Subgroups — C₃₁×(C₅⋊D₅)⋊D₁₁ #46802197

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×D₅₅	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₁₁×C₃₁	—	5	2	no	maximal
5	C₃₁×D₅₅	D₅	1	2	yes	complemented
6	D₅×C₁₁×C₃₁	—	5	2	no	—
7	D₅×C₁₁×C₃₁	—	10	2	no	—
8	C₅×D₁₁×C₃₁	—	5	2	no	—
9	D₅²×C₃₁	—	11	1	no	maximal, Hall
10	C₅×C₁₁×C₃₁	—	2	2	no	—
11	C₅×C₁₁×C₃₁	C₂×D₅	1	2	yes	complemented
12	C₃₁×C₅⋊D₅	D₁₁	1	1	yes	characteristic, complemented
13	C₅×D₅×C₃₁	—	11	2	no	—
14	C₂×D₁₁×C₃₁	—	25	1	no	Hall
15	(C₅⋊D₅)⋊D₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅²×C₃₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₃₁	—	25	1	no	—
18	D₁₁×C₃₁	—	5	2	no	—
19	C₂×D₅×C₃₁	—	55	2	no	—
20	C₁₁×C₅⋊D₅	C₂×C₃₁	1	1	yes	characteristic, complemented
21	C₅×D₅₅	C₂×C₃₁	1	2	yes	complemented
22	C₁₁×C₃₁	D₅²	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₃₁	—	55	2	no	—
24	D₅×C₃₁	—	5	2	no	—
25	D₅×C₃₁	—	10	2	no	—
26	D₅×C₃₁	—	11	2	no	—
27	C₅²×C₁₁	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
28	D₅×D₁₁	—	5	2	no	—
29	C₅×C₃₁	—	2	2	no	—
30	C₅×C₃₁	D₅×D₁₁	1	2	yes	complemented
31	C₂²×C₃₁	—	275	1	no	Hall
32	D₅₅	D₅×C₃₁	1	2	yes	complemented
33	C₅×D₁₁	—	5	2	no	—
34	D₅×C₁₁	—	5	2	no	—
35	D₅×C₁₁	—	10	2	no	—
36	D₅²	—	11	1	no	Hall
37	C₂×C₃₁	—	25	1	no	—
38	C₂×C₃₁	—	55	2	no	—
39	C₅×C₁₁	—	2	2	no	—
40	C₅×C₁₁	C₂×D₅×C₃₁	1	2	yes	complemented
41	C₅⋊D₅	D₁₁×C₃₁	1	1	yes	characteristic, complemented
42	C₅×D₅	—	11	2	no	—
43	C₂×D₁₁	—	25	1	no	Hall
44	C₃₁	(C₅⋊D₅)⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₅²	C₂×D₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	25	1	no	—
47	D₁₁	—	5	2	no	—
48	C₂×D₅	—	55	2	no	—
49	C₁₁	D₅²×C₃₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	55	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	—	11	2	no	—
54	C₅	—	2	2	no	—
55	C₅	D₅×D₁₁×C₃₁	1	2	yes	complemented
56	C₂²	—	275	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	55	2	no	—

	subgroup	G/H
center, hypercenter	C₃₁	(C₅⋊D₅)⋊D₁₁
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₃₁	C₂²
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×D₅₅	C₂	semidirect
2. C₁₁×C₃₁×C₅⋊D₅	C₂	semidirect
3. C₅²×C₁₁×C₃₁	C₂²	semidirect
5. C₃₁×D₅₅	D₅	semidirect
11. C₅×C₁₁×C₃₁	C₂×D₅	semidirect
12. C₃₁×C₅⋊D₅	D₁₁	semidirect
15. (C₅⋊D₅)⋊D₁₁	C₃₁	direct (N × H)
16. C₅²×C₃₁	C₂×D₁₁	semidirect
20. C₁₁×C₅⋊D₅	C₂×C₃₁	semidirect
21. C₅×D₅₅	C₂×C₃₁	semidirect
22. C₁₁×C₃₁	D₅²	semidirect
27. C₅²×C₁₁	C₂²×C₃₁	semidirect
30. C₅×C₃₁	D₅×D₁₁	semidirect
32. D₅₅	D₅×C₃₁	semidirect
40. C₅×C₁₁	C₂×D₅×C₃₁	semidirect
41. C₅⋊D₅	D₁₁×C₃₁	semidirect
44. C₃₁	(C₅⋊D₅)⋊D₁₁	direct (N × H)
45. C₅²	C₂×D₁₁×C₃₁	semidirect
49. C₁₁	D₅²×C₃₁	semidirect
55. C₅	D₅×D₁₁×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₁×D₅₅	2
C₁₁×C₃₁×C₅⋊D₅	2
D₅×D₁₁×C₃₁	5
D₅²×C₃₁	11
(C₅⋊D₅)⋊D₁₁	31

Subgroups — C31×(C5⋊D5)⋊D11 #46802197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×(C₅⋊D₅)⋊D₁₁ #46802197