Subgroups — C₂×D₁₁×C₁₅₁⋊C₅ #45684753

Order 33220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×C₁₅₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₅₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₁×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₁×C₁₅₁	C₂×C₅	1	2	yes	complemented
7	C₂²×C₁₅₁⋊C₅	—	11	1	no	maximal, Hall
8	C₁₁×C₁₅₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₅₁⋊C₅	—	11	2	no	—
10	C₂×C₁₅₁⋊C₅	D₁₁	1	1	yes	characteristic, direct product factor
11	C₁₅₁⋊C₅	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₅₁	—	11	1	no	Hall
13	C₂×C₁₅₁	—	11	2	no	—
14	C₂×C₁₅₁	C₅×D₁₁	1	1	yes	characteristic, complemented
15	C₂×C₅×D₁₁	—	151	1	no	maximal, Hall
16	C₁₅₁	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅×C₁₁	—	151	1	no	—
18	C₅×D₁₁	—	151	2	no	—
19	C₅×C₁₁	—	151	1	no	Hall
20	C₂×D₁₁	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₁	C₂×C₁₅₁⋊C₅	1	1	yes	characteristic, complemented
22	D₁₁	C₂×C₁₅₁⋊C₅	1	2	yes	direct product factor
23	C₂²×C₅	—	1661	1	no	Hall
24	C₁₁	C₂²×C₁₅₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	1661	2	no	—
26	C₂×C₅	—	151	1	no	—
27	C₅	—	151	1	no	Sylow
28	C₂²	—	11	1	no	Sylow
29	C₂	—	11	2	no	—
30	C₂	D₁₁×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₁×C₁₅₁⋊C₅
commutator, cosocle, hypocenter	C₁₁×C₁₅₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₅₁	C₂×C₅
LCS	G ▷ C₁₁×C₁₅₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₁×C₁₅₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₁×C₁₅₁⋊C₅	C₂	semidirect
3. C₁₁×C₁₅₁⋊C₅	C₂²	semidirect
4. C₂×D₁₁×C₁₅₁	C₅	semidirect
5. C₂×C₁₁×C₁₅₁	C₂×C₅	semidirect
6. D₁₁×C₁₅₁	C₂×C₅	semidirect
8. C₁₁×C₁₅₁	C₂²×C₅	semidirect
10. C₂×C₁₅₁⋊C₅	D₁₁	direct (N × H)
11. C₁₅₁⋊C₅	C₂×D₁₁	direct (N × H)
14. C₂×C₁₅₁	C₅×D₁₁	semidirect
16. C₁₅₁	C₂×C₅×D₁₁	semidirect
20. C₂×D₁₁	C₁₅₁⋊C₅	direct (N × H)
21. C₂×C₁₁	C₂×C₁₅₁⋊C₅	semidirect
22. D₁₁	C₂×C₁₅₁⋊C₅	direct (N × H)
24. C₁₁	C₂²×C₁₅₁⋊C₅	semidirect
30. C₂	D₁₁×C₁₅₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₁×C₁₅₁⋊C₅	2
C₂×C₁₁×C₁₅₁⋊C₅	2
C₂×D₁₁×C₁₅₁	5
C₂²×C₁₅₁⋊C₅	11
C₂×C₅×D₁₁	151

Subgroups — C2×D11×C151⋊C5 #45684753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁×C₁₅₁⋊C₅ #45684753