## Results (1-50 of at least 5000)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
30T1 $C_{30}$ $30$ $-1$ yes $C_2$, $C_3$, $C_5$, $C_6$, $C_{10}$, $C_{15}$
30T2 $C_5\times S_3$ $30$ $-1$ yes $C_2$, $S_3$, $C_5$, $S_3$, $C_{10}$, $S_3 \times C_5$ 15T4
30T3 $D_{15}$ $30$ $-1$ yes $C_2$, $S_3$, $D_{5}$, $S_3$, $D_5$, $D_{15}$ 15T2
30T4 $C_3\times D_5$ $30$ $-1$ yes $C_2$, $C_3$, $D_{5}$, $C_6$, $D_5$, $D_5\times C_3$ 15T3
30T5 $C_6\times D_5$ $60$ $-1$ yes $C_2$, $C_3$, $D_{5}$, $C_6$, $D_{10}$, $D_5\times C_3$ 30T5
30T6 $C_3:F_5$ $60$ $-1$ yes $C_2$, $S_3$, $F_5$, $S_3$, $F_5$, $C_{15} : C_4$ 15T6
30T7 $C_3\times F_5$ $60$ $-1$ yes $C_2$, $C_3$, $F_5$, $C_6$, $F_5$, $F_5\times C_3$ 15T8
30T8 $S_3\times D_5$ $60$ $-1$ yes $C_2$, $S_3$, $D_{5}$, $S_3$, $D_{10}$, $D_5\times S_3$ 15T7, 30T10, 30T13
30T9 $A_5$ $60$ $1$ no $A_5$, $\PSL(2,5)$, $A_{5}$, $A_5$ 5T4, 6T12, 10T7, 12T33, 15T5, 20T15
30T10 $S_3\times D_5$ $60$ $-1$ yes $C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_5$, $D_5\times S_3$ 15T7, 30T8, 30T13
30T11 $C_5\times A_4$ $60$ $1$ yes $C_3$, $C_5$, $A_4$, $C_{15}$ 20T14
30T12 $C_{10}\times S_3$ $60$ $-1$ yes $C_2$, $S_3$, $C_5$, $D_{6}$, $C_{10}$, $S_3 \times C_5$ 30T12
30T13 $S_3\times D_5$ $60$ $-1$ yes $C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_{10}$, $D_5\times S_3$ 15T7, 30T8, 30T10
30T14 $D_{30}$ $60$ $-1$ yes $C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_{10}$, $D_{15}$ 30T14
30T15 $C_{15}\times S_3$ $90$ $-1$ yes $C_2$, $C_5$, $S_3\times C_3$, $C_{10}$ 45T3
30T16 $C_3\times D_{15}$ $90$ $-1$ yes $C_2$, $D_{5}$, $S_3\times C_3$, $D_5$ 45T5
30T17 $C_2\times C_3:F_5$ $120$ $-1$ yes $C_2$, $S_3$, $F_5$, $D_{6}$, $F_{5}\times C_2$, $C_{15} : C_4$ 30T17
30T18 $C_{10}\times A_4$ $120$ $-1$ yes $C_3$, $C_5$, $A_4\times C_2$, $C_{15}$ 40T59
30T19 $C_5:S_4$ $120$ $1$ yes $S_3$, $D_{5}$, $S_4$, $D_{15}$ 20T33, 30T31, 40T63
30T20 $D_5\times A_4$ $120$ $-1$ yes $C_3$, $D_{5}$, $A_4\times C_2$, $D_5\times C_3$ 20T37, 30T28, 40T65
30T21 $C_2\times S_3\times D_5$ $120$ $-1$ yes $C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_{10}$, $D_5\times S_3$ 30T21 x 3
30T22 $S_5$ $120$ $-1$ no $S_5$, $\PGL(2,5)$, $S_5$ 5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T25, 30T27, 40T62
30T23 $S_3\times F_5$ $120$ $-1$ yes $C_2$, $S_3$, $F_5$, $D_{6}$, $F_{5}\times C_2$, $F_5 \times S_3$ 15T11, 30T24, 30T32
30T24 $S_3\times F_5$ $120$ $-1$ yes $C_2$, $S_3$, $F_5$, $D_{6}$, $F_5$, $F_5 \times S_3$ 15T11, 30T23, 30T32
