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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (1-50 of 1117 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
20T1 $C_{20}$ $20$ $-1$ ✓ $C_2$, $C_4$, $C_5$, $C_{10}$
20T2 $C_5:C_4$ $20$ $-1$ ✓ $C_2$, $C_4$, $D_{5}$, $D_5$
20T3 $C_2\times C_{10}$ $20$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_5$, $C_{10}$ x 3
20T4 $D_{10}$ $20$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $D_5$, $D_{10}$ x 2 10T3 x 2
20T5 $F_5$ $20$ $-1$ ✓ $C_2$, $C_4$, $F_5$, $F_5$ 5T3, 10T4
20T6 $C_4\times D_5$ $40$ $-1$ ✓ $C_2$, $C_4$, $D_{5}$, $D_{10}$ 20T6, 40T9
20T7 $C_5:D_4$ $40$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $D_{10}$ 20T11, 40T11
20T8 $C_2\times D_{10}$ $40$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $D_{10}$ x 3 20T8 x 3, 40T10
20T9 $C_2\times F_5$ $40$ $-1$ ✓ $C_2$, $C_4$, $F_5$, $F_5$ 10T5 x 2, 20T13, 40T14
20T10 $D_{20}$ $40$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $D_{10}$ 20T10, 40T12
20T11 $C_5:D_4$ $40$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $D_5$ 20T7, 40T11
20T12 $C_5\times D_4$ $40$ $-1$ ✓ $C_2$, $D_{4}$, $C_5$, $C_{10}$ 20T12, 40T6
20T13 $C_2\times F_5$ $40$ $1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $F_5$, $F_{5}\times C_2$ x 2 10T5 x 2, 20T9, 40T14
20T14 $C_5\times A_4$ $60$ $1$ ✓ $A_4$, $C_5$ 30T11
20T15 $A_5$ $60$ $1$ $A_5$, $A_{5}$ 5T4, 6T12, 10T7, 12T33, 15T5, 30T9
20T16 $C_2^2\times F_5$ $80$ $1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $F_{5}\times C_2$ x 3 20T16 x 3, 40T44 x 3, 40T56
20T17 $C_2^4:C_5$ $80$ $1$ ✓ $C_5$, $C_2^4 : C_5$ x 2 10T8 x 3, 16T178, 20T17 x 5, 20T23, 40T57 x 3
20T18 $C_{20}:C_4$ $80$ $-1$ ✓ $C_2$, $D_{4}$, $F_5$, $F_{5}\times C_2$ 20T18, 40T52, 40T54
20T19 $D_{10}:C_4$ $80$ $-1$ ✓ $C_2$, $D_{4}$, $F_5$, $F_{5}\times C_2$ 20T19, 20T22 x 2, 40T26, 40T45, 40T55 x 2
20T20 $C_4\times F_5$ $80$ $-1$ ✓ $C_2$, $C_4$, $F_5$, $F_{5}\times C_2$ 20T20 x 3, 40T53 x 2
20T21 $D_4\times D_5$ $80$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $D_{10}$ 20T21 x 3, 40T22 x 2, 40T39 x 2, 40T40 x 2
20T22 $D_{10}:C_4$ $80$ $-1$ ✓ $C_2$, $D_{4}$, $F_5$, $F_5$ 20T19 x 2, 20T22, 40T26, 40T45, 40T55 x 2
20T23 $C_2^4:C_5$ $80$ $1$ ✓ $C_5$, $C_2^4 : C_5$ x 3 10T8 x 3, 16T178, 20T17 x 6, 40T57 x 3
20T24 $C_5\times D_{10}$ $100$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_5\times C_5$ 20T24
20T25 $C_5:C_{20}$ $100$ $-1$ ✓ $C_2$, $C_4$, $D_5\times C_5$ 20T25
20T26 $C_5:F_5$ $100$ $-1$ ✓ $C_2$, $C_4$ 25T11
20T27 $C_5:F_5$ $100$ $-1$ ✓ $C_2$, $C_4$, $C_5^2 : C_4$ 10T10 x 2, 20T27, 25T10
20T28 $D_5^2$ $100$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_5^2$ 10T9 x 2, 20T28, 25T12
20T29 $C_5\times F_5$ $100$ $-1$ ✓ $C_2$, $C_4$ 25T7
20T30 $S_5$ $120$ $-1$ $S_5$, $S_5$ 5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
20T31 $C_2\times A_5$ $120$ $1$ $C_2$, $A_{5}$ 10T11, 12T75, 12T76, 20T36, 24T203, 30T29, 30T30, 40T61
