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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 120 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
10000.ca.10000.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
20000.dx.10000.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_5^3\times C_{10}):\OD_{16}$ $2^{5} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
20000.dz.10000.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_5^3\times C_{10}).\OD_{16}$ $2^{5} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
20000.ea.10000.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_5^3\times C_{10}).\OD_{16}$ $2^{5} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
40000.do.10000.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2.C_5^2:\OD_{16}$ $2^{6} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
40000.dp.10000.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_5^2:(C_{10}^2:\OD_{16})$ $2^{6} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
40000.dq.10000.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_5^4.C_2^3:C_8$ $2^{6} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
40000.dr.10000.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2.C_5^2:\OD_{16}$ $2^{6} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
50000.cf.10000.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_5^5.\OD_{16}$ $2^{4} \cdot 5^{5}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
50000.cg.10000._.A $C_5$ $5$ ✓ ✓ ✓ $C_5^5:\OD_{16}$ $2^{4} \cdot 5^{5}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
50000.ci.10000.A $C_5$ $5$ ✓ ✓ ✓ $C_5^5:\OD_{16}$ $2^{4} \cdot 5^{5}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
50000.cj.10000.A $C_5$ $5$ ✓ ✓ ✓ $C_5^5.\OD_{16}$ $2^{4} \cdot 5^{5}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$ ✓
80000.da.10000._.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_5^4:(C_2^3:\OD_{16})$ $2^{7} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
100000.q.10000.A $D_5$ $2 \cdot 5$ ✓ ✓ $C_5^5:(C_2\times \OD_{16})$ $2^{5} \cdot 5^{5}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
160000.bi.10000._.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_{10}^2.C_{10}^2:\OD_{16}$ $2^{8} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
160000.bn.10000.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_{10}^2.C_{10}^2:\OD_{16}$ $2^{8} \cdot 5^{4}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
250000.ck.10000._.B $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^6:\OD_{16}$ $2^{4} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
250000.cl.10000.A $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^6:\OD_{16}$ $2^{4} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
250000.co.10000.A $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^6:\OD_{16}$ $2^{4} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
250000.cq.10000._.B $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^6:\OD_{16}$ $2^{4} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
250000.cr.10000.A $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^6:\OD_{16}$ $2^{4} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
250000.cs.10000.A $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^6:\OD_{16}$ $2^{4} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
500000.l.10000.A $C_5:D_5$ $2 \cdot 5^{2}$ ✓ ✓ $C_5^6.C_4:C_8$ $2^{5} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
500000.cw.10000._.A $C_5:D_5$ $2 \cdot 5^{2}$ ✓ ✓ $C_5^6:(C_2\times \OD_{16})$ $2^{5} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
500000.dc.10000.A $C_5:D_5$ $2 \cdot 5^{2}$ ✓ ✓ $C_5^5.C_{40}:C_4$ $2^{5} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
500000.dg.10000.A $C_5:D_5$ $2 \cdot 5^{2}$ ✓ ✓ $C_5^6:(C_2\times \OD_{16})$ $2^{5} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
500000.dh.10000.A $C_5:D_5$ $2 \cdot 5^{2}$ ✓ ✓ $C_5^5.C_{40}:C_4$ $2^{5} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
500000.er.10000.A $C_5:D_5$ $2 \cdot 5^{2}$ ✓ ✓ $C_5^4.C_{10}^2:C_8$ $2^{5} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
1000000.dm.10000._.A $D_5^2$ $2^{2} \cdot 5^{2}$ ✓ ✓ $C_5^4.C_{10}^2:\OD_{16}$ $2^{6} \cdot 5^{6}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
1250000.bd.10000.A $C_5^3$ $5^{3}$ ✓ ✓ ✓ $C_5^7:\OD_{16}$ $2^{4} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
1250000.be.10000._.F $C_5^3$ $5^{3}$ ✓ ✓ ✓ $C_5^7:\OD_{16}$ $2^{4} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
1250000.bf.10000.A $C_5^3$ $5^{3}$ ✓ ✓ ✓ $C_5^7:\OD_{16}$ $2^{4} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
1250000.bg.10000.C $C_5^3$ $5^{3}$ ✓ ✓ ✓ $C_5^7:\OD_{16}$ $2^{4} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
1250000.bh.10000.A $C_5^3$ $5^{3}$ ✓ ✓ ✓ $C_5^7:\OD_{16}$ $2^{4} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
2500000.k.10000._.A $C_5^3:C_2$ $2 \cdot 5^{3}$ ✓ ✓ $C_5^7:(C_2\times \OD_{16})$ $2^{5} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
2500000.l.10000._.A $C_5^3:C_2$ $2 \cdot 5^{3}$ ✓ ✓ $C_5^7:(C_2\times \OD_{16})$ $2^{5} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
2500000.m.10000._.A $C_5^3:C_2$ $2 \cdot 5^{3}$ ✓ ✓ $C_5^6.C_{40}:C_4$ $2^{5} \cdot 5^{7}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.A $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.B $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.C $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.D $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.E $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.F $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.G $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.H $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.I $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.J $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.K $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.L $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
6250000.m.10000._.M $C_5^4$ $5^{4}$ ✓ ✓ $C_5^8.\OD_{16}$ $2^{4} \cdot 5^{8}$ $C_5^4.\OD_{16}$ $2^{4} \cdot 5^{4}$
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