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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 82 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
32.45.16.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3\times C_4$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
32.46.16.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2\times D_4$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
32.47.16.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2\times Q_8$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
32.48.16.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_4:C_2^2$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
32.49.16.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_4:C_2^2$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
32.50.16.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4.C_2^3$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
32.51.16.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^5$ $2^{5}$ $C_2^4$ $2^{4}$ ✓ ✓
48.51.16.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_2^2\times D_6$ $2^{4} \cdot 3$ $C_2^4$ $2^{4}$ ✓ ✓
48.52.16.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_2^3\times C_6$ $2^{4} \cdot 3$ $C_2^4$ $2^{4}$ ✓ ✓
80.51.16.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_2^2\times D_{10}$ $2^{4} \cdot 5$ $C_2^4$ $2^{4}$ ✓ ✓
80.52.16.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_2^3\times C_{10}$ $2^{4} \cdot 5$ $C_2^4$ $2^{4}$ ✓ ✓
112.42.16.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_2^2\times D_{14}$ $2^{4} \cdot 7$ $C_2^4$ $2^{4}$ ✓ ✓
112.43.16.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_2^3\times C_{14}$ $2^{4} \cdot 7$ $C_2^4$ $2^{4}$ ✓ ✓
176.41.16.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_2^2\times D_{22}$ $2^{4} \cdot 11$ $C_2^4$ $2^{4}$ ✓ ✓
176.42.16.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_2^3\times C_{22}$ $2^{4} \cdot 11$ $C_2^4$ $2^{4}$ ✓ ✓
208.50.16.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_2^2\times D_{26}$ $2^{4} \cdot 13$ $C_2^4$ $2^{4}$ ✓ ✓
208.51.16.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_2^3\times C_{26}$ $2^{4} \cdot 13$ $C_2^4$ $2^{4}$ ✓ ✓
272.53.16.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_2^2\times D_{34}$ $2^{4} \cdot 17$ $C_2^4$ $2^{4}$ ✓ ✓
272.54.16.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_2^3\times C_{34}$ $2^{4} \cdot 17$ $C_2^4$ $2^{4}$ ✓ ✓
304.41.16.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_2^2\times D_{38}$ $2^{4} \cdot 19$ $C_2^4$ $2^{4}$ ✓ ✓
304.42.16.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $C_2^3\times C_{38}$ $2^{4} \cdot 19$ $C_2^4$ $2^{4}$ ✓ ✓
368.41.16.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ $C_2^2\times D_{46}$ $2^{4} \cdot 23$ $C_2^4$ $2^{4}$ ✓ ✓
368.42.16.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ $C_2^3\times C_{46}$ $2^{4} \cdot 23$ $C_2^4$ $2^{4}$ ✓ ✓
