Subgroups — C₄×C₄₇×C₁₁⋊C₅ #23780266

Order 10340.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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