Subgroups — C₁₁×D₈₈₅ #34085694

Order 19470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₉₅	—	3	1	no	maximal, Hall
3	C₁₁×D₁₇₇	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₅₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₅₉	D₅	1	1	yes	characteristic, complemented, Hall
6	D₈₈₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₅₉	—	15	1	no	Hall
8	C₃×C₅×C₅₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₉	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₂₉₅	—	3	1	no	Hall
11	D₁₇₇	—	5	1	no	Hall
12	C₁₁×D₁₅	—	59	1	no	maximal, Hall
13	C₅×C₅₉	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅₉	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	D₅₉	1	1	yes	characteristic, complemented, Hall
16	D₅₉	—	15	1	no	Hall
17	D₅×C₁₁	—	177	1	no	Hall
18	D₃×C₁₁	—	295	1	no	Hall
19	C₅₉	C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₁₁	D₁₇₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₂₉₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	59	1	no	Hall
23	C₂×C₁₁	—	885	1	no	Hall
24	C₃×C₅	C₁₁×D₅₉	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₈₈₅	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	177	1	no	Hall
27	D₃	—	295	1	no	Hall
28	C₅	C₁₁×D₁₇₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₁×D₂₉₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	885	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₈₈₅
commutator, cosocle, hypocenter	C₃×C₅×C₅₉	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₅₉	C₂
LCS	G ▷ C₃×C₅×C₅₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₅₉	C₂	semidirect
4. C₅×C₁₁×C₅₉	D₃	semidirect
5. C₃×C₁₁×C₅₉	D₅	semidirect
6. D₈₈₅	C₁₁	direct (N × H)
8. C₃×C₅×C₅₉	C₂×C₁₁	semidirect
9. C₁₁×C₅₉	D₁₅	semidirect
13. C₅×C₅₉	D₃×C₁₁	semidirect
14. C₃×C₅₉	D₅×C₁₁	semidirect
15. C₃×C₅×C₁₁	D₅₉	semidirect
19. C₅₉	C₁₁×D₁₅	semidirect
20. C₅×C₁₁	D₁₇₇	semidirect
21. C₃×C₁₁	D₂₉₅	semidirect
24. C₃×C₅	C₁₁×D₅₉	semidirect
25. C₁₁	D₈₈₅	direct (N × H)
28. C₅	C₁₁×D₁₇₇	semidirect
29. C₃	C₁₁×D₂₉₅	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×C₅₉	2
C₁₁×D₂₉₅	3
C₁₁×D₁₇₇	5
D₈₈₅	11
C₁₁×D₁₅	59

Subgroups — C11×D885 #34085694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₈₈₅ #34085694