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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (27 matches)

  displayed columns for results
Label Name Order Parity Solvable Subfields Low Degree Siblings
4T4 $A_4$ $12$ $1$ ✓ 6T4, 12T4
4T5 $S_4$ $24$ $-1$ ✓ 6T7, 6T8, 8T14, 12T8, 12T9, 24T10
5T2 $D_{5}$ $10$ $1$ ✓ 10T2
5T3 $F_5$ $20$ $-1$ ✓ 10T4, 20T5
5T4 $A_5$ $60$ $1$ 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
5T5 $S_5$ $120$ $-1$ 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T2 $S_3$ $6$ $-1$ ✓ $C_2$, $S_3$ 3T2
6T3 $D_{6}$ $12$ $-1$ ✓ $C_2$, $S_3$ 6T3, 12T3
6T4 $A_4$ $12$ $1$ ✓ $C_3$ 4T4, 12T4
6T5 $S_3\times C_3$ $18$ $-1$ ✓ $C_2$ 9T4, 18T3
6T6 $A_4\times C_2$ $24$ $-1$ ✓ $C_3$ 8T13, 12T6, 12T7, 24T9
6T7 $S_4$ $24$ $1$ ✓ $S_3$ 4T5, 6T8, 8T14, 12T8, 12T9, 24T10
6T8 $S_4$ $24$ $-1$ ✓ $S_3$ 4T5, 6T7, 8T14, 12T8, 12T9, 24T10
6T9 $S_3^2$ $36$ $-1$ ✓ $C_2$ 9T8, 12T16, 18T9, 18T11 x 2, 36T13
6T10 $C_3^2:C_4$ $36$ $1$ ✓ $C_2$ 6T10, 9T9, 12T17 x 2, 18T10, 36T14
6T11 $S_4\times C_2$ $48$ $-1$ ✓ $S_3$ 6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2
6T12 $\PSL(2,5)$ $60$ $1$ 5T4, 10T7, 12T33, 15T5, 20T15, 30T9
6T13 $C_3^2:D_4$ $72$ $-1$ ✓ $C_2$ 6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2
6T14 $\PGL(2,5)$ $120$ $-1$ 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T15 $A_6$ $360$ $1$ 6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
6T16 $S_6$ $720$ $-1$ 6T16, 10T32, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96
7T2 $D_{7}$ $14$ $-1$ ✓ 14T2
7T3 $C_7:C_3$ $21$ $1$ ✓ 21T2
7T4 $F_7$ $42$ $-1$ ✓ 14T4, 21T4, 42T4
7T5 $\GL(3,2)$ $168$ $1$ 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
7T6 $A_7$ $2520$ $1$ 15T47 x 2, 21T33, 35T28, 42T294, 42T299
7T7 $S_7$ $5040$ $-1$ 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
  displayed columns for results

Results are complete for degrees $\leq 23$.