Subgroups — C₅×C₁₁⋊C₅×D₄₁ #36376992

Order 22550.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊C₅×D₄₁
commutator, cosocle, hypocenter	C₁₁×C₄₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₄₁	C₂×C₅
LCS	G ▷ C₁₁×C₄₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₁×C₁₁⋊C₅	C₂	semidirect
2. C₁₁⋊C₅×D₄₁	C₅	direct (N × H)
3. C₅×C₁₁×D₄₁	C₅	semidirect
4. C₅×C₁₁×C₄₁	C₂×C₅	semidirect
5. C₄₁×C₁₁⋊C₅	C₂×C₅	semidirect
8. C₁₁×D₄₁	C₅²	semidirect
10. C₁₁×C₄₁	C₂×C₅²	semidirect
12. C₅×D₄₁	C₁₁⋊C₅	direct (N × H)
13. C₅×C₁₁⋊C₅	D₄₁	direct (N × H)
15. C₅×C₄₁	C₂×C₁₁⋊C₅	semidirect
18. D₄₁	C₅×C₁₁⋊C₅	direct (N × H)
19. C₅×C₁₁	C₅×D₄₁	semidirect
20. C₁₁⋊C₅	C₅×D₄₁	direct (N × H)
22. C₄₁	C₂×C₅×C₁₁⋊C₅	semidirect
25. C₁₁	C₅²×D₄₁	semidirect
29. C₅	C₁₁⋊C₅×D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₄₁×C₁₁⋊C₅	2
C₁₁⋊C₅×D₄₁	5
C₅×C₁₁×D₄₁	5
C₅²×D₄₁	11
C₂×C₅×C₁₁⋊C₅	41

Subgroups — C5×C11⋊C5×D41 #36376992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊C₅×D₄₁ #36376992