Subgroups — C₁₁⋊C₅×D₂₈₇ #44538951

Order 31570.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₈₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊C₅×D₄₁	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×D₂₈₇	—	11	1	no	maximal, Hall
6	C₄₁×C₁₁⋊C₅	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₄₁	—	11	1	no	Hall
8	C₁₁×D₄₁	—	7	1	no	Hall
9	D₇×C₁₁⋊C₅	—	41	1	no	maximal, Hall
10	D₂₈₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₄₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
12	C₅×D₄₁	—	77	1	no	Hall
13	C₇×C₁₁⋊C₅	D₄₁	1	1	yes	characteristic, complemented, Hall
14	C₇×C₄₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
15	C₅×C₄₁	—	11	1	no	Hall
16	C₁₁×D₇	—	41	1	no	Hall
17	C₂×C₁₁⋊C₅	—	287	1	no	Hall
18	D₄₁	—	7	1	no	Hall
19	C₇×C₁₁	C₅×D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₅×D₇	—	451	1	no	Hall
21	C₁₁⋊C₅	D₂₈₇	1	1	yes	characteristic, direct product factor, Hall
22	C₄₁	D₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
23	C₅×C₇	—	11	1	no	Hall
24	C₂×C₁₁	—	287	1	no	Hall
25	D₇	—	41	1	no	Hall
26	C₁₁	C₅×D₂₈₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	3157	1	no	Hall
28	C₇	C₁₁⋊C₅×D₄₁	1	1	yes	characteristic, complemented, Sylow
29	C₅	—	11	1	no	Sylow
30	C₂	—	287	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₄₁	C₂×C₅
LCS	G ▷ C₇×C₁₁×C₄₁
UCS	C₁

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.