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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 98 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
5040.bh.1.a1.a1 $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_1$ $1$ ✓
5040.bh.2.a1.a1 $S_3\times D_5\times F_7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.2.b1.a1 $S_3\times C_{35}:C_{12}$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.2.c1.a1 $S_3\times C_{35}:C_{12}$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.2.d1.a1 $C_3\times F_5\times F_7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.2.e1.a1 $C_{15}:C_4\times F_7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.2.f1.a1 $D_{105}:C_{12}$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.2.g1.a1 $D_{105}:C_{12}$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
5040.bh.3.a1.a1 $S_3\times D_7\times F_5$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_3$ $3$ ✓
5040.bh.4.a1.a1 $C_{35}:C_6\times S_3$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.b1.a1 $D_{21}:C_{30}$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_4$ $2^{2}$ ✓
5040.bh.4.c1.a1 $D_{105}:C_6$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_4$ $2^{2}$ ✓
5040.bh.4.d1.a1 $C_{35}:C_6^2$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.e1.a1 $D_{105}:C_6$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.f1.a1 $C_{105}:C_{12}$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.g1.a1 $C_{105}:C_{12}$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.h1.a1 $C_{105}:C_{12}$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.i1.a1 $C_{105}:C_{12}$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5040.bh.4.j1.a1 $D_{15}\times F_7$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_4$ $2^{2}$ ✓
5040.bh.4.k1.a1 $D_{15}:F_7$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_4$ $2^{2}$ ✓
5040.bh.6.a1.a1 $D_{15}:D_{14}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.6.b1.a1 $D_{15}:C_{28}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.6.c1.a1 $C_{35}:C_4\times S_3$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.6.d1.a1 $D_{35}:C_{12}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.6.e1.a1 $C_{15}:C_4\times D_7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.6.f1.a1 $F_5\times F_7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $S_3$ $2 \cdot 3$
5040.bh.6.g1.a1 $F_5\times D_{21}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.6.h1.a1 $D_{105}:C_4$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5040.bh.8.a1.a1 $C_{21}:C_{30}$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
5040.bh.8.b1.a1 $C_{105}:C_6$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^3$ $2^{3}$ ✓
5040.bh.8.c1.a1 $C_{15}\times F_7$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
5040.bh.8.d1.a1 $C_{105}:C_6$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
5040.bh.8.e1.a1 $C_{21}:C_{30}$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
5040.bh.8.f1.a1 $C_{105}:C_6$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
5040.bh.8.g1.a1 $C_{105}:C_6$ $2 \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
5040.bh.12.a1.a1 $C_{21}:D_{10}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.b1.a1 $C_{15}:D_{14}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_{12}$ $2^{2} \cdot 3$ ✓
5040.bh.12.c1.a1 $S_3\times D_{35}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_{12}$ $2^{2} \cdot 3$ ✓
5040.bh.12.d1.a1 $C_{15}:D_{14}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.e1.a1 $D_5\times F_7$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $D_6$ $2^{2} \cdot 3$
5040.bh.12.f1.a1 $D_5\times D_{21}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.g1.a1 $F_5\times C_{21}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.h1.a1 $C_{15}:C_{28}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.i1.a1 $C_{105}:C_4$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.j1.a1 $C_{105}:C_4$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5040.bh.12.k1.a1 $C_{35}:C_{12}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $D_6$ $2^{2} \cdot 3$
5040.bh.12.l1.a1 $C_{35}:C_{12}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $D_6$ $2^{2} \cdot 3$
5040.bh.12.m1.a1 $D_7\times D_{15}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_{12}$ $2^{2} \cdot 3$ ✓
5040.bh.12.n1.a1 $C_{15}:D_{14}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_{12}$ $2^{2} \cdot 3$ ✓
5040.bh.16.a1.a1 $C_{105}:C_3$ $3^{2} \cdot 5 \cdot 7$ ✓ ✓ $S_3\times F_5\times F_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2\times C_4$ $2^{4}$ ✓
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