Subgroups — C₇×D₅×D₇₇ #24924775

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

	subgroup	G/H
center, hypercenter	C₇	D₅×D₇₇
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. C₇²×D₅×C₁₁	C₂	semidirect
3. C₅×C₇×D₇₇	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
6. D₅×D₇₇	C₇	direct (N × H)
10. C₇×D₇₇	D₅	direct (N × H)
12. D₃₈₅	C₂×C₇	semidirect
15. C₇×D₅×C₁₁	D₇	semidirect
16. C₇×D₅×C₁₁	C₂×C₇	semidirect
17. C₅×D₇₇	C₂×C₇	semidirect
19. C₇²×C₁₁	C₂×D₅	semidirect
21. C₇²×D₅	D₁₁	semidirect
24. C₅×C₇×C₁₁	C₂×D₇	semidirect
25. C₅×C₇×C₁₁	C₂²×C₇	semidirect
28. C₅×C₇²	C₂×D₁₁	semidirect
35. D₇₇	C₇×D₅	direct (N × H)
42. D₅×C₁₁	C₇×D₇	semidirect
47. C₇×C₁₁	D₅×D₇	semidirect
48. C₇×C₁₁	C₂×C₇×D₅	semidirect
54. C₇×D₅	C₇×D₁₁	semidirect
55. C₇×D₅	D₇₇	direct (N × H)
56. C₅×C₁₁	C₂×C₇×D₇	semidirect
57. C₇²	D₅×D₁₁	semidirect
60. C₅×C₇	C₂×C₇×D₁₁	semidirect
61. C₅×C₇	C₂×D₇₇	semidirect
75. C₁₁	C₇×D₅×D₇	semidirect
78. D₅	C₇×D₇₇	direct (N × H)
80. C₇	C₇×D₅×D₁₁	semidirect
81. C₇	D₅×D₇₇	direct (N × H)
82. C₅	C₂×C₇×D₇₇	semidirect

Subgroups — C7×D5×D77 #24924775

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₅×D₇₇ #24924775