Subgroups — C₇×D₁₁×D₃₅ #24924772

Order 10780.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₃₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₇×D₁₁	—	5	1	no	maximal, Hall
6	D₁₁×D₃₅	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₇×D₅×D₁₁	—	7	1	no	maximal
8	C₇×D₇₇	—	5	1	no	—
9	C₇×C₁₁×D₇	—	5	1	no	—
10	C₇²×D₁₁	D₅	1	1	yes	characteristic, complemented
11	C₂×C₇×D₃₅	—	11	1	no	maximal, Hall
12	D₃₈₅	C₂×C₇	1	1	yes	characteristic, complemented
13	C₁₁×D₃₅	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇×D₅₅	—	7	1	no	—
15	C₇×D₅×C₁₁	—	7	1	no	—
16	C₅×C₇×D₁₁	—	2	3	no	—
17	C₅×C₇×D₁₁	D₇	1	1	yes	characteristic, complemented
18	C₅×C₇×D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
19	C₇²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇²	—	11	1	no	—
21	C₇×D₃₅	—	11	1	no	—
22	C₇×D₃₅	D₁₁	1	1	yes	characteristic, direct product factor
23	C₅×C₇×C₁₁	—	2	3	no	—
24	C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented
25	C₅×C₇×C₁₁	C₂²×C₇	1	1	yes	characteristic, complemented
26	C₂×C₇×D₁₁	—	35	1	no	—
27	D₇×D₁₁	—	5	1	no	—
28	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	D₅×D₁₁	—	7	1	no	Hall
30	C₂×C₇×D₇	—	55	1	no	Hall
31	C₂×C₇×C₁₁	—	35	1	no	—
32	D₇₇	—	5	1	no	—
33	C₇×D₁₁	—	2	3	no	—
34	C₇×D₁₁	—	35	1	no	—
35	C₇×D₁₁	C₇×D₅	1	1	yes	characteristic, complemented
36	C₇×D₁₁	D₃₅	1	1	yes	characteristic, direct product factor
37	C₁₁×D₇	—	5	1	no	—
38	C₂×D₃₅	—	11	1	no	—
39	C₂×C₇×D₅	—	77	1	no	—
40	D₅₅	—	7	1	no	—
41	C₅×D₁₁	C₇×D₇	1	1	yes	characteristic, complemented
42	D₅×C₁₁	—	7	1	no	—
43	C₂×C₇²	—	11	1	no	—
44	C₇×D₇	—	5	1	no	—
45	C₇×D₇	—	55	1	no	—
46	C₇×C₁₁	—	2	3	no	—
47	C₇×C₁₁	C₂×C₇×D₅	1	1	yes	characteristic, complemented
48	C₇×C₁₁	C₂×D₃₅	1	1	yes	characteristic, complemented
49	C₂×C₅×C₇	—	11	1	no	—
50	C₂×C₅×C₇	—	11	1	no	—
51	C₂×C₅×C₇	—	22	3	no	—
52	D₃₅	—	11	1	no	—
53	D₃₅	C₇×D₁₁	1	1	yes	characteristic, direct product factor
54	C₇×D₅	—	7	1	no	—
55	C₇×D₅	—	77	1	no	—
56	C₅×C₁₁	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
57	C₇²	D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₁	—	35	1	no	Hall
59	C₅×C₇	—	2	3	no	—
60	C₅×C₇	D₇×D₁₁	1	1	yes	characteristic, complemented
61	C₅×C₇	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented
62	C₂²×C₇	—	385	1	no	—
63	C₂×D₇	—	55	1	no	—
64	C₂×C₁₁	—	35	1	no	—
65	D₁₁	—	35	1	no	—
66	D₁₁	C₇×D₃₅	1	1	yes	characteristic, direct product factor
67	C₂×D₅	—	77	1	no	Hall
68	C₂×C₇	—	11	1	no	—
69	C₂×C₇	—	11	1	no	—
70	C₂×C₇	—	22	3	no	—
71	C₂×C₇	—	35	1	no	—
72	C₂×C₇	—	385	1	no	—
73	D₇	—	5	1	no	—
74	D₇	—	55	1	no	—
75	C₁₁	C₂×C₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₅	—	11	1	no	—
77	D₅	—	7	1	no	—
78	D₅	—	77	1	no	—
79	C₇	—	2	3	no	—
80	C₇	C₇×D₅×D₁₁	1	1	yes	characteristic, complemented
81	C₇	D₁₁×D₃₅	1	1	yes	characteristic, direct product factor
82	C₅	C₇×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	385	1	no	Sylow
84	C₂	—	11	1	no	—
85	C₂	—	35	1	no	—
86	C₂	—	385	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₁₁×D₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₅×C₇×C₁₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₃₈₅	C₂	semidirect
2. C₇×C₁₁×D₃₅	C₂	semidirect
3. C₅×C₇²×D₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
6. D₁₁×D₃₅	C₇	direct (N × H)
10. C₇²×D₁₁	D₅	semidirect
12. D₃₈₅	C₂×C₇	semidirect
13. C₁₁×D₃₅	C₂×C₇	semidirect
17. C₅×C₇×D₁₁	D₇	semidirect
18. C₅×C₇×D₁₁	C₂×C₇	semidirect
19. C₇²×C₁₁	C₂×D₅	semidirect
22. C₇×D₃₅	D₁₁	direct (N × H)
24. C₅×C₇×C₁₁	C₂×D₇	semidirect
25. C₅×C₇×C₁₁	C₂²×C₇	semidirect
28. C₅×C₇²	C₂×D₁₁	semidirect
35. C₇×D₁₁	C₇×D₅	semidirect
36. C₇×D₁₁	D₃₅	direct (N × H)
41. C₅×D₁₁	C₇×D₇	semidirect
47. C₇×C₁₁	C₂×C₇×D₅	semidirect
48. C₇×C₁₁	C₂×D₃₅	semidirect
53. D₃₅	C₇×D₁₁	direct (N × H)
56. C₅×C₁₁	C₂×C₇×D₇	semidirect
57. C₇²	D₅×D₁₁	semidirect
60. C₅×C₇	D₇×D₁₁	semidirect
61. C₅×C₇	C₂×C₇×D₁₁	semidirect
66. D₁₁	C₇×D₃₅	direct (N × H)
75. C₁₁	C₂×C₇×D₃₅	semidirect
80. C₇	C₇×D₅×D₁₁	semidirect
81. C₇	D₁₁×D₃₅	direct (N × H)
82. C₅	C₇×D₇×D₁₁	semidirect

Subgroups — C7×D11×D35 #24924772

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₁₁×D₃₅ #24924772