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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 11568 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
32T1 $C_2\times \OD_{16}$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_8:C_2$ x 2, $C_4\times C_2^2$, $C_8: C_2$ x 2, $C_2 \times (C_8:C_2)$ x 2 16T15 x 2
32T2 $\OD_{16}:C_2$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $(C_8:C_2):C_2$ x 3 16T16 x 3
32T3 $(C_2\times C_4):C_4$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2$ x 6, $C_4\times C_2^2$, $Q_8 : C_2$ x 2, $C_4^2:C_2$ x 2 16T17 x 2
32T4 $C_2\times D_4:C_2$ $32$ $1$ ✓ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2$ x 6, $C_2^4$, $Q_8 : C_2$ x 2, $C_2 \times (C_4\times C_2):C_2$ x 6 16T18 x 6
32T5 $C_4\times D_4$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 3, $C_4\times C_2^2$, $D_4\times C_2$, $Q_8 : C_2$, $C_4 \times D_4$ x 4 16T19 x 4
32T6 $C_4.C_2^3$ $32$ $1$ ✓ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $C_2^4$, $(C_2 \times Q_8):C_2$ x 5 16T20 x 5
32T7 $C_2\times C_2^2:C_4$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 8, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 4, $D_4\times C_2$ x 8, $C_2^2:C_4$ x 8, $C_4\times C_2^2$, $D_4\times C_2$ x 2, $C_2^2 : C_4$ x 4, $C_2 \times (C_2^2:C_4)$ x 4 16T21 x 4
32T8 $\OD_{32}$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $C_8\times C_2$, $C_{16} : C_2$ 16T22
32T9 $Q_8:C_2^2$ $32$ $1$ ✓ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $C_2^3 : D_4 $ x 6, $C_2^4$, $Q_8 : C_2^2$ x 9 8T22 x 6, 16T23 x 9
32T10 $C_2^2:C_8$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_8$ x 2, $C_4\times C_2$, $D_4$ x 2, $C_8:C_2$, $C_2^2:C_4$ x 2, $C_8\times C_2$, $C_8: C_2$, $C_2^2 : C_4$, $C_2^2 : C_8$ x 2 16T24 x 2
32T11 $C_2^2\times D_4$ $32$ $1$ ✓ $C_2$ x 15, $C_2^2$ x 35, $D_{4}$ x 8, $C_2^3$ x 15, $D_4$ x 4, $D_4\times C_2$ x 24, $C_2^4$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$ x 8 16T25 x 8
32T12 $D_4:C_4$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $D_{8}$ x 2, $QD_{16}$, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $QD_{16}$, $D_{8}$, $D_4:C_4$ x 2 16T26 x 2
32T13 $C_4^2:C_2$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 9, $Q_8 : C_2$ x 3, $C_4^2:C_2$ 16T27
32T14 $C_4\wr C_2$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_2^2:C_4$ x 2, $C_4\wr C_2$ x 2, $C_2^2 : C_4$, $C_4\wr C_2$, $C_4\wr C_2$ 8T17 x 2, 16T28, 16T42
32T15 $C_2\times D_8$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_{8}$ x 4, $D_4\times C_2$ x 4, $D_4\times C_2$, $D_{8}$ x 2, $C_2\times D_8$ x 4 16T29 x 4
32T16 $C_4.D_4$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 6, $D_4\times C_2$, $Q_8 : C_2$ x 2, $C_4.D_4$ x 2 16T30 x 2
32T17 $C_2^2:Q_8$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $Q_8$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 3, $Q_8\times C_2$, $D_4\times C_2$, $Q_8 : C_2$, $C_2^2:Q_8$ x 2 16T31 x 2
32T18 $\SD_{16}:C_2$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $D_4\times C_2$, $\SD_{16}:C_2$, $\SD_{16}:C_2$ 16T32, 16T50
32T19 $C_2^2.D_4$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_2^2:C_4$ x 2, $C_2^3 : C_4 $ x 2, $C_2^3: C_4$, $C_2^3: C_4$, $C_2^2 : C_4$, $C_2^2.D_4$ x 2, $C_2^2.D_4$, $C_2^2.D_4$ 8T19 x 2, 8T20, 8T21, 16T33 x 2, 16T52, 16T53
32T20 $C_2^2:D_4$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 8, $C_2^3$, $D_4$ x 4, $D_4\times C_2$ x 8, $Q_8:C_2$ x 3, $D_4\times C_2$ x 2, $Q_8 : C_2$, $C_2^2:D_4$ x 2, $C_2^2:D_4$ x 2 16T34 x 2, 16T43 x 2
32T21 $C_8:C_2^2$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Z_8 : Z_8^\times$ x 2, $D_4\times C_2$, $C_8:C_2^2$, $C_8:C_2^2$ x 2, $C_8:C_2^2$ 8T15 x 2, 16T35, 16T38 x 2, 16T45
32T22 $C_2^3.C_4$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_2^2:C_4$ x 2, $(C_8:C_2):C_2$ x 2, $C_2^2 : C_4$, $C_2^3.C_4$, $C_2^3.C_4$ x 2 8T16 x 2, 16T36, 16T41 x 2
