# Tables of Imprimitive Sextics

## Cases where S contains one prime

 S C32 D4 S4×C2 C32 C4 C32 C22 A4×C2 S4- S4+ C32 C2 A4 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 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 1 5 txt gp {149} 2 2 txt gp {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 1 3 txt gp {211} 1 1 1 3 txt gp {223} 1 1 txt gp {227} 0 {229} 3 3 1 1 1 9 txt gp

## Cases where S contains two primes

 S C32 D4 S4×C2 C32 C4 C32 C22 A4×C2 S4- S4+ C32 C2 A4 D6 S3 C6 Total {2,3} 50 132 4 22 7 22 22 8 1 48 8 7 331 txt gp {2,5} 18 3 3 6 1 31 txt gp {3,5} 2 2 4 1 1 5 10 5 3 33 txt gp {2,7} 2 2 7 1 7 19 txt gp {3,7} 2 2 4 1 1 20 10 5 12 57 txt gp {5,7} 1 2 1 3 7 txt gp {2,11} 2 36 1 6 6 12 2 65 txt gp {3,11} 2 6 9 3 3 6 12 6 3 50 txt gp {5,11} 2 2 txt gp {7,11} 3 3 txt gp {2,13} 60 1 7 10 10 2 1 12 2 7 112 txt gp {3,13} 4 2 4 16 1 1 32 16 8 12 96 txt gp {5,13} 3 1 3 7 txt gp {7,13} 3 1 12 16 txt gp {11,13} 2 1 1 1 2 1 3 11 txt gp {2,17} 12 12 txt gp {3,17} 4 2 4 3 2 2 5 1 10 5 3 41 txt gp {5,17} 0 {7,17} 1 2 1 3 7 txt gp {11,17} 2 1 1 1 4 2 11 txt gp {13,17} 2 3 5 txt gp {2,19} 78 3 7 13 13 3 1 18 3 7 146 txt gp {3,19} 2 4 4 3 2 2 20 1 10 5 12 65 txt gp {5,19} 3 3 txt gp {7,19} 3 4 1 2 1 12 23 txt gp {11,19} 3 1 3 7 txt gp {13,19} 2 1 1 4 2 1 12 23 txt gp {17,19} 3 3 txt gp {2,23} 4 54 3 9 9 18 3 100 txt gp {3,23} 8 6 9 3 3 6 12 6 3 56 txt gp {5,23} 2 1 1 2 1 7 txt gp {7,23} 2 1 1 1 2 1 3 11 txt gp {11,23} 2 1 1 2 1 7 txt gp {13,23} 2 1 2 1 3 9 txt gp {17,23} 2 1 1 2 1 7 txt gp {19,23} 2 1 1 1 2 1 3 11 txt gp {2,29} 2 102 3 17 17 18 3 162 txt gp {3,29} 8 2 9 4 4 6 12 6 3 54 txt gp {5,29} 2 4 6 txt gp {7,29} 2 3 1 3 9 txt gp {11,29} 2 1 1 2 1 7 txt gp {13,29} 8 3 11 txt gp {17,29} 2 2 txt gp {19,29} 2 1 1 1 2 1 3 11 txt gp {23,29} 2 2 1 5 txt gp {2,31} 2 18 35 3 3 1 5 6 1 7 81 txt gp {3,31} 2 4 9 2 2 24 12 6 12 73 txt gp {5,31} 2 1 2 1 3 9 txt gp {7,31} 4 2 1 12 19 txt gp {11,31} 4 1 2 2 2 4 2 3 20 txt gp {13,31} 2 3 1 1 4 1 2 1 12 27 txt gp {17,31} 4 1 2 2 2 4 2 3 20 txt gp {19,31} 3 4 1 2 1 12 23 txt gp {23,31} 2 1 3 1 1 2 1 4 2 3 20 txt gp {29,31} 2 3 1 1 1 1 2 1 3 15 txt gp {2,37} 4 60 2 1 7 10 10 2 1 12 2 7 118 txt gp {3,37} 28 2 2 16 3 1 1 32 1 16 8 12 122 txt gp {5,37} 3 3 txt gp {7,37} 2 4 2 1 12 21 txt gp {11,37} 2 2 3 1 1 2 1 3 15 txt gp {13,37} 12 12 txt gp {17,37} 2 3 5 txt gp {19,37} 6 2 12 20 txt gp {23,37} 2 3 1 1 1 1 2 1 3 15 txt gp {29,37} 4 3 1 3 11 txt gp {31,37} 8 1 6 4 4 8 2 4 2 12 51 txt gp {2,41} 8 2 10 txt gp {3,41} 10 2 4 5 5 5 10 5 3 49 txt gp {5,41} 4 4 txt gp {7,41} 3 1 1 2 1 3 11 txt gp {11,41} 6 1 3 3 4 2 19 txt gp {13,41} 2 1 1 1 2 1 3 11 txt gp {17,41} 8 1 4 4 4 2 23 txt gp {19,41} 6 3 3 1 2 1 3 19 txt gp {23,41} 2 2 1 5 txt gp {29,41} 2 1 1 2 1 7 txt gp {31,41} 1 2 1 3 7 txt gp {37,41} 4 2 3 9 txt gp {2,43} 2 36 1 35 6 6 2 5 12 2 7 114 txt gp {3,43} 2 6 4 3 3 20 10 5 12 65 txt gp {5,43} 2 1 1 1 2 1 3 11 txt gp {7,43} 3 4 1 2 1 12 23 txt gp {11,43} 2 6 3 3 3 1 1 2 1 3 25 txt gp {13,43} 2 2 1 1 4 2 1 12 25 txt gp {17,43} 6 3 3 1 2 1 3 19 txt gp {19,43} 4 2 1 12 19 txt gp {23,43} 2 1 1 1 2 1 3 11 txt gp {29,43} 1 2 1 3 7 txt gp {31,43} 2 1 3 1 1 8 1 4 2 12 35 txt gp {37,43} 3 1 12 16 txt gp {41,43} 2 2 3 1 1 1 1 2 1 3 17 txt gp {2,47} 6 36 2 1 6 6 12 2 71 txt gp {3,47} 8 10 9 5 5 6 12 6 3 64 txt gp {5,47} 6 1 3 3 4 2 19 txt gp {7,47} 2 2 1 1 1 2 4 2 3 18 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} 1 4 2 7 txt gp {29,47} 4 1 2 2 4 2 15 txt gp {31,47} 2 6 3 3 3 1 1 2 1 3 25 txt gp {37,47} 2 3 1 1 2 1 3 13 txt gp {41,47} 2 1 1 1 4 2 11 txt gp {43,47} 6 3 3 3 1 1 2 1 3 23 txt gp {2,53} 2 126 4 3 21 21 18 3 198 txt gp {3,53} 2 2 4 3 1 1 5 1 10 5 3 37 txt gp {5,53} 0 {7,53} 6 3 3 1 2 1 3 19 txt gp {11,53} 2 2 txt gp {13,53} 2 2 3 