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

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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