Subgroups — C₇×D₅×C₁₁×D₇ #24924773

Order 10780.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₇×C₁₁	D₅×D₇
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×D₃₅	C₂	semidirect
2. C₇²×D₅×C₁₁	C₂	semidirect
3. C₅×C₇×C₁₁×D₇	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
7. D₅×C₁₁×D₇	C₇	direct (N × H)
10. C₇×C₁₁×D₇	D₅	direct (N × H)
11. C₇×D₅×D₇	C₁₁	direct (N × H)
13. C₁₁×D₃₅	C₂×C₇	semidirect
16. C₇×D₅×C₁₁	D₇	direct (N × H)
17. C₇×D₅×C₁₁	C₂×C₇	semidirect
18. C₅×C₁₁×D₇	C₂×C₇	semidirect
19. C₇²×C₁₁	C₂×D₅	semidirect
20. C₇×D₃₅	C₂×C₁₁	semidirect
21. C₇²×D₅	C₂×C₁₁	semidirect
22. C₅×C₇×D₇	C₂×C₁₁	semidirect
24. C₅×C₇×C₁₁	C₂×D₇	semidirect
25. C₅×C₇×C₁₁	C₂²×C₇	semidirect
28. C₅×C₇²	C₂²×C₁₁	semidirect
37. C₁₁×D₇	C₇×D₅	direct (N × H)
39. D₅×D₇	C₇×C₁₁	direct (N × H)
42. D₅×C₁₁	C₇×D₇	direct (N × H)
45. C₇×D₇	D₅×C₁₁	direct (N × H)
47. C₇×C₁₁	D₅×D₇	direct (N × H)
48. C₇×C₁₁	C₂×C₇×D₅	semidirect
50. D₃₅	C₂×C₇×C₁₁	semidirect
51. C₅×D₇	C₂×C₇×C₁₁	semidirect
54. C₇×D₅	C₁₁×D₇	direct (N × H)
55. C₇×D₅	C₂×C₇×C₁₁	semidirect
56. C₅×C₁₁	C₂×C₇×D₇	semidirect
57. C₇²	C₂×D₅×C₁₁	semidirect
60. C₅×C₇	C₂×C₁₁×D₇	semidirect
61. C₅×C₇	C₂²×C₇×C₁₁	semidirect
74. D₇	C₇×D₅×C₁₁	direct (N × H)
75. C₁₁	C₇×D₅×D₇	direct (N × H)
78. D₅	C₇×C₁₁×D₇	direct (N × H)
80. C₇	D₅×C₁₁×D₇	direct (N × H)
81. C₇	C₂×C₇×D₅×C₁₁	semidirect
82. C₅	C₂×C₇×C₁₁×D₇	semidirect

Subgroups — C7×D5×C11×D7 #24924773

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₅×C₁₁×D₇ #24924773