Subgroups — C₁₁×D₆₄₅ #28382000

Order 14190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₁₅	—	3	1	no	maximal, Hall
3	C₁₁×D₁₂₉	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₄₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₆₄₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₄₃	—	15	1	no	Hall
8	C₃×C₅×C₄₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₄₃	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₂₁₅	—	3	1	no	Hall
11	C₁₁×D₁₅	—	43	1	no	maximal, Hall
12	D₁₂₉	—	5	1	no	Hall
13	C₅×C₄₃	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₁	D₄₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄₃	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
16	D₅×C₁₁	—	129	1	no	Hall
17	D₄₃	—	15	1	no	Hall
18	D₃×C₁₁	—	215	1	no	Hall
19	C₅×C₁₁	D₁₂₉	1	1	yes	characteristic, complemented, Hall
20	C₄₃	C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₁	D₂₁₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	43	1	no	Hall
23	C₂×C₁₁	—	645	1	no	Hall
24	C₃×C₅	C₁₁×D₄₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₆₄₅	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	129	1	no	Hall
27	D₃	—	215	1	no	Hall
28	C₅	C₁₁×D₁₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₁×D₂₁₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	645	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₆₄₅
commutator, cosocle, hypocenter	C₃×C₅×C₄₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₄₃	C₂
LCS	G ▷ C₃×C₅×C₄₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₄₃	C₂	semidirect
4. C₅×C₁₁×C₄₃	D₃	semidirect
5. C₃×C₁₁×C₄₃	D₅	semidirect
6. D₆₄₅	C₁₁	direct (N × H)
8. C₃×C₅×C₄₃	C₂×C₁₁	semidirect
9. C₁₁×C₄₃	D₁₅	semidirect
13. C₅×C₄₃	D₃×C₁₁	semidirect
14. C₃×C₅×C₁₁	D₄₃	semidirect
15. C₃×C₄₃	D₅×C₁₁	semidirect
19. C₅×C₁₁	D₁₂₉	semidirect
20. C₄₃	C₁₁×D₁₅	semidirect
21. C₃×C₁₁	D₂₁₅	semidirect
24. C₃×C₅	C₁₁×D₄₃	semidirect
25. C₁₁	D₆₄₅	direct (N × H)
28. C₅	C₁₁×D₁₂₉	semidirect
29. C₃	C₁₁×D₂₁₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁×C₄₃	2
C₁₁×D₂₁₅	3
C₁₁×D₁₂₉	5
D₆₄₅	11
C₁₁×D₁₅	43

Subgroups — C11×D645 #28382000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₆₄₅ #28382000