Subgroups — C₁₁×D₁₀₄₅ #37527402

Order 22990.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₀₉	—	5	1	no	maximal, Hall
3	C₁₁²×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
4	D₁₀₄₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₁₁×D₉₅	—	11	1	no	maximal
6	C₁₁×D₅₅	—	19	1	no	maximal, Hall
7	C₅×C₁₁×C₁₉	—	2	5	no	—
8	C₅×C₁₁×C₁₉	D₁₁	1	1	yes	characteristic, complemented
9	C₅×C₁₁×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
10	C₅×C₁₁²	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₂₀₉	—	5	1	no	—
12	C₁₁×D₁₉	—	55	1	no	—
13	C₁₁×D₁₁	—	95	1	no	Hall
14	C₁₁×C₁₉	—	2	5	no	—
15	C₁₁×C₁₉	D₅×C₁₁	1	1	yes	characteristic, complemented
16	C₁₁×C₁₉	D₅₅	1	1	yes	characteristic, complemented
17	D₉₅	—	11	1	no	Hall
18	C₁₁²	D₉₅	1	1	yes	characteristic, complemented, Sylow
19	D₅₅	—	19	1	no	—
20	D₅×C₁₁	—	209	1	no	—
21	C₅×C₁₉	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₅×C₁₁	—	2	5	no	—
23	C₅×C₁₁	C₁₁×D₁₉	1	1	yes	characteristic, complemented
24	C₅×C₁₁	D₂₀₉	1	1	yes	characteristic, complemented
25	D₁₉	—	55	1	no	Hall
26	C₂×C₁₁	—	1045	1	no	—
27	D₁₁	—	95	1	no	—
28	C₁₉	C₁₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
29	C₁₁	—	2	5	no	—
30	C₁₁	C₁₁×D₉₅	1	1	yes	characteristic, complemented
31	C₁₁	D₁₀₄₅	1	1	yes	characteristic, direct product factor
32	D₅	—	209	1	no	Hall
33	C₅	C₁₁×D₂₀₉	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	1045	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₀₄₅
commutator, cosocle, hypocenter	C₅×C₁₁×C₁₉	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₉	C₂
LCS	G ▷ C₅×C₁₁×C₁₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁²×C₁₉	C₂	semidirect
3. C₁₁²×C₁₉	D₅	semidirect
4. D₁₀₄₅	C₁₁	direct (N × H)
8. C₅×C₁₁×C₁₉	D₁₁	semidirect
9. C₅×C₁₁×C₁₉	C₂×C₁₁	semidirect
10. C₅×C₁₁²	D₁₉	semidirect
15. C₁₁×C₁₉	D₅×C₁₁	semidirect
16. C₁₁×C₁₉	D₅₅	semidirect
18. C₁₁²	D₉₅	semidirect
21. C₅×C₁₉	C₁₁×D₁₁	semidirect
23. C₅×C₁₁	C₁₁×D₁₉	semidirect
24. C₅×C₁₁	D₂₀₉	semidirect
28. C₁₉	C₁₁×D₅₅	semidirect
30. C₁₁	C₁₁×D₉₅	semidirect
31. C₁₁	D₁₀₄₅	direct (N × H)
33. C₅	C₁₁×D₂₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁²×C₁₉	2
C₁₁×D₂₀₉	5
D₁₀₄₅	11
C₁₁×D₉₅	11
C₁₁×D₅₅	19

Subgroups — C11×D1045 #37527402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₀₄₅ #37527402