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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 196 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
20.2.10.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}$ $2^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
20.5.10.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{10}$ $2^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
20.5.10.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{10}$ $2^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
20.5.10.a1.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{10}$ $2^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
30.1.10.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_5\times S_3$ $2 \cdot 3 \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
30.4.10.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{30}$ $2 \cdot 3 \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.2.10.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_{50}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.3.10.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times D_5$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.5.10.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{10}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.5.10.a1.b1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{10}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.5.10.a1.c1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{10}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.5.10.a1.d1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{10}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.5.10.a1.e1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{10}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
50.5.10.a1.f1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{10}$ $2 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
70.2.10.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_5\times D_7$ $2 \cdot 5 \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓ ✓
70.4.10.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_{70}$ $2 \cdot 5 \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓ ✓
110.1.10.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $F_{11}$ $2 \cdot 5 \cdot 11$ $C_{10}$ $2 \cdot 5$ ✓ ✓
110.2.10.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{11}:C_{10}$ $2 \cdot 5 \cdot 11$ $C_{10}$ $2 \cdot 5$ ✓ ✓
110.4.10.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_5\times D_{11}$ $2 \cdot 5 \cdot 11$ $C_{10}$ $2 \cdot 5$ ✓ ✓
110.6.10.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_{110}$ $2 \cdot 5 \cdot 11$ $C_{10}$ $2 \cdot 5$ ✓ ✓
130.2.10.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_5\times D_{13}$ $2 \cdot 5 \cdot 13$ $C_{10}$ $2 \cdot 5$ ✓ ✓
130.4.10.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_{130}$ $2 \cdot 5 \cdot 13$ $C_{10}$ $2 \cdot 5$ ✓ ✓
160.235.10.a1.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2\wr C_5$ $2^{5} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓ ✓
170.2.10.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_5\times D_{17}$ $2 \cdot 5 \cdot 17$ $C_{10}$ $2 \cdot 5$ ✓ ✓
170.4.10.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_{170}$ $2 \cdot 5 \cdot 17$ $C_{10}$ $2 \cdot 5$ ✓ ✓
190.2.10.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_5\times D_{19}$ $2 \cdot 5 \cdot 19$ $C_{10}$ $2 \cdot 5$ ✓ ✓
190.4.10.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $C_{190}$ $2 \cdot 5 \cdot 19$ $C_{10}$ $2 \cdot 5$ ✓ ✓
230.2.10.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ $C_5\times D_{23}$ $2 \cdot 5 \cdot 23$ $C_{10}$ $2 \cdot 5$ ✓ ✓
230.4.10.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ $C_{230}$ $2 \cdot 5 \cdot 23$ $C_{10}$ $2 \cdot 5$ ✓ ✓
290.2.10.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ $C_5\times D_{29}$ $2 \cdot 5 \cdot 29$ $C_{10}$ $2 \cdot 5$ ✓ ✓
290.4.10.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $C_{290}$ $2 \cdot 5 \cdot 29$ $C_{10}$ $2 \cdot 5$ ✓ ✓
310.1.10.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{31}:C_{10}$ $2 \cdot 5 \cdot 31$ $C_{10}$ $2 \cdot 5$ ✓ ✓
310.2.10.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{31}:C_{10}$ $2 \cdot 5 \cdot 31$ $C_{10}$ $2 \cdot 5$ ✓ ✓
310.4.10.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_5\times D_{31}$ $2 \cdot 5 \cdot 31$ $C_{10}$ $2 \cdot 5$ ✓ ✓
310.6.10.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ ✓ $C_{310}$ $2 \cdot 5 \cdot 31$ $C_{10}$ $2 \cdot 5$ ✓ ✓
370.2.10.a1.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ $C_5\times D_{37}$ $2 \cdot 5 \cdot 37$ $C_{10}$ $2 \cdot 5$ ✓ ✓
370.4.10.a1.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ ✓ $C_{370}$ $2 \cdot 5 \cdot 37$ $C_{10}$ $2 \cdot 5$ ✓ ✓
410.1.10.a1.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ $C_{41}:C_{10}$ $2 \cdot 5 \cdot 41$ $C_{10}$ $2 \cdot 5$ ✓ ✓
410.2.10.a1.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ $C_{41}:C_{10}$ $2 \cdot 5 \cdot 41$ $C_{10}$ $2 \cdot 5$ ✓ ✓
410.4.10.a1.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ $C_5\times D_{41}$ $2 \cdot 5 \cdot 41$ $C_{10}$ $2 \cdot 5$ ✓ ✓
410.6.10.a1.a1 $C_{41}$ $41$ $41$ ✓ ✓ ✓ ✓ $C_{410}$ $2 \cdot 5 \cdot 41$ $C_{10}$ $2 \cdot 5$ ✓ ✓
430.2.10.a1.a1 $C_{43}$ $43$ $43$ ✓ ✓ ✓ $C_5\times D_{43}$ $2 \cdot 5 \cdot 43$ $C_{10}$ $2 \cdot 5$ ✓ ✓
430.4.10.a1.a1 $C_{43}$ $43$ $43$ ✓ ✓ ✓ ✓ $C_{430}$ $2 \cdot 5 \cdot 43$ $C_{10}$ $2 \cdot 5$ ✓ ✓
470.2.10.a1.a1 $C_{47}$ $47$ $47$ ✓ ✓ ✓ $C_5\times D_{47}$ $2 \cdot 5 \cdot 47$ $C_{10}$ $2 \cdot 5$ ✓ ✓
470.4.10.a1.a1 $C_{47}$ $47$ $47$ ✓ ✓ ✓ ✓ $C_{470}$ $2 \cdot 5 \cdot 47$ $C_{10}$ $2 \cdot 5$ ✓ ✓
530.2.10.a1.a1 $C_{53}$ $53$ $53$ ✓ ✓ ✓ $C_5\times D_{53}$ $2 \cdot 5 \cdot 53$ $C_{10}$ $2 \cdot 5$ ✓ ✓
530.4.10.a1.a1 $C_{53}$ $53$ $53$ ✓ ✓ ✓ ✓ $C_{530}$ $2 \cdot 5 \cdot 53$ $C_{10}$ $2 \cdot 5$ ✓ ✓
590.2.10.a1.a1 $C_{59}$ $59$ $59$ ✓ ✓ ✓ $C_5\times D_{59}$ $2 \cdot 5 \cdot 59$ $C_{10}$ $2 \cdot 5$ ✓ ✓
590.4.10.a1.a1 $C_{59}$ $59$ $59$ ✓ ✓ ✓ ✓ $C_{590}$ $2 \cdot 5 \cdot 59$ $C_{10}$ $2 \cdot 5$ ✓ ✓
600.144.10.a1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_5\times S_5$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓ ✓
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