Subgroups — C₅×C₁₁×D₂₈₅ #44535537

Order 31350.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₂₈₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₉	C₂	semidirect
3. C₁₁×D₂₈₅	C₅	direct (N × H)
5. C₅²×C₁₁×C₁₉	D₃	semidirect
7. C₃×C₅×C₁₁×C₁₉	D₅	semidirect
8. C₃×C₅×C₁₁×C₁₉	C₂×C₅	semidirect
9. C₅×D₂₈₅	C₁₁	direct (N × H)
13. C₃×C₅²×C₁₉	C₂×C₁₁	semidirect
16. C₅×C₁₁×C₁₉	C₅×D₃	semidirect
17. C₅×C₁₁×C₁₉	D₁₅	semidirect
19. C₃×C₅²×C₁₁	D₁₉	semidirect
20. C₃×C₁₁×C₁₉	C₅×D₅	semidirect
21. D₂₈₅	C₅×C₁₁	direct (N × H)
24. C₅²×C₁₉	D₃×C₁₁	semidirect
29. C₃×C₅×C₁₉	D₅×C₁₁	semidirect
30. C₃×C₅×C₁₉	C₂×C₅×C₁₁	semidirect
31. C₅²×C₁₁	D₅₇	semidirect
32. C₁₁×C₁₉	C₅×D₁₅	semidirect
36. C₃×C₅×C₁₁	C₅×D₁₉	semidirect
37. C₃×C₅×C₁₁	D₉₅	semidirect
43. C₅×C₁₉	C₅×D₃×C₁₁	semidirect
44. C₅×C₁₉	C₁₁×D₁₅	semidirect
45. C₃×C₅²	C₁₁×D₁₉	semidirect
47. C₃×C₁₉	C₅×D₅×C₁₁	semidirect
49. C₅×C₁₁	C₅×D₅₇	semidirect
50. C₅×C₁₁	D₂₈₅	direct (N × H)
53. C₃×C₁₁	C₅×D₉₅	semidirect
56. C₅²	C₁₁×D₅₇	semidirect
58. C₁₉	C₅×C₁₁×D₁₅	semidirect
60. C₃×C₅	C₅×C₁₁×D₁₉	semidirect
61. C₃×C₅	C₁₁×D₉₅	semidirect
62. C₁₁	C₅×D₂₈₅	direct (N × H)
67. C₅	C₅×C₁₁×D₅₇	semidirect
68. C₅	C₁₁×D₂₈₅	direct (N × H)
69. C₃	C₅×C₁₁×D₉₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁×C₁₉	2
C₅×C₁₁×D₉₅	3
C₁₁×D₂₈₅	5
C₅×C₁₁×D₅₇	5
C₅×D₂₈₅	11
C₅×C₁₁×D₁₅	19

Subgroups — C5×C11×D285 #44535537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₂₈₅ #44535537