Subgroups — C₇×D₇×D₅₅ #24924774

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×D₅₅	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	C₇×D₇×D₁₁	—	5	1	no	maximal, Hall
6	C₂×C₇×D₅₅	—	7	1	no	maximal
7	D₇×D₅₅	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₇×D₇₇	—	5	1	no	—
9	C₇×C₁₁×D₇	D₅	1	1	yes	characteristic, complemented
10	C₇²×D₁₁	—	5	1	no	—
11	C₇×D₅×D₇	—	11	1	no	maximal, Hall
12	C₂×C₅×C₇×C₁₁	—	7	1	no	—
13	D₃₈₅	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇×D₅₅	—	2	3	no	—
15	C₇×D₅₅	—	7	1	no	—
16	C₇×D₅₅	D₇	1	1	yes	characteristic, direct product factor
17	C₇×D₅₅	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	—	11	1	no	—
21	C₇²×D₅	—	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	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	C₂×D₅₅	—	7	1	no	Hall
30	C₂×C₇×D₇	—	55	1	no	Hall
31	C₂×C₇×C₁₁	—	7	1	no	—
32	D₇₇	—	5	1	no	—
33	C₇×D₁₁	—	5	1	no	—
34	C₇×D₁₁	—	5	1	no	—
35	C₇×D₁₁	—	10	3	no	—
36	C₇×D₁₁	—	35	1	no	—
37	C₁₁×D₇	C₇×D₅	1	1	yes	characteristic, complemented
38	C₂×C₇×D₅	—	77	1	no	—
39	D₅×D₇	—	11	1	no	—
40	C₂×C₅×C₁₁	—	7	1	no	—
41	D₅₅	—	7	1	no	—
42	D₅₅	C₇×D₇	1	1	yes	characteristic, direct product factor
43	C₂×C₇²	—	55	1	no	—
44	C₇×D₇	—	55	1	no	—
45	C₇×D₇	D₅₅	1	1	yes	characteristic, direct product factor
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	—	7	1	no	—
50	D₃₅	—	11	1	no	—
51	C₅×D₇	C₇×D₁₁	1	1	yes	characteristic, complemented
52	C₇×D₅	—	11	1	no	—
53	C₇×D₅	—	11	1	no	—
54	C₇×D₅	—	22	3	no	—
55	C₇×D₅	—	77	1	no	—
56	C₅×C₁₁	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
57	C₇²	C₂×D₅₅	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	—	7	1	no	—
65	D₁₁	—	5	1	no	—
66	D₁₁	—	35	1	no	—
67	C₂×D₅	—	77	1	no	Hall
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	55	1	no	—
70	C₂×C₇	—	55	1	no	—
71	C₂×C₇	—	110	3	no	—
72	C₂×C₇	—	385	1	no	—
73	D₇	—	55	1	no	—
74	D₇	C₇×D₅₅	1	1	yes	characteristic, direct product factor
75	C₁₁	C₇×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₅	—	7	1	no	—
77	D₅	—	11	1	no	—
78	D₅	—	77	1	no	—
79	C₇	—	2	3	no	—
80	C₇	D₇×D₅₅	1	1	yes	characteristic, direct product factor
81	C₇	C₂×C₇×D₅₅	1	1	yes	characteristic, complemented
82	C₅	C₇×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	385	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	55	1	no	—
86	C₂	—	385	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₇×D₅₅
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×D₅₅	C₂	semidirect
3. C₅×C₇×C₁₁×D₇	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
7. D₇×D₅₅	C₇	direct (N × H)
9. C₇×C₁₁×D₇	D₅	semidirect
13. D₃₈₅	C₂×C₇	semidirect
16. C₇×D₅₅	D₇	direct (N × H)
17. C₇×D₅₅	C₂×C₇	semidirect
18. C₅×C₁₁×D₇	C₂×C₇	semidirect
19. C₇²×C₁₁	C₂×D₅	semidirect
22. C₅×C₇×D₇	D₁₁	semidirect
24. C₅×C₇×C₁₁	C₂×D₇	semidirect
25. C₅×C₇×C₁₁	C₂²×C₇	semidirect
28. C₅×C₇²	C₂×D₁₁	semidirect
37. C₁₁×D₇	C₇×D₅	semidirect
42. D₅₅	C₇×D₇	direct (N × H)
45. C₇×D₇	D₅₅	direct (N × H)
47. C₇×C₁₁	D₅×D₇	semidirect
48. C₇×C₁₁	C₂×C₇×D₅	semidirect
51. C₅×D₇	C₇×D₁₁	semidirect
56. C₅×C₁₁	C₂×C₇×D₇	semidirect
57. C₇²	C₂×D₅₅	semidirect
60. C₅×C₇	D₇×D₁₁	semidirect
61. C₅×C₇	C₂×C₇×D₁₁	semidirect
74. D₇	C₇×D₅₅	direct (N × H)
75. C₁₁	C₇×D₅×D₇	semidirect
80. C₇	D₇×D₅₅	direct (N × H)
81. C₇	C₂×C₇×D₅₅	semidirect
82. C₅	C₇×D₇×D₁₁	semidirect

Subgroups — C7×D7×D55 #24924774

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₇×D₅₅ #24924774