30T25 $S_5$ $120$ $-1$ no $C_2$, $S_5$, $S_5$, $S_5$ 5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T27, 40T62
30T26 $C_6\times F_5$ $120$ $-1$ yes $C_2$, $C_3$, $F_5$, $C_6$, $F_{5}\times C_2$, $F_5\times C_3$ 30T26
30T27 $S_5$ $120$ $1$ no $S_5$, $S_5$, $S_5$ 5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 40T62
30T28 $D_5\times A_4$ $120$ $1$ yes $C_3$, $D_{5}$, $A_4$, $D_5\times C_3$ 20T37, 30T20, 40T65
30T29 $C_2\times A_5$ $120$ $-1$ no $A_5$, $A_5$ 10T11, 12T75, 12T76, 20T31, 20T36, 24T203, 30T30, 40T61
30T30 $C_2\times A_5$ $120$ $-1$ no $C_2$, $A_5$, $A_5\times C_2$, $A_5$ 10T11, 12T75, 12T76, 20T31, 20T36, 24T203, 30T29, 40T61
30T31 $C_5:S_4$ $120$ $-1$ yes $S_3$, $D_{5}$, $S_4$, $D_{15}$ 20T33, 30T19, 40T63
30T32 $S_3\times F_5$ $120$ $-1$ yes $C_2$, $S_3$, $F_5$, $S_3$, $F_{5}\times C_2$, $F_5 \times S_3$ 15T11, 30T23, 30T24
30T33 $C_5\times S_4$ $120$ $1$ yes $S_3$, $C_5$, $S_4$, $S_3 \times C_5$ 20T34, 30T34, 40T64
30T34 $C_5\times S_4$ $120$ $-1$ yes $S_3$, $C_5$, $S_4$, $S_3 \times C_5$ 20T34, 30T33, 40T64
30T35 $C_5^2:C_6$ $150$ $-1$ yes $C_2$, $C_3$, $C_6$, $(C_5^2 : C_3):C_2$ 15T12 x 2, 25T15, 30T35
30T36 $C_5\times D_{15}$ $150$ $-1$ yes $C_2$, $S_3$, $S_3$, $D_5\times C_5$ 30T36
30T37 $C_5^2:S_3$ $150$ $-1$ yes $C_2$, $S_3$, $S_3$, $(C_5^2 : C_3):C_2$ 15T13, 15T14, 25T16, 30T38
30T38 $C_5^2:S_3$ $150$ $-1$ yes $C_2$, $S_3$, $S_3$, $(C_5^2 : C_3):C_2$ 15T13, 15T14, 25T16, 30T37
30T39 $C_{15}\times D_5$ $150$ $-1$ yes $C_2$, $C_3$, $C_6$, $D_5\times C_5$ 30T39
30T40 $C_2\times C_5^2:C_3$ $150$ $-1$ yes $C_2$, $C_3$, $C_6$, $C_5^2 : C_3$ 30T40
30T41 $C_5\times S_3^2$ $180$ $-1$ yes $C_2$, $C_5$, $S_3^2$, $C_{10}$ 45T15
30T42 $S_3\times D_{15}$ $180$ $-1$ yes $C_2$, $D_{5}$, $S_3^2$, $D_{10}$ 45T13
30T43 $D_{15}:S_3$ $180$ $-1$ yes $C_2$, $D_{5}$, $S_3^2$, $D_5$ 45T21
30T44 $C_3\times S_3\times D_5$ $180$ $-1$ yes $C_2$, $D_{5}$, $S_3\times C_3$, $D_{10}$ 45T14
30T45 $C_3\times A_5$ $180$ $1$ no $C_3$, $A_{5}$ 15T15 x 2, 15T16, 18T90, 36T176, 45T16
30T46 $(C_3\times C_{15}):C_4$ $180$ $1$ yes $C_2$, $F_5$, $C_3^2:C_4$, $F_5$ 30T46, 45T27
30T47 $C_3\times C_3:F_5$ $180$ $-1$ yes $C_2$, $F_5$, $S_3\times C_3$, $F_5$ 45T18
30T48 $C_3^2:(C_5:C_4)$ $180$ $1$ yes $C_2$, $D_{5}$, $C_3^2:C_4$, $D_5$ 30T48, 45T26
30T49 $C_5\times C_3:S_3.C_2$ $180$ $1$ yes $C_2$, $C_5$, $C_3^2:C_4$, $C_{10}$ 30T49, 45T25
30T50 $F_{16}$ $240$ $1$ yes $C_3$, $C_5$, $C_{15}$ 16T447, 20T67
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Results are complete for degrees $\leq 23$.