Subgroups — C₇×D₁₃₆₅ #34062187

Order 19110.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₅₅	—	3	1	no	maximal, Hall
3	C₇×D₂₇₃	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	D₃	1	1	yes	characteristic, complemented, Hall
5	D₁₃₆₅	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×D₁₉₅	—	7	1	no	maximal
7	C₃×C₇²×C₁₃	D₅	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₀₅	—	13	1	no	maximal, Hall
9	C₃×C₅×C₇×C₁₃	—	2	3	no	—
10	C₃×C₅×C₇×C₁₃	D₇	1	1	yes	characteristic, complemented
11	C₃×C₅×C₇×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×D₉₁	—	15	1	no	Hall
13	D₄₅₅	—	3	1	no	—
14	C₇×D₆₅	—	21	1	no	—
15	C₃×C₅×C₇²	D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₁₃	D₁₅	1	1	yes	characteristic, complemented, Hall
17	D₂₇₃	—	5	1	no	—
18	C₇×D₃₉	—	35	1	no	—
19	C₇×D₃₅	—	39	1	no	Hall
20	C₅×C₇×C₁₃	—	2	3	no	—
21	C₅×C₇×C₁₃	D₃×C₇	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	D₂₁	1	1	yes	characteristic, complemented
23	D₁₉₅	—	7	1	no	Hall
24	C₇×D₂₁	—	65	1	no	Hall
25	C₃×C₇×C₁₃	—	2	3	no	—
26	C₃×C₇×C₁₃	C₇×D₅	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₃	D₃₅	1	1	yes	characteristic, complemented
28	C₅×C₇²	D₃₉	1	1	yes	characteristic, complemented, Hall
29	D₁₀₅	—	13	1	no	—
30	C₇×D₁₅	—	91	1	no	—
31	C₃×C₅×C₁₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
32	D₉₁	—	15	1	no	—
33	C₇×D₁₃	—	105	1	no	—
34	C₃×C₇²	D₆₅	1	1	yes	characteristic, complemented, Hall
35	D₆₅	—	21	1	no	Hall
36	C₃×C₅×C₇	—	2	3	no	—
37	C₃×C₅×C₇	C₇×D₁₃	1	1	yes	characteristic, complemented
38	C₃×C₅×C₇	D₉₁	1	1	yes	characteristic, complemented
39	C₇×D₇	—	195	1	no	Hall
40	C₇×C₁₃	—	2	3	no	—
41	C₇×C₁₃	C₇×D₁₅	1	1	yes	characteristic, complemented
42	C₇×C₁₃	D₁₀₅	1	1	yes	characteristic, complemented
43	D₃₉	—	35	1	no	Hall
44	D₃₅	—	39	1	no	—
45	C₇×D₅	—	273	1	no	—
46	C₅×C₁₃	C₇×D₂₁	1	1	yes	characteristic, complemented, Hall
47	C₇²	D₁₉₅	1	1	yes	characteristic, complemented, Sylow
48	D₂₁	—	65	1	no	—
49	D₃×C₇	—	455	1	no	—
50	C₃×C₁₃	C₇×D₃₅	1	1	yes	characteristic, complemented, Hall
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	C₇×D₃₉	1	1	yes	characteristic, complemented
53	C₅×C₇	D₂₇₃	1	1	yes	characteristic, complemented
54	D₁₅	—	91	1	no	Hall
55	D₁₃	—	105	1	no	Hall
56	C₃×C₇	—	2	3	no	—
57	C₃×C₇	C₇×D₆₅	1	1	yes	characteristic, complemented
58	C₃×C₇	D₄₅₅	1	1	yes	characteristic, complemented
59	C₃×C₅	C₇×D₉₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₇	—	1365	1	no	—
61	D₇	—	195	1	no	—
62	C₁₃	C₇×D₁₀₅	1	1	yes	characteristic, complemented, Sylow
63	D₅	—	273	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	C₇×D₁₉₅	1	1	yes	characteristic, complemented
66	C₇	D₁₃₆₅	1	1	yes	characteristic, direct product factor
67	D₃	—	455	1	no	Hall
68	C₅	C₇×D₂₇₃	1	1	yes	characteristic, complemented, Sylow
69	C₃	C₇×D₄₅₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	1365	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₃₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₇×C₁₃	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₇×C₁₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₃	C₂	semidirect
4. C₅×C₇²×C₁₃	D₃	semidirect
5. D₁₃₆₅	C₇	direct (N × H)
7. C₃×C₇²×C₁₃	D₅	semidirect
10. C₃×C₅×C₇×C₁₃	D₇	semidirect
11. C₃×C₅×C₇×C₁₃	C₂×C₇	semidirect
15. C₃×C₅×C₇²	D₁₃	semidirect
16. C₇²×C₁₃	D₁₅	semidirect
21. C₅×C₇×C₁₃	D₃×C₇	semidirect
22. C₅×C₇×C₁₃	D₂₁	semidirect
26. C₃×C₇×C₁₃	C₇×D₅	semidirect
27. C₃×C₇×C₁₃	D₃₅	semidirect
28. C₅×C₇²	D₃₉	semidirect
31. C₃×C₅×C₁₃	C₇×D₇	semidirect
34. C₃×C₇²	D₆₅	semidirect
37. C₃×C₅×C₇	C₇×D₁₃	semidirect
38. C₃×C₅×C₇	D₉₁	semidirect
41. C₇×C₁₃	C₇×D₁₅	semidirect
42. C₇×C₁₃	D₁₀₅	semidirect
46. C₅×C₁₃	C₇×D₂₁	semidirect
47. C₇²	D₁₉₅	semidirect
50. C₃×C₁₃	C₇×D₃₅	semidirect
52. C₅×C₇	C₇×D₃₉	semidirect
53. C₅×C₇	D₂₇₃	semidirect
57. C₃×C₇	C₇×D₆₅	semidirect
58. C₃×C₇	D₄₅₅	semidirect
59. C₃×C₅	C₇×D₉₁	semidirect
62. C₁₃	C₇×D₁₀₅	semidirect
65. C₇	C₇×D₁₉₅	semidirect
66. C₇	D₁₃₆₅	direct (N × H)
68. C₅	C₇×D₂₇₃	semidirect
69. C₃	C₇×D₄₅₅	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×C₁₃	2
C₇×D₄₅₅	3
C₇×D₂₇₃	5
D₁₃₆₅	7
C₇×D₁₉₅	7
C₇×D₁₀₅	13

Subgroups — C7×D1365 #34062187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₃₆₅ #34062187