7 24 txt gp {3,61} 28 2 16 32 16 8 12 114 txt gp {5,61} 4 3 7 txt gp {7,61} 12 12 txt gp {11,61} 1 2 1 3 7 txt gp {13,61} 4 4 4 2 1 12 27 txt gp {17,61} 3 3 txt gp {19,61} 2 4 2 1 12 21 txt gp {23,61} 1 2 4 2 3 12 txt gp {29,61} 3 3 txt gp {31,61} 4 2 1 12 19 txt gp {37,61} 12 12 txt gp {41,61} 2 2 3 7 txt gp {43,61} 12 12 txt gp {47,61} 2 1 2 4 2 3 14 txt gp {53,61} 1 2 1 3 7 txt gp {59,61} 1 2 4 2 3 12 txt gp {2,67} 8 1 2 12 2 7 32 txt gp {3,67} 2 4 20 10 5 12 53 txt gp {5,67} 1 2 4 2 3 12 txt gp {7,67} 1 8 4 2 12 27 txt gp {11,67} 1 2 4 2 3 12 txt gp {13,67} 12 12 txt gp {17,67} 3 3 txt gp {19,67} 4 2 1 12 19 txt gp {23,67} 1 2 1 3 7 txt gp {29,67} 2 3 5 txt gp {31,67} 4 2 1 12 19 txt gp {37,67} 2 1 8 4 2 12 29 txt gp {41,67} 1 2 4 2 3 12 txt gp {43,67} 4 2 1 12 19 txt gp {47,67} 2 3 5 txt gp {53,67} 1 2 1 3 7 txt gp {59,67} 1 2 1 3 7 txt gp {61,67} 4 2 1 12 19 txt gp

## Cases where S contains three primes

 S C32 D4 C32 C4 C32 C22 C32 C2 D6 S3 C6 Total {2,3,5} 624 44 375 31 434 31 15 1554 txt gp {2,3,7} 642 28 345 120 420 30 60 1645 txt gp {2,5,7} 32 2 15 6 84 6 15 160 txt gp {3,5,7} 54 4 106 80 120 20 28 412 txt gp {2,3,11} 878 8 493 35 490 35 15 1954 txt gp {2,5,11} 44 4 21 98 7 174 txt gp {3,5,11} 76 6 163 23 138 23 7 436 txt gp {2,7,11} 86 6 10 5 70 5 15 197 txt gp {3,7,11} 30 93 76 114 19 28 360 txt gp {5,7,11} 8 1 2 12 2 7 32 txt gp {2,3,13} 632 46 345 120 420 30 60 1653 txt gp {2,5,13} 62 6 15 6 84 6 15 194 txt gp {3,5,13} 44 14 106 80 120 20 28 412 txt gp {2,7,13} 42 2 15 24 84 6 60 233 txt gp {3,7,13} 76 6 87 247 114 19 91 640 txt gp {5,7,13} 4 1 8 12 2 28 55 txt gp {2,11,13} 48 2 30 9 126 9 15 239 txt gp {3,11,13} 46 24 147 88 132 22 28 487 txt gp {5,11,13} 6 2 3 3 18 3 7 42 txt gp {7,11,13} 2 3 12 18 3 28 66 txt gp {2,3,17} 852 66 493 35 490 35 15 1986 txt gp {2,5,17} 70 8 15 84 6 183 txt gp {3,5,17} 44 14 147 22 132 22 7 388 txt gp {2,7,17} 108 6 10 5 70 5 15 219 txt gp {3,7,17} 54 4 106 80 120 20 28 412 txt gp {5,7,17} 2 2 4 24 4 7 43 txt gp {2,11,17} 74 4 30 126 9 243 txt gp {3,11,17} 58 4 126 21 126 21 7 363 txt gp {5,11,17} 4 2 3 18 3 30 txt gp {7,11,17} 6 10 5 30 5 7 63 txt gp {2,13,17} 168 16 3 3 42 3 15 250 txt gp {3,13,17} 188 52 334 128 192 32 28 954 txt gp {5,13,17} 14 6 1 6 1 7 35 txt gp {7,13,17} 2 4 3 12 18 3 28 70 txt gp {11,13,17} 4 4 6 4 24 4 7 53 txt gp {2,3,19} 894 8 459 136 476 34 60 2067 txt gp {2,5,19} 48 2 22 8 112 8 15 215 txt gp {3,5,19} 64 4 147 88 132 22 28 485 txt gp {2,7,19} 46 2 15 28 98 7 60 256 txt gp {3,7,19} 160 163 299 138 23 91 874 txt gp {5,7,19} 4 3 12 18 3 28 68 txt gp {2,11,19} 85 39 10 140 10 15 299 txt gp {3,11,19} 30 75 72 108 18 28 331 txt gp {5,11,19} 44 7 51 txt gp {7,11,19} 10 4 6 1 28 49 txt gp {2,13,19} 54 2 21 28 98 7 60 270 txt gp {3,13,19} 76 6 106 260 120 20 91 679 txt gp {5,13,19} 4 2 3 12 18 3 28 70 txt gp {7,13,19} 4 3 39 18 3 91 158 txt gp {11,13,19} 6 3 12 18 3 28 70 txt gp {2,17,19} 156 4 10 5 70 5 15 265 txt gp {3,17,19} 58 4 147 88 132 22 28 479 txt gp {5,17,19} 10 4 10 5 30 5 7 71 txt gp {7,17,19} 6 2 1 8 12 2 28 59 txt gp {11,17,19} 6 2 3 3 18 3 7 42 txt gp {13,17,19} 18 2 1 8 12 2 28 71 txt gp

## Cases where S contains four primes

 S C32 D4 C32 C4 C32 C22 C32 C2 D6 S3 C6 Total {2,3,5,7} 6967 128 4498 416 3120 104 124 15357 txt gp