Subgroups — C₅×D₇×D₇₇ #24924759

Order 10780.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇⋊D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₁×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₇₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×D₇₇	—	7	1	no	maximal
7	C₅×D₇×D₁₁	—	7	1	no	maximal
8	C₇⋊D₇₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₇×D₇₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₇×C₁₁×D₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×D₇²	—	11	1	no	maximal, Hall
12	C₂×C₅×C₇×C₁₁	—	7	1	no	—
13	C₅×D₇₇	—	7	1	no	—
14	C₅×D₇₇	—	7	1	no	—
15	C₅×D₇₇	—	14	3	no	—
16	C₅×D₇₇	D₇	1	1	yes	characteristic, direct product factor
17	C₅×C₁₁×D₇	D₇	1	1	yes	characteristic, complemented
18	C₅×C₇×D₁₁	—	7	1	no	—
19	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₇⋊D₇	—	11	1	no	—
21	C₅×C₇×D₇	—	11	1	no	—
22	C₅×C₇×D₇	D₁₁	1	1	yes	characteristic, complemented
23	C₅×C₇×C₁₁	—	2	3	no	—
24	C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented
25	C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented
26	C₂×D₇₇	—	7	1	no	—
27	D₇×D₁₁	—	7	1	no	—
28	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×D₁₁	—	49	1	no	Hall
30	D₇²	—	11	1	no	Hall
31	C₂×C₇×C₁₁	—	7	1	no	—
32	D₇₇	—	7	1	no	—
33	D₇₇	—	7	1	no	—
34	D₇₇	—	14	3	no	—
35	D₇₇	C₅×D₇	1	1	yes	characteristic, direct product factor
36	C₇×D₁₁	—	7	1	no	—
37	C₁₁×D₇	C₅×D₇	1	1	yes	characteristic, complemented
38	C₂×C₅×D₇	—	77	1	no	—
39	C₂×C₅×D₇	—	77	1	no	—
40	C₂×C₅×C₁₁	—	7	1	no	—
41	C₅×D₁₁	—	7	1	no	—
42	C₅×D₁₁	—	49	1	no	—
43	C₇⋊D₇	—	11	1	no	—
44	C₇×D₇	—	11	1	no	—
45	C₇×D₇	C₅×D₁₁	1	1	yes	characteristic, complemented
46	C₇×C₁₁	—	2	3	no	—
47	C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented
48	C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented
49	C₂×C₅×C₇	—	7	1	no	—
50	C₂×C₅×C₇	—	77	1	no	—
51	C₅×D₇	—	11	1	no	—
52	C₅×D₇	—	77	1	no	—
53	C₅×D₇	—	77	1	no	—
54	C₅×D₇	—	154	3	no	—
55	C₅×D₇	D₇₇	1	1	yes	characteristic, direct product factor
56	C₅×C₁₁	D₇²	1	1	yes	characteristic, complemented, Hall
57	C₇²	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₁	—	49	1	no	Hall
59	C₅×C₇	—	2	3	no	—
60	C₅×C₇	D₇×D₁₁	1	1	yes	characteristic, complemented
61	C₅×C₇	C₂×D₇₇	1	1	yes	characteristic, complemented
62	C₂×D₇	—	77	1	no	—
63	C₂×D₇	—	77	1	no	—
64	C₂×C₁₁	—	7	1	no	—
65	D₁₁	—	7	1	no	—
66	D₁₁	—	49	1	no	—
67	C₂²×C₅	—	539	1	no	Hall
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	77	1	no	—
70	D₇	—	11	1	no	—
71	D₇	—	77	1	no	—
72	D₇	—	77	1	no	—
73	D₇	—	154	3	no	—
74	D₇	C₅×D₇₇	1	1	yes	characteristic, direct product factor
75	C₁₁	C₅×D₇²	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₅	—	7	1	no	—
77	C₂×C₅	—	539	1	no	—
78	C₂×C₅	—	77	1	no	—
79	C₇	—	2	3	no	—
80	C₇	C₅×D₇×D₁₁	1	1	yes	characteristic, complemented
81	C₇	C₂×C₅×D₇₇	1	1	yes	characteristic, complemented
82	C₅	D₇×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²	—	539	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	539	1	no	—
86	C₂	—	77	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₇×D₇₇
commutator, cosocle, hypocenter	C₇²×C₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇⋊D₇₇	C₂	semidirect
2. C₅×C₇×D₇₇	C₂	semidirect
3. C₅×C₇×C₁₁×D₇	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
5. D₇×D₇₇	C₅	direct (N × H)
8. C₇⋊D₇₇	C₂×C₅	semidirect
9. C₇×D₇₇	C₂×C₅	semidirect
10. C₇×C₁₁×D₇	C₂×C₅	semidirect
16. C₅×D₇₇	D₇	direct (N × H)
17. C₅×C₁₁×D₇	D₇	semidirect
19. C₇²×C₁₁	C₂²×C₅	semidirect
22. C₅×C₇×D₇	D₁₁	semidirect
24. C₅×C₇×C₁₁	C₂×D₇	semidirect
25. C₅×C₇×C₁₁	C₂×D₇	semidirect
28. C₅×C₇²	C₂×D₁₁	semidirect
35. D₇₇	C₅×D₇	direct (N × H)
37. C₁₁×D₇	C₅×D₇	semidirect
45. C₇×D₇	C₅×D₁₁	semidirect
47. C₇×C₁₁	C₂×C₅×D₇	semidirect
48. C₇×C₁₁	C₂×C₅×D₇	semidirect
55. C₅×D₇	D₇₇	direct (N × H)
56. C₅×C₁₁	D₇²	semidirect
57. C₇²	C₂×C₅×D₁₁	semidirect
60. C₅×C₇	D₇×D₁₁	semidirect
61. C₅×C₇	C₂×D₇₇	semidirect
74. D₇	C₅×D₇₇	direct (N × H)
75. C₁₁	C₅×D₇²	semidirect
80. C₇	C₅×D₇×D₁₁	semidirect
81. C₇	C₂×C₅×D₇₇	semidirect
82. C₅	D₇×D₇₇	direct (N × H)

Subgroups — C5×D7×D77 #24924759

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₇×D₇₇ #24924759