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