Subgroups — C₁₁⋊C₅×D₂₈₅ #44535487

Order 31350.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊C₅×D₉₅	—	3	1	no	maximal, Hall
3	C₁₁⋊C₅×D₅₇	—	5	1	no	maximal
4	C₁₁×D₂₈₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅×C₁₉×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₉×C₁₁⋊C₅	—	2	2	no	—
7	C₃×C₁₉×C₁₁⋊C₅	D₅	1	1	yes	characteristic, complemented
8	C₃×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₂₈₅	—	11	1	no	maximal, Hall
10	D₁₉×C₁₁⋊C₅	—	15	1	no	—
11	C₁₁×D₉₅	—	3	1	no	—
12	D₁₅×C₁₁⋊C₅	—	19	1	no	maximal, Hall
13	C₃×C₅²×C₁₉	—	11	1	no	Hall
14	C₁₁×D₅₇	—	5	1	no	Hall
15	C₅×C₁₁×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
16	C₁₉×C₁₁⋊C₅	—	2	2	no	—
17	C₁₉×C₁₁⋊C₅	D₁₅	1	1	yes	characteristic, complemented
18	C₅×D₉₅	—	33	1	no	Hall
19	C₃×C₅×C₁₁⋊C₅	D₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
21	D₂₈₅	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
22	C₅×D₅₇	—	55	1	no	—
23	D₅×C₁₁⋊C₅	—	57	1	no	Hall
24	C₅²×C₁₉	—	11	1	no	Hall
25	C₁₁×D₁₉	—	15	1	no	Hall
26	C₁₁×D₁₅	—	19	1	no	—
27	D₃×C₁₁⋊C₅	—	95	1	no	—
28	C₃×C₅×C₁₉	—	11	1	no	—
29	C₃×C₅×C₁₉	—	22	2	no	—
30	C₃×C₅×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
31	C₅×C₁₁⋊C₅	D₅₇	1	1	yes	characteristic, complemented, Hall
32	C₁₁×C₁₉	C₅×D₁₅	1	1	yes	characteristic, complemented, Hall
33	D₉₅	—	3	1	no	—
34	C₅×D₁₉	—	165	1	no	—
35	C₃×C₅×C₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented
36	C₃×C₁₁⋊C₅	—	2	2	no	—
37	C₃×C₁₁⋊C₅	D₉₅	1	1	yes	characteristic, complemented
38	C₅×D₁₅	—	209	1	no	Hall
39	D₅₇	—	5	1	no	Hall
40	D₅×C₁₁	—	57	1	no	—
41	C₂×C₁₁⋊C₅	—	285	1	no	—
42	C₅×C₁₉	—	11	1	no	—
43	C₅×C₁₉	—	22	2	no	—
44	C₅×C₁₉	D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
45	C₃×C₅²	—	11	1	no	Hall
46	D₃×C₁₁	—	95	1	no	Hall
47	C₃×C₁₉	D₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
48	C₅×C₁₁	C₅×D₅₇	1	1	yes	characteristic, complemented
49	C₁₁⋊C₅	—	2	2	no	—
50	C₁₁⋊C₅	D₂₈₅	1	1	yes	characteristic, direct product factor
51	C₅×D₅	—	627	1	no	Hall
52	D₁₉	—	15	1	no	Hall
53	C₃×C₁₁	C₅×D₉₅	1	1	yes	characteristic, complemented, Hall
54	D₁₅	—	19	1	no	—
55	C₅×D₃	—	1045	1	no	—
56	C₅²	—	11	1	no	Sylow
57	C₂×C₁₁	—	285	1	no	Hall
58	C₁₉	D₁₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₅	—	11	1	no	—
60	C₃×C₅	—	22	2	no	—
61	C₃×C₅	D₁₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented
62	C₁₁	C₅×D₂₈₅	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₅	—	3135	1	no	—
64	D₅	—	57	1	no	—
65	D₃	—	95	1	no	Hall
66	C₅	—	11	1	no	—
67	C₅	—	22	2	no	—
68	C₅	C₁₁⋊C₅×D₅₇	1	1	yes	characteristic, complemented
69	C₃	C₁₁⋊C₅×D₉₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	285	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₁×C₁₉	C₂×C₅
LCS	G ▷ C₃×C₅×C₁₁×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₁₁⋊C₅	C₂	semidirect
4. C₁₁×D₂₈₅	C₅	semidirect
5. C₅×C₁₉×C₁₁⋊C₅	D₃	semidirect
7. C₃×C₁₉×C₁₁⋊C₅	D₅	semidirect
8. C₃×C₅×C₁₁×C₁₉	C₂×C₅	semidirect
15. C₅×C₁₁×C₁₉	C₅×D₃	semidirect
17. C₁₉×C₁₁⋊C₅	D₁₅	semidirect
19. C₃×C₅×C₁₁⋊C₅	D₁₉	semidirect
20. C₃×C₁₁×C₁₉	C₅×D₅	semidirect
21. D₂₈₅	C₁₁⋊C₅	direct (N × H)
30. C₃×C₅×C₁₉	C₂×C₁₁⋊C₅	semidirect
31. C₅×C₁₁⋊C₅	D₅₇	semidirect
32. C₁₁×C₁₉	C₅×D₁₅	semidirect
35. C₃×C₅×C₁₁	C₅×D₁₉	semidirect
37. C₃×C₁₁⋊C₅	D₉₅	semidirect
44. C₅×C₁₉	D₃×C₁₁⋊C₅	semidirect
47. C₃×C₁₉	D₅×C₁₁⋊C₅	semidirect
48. C₅×C₁₁	C₅×D₅₇	semidirect
50. C₁₁⋊C₅	D₂₈₅	direct (N × H)
53. C₃×C₁₁	C₅×D₉₅	semidirect
58. C₁₉	D₁₅×C₁₁⋊C₅	semidirect
61. C₃×C₅	D₁₉×C₁₁⋊C₅	semidirect
62. C₁₁	C₅×D₂₈₅	semidirect
68. C₅	C₁₁⋊C₅×D₅₇	semidirect
69. C₃	C₁₁⋊C₅×D₉₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉×C₁₁⋊C₅	2
C₁₁⋊C₅×D₉₅	3
C₁₁⋊C₅×D₅₇	5
C₁₁×D₂₈₅	5
C₅×D₂₈₅	11
D₁₅×C₁₁⋊C₅	19

Subgroups — C11⋊C5×D285 #44535487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊C₅×D₂₈₅ #44535487