Subgroups — C₇²×D₅×D₁₁ #24924771

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₅×C₁₁	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	C₂×C₇²×D₁₁	—	5	1	no	maximal, Hall
6	C₇×D₅×D₁₁	C₇	1	8	yes	maximal, direct product factor
7	C₂×C₇²×C₁₁	—	5	1	no	—
8	C₇²×D₁₁	—	5	1	no	—
9	C₇²×D₁₁	D₅	1	1	yes	characteristic, direct product factor
10	C₂×C₇²×D₅	—	11	1	no	maximal, Hall
11	C₇×D₅₅	C₂×C₇	1	8	yes	complemented
12	C₇×D₅×C₁₁	C₂×C₇	1	8	yes	complemented
13	C₅×C₇×D₁₁	C₂×C₇	1	8	yes	complemented
14	C₇²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₇²	—	11	1	no	—
16	C₇²×D₅	—	11	1	no	—
17	C₇²×D₅	D₁₁	1	1	yes	characteristic, direct product factor
18	C₅×C₇×C₁₁	C₂²×C₇	1	8	yes	complemented
19	C₂×C₇×D₁₁	—	5	8	no	—
20	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	D₅×D₁₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₇²	—	55	1	no	Hall
23	C₂×C₇×C₁₁	—	5	8	no	—
24	C₇×D₁₁	—	5	8	no	—
25	C₇×D₁₁	C₇×D₅	1	8	yes	direct product factor
26	C₂×C₇×D₅	—	11	8	no	—
27	D₅₅	C₂×C₇²	1	1	yes	characteristic, complemented
28	C₅×D₁₁	C₂×C₇²	1	1	yes	characteristic, complemented
29	D₅×C₁₁	C₂×C₇²	1	1	yes	characteristic, complemented
30	C₂×C₇²	—	5	1	no	—
31	C₂×C₇²	—	11	1	no	—
32	C₂×C₇²	—	55	1	no	—
33	C₇×C₁₁	C₂×C₇×D₅	1	8	yes	complemented
34	C₂×C₅×C₇	—	11	8	no	—
35	C₇×D₅	—	11	8	no	—
36	C₇×D₅	C₇×D₁₁	1	8	yes	direct product factor
37	C₅×C₁₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
38	C₇²	D₅×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₁₁	—	5	1	no	Hall
40	C₅×C₇	C₂×C₇×D₁₁	1	8	yes	complemented
41	C₂²×C₇	—	55	8	no	—
42	C₂×C₁₁	—	5	1	no	—
43	D₁₁	—	5	1	no	—
44	D₁₁	C₇²×D₅	1	1	yes	characteristic, direct product factor
45	C₂×D₅	—	11	1	no	Hall
46	C₂×C₇	—	5	8	no	—
47	C₂×C₇	—	11	8	no	—
48	C₂×C₇	—	55	8	no	—
49	C₁₁	C₂×C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	11	1	no	—
51	D₅	—	11	1	no	—
52	D₅	C₇²×D₁₁	1	1	yes	characteristic, direct product factor
53	C₇	C₇×D₅×D₁₁	1	8	yes	direct product factor
54	C₅	C₂×C₇²×D₁₁	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	55	1	no	Sylow
56	C₂	—	5	1	no	—
57	C₂	—	11	1	no	—
58	C₂	—	55	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×D₅₅	C₂	semidirect
2. C₇²×D₅×C₁₁	C₂	semidirect
3. C₅×C₇²×D₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
6. C₇×D₅×D₁₁	C₇	direct (N × H)
9. C₇²×D₁₁	D₅	direct (N × H)
11. C₇×D₅₅	C₂×C₇	semidirect
12. C₇×D₅×C₁₁	C₂×C₇	semidirect
13. C₅×C₇×D₁₁	C₂×C₇	semidirect
14. C₇²×C₁₁	C₂×D₅	semidirect
17. C₇²×D₅	D₁₁	direct (N × H)
18. C₅×C₇×C₁₁	C₂²×C₇	semidirect
20. C₅×C₇²	C₂×D₁₁	semidirect
21. D₅×D₁₁	C₇²	direct (N × H)
25. C₇×D₁₁	C₇×D₅	direct (N × H)
27. D₅₅	C₂×C₇²	semidirect
28. C₅×D₁₁	C₂×C₇²	semidirect
29. D₅×C₁₁	C₂×C₇²	semidirect
33. C₇×C₁₁	C₂×C₇×D₅	semidirect
36. C₇×D₅	C₇×D₁₁	direct (N × H)
37. C₅×C₁₁	C₂²×C₇²	semidirect
38. C₇²	D₅×D₁₁	direct (N × H)
40. C₅×C₇	C₂×C₇×D₁₁	semidirect
44. D₁₁	C₇²×D₅	direct (N × H)
49. C₁₁	C₂×C₇²×D₅	semidirect
52. D₅	C₇²×D₁₁	direct (N × H)
53. C₇	C₇×D₅×D₁₁	direct (N × H)
54. C₅	C₂×C₇²×D₁₁	semidirect

Subgroups — C72×D5×D11 #24924771

Conjugacy classes of subgroups

Complements

Subgroups — C₇²×D₅×D₁₁ #24924771