20T32 $S_5$ $120$ $1$ $C_2$, $S_5$ 5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
20T33 $C_5:S_4$ $120$ $-1$ ✓ $S_4$, $D_{5}$ 30T19, 30T31, 40T63
20T34 $C_5\times S_4$ $120$ $-1$ ✓ $S_4$, $C_5$ 30T33, 30T34, 40T64
20T35 $S_5$ $120$ $-1$ $S_5$ 5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 24T202, 30T22, 30T25, 30T27, 40T62
20T36 $C_2\times A_5$ $120$ $1$ $A_{5}$ 10T11, 12T75, 12T76, 20T31, 24T203, 30T29, 30T30, 40T61
20T37 $D_5\times A_4$ $120$ $1$ ✓ $A_4$, $D_{5}$ 30T20, 30T28, 40T65
20T38 $C_2^4:D_5$ $160$ $-1$ ✓ $D_{5}$, $(C_2^4 : C_5) : C_2$ 10T15 x 3, 10T16 x 3, 16T415, 20T38 x 5, 20T39, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146
20T39 $C_2^4:D_5$ $160$ $1$ ✓ $D_{5}$, $(C_2^4 : C_5) : C_2$ x 3 10T15 x 3, 10T16 x 3, 16T415, 20T38 x 6, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146
20T40 $C_2\wr C_5$ $160$ $1$ ✓ $C_5$, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 2 10T14 x 3, 20T40 x 11, 20T41 x 6, 20T44 x 3, 20T46 x 3, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3
20T41 $C_2\wr C_5$ $160$ $1$ ✓ $C_5$, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ 10T14 x 3, 20T40 x 12, 20T41 x 5, 20T44 x 3, 20T46 x 3, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3
20T42 $D_4\times F_5$ $160$ $-1$ ✓ $C_2$, $D_{4}$, $F_5$, $F_{5}\times C_2$ 20T42 x 3, 40T109 x 2, 40T110 x 2, 40T112, 40T118 x 2, 40T119 x 2
20T43 $C_2^4:D_5$ $160$ $1$ ✓ $C_2$, $D_{5}$, $D_5$, $(C_2^4 : C_5) : C_2$, $(C_2^4 : C_5) : C_2$ 10T15 x 3, 10T16 x 3, 16T415, 20T38 x 6, 20T39, 20T43 x 2, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146
20T44 $C_2\wr C_5$ $160$ $1$ ✓ $C_2$, $C_5$, $C_{10}$, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ 10T14 x 3, 20T40 x 12, 20T41 x 6, 20T44 x 2, 20T46 x 3, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3
20T45 $C_2^4:D_5$ $160$ $1$ ✓ $D_{5}$, $(C_2^4 : C_5) : C_2$, $(C_2^4 : C_5) : C_2$ x 2 10T15 x 3, 10T16 x 3, 16T415, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 2, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146
20T46 $C_2\wr C_5$ $160$ $1$ ✓ $C_5$, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 2 10T14 x 3, 20T40 x 12, 20T41 x 6, 20T44 x 3, 20T46 x 2, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3
20T47 $C_5^2:Q_8$ $200$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_5^2 : Q_8$ 10T20 x 3, 20T47 x 2, 25T17, 40T166 x 3
20T48 $D_5\wr C_2$ $200$ $-1$ ✓ $C_2$, $D_{4}$, $D_5^2 : C_2$ 10T19, 10T21 x 2, 20T48, 20T50 x 2, 20T55, 20T57 x 2, 25T21, 40T167 x 2, 40T170
20T49 $C_{10}:F_5$ $200$ $-1$ ✓ $C_2$, $C_4$, $C_5^2 : C_4$ 20T49, 20T52 x 2, 40T157 x 2
20T50 $D_5\wr C_2$ $200$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_5^2 : C_2$ 10T19, 10T21 x 2, 20T48 x 2, 20T50, 20T55, 20T57 x 2, 25T21, 40T167 x 2, 40T170
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Results are complete for degrees $\leq 23$.