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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (26 matches)

  displayed columns for results
Label Name Order Parity Solvable Subfields Low Degree Siblings
16T1829 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $D_{4}$ 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
16T1831 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$ x 3, $C_2^2$ 16T1829, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14179 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14180 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14181 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14182 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14183 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14184 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14185 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14186 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14426 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14430 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14434 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14438 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14442 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14446 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14450 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
24T14454 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $C_2$, $C_3^2:D_4$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
36T14677 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $S_3^2:C_2$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
36T14678 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $S_3^2:C_2$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
36T14679 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $S_3^2:C_2$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
36T14680 $C_2^5.S_4\wr C_2$ $36864$ $1$ ✓ $C_2$, $S_3^2:C_2$, $S_3^2:C_2^2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
36T15146 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $S_3^2:C_2$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146, 36T15148 x 2, 36T15151 x 2, 36T15153 x 2
36T15148 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $S_3^2:C_2$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148, 36T15151 x 2, 36T15153 x 2
36T15151 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $S_3^2:C_2$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151, 36T15153 x 2
36T15153 $C_2^5.S_4\wr C_2$ $36864$ $-1$ ✓ $S_3^2:C_2$, $S_4\wr C_2$ 16T1829, 16T1831, 24T14179, 24T14180, 24T14181, 24T14182, 24T14183, 24T14184, 24T14185, 24T14186, 24T14426, 24T14430, 24T14434, 24T14438, 24T14442, 24T14446, 24T14450, 24T14454, 32T1515105 x 2, 32T1515113, 32T1515177, 32T1515178, 32T1515179, 32T1515183, 32T1515184, 32T1515185, 36T14677 x 2, 36T14678 x 2, 36T14679 x 2, 36T14680 x 2, 36T15146 x 2, 36T15148 x 2, 36T15151 x 2, 36T15153
  displayed columns for results

Results are complete for degrees $\leq 23$.