Subgroups — D₅×C₁₁⋊C₅×C₆₁ #46776708

Order 33550.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊C₅×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₁×C₆₁	C₅	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊C₅×C₆₁	—	5	1	no	maximal
4	C₅×C₁₁×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₁⋊C₅×C₆₁	—	2	2	no	—
6	C₁₁⋊C₅×C₆₁	D₅	1	1	yes	characteristic, direct product factor
7	C₅×D₅×C₆₁	—	11	1	no	maximal, Hall
8	C₅²×C₆₁	—	11	1	no	Hall
9	C₂×C₁₁×C₆₁	—	5	1	no	Hall
10	C₁₁×C₆₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₆₁	—	55	1	no	—
12	D₅×C₆₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
13	D₅×C₁₁⋊C₅	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₆₁	—	11	1	no	—
15	C₅×C₆₁	—	22	2	no	—
16	C₅×C₆₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
17	C₅×C₁₁⋊C₅	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₆₁	—	5	1	no	Hall
19	D₅×C₁₁	C₅×C₆₁	1	1	yes	characteristic, complemented
20	C₂×C₁₁⋊C₅	—	5	1	no	—
21	C₆₁	D₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₅×C₁₁	C₂×C₅×C₆₁	1	1	yes	characteristic, complemented
23	C₁₁⋊C₅	—	2	2	no	—
24	C₁₁⋊C₅	D₅×C₆₁	1	1	yes	characteristic, direct product factor
25	C₅×D₅	—	11	1	no	Hall
26	C₅²	—	11	1	no	Sylow
27	C₂×C₁₁	—	5	1	no	Hall
28	C₁₁	C₅×D₅×C₆₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	55	1	no	—
30	D₅	C₁₁⋊C₅×C₆₁	1	1	yes	characteristic, direct product factor
31	C₅	—	11	1	no	—
32	C₅	—	22	2	no	—
33	C₅	C₂×C₁₁⋊C₅×C₆₁	1	1	yes	characteristic, complemented
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₁	D₅×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₅×C₆₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₆₁	C₂×C₅
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₆₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁⋊C₅×C₆₁	C₂	semidirect
2. D₅×C₁₁×C₆₁	C₅	semidirect
4. C₅×C₁₁×C₆₁	C₂×C₅	semidirect
6. C₁₁⋊C₅×C₆₁	D₅	direct (N × H)
10. C₁₁×C₆₁	C₅×D₅	semidirect
12. D₅×C₆₁	C₁₁⋊C₅	direct (N × H)
13. D₅×C₁₁⋊C₅	C₆₁	direct (N × H)
16. C₅×C₆₁	C₂×C₁₁⋊C₅	semidirect
17. C₅×C₁₁⋊C₅	C₂×C₆₁	semidirect
19. D₅×C₁₁	C₅×C₆₁	semidirect
21. C₆₁	D₅×C₁₁⋊C₅	direct (N × H)
22. C₅×C₁₁	C₂×C₅×C₆₁	semidirect
24. C₁₁⋊C₅	D₅×C₆₁	direct (N × H)
28. C₁₁	C₅×D₅×C₆₁	semidirect
30. D₅	C₁₁⋊C₅×C₆₁	direct (N × H)
33. C₅	C₂×C₁₁⋊C₅×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁⋊C₅×C₆₁	2
D₅×C₁₁×C₆₁	5
C₂×C₁₁⋊C₅×C₆₁	5
C₅×D₅×C₆₁	11
D₅×C₁₁⋊C₅	61

Subgroups — D5×C11⋊C5×C61 #46776708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁⋊C₅×C₆₁ #46776708