1 3 11 txt gp {17,53} 2 2 txt gp {19,53} 2 1 1 1 2 4 2 3 16 txt gp {23,53} 10 3 5 5 6 3 32 txt gp {29,53} 2 2 4 txt gp {31,53} 2 1 1 4 8 4 3 23 txt gp {37,53} 8 3 11 txt gp {41,53} 0 {43,53} 2 6 3 3 1 2 1 3 21 txt gp {47,53} 4 2 1 1 2 1 11 txt gp {2,59} 2 144 6 24 24 24 4 228 txt gp {3,59} 8 4 9 2 2 6 12 6 3 52 txt gp {5,59} 2 2 1 1 2 1 9 txt gp {7,59} 4 4 2 2 5 10 5 3 35 txt gp {11,59} 2 1 1 2 1 7 txt gp {13,59} 2 1 1 1 2 1 3 11 txt gp {17,59} 2 6 3 3 2 1 17 txt gp {19,59} 4 1 2 2 2 4 2 3 20 txt gp {23,59} 8 1 4 4 4 2 23 txt gp {29,59} 4 2 1 1 2 1 11 txt gp {31,59} 6 1 3 3 2 4 2 3 24 txt gp {37,59} 8 1 4 4 2 4 2 3 28 txt gp {41,59} 2 2 1 1 2 1 9 txt gp {43,59} 8 6 3 3 3 1 1 2 1 3 31 txt gp {47,59} 2 1 1 2 1 7 txt gp {53,59} 2 4 2 1 2 2 4 2 19 txt gp {2,61} 60 1 7 10 10 2 1 12 2 7 112 txt gp {3,61} 28 4 2 16 3 2 2 32 1 16 8 12 126 txt gp {5,61} 4 3 7 txt gp {7,61} 12 12 txt gp {11,61} 2 3 1 1 1 1 2 1 3 15 txt gp {13,61} 4 6 4 3 3 4 2 1 12 39 txt gp {17,61} 3 3 txt gp {19,61} 2 2 1 1 4 2 1 12 25 txt gp {23,61} 4 1 3 2 2 2 1 4 2 3 24 txt gp {29,61} 3 3 txt gp {31,61} 2 3 1 1 4 1 2 1 12 27 txt gp {37,61} 3 1 12 16 txt gp {41,61} 2 2 3 1 3 11 txt gp {43,61} 12 12 txt gp {47,61} 2 8 1 4 4 2 4 2 3 30 txt gp {53,61} 6 3 3 3 1 1 2 1 3 23 txt gp {59,61} 4 1 2 2 2 4 2 3 20 txt gp {2,67} 8 36 1 7 6 6 2 1 12 2 7 88 txt gp {3,67} 2 12 4 3 6 6 20 1 10 5 12 81 txt gp {5,67} 4 1 3 2 2 2 1 4 2 3 24 txt gp {7,67} 6 1 3 3 8 4 2 12 39 txt gp {11,67} 2 1 1 1 2 4 2 3 16 txt gp {13,67} 12 12 txt gp {17,67} 3 3 txt gp {19,67} 2 1 1 4 2 1 12 23 txt gp {23,67} 2 1 1 1 2 1 3 11 txt gp {29,67} 2 3 5 txt gp {31,67} 6 3 3 3 4 1 2 1 12 35 txt gp {37,67} 2 8 1 4 4 8 4 2 12 45 txt gp {41,67} 4 1 2 2 2 4 2 3 20 txt gp {43,67} 6 6 3 3 4 2 2 1 12 39 txt gp {47,67} 2 3 5 txt gp {53,67} 6 3 3 3 1 1 2 1 3 23 txt gp {59,67} 2 3 1 1 1 1 2 1 3 15 txt gp {61,67} 2 1 1 4 2 1 12 23 txt gp

