Subgroups — C₁₁×D₁₄₅₅ #44544967

Order 32010.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₄₈₅	—	3	1	no	maximal, Hall
3	C₁₁×D₂₉₁	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₉₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₉₇	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₄₅₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₉₇	—	15	1	no	Hall
8	C₃×C₅×C₉₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₉₇	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₄₈₅	—	3	1	no	Hall
11	D₂₉₁	—	5	1	no	Hall
12	C₅×C₉₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₁₅	—	97	1	no	maximal, Hall
14	C₃×C₉₇	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	D₉₇	—	15	1	no	Hall
16	C₃×C₅×C₁₁	D₉₇	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₁	—	291	1	no	Hall
18	C₉₇	C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
19	D₃×C₁₁	—	485	1	no	Hall
20	C₅×C₁₁	D₂₉₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₄₈₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	97	1	no	Hall
23	C₂×C₁₁	—	1455	1	no	Hall
24	C₃×C₅	C₁₁×D₉₇	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₁₄₅₅	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	291	1	no	Hall
27	D₃	—	485	1	no	Hall
28	C₅	C₁₁×D₂₉₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₁×D₄₈₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	1455	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₄₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₉₇	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₉₇	C₂
LCS	G ▷ C₃×C₅×C₉₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₉₇	C₂	semidirect
4. C₅×C₁₁×C₉₇	D₃	semidirect
5. C₃×C₁₁×C₉₇	D₅	semidirect
6. D₁₄₅₅	C₁₁	direct (N × H)
8. C₃×C₅×C₉₇	C₂×C₁₁	semidirect
9. C₁₁×C₉₇	D₁₅	semidirect
12. C₅×C₉₇	D₃×C₁₁	semidirect
14. C₃×C₉₇	D₅×C₁₁	semidirect
16. C₃×C₅×C₁₁	D₉₇	semidirect
18. C₉₇	C₁₁×D₁₅	semidirect
20. C₅×C₁₁	D₂₉₁	semidirect
21. C₃×C₁₁	D₄₈₅	semidirect
24. C₃×C₅	C₁₁×D₉₇	semidirect
25. C₁₁	D₁₄₅₅	direct (N × H)
28. C₅	C₁₁×D₂₉₁	semidirect
29. C₃	C₁₁×D₄₈₅	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×C₉₇	2
C₁₁×D₄₈₅	3
C₁₁×D₂₉₁	5
D₁₄₅₅	11
C₁₁×D₁₅	97

Subgroups — C11×D1455 #44544967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₄₅₅ #44544967