Subgroups — C₁₁×(C₅⋊D₅)⋊D₃₁ #46802192

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×D₁₅₅	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×C₁₁×D₃₁	—	5	2	no	maximal
5	C₁₁×D₁₅₅	D₅	1	2	yes	complemented
6	D₅×C₁₁×C₃₁	—	5	2	no	—
7	D₅×C₁₁×C₃₁	—	10	2	no	—
8	C₅×C₁₁×D₃₁	—	5	2	no	—
9	(C₅⋊D₅)⋊D₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₁×C₃₁	—	2	2	no	—
11	C₅×C₁₁×C₃₁	C₂×D₅	1	2	yes	complemented
12	C₃₁×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₅×D₁₅₅	C₂×C₁₁	1	2	yes	complemented
14	C₂×C₁₁×D₃₁	—	25	1	no	Hall
15	D₅²×C₁₁	—	31	1	no	maximal, Hall
16	C₅²×C₃₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₃₁	—	25	1	no	—
18	C₁₁×D₃₁	—	5	2	no	—
19	D₅×D₃₁	—	5	2	no	—
20	C₁₁×C₅⋊D₅	D₃₁	1	1	yes	characteristic, complemented
21	C₅×D₅×C₁₁	—	31	2	no	—
22	C₁₁×C₃₁	D₅²	1	1	yes	characteristic, complemented, Hall
23	D₁₅₅	D₅×C₁₁	1	2	yes	complemented
24	C₅×D₃₁	—	5	2	no	—
25	D₅×C₃₁	—	5	2	no	—
26	D₅×C₃₁	—	10	2	no	—
27	C₅²×C₁₁	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₅×C₁₁	—	155	2	no	—
29	C₅×C₃₁	—	2	2	no	—
30	C₅×C₃₁	C₂×D₅×C₁₁	1	2	yes	complemented
31	C₂×D₃₁	—	25	1	no	Hall
32	C₂×C₅×C₁₁	—	155	2	no	—
33	D₅×C₁₁	—	5	2	no	—
34	D₅×C₁₁	—	10	2	no	—
35	D₅×C₁₁	—	31	2	no	—
36	D₅²	—	31	1	no	Hall
37	C₂×C₃₁	—	25	1	no	—
38	D₃₁	—	5	2	no	—
39	C₅×C₁₁	—	2	2	no	—
40	C₅×C₁₁	D₅×D₃₁	1	2	yes	complemented
41	C₅⋊D₅	C₁₁×D₃₁	1	1	yes	characteristic, complemented
42	C₅×D₅	—	31	2	no	—
43	C₂²×C₁₁	—	775	1	no	Hall
44	C₃₁	D₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₅²	C₂×C₁₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	25	1	no	—
47	C₂×C₁₁	—	155	2	no	—
48	C₂×D₅	—	155	2	no	—
49	C₁₁	(C₅⋊D₅)⋊D₃₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₅	—	155	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	—	31	2	no	—
54	C₅	—	2	2	no	—
55	C₅	D₅×C₁₁×D₃₁	1	2	yes	complemented
56	C₂²	—	775	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	155	2	no	—

	subgroup	G/H
center, hypercenter	C₁₁	(C₅⋊D₅)⋊D₃₁
commutator, cosocle, hypocenter	C₅²×C₃₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₃₁	C₂²
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×D₁₅₅	C₂	semidirect
2. C₁₁×C₃₁×C₅⋊D₅	C₂	semidirect
3. C₅²×C₁₁×C₃₁	C₂²	semidirect
5. C₁₁×D₁₅₅	D₅	semidirect
9. (C₅⋊D₅)⋊D₃₁	C₁₁	direct (N × H)
11. C₅×C₁₁×C₃₁	C₂×D₅	semidirect
12. C₃₁×C₅⋊D₅	C₂×C₁₁	semidirect
13. C₅×D₁₅₅	C₂×C₁₁	semidirect
16. C₅²×C₃₁	C₂²×C₁₁	semidirect
20. C₁₁×C₅⋊D₅	D₃₁	semidirect
22. C₁₁×C₃₁	D₅²	semidirect
23. D₁₅₅	D₅×C₁₁	semidirect
27. C₅²×C₁₁	C₂×D₃₁	semidirect
30. C₅×C₃₁	C₂×D₅×C₁₁	semidirect
40. C₅×C₁₁	D₅×D₃₁	semidirect
41. C₅⋊D₅	C₁₁×D₃₁	semidirect
44. C₃₁	D₅²×C₁₁	semidirect
45. C₅²	C₂×C₁₁×D₃₁	semidirect
49. C₁₁	(C₅⋊D₅)⋊D₃₁	direct (N × H)
55. C₅	D₅×C₁₁×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×D₁₅₅	2
C₁₁×C₃₁×C₅⋊D₅	2
D₅×C₁₁×D₃₁	5
(C₅⋊D₅)⋊D₃₁	11
D₅²×C₁₁	31

Subgroups — C11×(C5⋊D5)⋊D31 #46802192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×(C₅⋊D₅)⋊D₃₁ #46802192