Subgroups — C₁₁×D₁₉×C₁₁⋊C₅ #37527366

Order 22990.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₁	D₁₉×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁²×C₁₉	C₂×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₁₁⋊C₅	C₂	semidirect
2. C₁₁²×D₁₉	C₅	semidirect
3. C₁₁²×C₁₉	C₂×C₅	semidirect
4. D₁₉×C₁₁⋊C₅	C₁₁	direct (N × H)
8. C₁₉×C₁₁⋊C₅	C₂×C₁₁	semidirect
9. C₁₁×C₁₁⋊C₅	D₁₉	direct (N × H)
11. C₁₁×D₁₉	C₁₁⋊C₅	direct (N × H)
12. C₁₁×D₁₉	C₅×C₁₁	semidirect
15. C₁₁×C₁₉	C₂×C₁₁⋊C₅	semidirect
16. C₁₁×C₁₉	C₂×C₅×C₁₁	semidirect
18. C₁₁²	C₅×D₁₉	semidirect
23. C₁₁⋊C₅	C₁₁×D₁₉	direct (N × H)
24. D₁₉	C₁₁×C₁₁⋊C₅	direct (N × H)
28. C₁₉	C₂×C₁₁×C₁₁⋊C₅	semidirect
30. C₁₁	C₅×C₁₁×D₁₉	semidirect
31. C₁₁	D₁₉×C₁₁⋊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
C₁₁×C₁₉×C₁₁⋊C₅	2
C₁₁²×D₁₉	5
D₁₉×C₁₁⋊C₅	11
C₅×C₁₁×D₁₉	11
C₂×C₁₁×C₁₁⋊C₅	19

Subgroups — C11×D19×C11⋊C5 #37527366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₉×C₁₁⋊C₅ #37527366