Subgroups — C₅²×C₃⋊D₂₃₁ #46831677

Order 34650.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₂₃₁	—	3	4	no	maximal
3	C₅×C₃⋊D₂₃₁	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₇×C₁₁	D₃	1	4	yes	complemented
5	C₅²×C₃⋊D₃₃	—	7	1	no	maximal, Hall
6	C₅²×D₇₇	—	9	1	no	Hall
7	C₃²×C₅×C₇×C₁₁	C₂×C₅	1	6	yes	complemented
8	C₅²×C₃⋊D₂₁	—	11	1	no	maximal, Hall
9	C₃²×C₅²×C₁₁	D₇	1	1	yes	characteristic, complemented, Hall
10	C₅×D₂₃₁	—	3	24	no	—
11	C₅²×C₇×C₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	C₅²×D₃₃	—	21	4	no	—
13	C₃²×C₅²×C₇	D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃⋊D₂₃₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₇×C₁₁	C₅×D₃	1	24	yes	complemented
16	C₅²×D₂₁	—	33	4	no	—
17	C₅×C₃⋊D₃₃	—	7	6	no	—
18	C₃×C₅²×C₁₁	D₂₁	1	4	yes	complemented
19	C₅×D₇₇	—	9	6	no	—
20	C₃²×C₇×C₁₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
21	C₅×C₃⋊D₂₁	—	11	6	no	—
22	C₅²×D₁₁	—	63	1	no	Hall
23	C₃×C₅²×C₇	D₃₃	1	4	yes	complemented
24	C₃²×C₅×C₁₁	C₅×D₇	1	6	yes	complemented
25	D₂₃₁	—	3	4	no	—
26	C₅²×C₃⋊D₃	—	77	1	no	Hall
27	C₅×C₇×C₁₁	C₅×C₃⋊D₃	1	6	yes	complemented
28	C₅²×D₇	—	99	1	no	Hall
29	C₅×D₃₃	—	21	24	no	—
30	C₃²×C₅×C₇	C₅×D₁₁	1	6	yes	complemented
31	C₅²×C₁₁	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₅²×D₃	1	4	yes	complemented
33	C₃²×C₅²	D₇₇	1	1	yes	characteristic, complemented, Hall
34	C₅×D₂₁	—	33	24	no	—
35	C₃⋊D₃₃	—	7	1	no	Hall
36	C₅²×C₇	C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₁	C₅×D₂₁	1	24	yes	complemented
38	D₇₇	—	9	1	no	Hall
39	C₅²×D₃	—	231	4	no	—
40	C₃⋊D₂₁	—	11	1	no	Hall
41	C₅×D₁₁	—	63	6	no	—
42	C₃×C₅×C₇	C₅×D₃₃	1	24	yes	complemented
43	C₃²×C₁₁	C₅²×D₇	1	1	yes	characteristic, complemented, Hall
44	C₅×C₃⋊D₃	—	77	6	no	—
45	C₇×C₁₁	C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅²	D₂₃₁	1	4	yes	complemented
47	C₅×D₇	—	99	6	no	—
48	D₃₃	—	21	4	no	—
49	C₃²×C₇	C₅²×D₁₁	1	1	yes	characteristic, complemented, Hall
50	C₅×C₁₁	C₅×C₃⋊D₂₁	1	6	yes	complemented
51	C₂×C₅²	—	693	1	no	Hall
52	C₃²×C₅	C₅×D₇₇	1	6	yes	complemented
53	D₂₁	—	33	4	no	—
54	C₅×C₇	C₅×C₃⋊D₃₃	1	6	yes	complemented
55	C₃×C₁₁	C₅²×D₂₁	1	4	yes	complemented
56	C₅×D₃	—	231	24	no	—
