Tables of Quintics unramified outside S



Cases where S contains one prime

S S5 A5 F5 D5 C5 Total    
{2}           0    
{3}           0    
{5}     2   1 3 txt gp
{7}           0    
{11}         1 1 txt gp
{13}           0    
{17}           0    
{19}           0    
{23}           0    
{29}           0    
{31}         1 1 txt gp
{37}           0    
{41}         1 1 txt gp
{43}           0    
{47}       1   1 txt gp
{53}           0    
{59}           0    
{61}         1 1 txt gp
{67}           0    
{71}         1 1 txt gp
{73}           0    
{79}       1   1 txt gp
{83}           0    
{89}           0    
{97}           0    
{101} 1   1   1 3 txt gp
{103}       1   1 txt gp
{107}           0    
{109}           0    
{113}           0    
{127}       1   1 txt gp
{131}       1 1 2 txt gp
{137}           0    
{139}           0    
{149}           0    
{151} 1       1 2 txt gp
{157}     1     1 txt gp
{163}           0    
{167}           0    
{173}     1     1 txt gp
{179}       1   1 txt gp
{181}     1   1 2 txt gp
{191}         1 1 txt gp
{193}           0    
{197}     1     1 txt gp
{199}           0    
{211}         1 1 txt gp
{223}           0    
{227}       1   1 txt gp
{229}           0    
{233}           0    
{239}       1   1 txt gp
{241}         1 1 txt gp
{251}         1 1 txt gp
{257}           0    
{263}           0    
{269} 1         1 txt gp
{271}         1 1 txt gp
{277}           0    
{281} 1       1 2 txt gp
{283}           0    
{293}           0    
{307}           0    
{311}         1 1 txt gp
{313}           0    
{317} 1         1 txt gp
{331}         1 1 txt gp
{337}           0    
{347}       1   1 txt gp
{349}     1     1 txt gp
{353}           0    
{359}           0    
{367}           0    
{373}     1     1 txt gp
{379}           0    
{383}           0    
{389}           0    
{397}           0    
{401} 1     1 1 3 txt gp
{409}           0    
{419}           0    
{421}     1   1 2 txt gp



