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Label Name Order Parity Solvable Subfields Low Degree Siblings
3T2 $S_3$ $6$ $-1$ yes 6T2
4T2 $C_2^2$ $4$ $1$ yes $C_2$ x 3
4T3 $D_{4}$ $8$ $-1$ yes $C_2$ 4T3, 8T4
4T4 $A_4$ $12$ $1$ yes 6T4, 12T4
4T5 $S_4$ $24$ $-1$ yes 6T7, 6T8, 8T14, 12T8, 12T9, 24T10
5T2 $D_{5}$ $10$ $1$ yes 10T2
5T3 $F_5$ $20$ $-1$ yes 10T4, 20T5
5T4 $A_5$ $60$ $1$ no 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
5T5 $S_5$ $120$ $-1$ no 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T2 $S_3$ $6$ $-1$ yes $C_2$, $S_3$ 3T2
6T3 $D_{6}$ $12$ $-1$ yes $C_2$, $S_3$ 6T3, 12T3
6T4 $A_4$ $12$ $1$ yes $C_3$ 4T4, 12T4
6T5 $S_3\times C_3$ $18$ $-1$ yes $C_2$ 9T4, 18T3
6T6 $A_4\times C_2$ $24$ $-1$ yes $C_3$ 8T13, 12T6, 12T7, 24T9
6T7 $S_4$ $24$ $1$ yes $S_3$ 4T5, 6T8, 8T14, 12T8, 12T9, 24T10
6T8 $S_4$ $24$ $-1$ yes $S_3$ 4T5, 6T7, 8T14, 12T8, 12T9, 24T10
6T9 $S_3^2$ $36$ $-1$ yes $C_2$ 9T8, 12T16, 18T9, 18T11 x 2, 36T13
6T10 $C_3^2:C_4$ $36$ $1$ yes $C_2$ 6T10, 9T9, 12T17 x 2, 18T10, 36T14
6T11 $S_4\times C_2$ $48$ $-1$ yes $S_3$ 6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2
6T12 $\PSL(2,5)$ $60$ $1$ no 5T4, 10T7, 12T33, 15T5, 20T15, 30T9
6T13 $C_3^2:D_4$ $72$ $-1$ yes $C_2$ 6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2
6T14 $\PGL(2,5)$ $120$ $-1$ no 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T15 $A_6$ $360$ $1$ no 6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
6T16 $S_6$ $720$ $-1$ no 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 $D_{7}$ $14$ $-1$ yes 14T2
7T3 $C_7:C_3$ $21$ $1$ yes 21T2
7T4 $F_7$ $42$ $-1$ yes 14T4, 21T4, 42T4
7T5 $\GL(3,2)$ $168$ $1$ no 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
7T6 $A_7$ $2520$ $1$ no 15T47 x 2, 21T33, 35T28, 42T294, 42T299
7T7 $S_7$ $5040$ $-1$ no 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
8T2 $C_4\times C_2$ $8$ $1$ yes $C_2$ x 3, $C_4$ x 2, $C_2^2$
8T3 $C_2^3$ $8$ $1$ yes $C_2$ x 7, $C_2^2$ x 7
8T4 $D_4$ $8$ $1$ yes $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 4T3 x 2
8T5 $Q_8$ $8$ $1$ yes $C_2$ x 3, $C_2^2$
8T6 $D_{8}$ $16$ $-1$ yes $C_2$, $D_{4}$ 8T6, 16T13
8T7 $C_8:C_2$ $16$ $-1$ yes $C_2$, $C_4$ 16T6
8T8 $QD_{16}$ $16$ $-1$ yes $C_2$, $D_{4}$ 16T12
8T9 $D_4\times C_2$ $16$ $1$ yes $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 8T9 x 3, 16T9
8T10 $C_2^2:C_4$ $16$ $1$ yes $C_2$, $C_4$, $D_{4}$ x 2 8T10, 16T10
8T11 $Q_8:C_2$ $16$ $1$ yes $C_2$ x 3, $C_2^2$ 8T11 x 2, 16T11
8T12 $\SL(2,3)$ $24$ $1$ yes $A_4$ 24T7
8T13 $A_4\times C_2$ $24$ $1$ yes $C_2$, $A_4$ 6T6, 12T6, 12T7, 24T9
8T14 $S_4$ $24$ $1$ yes $C_2$, $S_4$ 4T5, 6T7, 6T8, 12T8, 12T9, 24T10
8T15 $Z_8 : Z_8^\times$ $32$ $-1$ yes $C_2$, $D_{4}$ 8T15, 16T35, 16T38 x 2, 16T45, 32T21
8T16 $(C_8:C_2):C_2$ $32$ $-1$ yes $C_2$, $C_4$ 8T16, 16T36, 16T41 x 2, 32T22
8T17 $C_4\wr C_2$ $32$ $-1$ yes $C_2$, $D_{4}$ 8T17, 16T28, 16T42, 32T14
8T18 $C_2^2 \wr C_2$ $32$ $1$ yes $C_2$, $D_{4}$ x 3 8T18 x 7, 16T39 x 6, 16T46, 32T24
8T19 $C_2^3 : C_4 $ $32$ $1$ yes $C_2$, $D_{4}$ 8T19, 8T20, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T20 $C_2^3: C_4$ $32$ $1$ yes $C_2$, $C_4$ 8T19 x 2, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T21 $C_2^3: C_4$ $32$ $-1$ yes $C_2$ x 3, $C_2^2$ 8T19 x 2, 8T20, 16T33 x 2, 16T52, 16T53, 32T19
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Results are complete for degrees $\leq 23$.