Subgroups — C₅×C₇×D₇×D₁₁ #24924756

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

	subgroup	G/H
center, hypercenter	C₅×C₇	D₇×D₁₁
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₅×C₇

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×C₁₁×D₇	C₂	semidirect
3. C₅×C₇²×D₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
5. C₇×D₇×D₁₁	C₅	direct (N × H)
7. C₅×D₇×D₁₁	C₇	direct (N × H)
8. C₇×D₇₇	C₂×C₅	semidirect
9. C₇×C₁₁×D₇	C₂×C₅	semidirect
10. C₇²×D₁₁	C₂×C₅	semidirect
13. C₅×D₇₇	C₂×C₇	semidirect
14. C₅×C₁₁×D₇	C₂×C₇	semidirect
17. C₅×C₇×D₁₁	D₇	direct (N × H)
18. C₅×C₇×D₁₁	C₂×C₇	semidirect
19. C₇²×C₁₁	C₂²×C₅	semidirect
22. C₅×C₇×D₇	D₁₁	direct (N × H)
24. C₅×C₇×C₁₁	C₂×D₇	semidirect
25. C₅×C₇×C₁₁	C₂²×C₇	semidirect
27. D₇×D₁₁	C₅×C₇	direct (N × H)
28. C₅×C₇²	C₂×D₁₁	semidirect
32. D₇₇	C₂×C₅×C₇	semidirect
35. C₇×D₁₁	C₅×D₇	direct (N × H)
36. C₇×D₁₁	C₂×C₅×C₇	semidirect
37. C₁₁×D₇	C₂×C₅×C₇	semidirect
42. C₅×D₁₁	C₇×D₇	direct (N × H)
45. C₇×D₇	C₅×D₁₁	direct (N × H)
47. C₇×C₁₁	C₂×C₅×D₇	semidirect
48. C₇×C₁₁	C₂²×C₅×C₇	semidirect
55. C₅×D₇	C₇×D₁₁	direct (N × H)
56. C₅×C₁₁	C₂×C₇×D₇	semidirect
57. C₇²	C₂×C₅×D₁₁	semidirect
60. C₅×C₇	D₇×D₁₁	direct (N × H)
61. C₅×C₇	C₂×C₇×D₁₁	semidirect
66. D₁₁	C₅×C₇×D₇	direct (N × H)
74. D₇	C₅×C₇×D₁₁	direct (N × H)
75. C₁₁	C₂×C₅×C₇×D₇	semidirect
80. C₇	C₅×D₇×D₁₁	direct (N × H)
81. C₇	C₂×C₅×C₇×D₁₁	semidirect
82. C₅	C₇×D₇×D₁₁	direct (N × H)

Subgroups — C5×C7×D7×D11 #24924756

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₇×D₇×D₁₁ #24924756