57	C₅²	C₃⋊D₂₃₁	1	1	yes	characteristic, direct product factor, Sylow
58	D₁₁	—	63	1	no	Hall
59	C₃×C₇	C₅²×D₃₃	1	4	yes	complemented
60	C₃⋊D₃	—	77	1	no	Hall
61	C₃×C₅	C₅×D₂₃₁	1	24	yes	complemented
62	D₇	—	99	1	no	Hall
63	C₁₁	C₅²×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	—	693	6	no	—
65	C₃²	C₅²×D₇₇	1	1	yes	characteristic, complemented, Sylow
66	C₇	C₅²×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
67	D₃	—	231	4	no	—
68	C₅	C₅×C₃⋊D₂₃₁	1	6	yes	direct product factor
69	C₃	C₅²×D₂₃₁	1	4	yes	complemented
70	C₂	—	693	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	C₃⋊D₂₃₁
commutator, cosocle, hypocenter	C₃²×C₇×C₁₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇×C₁₁	C₂
LCS	G ▷ C₃²×C₇×C₁₁
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇×C₁₁	C₂	semidirect
3. C₅×C₃⋊D₂₃₁	C₅	direct (N × H)
4. C₃×C₅²×C₇×C₁₁	D₃	semidirect
7. C₃²×C₅×C₇×C₁₁	C₂×C₅	semidirect
9. C₃²×C₅²×C₁₁	D₇	semidirect
11. C₅²×C₇×C₁₁	C₃⋊D₃	semidirect
13. C₃²×C₅²×C₇	D₁₁	semidirect
14. C₃⋊D₂₃₁	C₅²	direct (N × H)
15. C₃×C₅×C₇×C₁₁	C₅×D₃	semidirect
18. C₃×C₅²×C₁₁	D₂₁	semidirect
20. C₃²×C₇×C₁₁	C₂×C₅²	semidirect
23. C₃×C₅²×C₇	D₃₃	semidirect
24. C₃²×C₅×C₁₁	C₅×D₇	semidirect
27. C₅×C₇×C₁₁	C₅×C₃⋊D₃	semidirect
30. C₃²×C₅×C₇	C₅×D₁₁	semidirect
31. C₅²×C₁₁	C₃⋊D₂₁	semidirect
32. C₃×C₇×C₁₁	C₅²×D₃	semidirect
33. C₃²×C₅²	D₇₇	semidirect
36. C₅²×C₇	C₃⋊D₃₃	semidirect
37. C₃×C₅×C₁₁	C₅×D₂₁	semidirect
42. C₃×C₅×C₇	C₅×D₃₃	semidirect
43. C₃²×C₁₁	C₅²×D₇	semidirect
45. C₇×C₁₁	C₅²×C₃⋊D₃	semidirect
46. C₃×C₅²	D₂₃₁	semidirect
49. C₃²×C₇	C₅²×D₁₁	semidirect
50. C₅×C₁₁	C₅×C₃⋊D₂₁	semidirect
52. C₃²×C₅	C₅×D₇₇	semidirect
54. C₅×C₇	C₅×C₃⋊D₃₃	semidirect
55. C₃×C₁₁	C₅²×D₂₁	semidirect
57. C₅²	C₃⋊D₂₃₁	direct (N × H)
59. C₃×C₇	C₅²×D₃₃	semidirect
61. C₃×C₅	C₅×D₂₃₁	semidirect
63. C₁₁	C₅²×C₃⋊D₂₁	semidirect
65. C₃²	C₅²×D₇₇	semidirect
66. C₇	C₅²×C₃⋊D₃₃	semidirect
68. C₅	C₅×C₃⋊D₂₃₁	direct (N × H)
69. C₃	C₅²×D₂₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×C₇×C₁₁	2
C₅²×D₂₃₁	3
C₅×C₃⋊D₂₃₁	5
C₅²×C₃⋊D₃₃	7
C₅²×C₃⋊D₂₁	11

Subgroups — C52×C3⋊D231 #46831677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊D₂₃₁ #46831677