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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 (42 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
42998169600000000.ey.1.a1.a1 $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_1$ $1$ ✓
85996339200000000.dw.2._.N $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.ee.2._.J $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.ee.2._.Z $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.en.2._.N $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2^2.D_4^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.hk.2._.D $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4^2.C_4:D_4$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.hn.2._.C $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4^2.(C_4\times D_4)$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.hu.2._.D $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4^2:C_4.D_4$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
85996339200000000.hy.2._.C $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4:D_4.D_4$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.4._.DG $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.FS $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cx.4._.HU $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^2.D_4.C_2^3$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
171992678400000000.cx.4._.JQ $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^2.D_4.C_2^3$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
171992678400000000.ge.4._.N $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.C_4^2.C_2^2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.ge.4._.U $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.C_4^2.C_2^2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.gh.4._.L $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.C_2^5.C_2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.gh.4._.Z $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.C_2^5.C_2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.gm.4._.N $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^5.D_4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.gn.4._.M $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4^2.D_4^2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.gn.4._.BG $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4^2.D_4^2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.gq.4._.BI $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4^2.D_4^2$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
257989017600000000.m.6._.D $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2^4.C_2^4.S_3$ $2^{25} \cdot 3^{9} \cdot 5^{8}$ $2 \cdot 3$ $-$
257989017600000000.q.6._.D $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.S_4$ $2^{25} \cdot 3^{9} \cdot 5^{8}$ $2 \cdot 3$ $-$
343985356800000000.ec.8._.D $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.D_4^2.C_2$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
343985356800000000.ec.8._.I $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.D_4^2.C_2$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
343985356800000000.ec.8._.L $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.D_4^2.C_2$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
343985356800000000.ec.8._.S $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4^2.D_4^2.C_2$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
343985356800000000.el.8._.HK $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2^4.C_2^5.C_4$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
343985356800000000.em.8._.GD $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^2.C_2^4.C_2^3$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
343985356800000000.fq.8._.CL $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.C_2^2\wr C_2$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
343985356800000000.ft.8._.CC $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^2.C_4^2.D_4$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
343985356800000000.gd.8._.CL $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^2.C_2^4.C_2^3$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
343985356800000000.ge.8._.BX $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^2.C_2^4.C_2^3$ $2^{27} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
515978035200000000.q.12._.L $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.S_4.C_2$ $2^{26} \cdot 3^{9} \cdot 5^{8}$ $2^{2} \cdot 3$ $-$
515978035200000000.q.12._.T $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.S_4.C_2$ $2^{26} \cdot 3^{9} \cdot 5^{8}$ $2^{2} \cdot 3$ $-$
515978035200000000.u.12._.T $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.S_4.C_2$ $2^{26} \cdot 3^{9} \cdot 5^{8}$ $2^{2} \cdot 3$ $-$
515978035200000000.u.12._.BA $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.S_4.C_2$ $2^{26} \cdot 3^{9} \cdot 5^{8}$ $2^{2} \cdot 3$ $-$
515978035200000000.v.12._.N $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.S_4.C_2$ $2^{26} \cdot 3^{9} \cdot 5^{8}$ $2^{2} \cdot 3$ $-$
515978035200000000.bc.12._.O $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.Q_8^2.C_2.S_4$ $2^{26} \cdot 3^{9} \cdot 5^{8}$ $2^{2} \cdot 3$ $-$
1031956070400000000.x.24._.BE $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.A_4.D_4$ $2^{27} \cdot 3^{9} \cdot 5^{8}$ $2^{3} \cdot 3$ $-$
1031956070400000000.ba.24._.Y $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_4^3.A_4.D_4$ $2^{27} \cdot 3^{9} \cdot 5^{8}$ $2^{3} \cdot 3$ $-$
3611846246400000000.c.84._.L $A_5^8.C_2\wr C_4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2.C_2^6.\PSL(2,7)$ $2^{26} \cdot 3^{9} \cdot 5^{8} \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
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