Subgroups — C₃²×C₅⋊D₃₈₅ #46831661

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	C₃×C₅⋊D₃₈₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₃₈₅	—	5	6	no	maximal
4	C₃×C₅²×C₇×C₁₁	C₂×C₃	1	4	yes	complemented
5	C₃²×C₅⋊D₅₅	—	7	1	no	maximal, Hall
6	C₅⋊D₃₈₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇×C₁₁	D₅	1	6	yes	complemented
8	C₃²×C₅⋊D₃₅	—	11	1	no	maximal, Hall
9	C₃²×C₅²×C₁₁	D₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃₈₅	—	5	24	no	—
11	C₅²×C₇×C₁₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅⋊D₅₅	—	7	4	no	—
13	C₃²×C₅²×C₇	D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃²×D₇₇	—	25	1	no	Hall
15	C₃×C₅×C₇×C₁₁	C₃×D₅	1	24	yes	complemented
16	C₃×C₅⋊D₃₅	—	11	4	no	—
17	C₃²×D₅₅	—	35	6	no	—
18	C₃×C₅²×C₁₁	C₃×D₇	1	4	yes	complemented
19	D₃₈₅	—	5	6	no	—
20	C₃²×C₇×C₁₁	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
21	C₃²×D₃₅	—	55	6	no	—
22	C₅⋊D₅₅	—	7	1	no	Hall
23	C₃×C₅²×C₇	C₃×D₁₁	1	4	yes	complemented
24	C₃²×C₅×C₁₁	D₃₅	1	6	yes	complemented
25	C₃×D₇₇	—	25	4	no	—
26	C₃²×C₅⋊D₅	—	77	1	no	Hall
27	C₅×C₇×C₁₁	C₃²×D₅	1	6	yes	complemented
28	C₅⋊D₃₅	—	11	1	no	Hall
29	C₃×D₅₅	—	35	24	no	—
30	C₃²×C₅×C₇	D₅₅	1	6	yes	complemented
31	C₅²×C₁₁	C₃²×D₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₃×C₅⋊D₅	1	4	yes	complemented
33	C₃²×C₅²	D₇₇	1	1	yes	characteristic, complemented, Hall
34	C₃×D₃₅	—	55	24	no	—
35	C₃²×D₁₁	—	175	1	no	Hall
36	C₅²×C₇	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₁	C₃×D₃₅	1	24	yes	complemented
38	D₇₇	—	25	1	no	Hall
39	C₃×C₅⋊D₅	—	77	4	no	—
40	C₃²×D₇	—	275	1	no	Hall
41	D₅₅	—	35	6	no	—
42	C₃×C₅×C₇	C₃×D₅₅	1	24	yes	complemented
43	C₃²×C₁₁	C₅⋊D₃₅	1	1	yes	characteristic, complemented, Hall
44	C₃²×D₅	—	385	6	no	—
45	C₇×C₁₁	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅²	C₃×D₇₇	1	4	yes	complemented
47	D₃₅	—	55	6	no	—
48	C₃×D₁₁	—	175	4	no	—
49	C₃²×C₇	C₅⋊D₅₅	1	1	yes	characteristic, complemented, Hall
50	C₅×C₁₁	C₃²×D₃₅	1	6	yes	complemented
51	C₅⋊D₅	—	77	1	no	Hall
52	C₃²×C₅	D₃₈₅	1	6	yes	complemented
53	C₃×D₇	—	275	4	no	—
54	C₅×C₇	C₃²×D₅₅	1	6	yes	complemented
55	C₃×C₁₁	C₃×C₅⋊D₃₅	1	4	yes	complemented
56	C₃×D₅	—	385	24	no	—
57	C₅²	C₃²×D₇₇	1	1	yes	characteristic, complemented, Sylow
58	D₁₁	—	175	1	no	Hall
59	C₃×C₇	C₃×C₅⋊D₅₅	1	4	yes	complemented
60	C₂×C₃²	—	1925	1	no	Hall
61	C₃×C₅	C₃×D₃₈₅	1	24	yes	complemented
62	D₇	—	275	1	no	Hall
63	C₁₁	C₃²×C₅⋊D₃₅	1	1	yes	characteristic, complemented, Sylow
64	D₅	—	385	6	no	—
65	C₃²	C₅⋊D₃₈₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₇	C₃²×C₅⋊D₅₅	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	—	1925	4	no	—
68	C₅	C₃²×D₃₈₅	1	6	yes	complemented
69	C₃	C₃×C₅⋊D₃₈₅	1	4	yes	direct product factor
70	C₂	—	1925	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊D₃₈₅
commutator, cosocle, hypocenter	C₅²×C₇×C₁₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇×C₁₁	C₂
LCS	G ▷ C₅²×C₇×C₁₁
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇×C₁₁	C₂	semidirect
2. C₃×C₅⋊D₃₈₅	C₃	direct (N × H)
4. C₃×C₅²×C₇×C₁₁	C₂×C₃	semidirect
6. C₅⋊D₃₈₅	C₃²	direct (N × H)
7. C₃²×C₅×C₇×C₁₁	D₅	semidirect
9. C₃²×C₅²×C₁₁	D₇	semidirect
11. C₅²×C₇×C₁₁	C₂×C₃²	semidirect
13. C₃²×C₅²×C₇	D₁₁	semidirect
15. C₃×C₅×C₇×C₁₁	C₃×D₅	semidirect
18. C₃×C₅²×C₁₁	C₃×D₇	semidirect
20. C₃²×C₇×C₁₁	C₅⋊D₅	semidirect
23. C₃×C₅²×C₇	C₃×D₁₁	semidirect
24. C₃²×C₅×C₁₁	D₃₅	semidirect
27. C₅×C₇×C₁₁	C₃²×D₅	semidirect
30. C₃²×C₅×C₇	D₅₅	semidirect
31. C₅²×C₁₁	C₃²×D₇	semidirect
32. C₃×C₇×C₁₁	C₃×C₅⋊D₅	semidirect
33. C₃²×C₅²	D₇₇	semidirect
36. C₅²×C₇	C₃²×D₁₁	semidirect
37. C₃×C₅×C₁₁	C₃×D₃₅	semidirect
42. C₃×C₅×C₇	C₃×D₅₅	semidirect
43. C₃²×C₁₁	C₅⋊D₃₅	semidirect
45. C₇×C₁₁	C₃²×C₅⋊D₅	semidirect
46. C₃×C₅²	C₃×D₇₇	semidirect
49. C₃²×C₇	C₅⋊D₅₅	semidirect
50. C₅×C₁₁	C₃²×D₃₅	semidirect
52. C₃²×C₅	D₃₈₅	semidirect
54. C₅×C₇	C₃²×D₅₅	semidirect
55. C₃×C₁₁	C₃×C₅⋊D₃₅	semidirect
57. C₅²	C₃²×D₇₇	semidirect
59. C₃×C₇	C₃×C₅⋊D₅₅	semidirect
61. C₃×C₅	C₃×D₃₈₅	semidirect
63. C₁₁	C₃²×C₅⋊D₃₅	semidirect
65. C₃²	C₅⋊D₃₈₅	direct (N × H)
66. C₇	C₃²×C₅⋊D₅₅	semidirect
68. C₅	C₃²×D₃₈₅	semidirect
69. C₃	C₃×C₅⋊D₃₈₅	direct (N × H)

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
C₃×C₅⋊D₃₈₅	3
C₃²×D₃₈₅	5
C₃²×C₅⋊D₅₅	7
C₃²×C₅⋊D₃₅	11

Subgroups — C32×C5⋊D385 #46831661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅⋊D₃₈₅ #46831661