Cases where S contains two primes

S S5 A5 F5 D5 C5 Total    
{2,3} 5   1     6 txt gp
{2,5} 38 5 19 4 1 67 txt gp
{3,5} 22 6 7 2 1 38 txt gp
{2,7} 2         2 txt gp
{3,7}           0    
{5,7} 4   7 2 1 14 txt gp
{2,11} 2   1 1 1 5 txt gp
{3,11}   2     1 3 txt gp
{5,11} 5   13 3 6 27 txt gp
{7,11} 1     1 1 3 txt gp
{2,13} 4   6     10 txt gp
{3,13}           0    
{5,13} 9 1 13   1 24 txt gp
{7,13}     1     1 txt gp
{11,13}       1 1 2 txt gp
{2,17} 3 1       4 txt gp
{3,17} 1 1 1     3 txt gp
{5,17} 12   14   1 27 txt gp
{7,17}       1   1 txt gp
{11,17}         1 1 txt gp
{13,17}     1     1 txt gp
{2,19} 2 1 1 1   5 txt gp
{3,19} 4 3       7 txt gp
{5,19} 8   13 2 1 24 txt gp
{7,19}       1   1 txt gp
{11,19} 1     2 1 4 txt gp
{13,19} 1         1 txt gp
{17,19} 1         1 txt gp
{2,23} 5   1     6 txt gp
{3,23}   1       1 txt gp
{5,23} 8   7 2 1 18 txt gp
{7,23} 1         1 txt gp
{11,23} 1       1 2 txt gp
{13,23}           0    
{17,23}     1     1 txt gp
{19,23} 2     1   3 txt gp
{2,29} 6 2 2 1   11 txt gp
{3,29}   3 1 1   5 txt gp
{5,29} 8   23   1 32 txt gp
{7,29} 2         2 txt gp
{11,29}       2 1 3 txt gp
{13,29} 2 1 1     4 txt gp
{17,29} 3 2 2     7 txt gp
{19,29}     1 1   2 txt gp
{23,29} 1 2       3 txt gp
{2,31} 3 1     1 5 txt gp
{3,31} 1 3   1 1 6 txt gp
{5,31} 9 1 13 3 6 32 txt gp
{7,31}         1 1 txt gp
{11,31}       1 6 7 txt gp
{13,31}   2     1 3 txt gp
{17,31}   1 1   1 3 txt gp
{19,31} 3       1 4 txt gp
{23,31}       1 1 2 txt gp
{29,31}       1 1 2 txt gp
{2,37} 6   3 1   10 txt gp
{3,37} 2         2 txt gp
{5,37} 13 1 14 1 1 30 txt gp
{7,37}           0    
{11,37} 1       1 2 txt gp
{13,37} 3   4     7 txt gp
{17,37} 3   2     5 txt gp
{19,37}           0    
{23,37} 1   1 1   3 txt gp
{29,37} 2   2 1   5 txt gp
{31,37} 1       1 2 txt gp
{2,41} 9 2 3 2 1 17 txt gp
{3,41} 2 2     1 5 txt gp
{5,41} 12 2 24 1 6 45 txt gp
{7,41} 2   1   1 4 txt gp
{11,41}         6 6 txt gp
{13,41} 2   2   1 5 txt gp
{17,41} 4 1 1   1 7 txt gp
{19,41} 1 1   1 1 4 txt gp
{23,41}   1   1 1 3 txt gp
{29,41} 3   1   1 5 txt gp
{31,41}       2 6 8 txt gp
{37,41} 2       1 3 txt gp
{2,43} 14 1 2 1   18 txt gp
{3,43} 6 3       9 txt gp
{5,43} 11 1 7 2 1 22 txt gp
{7,43} 2         2 txt gp
{11,43} 1 1   1 1 4 txt gp
{13,43}           0    
{17,43} 1         1 txt gp
{19,43}       2   2 txt gp
{23,43} 2         2 txt gp
{29,43} 1   1 1   3 txt gp
{31,43} 4     1 1 6 txt gp
{37,43} 3   1     4 txt gp
{41,43} 1 1 1 1 1 5 txt gp
{2,47} 10     1   11 txt gp
{3,47} 3     1   4 txt gp
{5,47} 8   8 2 1 19 txt gp
{7,47}       1   1 txt gp
{11,47} 1     1 1 3 txt gp
{13,47} 1   1 2   4 txt gp
{17,47}       1   1 txt gp
{19,47} 1     1   2 txt gp
{23,47}       1   1 txt gp
{29,47} 1   1 1   3 txt gp
{31,47} 1     1 1 3 txt gp
{37,47}     1 2   3 txt gp
{41,47}     2 1 1 4 txt gp
{43,47}       1   1 txt gp
{2,53} 11   3     14 txt gp
{3,53} 5   1 1   7 txt gp
{5,53} 14 2 14 1 1 32 txt gp
{7,53}           0    
{11,53}   1     1 2 txt gp
{13,53}           0    
{17,53} 1   2     3 txt gp
{19,53} 1     1   2 txt gp
{23,53}   1 1     2 txt gp
{29,53}     2     2 txt gp
{31,53}       1 1 2 txt gp
{37,53} 2         2 txt gp
{41,53} 2   1   1 4 txt gp
{43,53}           0    
{47,53} 1     1   2 txt gp
{2,59} 8 1 1 1   11 txt gp
{3,59} 3 3   1   7 txt gp
{5,59} 8 2 13 2 1 26 txt gp
{7,59}       1   1 txt gp
{11,59} 1       1 2 txt gp
{13,59}   1   1   2 txt gp
{17,59} 1 2 1     4 txt gp
{19,59} 1     1   2 txt gp
{23,59} 1         1 txt gp
{29,59} 2         2 txt gp
{31,59}   1     1 2 txt gp
{37,59} 2         2 txt gp
{41,59}       1 1 2 txt gp
