Subgroups — C₁₁×Dic₅×C₄₇ #23780270

Order 10340.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₁×C₄₇	—	5	1	no	maximal, Hall
4	C₂×C₁₁×C₄₇	D₅	1	1	yes	characteristic
5	Dic₅×C₄₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₄₇	Dic₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₄₇	C₂×C₁₁	1	1	yes	characteristic
8	C₅×C₄₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×Dic₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₄₇	—	5	1	no	Hall
11	C₂×C₅×C₁₁	C₂×C₄₇	1	1	yes	characteristic
12	C₂×C₄₇	D₅×C₁₁	1	1	yes	characteristic
13	C₅×C₁₁	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₄₇	C₁₁×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₄×C₁₁	—	5	1	no	Hall
16	C₂×C₁₁	D₅×C₄₇	1	1	yes	characteristic
17	Dic₅	C₁₁×C₄₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	Dic₅×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₁×C₄₇	1	1	yes	characteristic
20	C₅	C₄×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	D₅×C₁₁×C₄₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.