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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 384 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
8400.i.1.a1.a1 $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_1$ $1$ ✓
8400.i.2.a1.a1 $D_{210}:C_{10}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.2.a1.b1 $D_{210}:C_{10}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.2.b1.a1 $C_{10}\times C_{420}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.2.c1.a1 $C_{20}\times D_{105}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.2.c1.b1 $C_{20}\times D_{105}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.2.d1.a1 $C_5\times D_{420}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.2.e1.a1 $C_{420}.C_{10}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
8400.i.3.a1.a1 $D_{140}:C_{10}$ $2^{4} \cdot 5^{2} \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $3$ $-$
8400.i.4.a1.a1 $C_{10}\times C_{210}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.4.b1.a1 $C_5\times D_{210}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.4.b1.b1 $C_5\times D_{210}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.4.c1.a1 $C_5\times C_{420}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.4.d1.a1 $C_5\times C_{420}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.4.e1.a1 $C_{105}:C_{20}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.4.e1.b1 $C_{105}:C_{20}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
8400.i.5.a1.a1 $D_{420}:C_2$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5$ $5$ ✓
8400.i.5.b1.a1 $D_{84}:C_{10}$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $5$ $-$
8400.i.6.a1.a1 $C_{10}\times C_{140}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $S_3$ $2 \cdot 3$
8400.i.6.b1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.6.b1.b1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.6.c1.a1 $C_{20}\times D_{35}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.6.c1.b1 $C_{20}\times D_{35}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.6.d1.a1 $C_5\times D_{140}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.6.e1.a1 $C_{140}.C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.7.a1.a1 $D_{60}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2}$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $7$ $-$
8400.i.8.a1.a1 $C_5\times C_{210}$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2^3$ $2^{3}$ ✓
8400.i.8.b1.a1 $C_5\times C_{210}$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2^{3}$ $-$
8400.i.8.c1.a1 $C_5\times D_{105}$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2^{3}$ $-$
8400.i.8.c1.b1 $C_5\times D_{105}$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2^{3}$ $-$
8400.i.10.a1.a1 $C_{105}:D_4$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.a1.b1 $C_{105}:D_4$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.b1.a1 $C_2\times C_{420}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $D_5$ $2 \cdot 5$
8400.i.10.c1.a1 $C_2\times C_{420}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.d1.a1 $C_4\times D_{105}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.d1.b1 $C_4\times D_{105}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.e1.a1 $D_{420}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.f1.a1 $C_{105}:Q_8$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
8400.i.10.g1.a1 $C_{105}:D_4$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.g1.b1 $C_{105}:D_4$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.h1.a1 $C_2\times C_{420}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.h1.b1 $C_2\times C_{420}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.i1.a1 $C_{20}\times D_{21}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.i1.b1 $C_{20}\times D_{21}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.j1.a1 $C_5\times D_{84}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.10.k1.a1 $C_{105}:Q_8$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 5$ $-$
8400.i.12.a1.a1 $C_{10}\times C_{70}$ $2^{2} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
8400.i.12.b1.a1 $C_5\times C_{140}$ $2^{2} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
8400.i.12.c1.a1 $C_5\times C_{140}$ $2^{2} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
8400.i.12.d1.a1 $C_5\times D_{70}$ $2^{2} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2^{2} \cdot 3$ $-$
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