{43,59} 2         2 txt gp
{47,59} 4     1   5 txt gp
{53,59} 3   2     5 txt gp
{2,61} 13 1 3 2 1 20 txt gp
{3,61} 3 1   1 1 6 txt gp
{5,61} 15   24 1 6 46 txt gp
{7,61}     2   1 3 txt gp
{11,61}       1 6 7 txt gp
{13,61}     3   1 4 txt gp
{17,61}   1 2   1 4 txt gp
{19,61} 1   2 1 1 5 txt gp
{23,61} 1   1   1 3 txt gp
{29,61} 3 1     1 5 txt gp
{31,61} 2     1 6 9 txt gp
{37,61} 2 1 3   1 7 txt gp
{41,61} 3 1 1   6 11 txt gp
{43,61} 1   1   1 3 txt gp
{47,61}       1 1 2 txt gp
{53,61} 3   2   1 6 txt gp
{59,61}       1 1 2 txt gp
{2,67} 13 2 1     16 txt gp
{3,67} 2 1       3 txt gp
{5,67} 13 1 7 2 1 24 txt gp
{7,67} 1         1 txt gp
{11,67}         1 1 txt gp
{13,67}     1     1 txt gp
{17,67}     1     1 txt gp
{19,67} 3         3 txt gp
{23,67}           0    
{29,67} 3         3 txt gp
{31,67} 2       1 3 txt gp
{37,67}     1     1 txt gp
{41,67}     1   1 2 txt gp
{43,67} 1         1 txt gp
{47,67} 3 1   1   5 txt gp
{53,67}     1     1 txt gp
{59,67}           0    
{61,67} 2   1 1 1 5 txt gp
{2,71} 8 1 2   1 12 txt gp
{3,71} 8 2     1 11 txt gp
{5,71} 14 1 13 3 6 37 txt gp
{7,71} 3     1 1 5 txt gp
{11,71} 1     1 6 8 txt gp
{13,71}       1 1 2 txt gp
{17,71} 1       1 2 txt gp
{19,71} 2 1     1 4 txt gp
{23,71}       1 1 2 txt gp
{29,71} 1 1     1 3 txt gp
{31,71} 1 4   1 6 12 txt gp
{37,71}   2 2 1 1 6 txt gp
{41,71} 1       6 7 txt gp
{43,71} 2       1 3 txt gp
{47,71}       1 1 2 txt gp
{53,71} 1       1 2 txt gp
{59,71} 1 2   2 1 6 txt gp
{61,71} 3 1     6 10 txt gp
{67,71} 4     2 1 7 txt gp
{2,73} 5 1 2     8 txt gp
{3,73} 3         3 txt gp
{5,73} 9 1 14 1 1 26 txt gp
{7,73}   1       1 txt gp
{11,73} 1   1 1 1 4 txt gp
{13,73} 1   2     3 txt gp
{17,73} 2   1     3 txt gp
{19,73}           0    
{23,73}           0    
{29,73} 4 1 2     7 txt gp
{31,73}         1 1 txt gp
{37,73}           0    
{41,73} 1 2 1   1 5 txt gp
{43,73} 2 1 1 1   5 txt gp
{47,73}   1   1   2 txt gp
{53,73} 2   5     7 txt gp
{59,73} 1   2     3 txt gp
{61,73} 2 1 1   1 5 txt gp
{67,73}       1   1 txt gp
{71,73}     1 1 1 3 txt gp
{2,79} 11 4 2 3   20 txt gp
{3,79} 2 4   1   7 txt gp
{5,79} 14 2 13 2 1 32 txt gp
{7,79} 1     1   2 txt gp
{11,79}       2 1 3 txt gp
{13,79}   1   1   2 txt gp
{17,79}       2   2 txt gp
{19,79} 1 2   2   5 txt gp
{23,79}       2   2 txt gp
{29,79} 2     1   3 txt gp
{31,79}       2 1 3 txt gp
{37,79} 3     1   4 txt gp
{41,79} 2 3 1 2 1 9 txt gp
{43,79} 4     1   5 txt gp
{47,79} 1     2   3 txt gp
{53,79} 1 1   1   3 txt gp
{59,79} 2 1   1   4 txt gp
{61,79} 1     1 1 3 txt gp
{67,79} 2     2   4 txt gp
{71,79} 4     1 1 6 txt gp
{73,79}     1 1   2 txt gp
{2,83} 10   3 1   14 txt gp
{3,83} 4 1       5 txt gp
{5,83} 11   8 2 1 22 txt gp
{7,83}           0    
{11,83} 1     1 1 3 txt gp
{13,83}     1     1 txt gp
{17,83}           0    
{19,83} 1     1   2 txt gp
{23,83} 2         2 txt gp
{29,83}       1   1 txt gp
{31,83} 2     1 1 4 txt gp
{37,83} 4         4 txt gp
{41,83} 1     1 1 3 txt gp
{43,83} 1         1 txt gp
{47,83} 3     1   4 txt gp
{53,83} 3 1 1 1   6 txt gp
{59,83} 1         1 txt gp
{61,83}       1 1 2 txt gp
{67,83} 2 1       3 txt gp
{71,83} 1       1 2 txt gp
{73,83}           0    
{79,83}   2   2   4 txt gp



Cases where S contains three primes

S S5 A5 F5 D5 C5 Total    
{2,3,5} 1353 62 82 8 1 1506 txt gp
{2,3,7} 153 1 2     156 txt gp
{2,5,7} 453 15 83 9 1 561 txt gp
{3,5,7} 205 25 41 4 1 276 txt gp
{2,3,11} 150 17 4 2 1 174 txt gp
{2,5,11} 468 36 72 19 6 601 txt gp
{3,5,11} 204 48 45 5 6 308 txt gp
{2,7,11} 58 4 1 2 1 66 txt gp
{3,7,11} 21 6   1 1 29 txt gp
{5,7,11} 67 4 27 15 6 119 txt gp