Subgroups — C₅×C₁₁×D₁₁×C₂₃ #42123739

Order 27830.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₁×C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₁×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₅×C₁₁×C₂₃	—	11	1	no	maximal
6	C₅×C₁₁×C₂₃	—	2	5	no	—
7	C₅×C₁₁×C₂₃	D₁₁	1	1	yes	characteristic, direct product factor
8	C₅×C₁₁×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	C₅×C₁₁×D₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₁²	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₂₃	—	11	1	no	—
12	D₁₁×C₂₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor
13	C₁₁×C₂₃	—	2	5	no	—
14	C₁₁×C₂₃	C₅×D₁₁	1	1	yes	characteristic, direct product factor
15	C₁₁×C₂₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
16	C₁₁×D₁₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₂₃	—	11	1	no	Hall
18	C₁₁²	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₂₃	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₁	—	11	1	no	—
21	C₅×D₁₁	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor
22	C₅×C₁₁	—	2	5	no	—
23	C₅×C₁₁	D₁₁×C₂₃	1	1	yes	characteristic, direct product factor
24	C₅×C₁₁	C₂×C₁₁×C₂₃	1	1	yes	characteristic, complemented
25	C₂×C₂₃	—	11	1	no	Hall
26	C₂₃	C₅×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	—	11	1	no	—
28	D₁₁	C₅×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor
29	C₁₁	—	2	5	no	—
30	C₁₁	C₂×C₅×C₁₁×C₂₃	1	1	yes	characteristic, complemented
31	C₁₁	C₅×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor
32	C₂×C₅	—	11	1	no	Hall
33	C₅	C₁₁×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁×C₂₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₂₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₁₁×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁²×C₂₃	C₂	semidirect
2. C₁₁×D₁₁×C₂₃	C₅	direct (N × H)
3. C₁₁²×C₂₃	C₂×C₅	semidirect
4. C₅×D₁₁×C₂₃	C₁₁	direct (N × H)
7. C₅×C₁₁×C₂₃	D₁₁	direct (N × H)
8. C₅×C₁₁×C₂₃	C₂×C₁₁	semidirect
9. C₅×C₁₁×D₁₁	C₂₃	direct (N × H)
10. C₅×C₁₁²	C₂×C₂₃	semidirect
12. D₁₁×C₂₃	C₅×C₁₁	direct (N × H)
14. C₁₁×C₂₃	C₅×D₁₁	direct (N × H)
15. C₁₁×C₂₃	C₂×C₅×C₁₁	semidirect
16. C₁₁×D₁₁	C₅×C₂₃	direct (N × H)
18. C₁₁²	C₂×C₅×C₂₃	semidirect
19. C₅×C₂₃	C₁₁×D₁₁	direct (N × H)
21. C₅×D₁₁	C₁₁×C₂₃	direct (N × H)
23. C₅×C₁₁	D₁₁×C₂₃	direct (N × H)
24. C₅×C₁₁	C₂×C₁₁×C₂₃	semidirect
26. C₂₃	C₅×C₁₁×D₁₁	direct (N × H)
28. D₁₁	C₅×C₁₁×C₂₃	direct (N × H)
30. C₁₁	C₂×C₅×C₁₁×C₂₃	semidirect
31. C₁₁	C₅×D₁₁×C₂₃	direct (N × H)
33. C₅	C₁₁×D₁₁×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁²×C₂₃	2
C₁₁×D₁₁×C₂₃	5
C₅×D₁₁×C₂₃	11
C₂×C₅×C₁₁×C₂₃	11
C₅×C₁₁×D₁₁	23

Subgroups — C5×C11×D11×C23 #42123739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₁₁×C₂₃ #42123739