Subgroups — C₂₅×D₂₃₁ #26040451

Order 11550.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₅×D₇₇	—	3	1	no	maximal, Hall
3	C₅×D₂₃₁	C₅	1	1	yes	maximal, characteristic
4	C₇×C₁₁×C₂₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₂₅×D₃₃	—	7	1	no	maximal, Hall
6	C₃×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic
7	C₂₅×D₂₁	—	11	1	no	maximal, Hall
8	C₃×C₁₁×C₂₅	D₇	1	1	yes	characteristic, complemented, Hall
9	C₅×D₇₇	—	3	1	no	—
10	D₁₁×C₂₅	—	21	1	no	Hall
11	C₃×C₇×C₂₅	D₁₁	1	1	yes	characteristic, complemented, Hall
12	D₂₃₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₇×C₁₁	C₅×D₃	1	1	yes	characteristic
14	D₇×C₂₅	—	33	1	no	Hall
15	C₅×D₃₃	—	7	1	no	—
16	C₁₁×C₂₅	D₂₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
18	C₅×D₂₁	—	11	1	no	—
19	C₇×C₂₅	D₃₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅×C₁₁	C₅×D₇	1	1	yes	characteristic
21	D₇₇	—	3	1	no	Hall
22	D₃×C₂₅	—	77	1	no	Hall
23	C₅×D₁₁	—	21	1	no	—
24	C₃×C₅×C₇	C₅×D₁₁	1	1	yes	characteristic
25	C₇×C₁₁	D₃×C₂₅	1	1	yes	characteristic, complemented, Hall
26	C₃×C₂₅	D₇₇	1	1	yes	characteristic, complemented, Hall
27	C₅×D₇	—	33	1	no	—
28	D₃₃	—	7	1	no	Hall
29	C₅×C₁₁	C₅×D₂₁	1	1	yes	characteristic
30	C₂×C₂₅	—	231	1	no	Hall
31	D₂₁	—	11	1	no	Hall
32	C₅×C₇	C₅×D₃₃	1	1	yes	characteristic
33	C₃×C₁₁	D₇×C₂₅	1	1	yes	characteristic, complemented, Hall
34	C₅×D₃	—	77	1	no	—
35	C₂₅	D₂₃₁	1	1	yes	characteristic, direct product factor, Sylow
36	D₁₁	—	21	1	no	Hall
37	C₃×C₇	D₁₁×C₂₅	1	1	yes	characteristic, complemented, Hall
38	C₃×C₅	C₅×D₇₇	1	1	yes	characteristic
39	D₇	—	33	1	no	Hall
40	C₁₁	C₂₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	231	1	no	—
42	C₇	C₂₅×D₃₃	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	77	1	no	Hall
44	C₅	C₅×D₂₃₁	1	1	yes	characteristic
45	C₃	C₂₅×D₇₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	231	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅	D₂₃₁
commutator, hypocenter	C₃×C₇×C₁₁	C₂×C₂₅
Frattini	C₅	C₅×D₂₃₁
Fitting	C₃×C₇×C₁₁×C₂₅	C₂
socle, cosocle	C₃×C₅×C₇×C₁₁	C₂×C₅
prime radical	C₅×D₂₃₁	C₅
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₂₅	C₂	semidirect
4. C₇×C₁₁×C₂₅	D₃	semidirect
8. C₃×C₁₁×C₂₅	D₇	semidirect
11. C₃×C₇×C₂₅	D₁₁	semidirect
12. D₂₃₁	C₂₅	direct (N × H)
16. C₁₁×C₂₅	D₂₁	semidirect
17. C₃×C₇×C₁₁	C₂×C₂₅	semidirect
19. C₇×C₂₅	D₃₃	semidirect
25. C₇×C₁₁	D₃×C₂₅	semidirect
26. C₃×C₂₅	D₇₇	semidirect
33. C₃×C₁₁	D₇×C₂₅	semidirect
35. C₂₅	D₂₃₁	direct (N × H)
37. C₃×C₇	D₁₁×C₂₅	semidirect
40. C₁₁	C₂₅×D₂₁	semidirect
42. C₇	C₂₅×D₃₃	semidirect
45. C₃	C₂₅×D₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₁×C₂₅	2
C₂₅×D₇₇	3
C₅×D₂₃₁	5
C₂₅×D₃₃	7
C₂₅×D₂₁	11

Subgroups — C25×D231 #26040451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×D₂₃₁ #26040451