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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 68 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
51840.cr.1.a1.a1 $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_1$ $1$ ✓
51840.cr.2.a1.a1 $C_3^4:D_{10}.\SD_{16}$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.2.b1.a1 $C_2\times C_3^4.(C_8.F_5)$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.2.c1.a1 $C_2\times C_3^4.C_{80}.C_2$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.2.d1.a1 $F_{81}:C_4$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.2.d1.b1 $F_{81}:C_4$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.2.d1.c1 $F_{81}:C_4$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.2.d1.d1 $F_{81}:C_4$ $2^{6} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2$ $2$ ✓
51840.cr.4.a1.a1 $C_2\times C_3^4.(C_8\times D_5)$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.b1.a1 $C_2\times F_{81}$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
51840.cr.4.c1.a1 $C_2\times C_3^4.C_{40}.C_2$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
51840.cr.4.d1.a1 $C_3^4:C_{40}:C_4$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.d1.b1 $C_3^4:C_{40}:C_4$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.e1.a1 $C_3^4.(C_8.F_5)$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.e1.b1 $C_3^4.(C_8.F_5)$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.f1.a1 $C_3^4.C_{80}.C_2$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.f1.b1 $C_3^4.C_{80}.C_2$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
51840.cr.4.g1.a1 $C_3^4.C_{80}.C_2$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
51840.cr.4.g1.b1 $C_3^4.C_{80}:C_2$ $2^{5} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
51840.cr.8.a1.a1 $C_2\times C_3^4.D_{10}.C_2$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $D_4$ $2^{3}$
51840.cr.8.b1.a1 $C_2\times C_3^4:C_{40}$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
51840.cr.8.c1.a1 $C_2\times C_3^4:C_5.C_8$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $Q_8$ $2^{3}$
51840.cr.8.d1.a1 $C_3^4:(C_8\times D_5)$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^3$ $2^{3}$ ✓
51840.cr.8.e1.a1 $C_3^4:(C_8\times D_5)$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $D_4$ $2^{3}$
51840.cr.8.f1.a1 $C_3^4:(C_8\times D_5)$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
51840.cr.8.g1.a1 $C_3^4:(C_8\times D_5)$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $Q_8$ $2^{3}$
51840.cr.8.h1.a1 $F_{81}$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
51840.cr.8.h1.b1 $F_{81}$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
51840.cr.8.i1.a1 $C_3^4.C_{40}.C_2$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
51840.cr.8.i1.b1 $C_3^4.C_{40}.C_2$ $2^{4} \cdot 3^{4} \cdot 5$ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
51840.cr.16.a1.a1 $C_2\times C_3^4:D_{10}$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $\SD_{16}$ $2^{4}$
51840.cr.16.b1.a1 $C_2\times C_3^4:C_{20}$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4:C_4$ $2^{4}$
51840.cr.16.c1.a1 $C_2\times C_3^4:(C_5:C_4)$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $\SD_{16}$ $2^{4}$
51840.cr.16.d1.a1 $C_3^4:(C_4\times D_5)$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times D_4$ $2^{4}$
51840.cr.16.e1.a1 $C_3^4:(C_4\times D_5)$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $\SD_{16}$ $2^{4}$
51840.cr.16.f1.a1 $C_3^4:(C_4\times D_5)$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4:C_4$ $2^{4}$
51840.cr.16.g1.a1 $C_3^4:(C_4\times D_5)$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $\SD_{16}$ $2^{4}$
51840.cr.16.h1.a1 $C_3^4:C_{40}$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2\times C_4$ $2^{4}$ ✓
51840.cr.16.i1.a1 $C_3^4:C_{40}$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4:C_4$ $2^{4}$
51840.cr.16.j1.a1 $C_3^4:C_5:C_8$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_4:C_4$ $2^{4}$
51840.cr.16.k1.a1 $C_3^4:C_5:C_8$ $2^{3} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times Q_8$ $2^{4}$
51840.cr.20.a1.a1 $C_2\times C_3^4:C_{16}$ $2^{5} \cdot 3^{4}$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $F_5$ $2^{2} \cdot 5$
51840.cr.32.a1.a1 $C_2\times C_3^4:C_{10}$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_8:C_4$ $2^{5}$
51840.cr.32.b1.a1 $C_3^4:D_{10}$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times \SD_{16}$ $2^{5}$
51840.cr.32.c1.a1 $C_3^4:D_{10}$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_8:C_4$ $2^{5}$
51840.cr.32.d1.a1 $C_3^4:C_{20}$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2^2.D_4$ $2^{5}$
51840.cr.32.e1.a1 $C_3^4:C_{20}$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_8:C_4$ $2^{5}$
51840.cr.32.f1.a1 $C_3^4:C_5:C_4$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times \SD_{16}$ $2^{5}$
51840.cr.32.g1.a1 $C_3^4:C_5:C_4$ $2^{2} \cdot 3^{4} \cdot 5$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_8:C_4$ $2^{5}$
51840.cr.40.a1.a1 $C_2\times C_3^2:F_9$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_2\times F_{81}:C_4$ $2^{7} \cdot 3^{4} \cdot 5$ $C_2\times F_5$ $2^{3} \cdot 5$
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