Subgroups — C₇×D₁₁₅₅ #30633573

Order 16170.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₈₅	—	3	1	no	maximal, Hall
3	C₇×D₂₃₁	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₁	D₃	1	1	yes	characteristic, complemented, Hall
5	D₁₁₅₅	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×D₁₆₅	—	7	1	no	maximal
7	C₃×C₇²×C₁₁	D₅	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₀₅	—	11	1	no	maximal, Hall
9	C₃×C₅×C₇×C₁₁	—	2	3	no	—
10	C₃×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic, complemented
11	C₃×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×D₇₇	—	15	1	no	Hall
13	D₃₈₅	—	3	1	no	—
14	C₇×D₅₅	—	21	1	no	—
15	C₃×C₅×C₇²	D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₁₁	D₁₅	1	1	yes	characteristic, complemented, Hall
17	C₇×D₃₅	—	33	1	no	Hall
18	D₂₃₁	—	5	1	no	—
19	C₇×D₃₃	—	35	1	no	—
20	C₅×C₇×C₁₁	—	2	3	no	—
21	C₅×C₇×C₁₁	D₃×C₇	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₁	D₂₁	1	1	yes	characteristic, complemented
23	D₁₆₅	—	7	1	no	Hall
24	C₇×D₂₁	—	55	1	no	Hall
25	C₅×C₇²	D₃₃	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₁	—	2	3	no	—
27	C₃×C₇×C₁₁	C₇×D₅	1	1	yes	characteristic, complemented
28	C₃×C₇×C₁₁	D₃₅	1	1	yes	characteristic, complemented
29	D₁₀₅	—	11	1	no	—
30	C₇×D₁₅	—	77	1	no	—
31	C₃×C₅×C₁₁	C₇×D₇	1	1	yes	characteristic, complemented, Hall
32	D₇₇	—	15	1	no	—
33	C₇×D₁₁	—	105	1	no	—
34	C₃×C₇²	D₅₅	1	1	yes	characteristic, complemented, Hall
35	D₅₅	—	21	1	no	Hall
36	C₃×C₅×C₇	—	2	3	no	—
37	C₃×C₅×C₇	C₇×D₁₁	1	1	yes	characteristic, complemented
38	C₃×C₅×C₇	D₇₇	1	1	yes	characteristic, complemented
39	C₇×D₇	—	165	1	no	Hall
40	C₇×C₁₁	—	2	3	no	—
41	C₇×C₁₁	C₇×D₁₅	1	1	yes	characteristic, complemented
42	C₇×C₁₁	D₁₀₅	1	1	yes	characteristic, complemented
43	D₃₅	—	33	1	no	—
44	C₇×D₅	—	231	1	no	—
45	D₃₃	—	35	1	no	Hall
46	C₅×C₁₁	C₇×D₂₁	1	1	yes	characteristic, complemented, Hall
47	C₇²	D₁₆₅	1	1	yes	characteristic, complemented, Sylow
48	D₂₁	—	55	1	no	—
49	D₃×C₇	—	385	1	no	—
50	C₅×C₇	—	2	3	no	—
51	C₅×C₇	C₇×D₃₃	1	1	yes	characteristic, complemented
52	C₅×C₇	D₂₃₁	1	1	yes	characteristic, complemented
53	C₃×C₁₁	C₇×D₃₅	1	1	yes	characteristic, complemented, Hall
54	D₁₅	—	77	1	no	Hall
55	D₁₁	—	105	1	no	Hall
56	C₃×C₇	—	2	3	no	—
57	C₃×C₇	C₇×D₅₅	1	1	yes	characteristic, complemented
58	C₃×C₇	D₃₈₅	1	1	yes	characteristic, complemented
59	C₃×C₅	C₇×D₇₇	1	1	yes	characteristic, complemented, Hall
60	C₂×C₇	—	1155	1	no	—
61	D₇	—	165	1	no	—
62	C₁₁	C₇×D₁₀₅	1	1	yes	characteristic, complemented, Sylow
63	D₅	—	231	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	C₇×D₁₆₅	1	1	yes	characteristic, complemented
66	C₇	D₁₁₅₅	1	1	yes	characteristic, direct product factor
67	D₃	—	385	1	no	Hall
68	C₅	C₇×D₂₃₁	1	1	yes	characteristic, complemented, Sylow
69	C₃	C₇×D₃₈₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	1155	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₁₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₇×C₁₁	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₃×C₅×C₇×C₁₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	D₃	semidirect
5. D₁₁₅₅	C₇	direct (N × H)
7. C₃×C₇²×C₁₁	D₅	semidirect
10. C₃×C₅×C₇×C₁₁	D₇	semidirect
11. C₃×C₅×C₇×C₁₁	C₂×C₇	semidirect
15. C₃×C₅×C₇²	D₁₁	semidirect
16. C₇²×C₁₁	D₁₅	semidirect
21. C₅×C₇×C₁₁	D₃×C₇	semidirect
22. C₅×C₇×C₁₁	D₂₁	semidirect
25. C₅×C₇²	D₃₃	semidirect
27. C₃×C₇×C₁₁	C₇×D₅	semidirect
28. C₃×C₇×C₁₁	D₃₅	semidirect
31. C₃×C₅×C₁₁	C₇×D₇	semidirect
34. C₃×C₇²	D₅₅	semidirect
37. C₃×C₅×C₇	C₇×D₁₁	semidirect
38. C₃×C₅×C₇	D₇₇	semidirect
41. C₇×C₁₁	C₇×D₁₅	semidirect
42. C₇×C₁₁	D₁₀₅	semidirect
46. C₅×C₁₁	C₇×D₂₁	semidirect
47. C₇²	D₁₆₅	semidirect
51. C₅×C₇	C₇×D₃₃	semidirect
52. C₅×C₇	D₂₃₁	semidirect
53. C₃×C₁₁	C₇×D₃₅	semidirect
57. C₃×C₇	C₇×D₅₅	semidirect
58. C₃×C₇	D₃₈₅	semidirect
59. C₃×C₅	C₇×D₇₇	semidirect
62. C₁₁	C₇×D₁₀₅	semidirect
65. C₇	C₇×D₁₆₅	semidirect
66. C₇	D₁₁₅₅	direct (N × H)
68. C₅	C₇×D₂₃₁	semidirect
69. C₃	C₇×D₃₈₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₁	2
C₇×D₃₈₅	3
C₇×D₂₃₁	5
D₁₁₅₅	7
C₇×D₁₆₅	7
C₇×D₁₀₅	11

Subgroups — C7×D1155 #30633573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₁₅₅ #30633573