464.50.16.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ $C_2^2\times D_{58}$ $2^{4} \cdot 29$ $C_2^4$ $2^{4}$ ✓ ✓
464.51.16.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $C_2^3\times C_{58}$ $2^{4} \cdot 29$ $C_2^4$ $2^{4}$ ✓ ✓
496.41.16.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_2^2\times D_{62}$ $2^{4} \cdot 31$ $C_2^4$ $2^{4}$ ✓ ✓
496.42.16.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ ✓ $C_2^3\times C_{62}$ $2^{4} \cdot 31$ $C_2^4$ $2^{4}$ ✓ ✓
592.50.16.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ $C_2^2\times D_{74}$ $2^{4} \cdot 37$ $C_2^4$ $2^{4}$ ✓ ✓
592.51.16.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ ✓ $C_2^3\times C_{74}$ $2^{4} \cdot 37$ $C_2^4$ $2^{4}$ ✓ ✓
656.52.16.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ $C_2^2\times D_{82}$ $2^{4} \cdot 41$ $C_2^4$ $2^{4}$ ✓ ✓
656.53.16.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ ✓ $C_2^3\times C_{82}$ $2^{4} \cdot 41$ $C_2^4$ $2^{4}$ ✓ ✓
688.41.16.a1 $C_{43}$ $43$ $43$ ✓ ✓ ✓ $C_2^2\times D_{86}$ $2^{4} \cdot 43$ $C_2^4$ $2^{4}$ ✓ ✓
688.42.16.a1 $C_{43}$ $43$ $43$ ✓ ✓ ✓ ✓ $C_2^3\times C_{86}$ $2^{4} \cdot 43$ $C_2^4$ $2^{4}$ ✓ ✓
752.41.16.a1 $C_{47}$ $47$ $47$ ✓ ✓ ✓ $C_2^2\times D_{94}$ $2^{4} \cdot 47$ $C_2^4$ $2^{4}$ ✓ ✓
752.42.16.a1 $C_{47}$ $47$ $47$ ✓ ✓ ✓ ✓ $C_2^3\times C_{94}$ $2^{4} \cdot 47$ $C_2^4$ $2^{4}$ ✓ ✓
848.50.16.a1 $C_{53}$ $53$ $53$ ✓ ✓ ✓ $C_2^2\times D_{106}$ $2^{4} \cdot 53$ $C_2^4$ $2^{4}$ ✓ ✓
848.51.16.a1 $C_{53}$ $53$ $53$ ✓ ✓ ✓ ✓ $C_2^3\times C_{106}$ $2^{4} \cdot 53$ $C_2^4$ $2^{4}$ ✓ ✓
944.41.16.a1 $C_{59}$ $59$ $59$ ✓ ✓ ✓ $C_2^2\times D_{118}$ $2^{4} \cdot 59$ $C_2^4$ $2^{4}$ ✓ ✓
944.42.16.a1 $C_{59}$ $59$ $59$ ✓ ✓ ✓ ✓ $C_2^3\times C_{118}$ $2^{4} \cdot 59$ $C_2^4$ $2^{4}$ ✓ ✓
960.11355.16.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_2^3\times S_5$ $2^{6} \cdot 3 \cdot 5$ $C_2^4$ $2^{4}$ ✓ ✓
960.11356.16.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_2^4\times A_5$ $2^{6} \cdot 3 \cdot 5$ $C_2^4$ $2^{4}$ ✓ ✓
976.50.16.a1 $C_{61}$ $61$ $61$ ✓ ✓ ✓ $C_2^2\times D_{122}$ $2^{4} \cdot 61$ $C_2^4$ $2^{4}$ ✓ ✓
976.51.16.a1 $C_{61}$ $61$ $61$ ✓ ✓ ✓ ✓ $C_2^3\times C_{122}$ $2^{4} \cdot 61$ $C_2^4$ $2^{4}$ ✓ ✓
1072.14.16.a1 $C_{67}$ $67$ $67$ ✓ ✓ ✓ ✓ $C_2^3\times C_{134}$ $2^{4} \cdot 67$ $C_2^4$ $2^{4}$ ✓ ✓
1072.42.16.a1 $C_{67}$ $67$ $67$ ✓ ✓ ✓ $C_2^2\times D_{134}$ $2^{4} \cdot 67$ $C_2^4$ $2^{4}$ ✓ ✓
1136.14.16.a1 $C_{71}$ $71$ $71$ ✓ ✓ ✓ ✓ $C_2^3\times C_{142}$ $2^{4} \cdot 71$ $C_2^4$ $2^{4}$ ✓ ✓
1136.42.16.a1 $C_{71}$ $71$ $71$ ✓ ✓ ✓ $C_2^2\times D_{142}$ $2^{4} \cdot 71$ $C_2^4$ $2^{4}$ ✓ ✓
1168.14.16.a1 $C_{73}$ $73$ $73$ ✓ ✓ ✓ ✓ $C_2^3\times C_{146}$ $2^{4} \cdot 73$ $C_2^4$ $2^{4}$ ✓ ✓
1168.42.16.a1 $C_{73}$ $73$ $73$ ✓ ✓ ✓ $C_2^2\times D_{146}$ $2^{4} \cdot 73$ $C_2^4$ $2^{4}$ ✓ ✓
1264.14.16.a1 $C_{79}$ $79$ $79$ ✓ ✓ ✓ ✓ $C_2^3\times C_{158}$ $2^{4} \cdot 79$ $C_2^4$ $2^{4}$ ✓ ✓
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