Subgroups — C₁₁×D₁₂₆₅ #42123746

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×D₂₅₃	—	5	1	no	maximal, Hall
3	C₁₁²×C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
4	D₁₂₆₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₁₁×D₁₁₅	—	11	1	no	maximal
6	C₅×C₁₁×C₂₃	—	2	5	no	—
7	C₅×C₁₁×C₂₃	D₁₁	1	1	yes	characteristic, complemented
8	C₅×C₁₁×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	C₁₁×D₅₅	—	23	1	no	maximal, Hall
10	C₅×C₁₁²	D₂₃	1	1	yes	characteristic, complemented, Hall
11	D₂₅₃	—	5	1	no	—
12	C₁₁×D₂₃	—	55	1	no	—
13	C₁₁×C₂₃	—	2	5	no	—
14	C₁₁×C₂₃	D₅×C₁₁	1	1	yes	characteristic, complemented
15	C₁₁×C₂₃	D₅₅	1	1	yes	characteristic, complemented
16	C₁₁×D₁₁	—	115	1	no	Hall
17	D₁₁₅	—	11	1	no	Hall
18	C₁₁²	D₁₁₅	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₂₃	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₅₅	—	23	1	no	—
21	D₅×C₁₁	—	253	1	no	—
22	C₅×C₁₁	—	2	5	no	—
23	C₅×C₁₁	C₁₁×D₂₃	1	1	yes	characteristic, complemented
24	C₅×C₁₁	D₂₅₃	1	1	yes	characteristic, complemented
25	D₂₃	—	55	1	no	Hall
26	C₂₃	C₁₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	1265	1	no	—
28	D₁₁	—	115	1	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	C₁₁×D₁₁₅	1	1	yes	characteristic, complemented
31	C₁₁	D₁₂₆₅	1	1	yes	characteristic, direct product factor
32	D₅	—	253	1	no	Hall
33	C₅	C₁₁×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	1265	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₂₆₅
commutator, cosocle, hypocenter	C₅×C₁₁×C₂₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₂₃	C₂
LCS	G ▷ C₅×C₁₁×C₂₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁²×C₂₃	C₂	semidirect
3. C₁₁²×C₂₃	D₅	semidirect
4. D₁₂₆₅	C₁₁	direct (N × H)
7. C₅×C₁₁×C₂₃	D₁₁	semidirect
8. C₅×C₁₁×C₂₃	C₂×C₁₁	semidirect
10. C₅×C₁₁²	D₂₃	semidirect
14. C₁₁×C₂₃	D₅×C₁₁	semidirect
15. C₁₁×C₂₃	D₅₅	semidirect
18. C₁₁²	D₁₁₅	semidirect
19. C₅×C₂₃	C₁₁×D₁₁	semidirect
23. C₅×C₁₁	C₁₁×D₂₃	semidirect
24. C₅×C₁₁	D₂₅₃	semidirect
26. C₂₃	C₁₁×D₅₅	semidirect
30. C₁₁	C₁₁×D₁₁₅	semidirect
31. C₁₁	D₁₂₆₅	direct (N × H)
33. C₅	C₁₁×D₂₅₃	semidirect

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×D₂₅₃	5
D₁₂₆₅	11
C₁₁×D₁₁₅	11
C₁₁×D₅₅	23

Subgroups — C11×D1265 #42123746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₂₆₅ #42123746