## Cases where S contains three primes

 S C32 D4 S4×C2 C32 C4 C32 C22 A4×C2 S4- S4+ C32 C2 A4 D6 S3 C6 Total {2,3,5} 624 2002 44 375 15 143 143 31 1 434 31 15 3858 txt gp {2,3,7} 642 2100 28 345 120 150 150 120 8 420 30 60 4173 txt gp {2,5,7} 32 532 2 15 15 38 38 6 1 84 6 15 784 txt gp {3,5,7} 54 66 4 106 7 11 11 80 1 120 20 28 508 txt gp {2,3,11} 878 2394 8 493 15 171 171 35 1 490 35 15 4706 txt gp {2,5,11} 44 630 4 21 45 45 98 7 894 txt gp {3,5,11} 76 90 6 163 15 15 23 138 23 7 556 txt gp {2,7,11} 86 602 6 10 15 43 43 5 1 70 5 15 901 txt gp {3,7,11} 30 102 93 7 17 17 76 1 114 19 28 504 txt gp {5,7,11} 8 6 1 1 1 2 12 2 7 40 txt gp {2,3,13} 632 2100 46 345 120 150 150 120 8 420 30 60 4181 txt gp {2,5,13} 62 532 6 15 75 38 38 6 5 84 6 15 882 txt gp {3,5,13} 44 72 14 106 7 12 12 80 1 120 20 28 516 txt gp {2,7,13} 42 700 2 15 180 50 50 24 12 84 6 60 1225 txt gp {3,7,13} 76 78 6 87 21 13 13 247 3 114 19 91 768 txt gp {5,7,13} 4 12 1 14 2 2 8 2 12 2 28 87 txt gp {2,11,13} 48 1050 2 30 15 75 75 9 1 126 9 15 1455 txt gp {3,11,13} 46 120 24 147 7 20 20 88 1 132 22 28 655 txt gp {5,11,13} 6 30 2 3 7 5 5 3 1 18 3 7 90 txt gp {7,11,13} 2 30 3 14 5 5 12 2 18 3 28 122 txt gp {2,3,17} 852 2590 66 493 75 185 185 35 5 490 35 15 5026 txt gp {2,5,17} 70 644 8 15 46 46 84 6 919 txt gp {3,5,17} 44 108 14 147 7 18 18 22 1 132 22 7 540 txt gp {2,7,17} 108 546 6 10 15 39 39 5 1 70 5 15 859 txt gp {3,7,17} 54 90 4 106 7 15 15 80 1 120 20 28 540 txt gp {5,7,17} 2 12 2 2 2 4 24 4 7 59 txt gp {2,11,17} 74 714 4 30 51 51 126 9 1059 txt gp {3,11,17} 58 126 4 126 7 21 21 21 1 126 21 7 539 txt gp {5,11,17} 4 36 2 3 6 6 18 3 78 txt gp {7,11,17} 6 66 10 11 11 5 30 5 7 151 txt gp {2,13,17} 168 238 16 3 15 17 17 3 1 42 3 15 538 txt gp {3,13,17} 188 108 52 334 7 18 18 128 1 192 32 28 1106 txt gp {5,13,17} 14 6 6 7 1 1 1 1 6 1 7 51 txt gp {7,13,17} 2 30 4 3 14 5 5 12 2 18 3 28 126 txt gp {11,13,17} 4 24 4 6 4 4 4 24 4 7 85 txt gp {2,3,19} 894 2324 8 459 180 166 166 136 12 476 34 60 4915 txt gp {2,5,19} 48 672 2 22 15 48 48 8 1 112 8 15 999 txt gp {3,5,19} 64 108 4 147 14 18 18 88 2 132 22 28 645 txt gp {2,7,19} 46 518 2 15 180 37 37 28 12 98 7 60 1040 txt gp {3,7,19} 160 102 163 28 17 17 299 4 138 23 91 1042 txt gp {5,7,19} 4 24 3 14 4 4 12 2 18 3 28 116 txt gp {2,11,19} 85 1092 39 75 78 78 10 5 140 10 15 1627 txt gp {3,11,19} 30 96 75 14 16 16 72 2 108 18 28 475 txt gp {5,11,19} 44 7 1 7 59 txt gp {7,11,19} 10 35 4 5 6 1 28 89 txt gp {2,13,19} 54 798 2 21 120 57 57 28 8 98 7 60 1310 txt gp {3,13,19} 76 138 6 106 21 23 23 260 3 120 20 91 887 txt gp {5,13,19} 4 42 2 3 7 7 7 12 1 18 3 28 134 txt gp {7,13,19} 4 30 3 21 5 5 39 3 18 3 91 222 txt gp {11,13,19} 6 42 3 7 7 7 12 1 18 3 28 134 txt gp {2,17,19} 156 546 4 10 15 39 39 5 1 70 5 15 905 txt gp {3,17,19} 58 114 4 147 35 19 19 88 5 132 22 28 671 txt gp {5,17,19} 10 66 4 10 11 11 5 30 5 7 159 txt gp {7,17,19} 6 24 2 1 14 4 4 8 2 12 2 28 107 txt gp {11,17,19} 6 18 2 3 7 3 3 3 1 18 3 7 74 txt gp {13,17,19} 18 12 2 1 7 2 2 8 1 12 2 28 95 txt gp

## Cases where S contains four primes

 S C32 D4 S4×C2 C32 C4 C32 C22 A4×C2 S4- S4+ C32 C2 A4 D6 S3 C6 Total {2,3,5,7} 6967 26820 128 4498 372 894 894 416 12 3120 104 124 44349 txt gp