Subgroups — C₁₁×C₅⋊D₅×D₃₁ #46802200

Order 34100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Subgroups — C11×C5⋊D5×D31 #46802200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₅⋊D₅×D₃₁ #46802200