32T23 $(C_2^2\times C_4):C_2$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 6, $D_4\times C_2$, $Q_8 : C_2$ x 2, $(C_2^2\times C_4):C_2$, $(C_2^2\times C_4):C_2$ x 2 16T37, 16T54 x 2
32T24 $C_2^2\wr C_2$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 6, $D_4\times C_2$ x 12, $C_2^2 \wr C_2$ x 8, $D_4\times C_2$ x 3, $C_2^2\wr C_2$ x 6, $C_2^2\wr C_2$ 8T18 x 8, 16T39 x 6, 16T46
32T25 $\OD_{16}.C_2$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $\OD_{16}.C_2$ 16T40
32T26 $D_8:C_2$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $D_4\times C_2$, $D_8:C_2$ x 2, $D_8:C_2$ 16T44 x 2, 16T47
32T27 $C_2\times \SD_{16}$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $QD_{16}$ x 2, $D_4\times C_2$ x 4, $D_4\times C_2$, $QD_{16}$ x 2, $C_2\times \SD_{16}$ x 2 16T48 x 2
32T28 $C_8.C_4$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_4:C_4$, $C_8.C_4$ 16T49
32T29 $C_4:D_4$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 6, $D_4\times C_2$ x 12, $D_4\times C_2$ x 3, $C_4^2:C_2$ x 4 16T51 x 4
32T30 $\SD_{32}$ $32$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$, $\SD_{32}$ 16T55
32T31 $D_{16}$ $32$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$, $D_{16}$ x 2 16T56 x 2
32T32 $C_2\times C_{16}$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $C_{16}$ x 2, $C_8\times C_2$
32T33 $C_{32}$ $32$ $-1$ ✓ $C_2$, $C_4$, $C_8$, $C_{16}$
32T34 $C_2^3\times C_4$ $32$ $1$ ✓ $C_2$ x 15, $C_4$ x 8, $C_2^2$ x 35, $C_4\times C_2$ x 28, $C_2^3$ x 15, $C_4\times C_2^2$ x 14, $C_2^4$
32T35 $C_2\times C_4:C_4$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 2, $Q_8$ x 2, $D_4\times C_2$ x 4, $C_4\times C_2^2$, $Q_8\times C_2$, $C_4:C_4$ x 4, $D_4\times C_2$
32T36 $C_2\times C_4^2$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 12, $C_2^2$ x 7, $C_4\times C_2$ x 18, $C_2^3$, $C_4\times C_2^2$ x 3, $C_4^2$ x 4
32T37 $C_2^2\times C_8$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_8$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $C_8\times C_2$ x 6
32T38 $C_4\times Q_8$ $32$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8$ x 2, $Q_8:C_2$ x 3, $C_4\times C_2^2$, $Q_8\times C_2$, $Q_8 : C_2$
32T39 $C_2^5$ $32$ $1$ ✓ $C_2$ x 31, $C_2^2$ x 155, $C_2^3$ x 155, $C_2^4$ x 31
32T40 $C_2^2\times Q_8$ $32$ $1$ ✓ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8$ x 4, $C_2^4$, $Q_8\times C_2$ x 6
32T41 $C_2.C_4^2$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $D_{4}$ x 6, $C_4\times C_2$ x 3, $D_4$ x 3, $Q_8$, $C_2^2:C_4$ x 6, $C_4^2$, $C_4:C_4$ x 3, $C_2^2 : C_4$ x 3
32T42 $C_2.\OD_{16}$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3, $C_8:C_2$ x 2, $C_4^2$, $C_8: C_2$ x 2
32T43 $C_4\times C_8$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_8$ x 4, $C_4\times C_2$ x 3, $C_4^2$, $C_8\times C_2$ x 2
32T44 $C_4:C_8$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_8$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_8:C_2$, $C_8\times C_2$, $C_8: C_2$, $C_4:C_4$
32T45 $C_4:Q_8$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $Q_8$ x 4, $D_4\times C_2$ x 4, $Q_8\times C_2$ x 2, $D_4\times C_2$
32T46 $C_4.Q_8$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2, $Q_8:C_2$ x 6, $Q_8\times C_2$, $Q_8 : C_2$ x 2
32T47 $C_8:C_4$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $QD_{16}$ x 2, $C_4:C_4$, $QD_{16}$ x 2
32T48 $C_2.D_8$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $D_{8}$ x 2, $C_4:C_4$, $D_{8}$, $Q_{16}$
32T49 $C_2\times Q_{16}$ $32$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $D_4\times C_2$, $Q_{16}$ x 2
32T50 $Q_8:C_4$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $QD_{16}$, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $QD_{16}$, $Q_{16}$
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Results are complete for degrees $\leq 23$.