Subgroups — C₅×(C₄₁⋊C₅)⋊D₁₁ #36376993

Order 22550.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₄₁⋊C₅)⋊D₁₁	C₅	1	5	yes	maximal, direct product factor
3	C₅×D₄₅₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₁×C₄₁⋊C₅	C₂×C₅	1	5	yes	complemented
6	C₅×D₄₁⋊C₅	—	11	1	no	maximal, Hall
7	C₅×C₄₁⋊C₅	D₁₁	1	1	yes	characteristic, complemented, Hall
8	D₄₅₁	C₅²	1	1	yes	characteristic, complemented, Hall
9	C₅²×D₁₁	—	41	1	no	maximal, Hall
10	C₁₁×C₄₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
11	C₅×D₄₁	—	11	1	no	—
12	D₄₁⋊C₅	—	11	5	no	—
13	C₅²×C₁₁	—	41	1	no	Hall
14	C₅×C₄₁	C₅×D₁₁	1	1	yes	characteristic, complemented
15	C₄₁⋊C₅	C₅×D₁₁	1	5	yes	complemented
16	C₅×D₁₁	—	41	5	no	—
17	C₅×D₁₁	—	41	1	no	—
18	D₄₁	—	11	1	no	Hall
19	C₅×C₁₁	—	41	5	no	—
20	C₅×C₁₁	D₄₁⋊C₅	1	1	yes	characteristic, complemented
21	C₂×C₅²	—	451	1	no	Hall
22	C₄₁	C₅²×D₁₁	1	1	yes	characteristic, complemented, Sylow
23	C₅²	—	41	1	no	Sylow
24	D₁₁	—	41	1	no	Hall
25	C₁₁	C₅×D₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	451	5	no	—
27	C₂×C₅	—	2255	1	no	—
28	C₅	—	41	5	no	—
29	C₅	(C₄₁⋊C₅)⋊D₁₁	1	1	yes	characteristic, direct product factor
30	C₂	—	2255	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	(C₄₁⋊C₅)⋊D₁₁
commutator, cosocle, hypocenter	C₁₁×C₄₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₄₁	C₂×C₅
LCS	G ▷ C₁₁×C₄₁
UCS	C₁ ◁ C₅

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.