Subgroups — D₁₁×C₃₁×C₅⋊D₅ #46802202

Order 34100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃₁	D₁₁×C₅⋊D₅
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. C₅²×D₁₁×C₃₁	C₂	semidirect
2. C₁₁×C₃₁×C₅⋊D₅	C₂	semidirect
3. C₃₁×C₅⋊D₅₅	C₂	semidirect
4. C₅²×C₁₁×C₃₁	C₂²	semidirect
8. C₅×D₁₁×C₃₁	D₅	semidirect
10. C₅×C₁₁×C₃₁	C₂×D₅	semidirect
13. C₃₁×C₅⋊D₅	D₁₁	direct (N × H)
15. D₁₁×C₅⋊D₅	C₃₁	direct (N × H)
16. C₅²×C₃₁	C₂×D₁₁	semidirect
19. D₁₁×C₃₁	C₅⋊D₅	direct (N × H)
21. C₅⋊D₅₅	C₂×C₃₁	semidirect
22. C₁₁×C₅⋊D₅	C₂×C₃₁	semidirect
23. C₅²×D₁₁	C₂×C₃₁	semidirect
24. C₁₁×C₃₁	C₂×C₅⋊D₅	semidirect
28. C₅²×C₁₁	C₂²×C₃₁	semidirect
30. C₅×C₃₁	D₅×D₁₁	semidirect
33. C₅×D₁₁	D₅×C₃₁	semidirect
39. C₅×C₁₁	C₂×D₅×C₃₁	semidirect
42. C₅⋊D₅	D₁₁×C₃₁	direct (N × H)
44. C₃₁	D₁₁×C₅⋊D₅	direct (N × H)
45. C₅²	C₂×D₁₁×C₃₁	semidirect
48. D₁₁	C₃₁×C₅⋊D₅	direct (N × H)
50. C₁₁	C₂×C₃₁×C₅⋊D₅	semidirect
54. 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
C₅²×D₁₁×C₃₁	2
C₁₁×C₃₁×C₅⋊D₅	2
C₃₁×C₅⋊D₅₅	2
D₅×D₁₁×C₃₁	5
C₂×C₃₁×C₅⋊D₅	11
D₁₁×C₅⋊D₅	31

Subgroups — D11×C31×C5⋊D5 #46802202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×C₃₁×C₅⋊D₅ #46802202