Subgroups — C₅×D₁₁×C₇⋊D₇ #24924757

Order 10780.

200 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×C₁₁×C₇⋊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	D₁₁×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₇×D₁₁	—	7	8	no	maximal
7	C₇⋊D₇₇	C₂×C₅	1	1	yes	characteristic, complemented
8	C₁₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₇²×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×C₅×C₇⋊D₇	—	11	1	no	maximal, Hall
11	C₅×D₇₇	—	7	8	no	—
12	C₅×C₁₁×D₇	—	7	8	no	—
13	C₅×C₇×D₁₁	D₇	1	8	yes	complemented
14	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₇²	—	11	1	no	—
16	C₅×C₇⋊D₇	—	11	1	no	—
17	C₅×C₇⋊D₇	D₁₁	1	1	yes	characteristic, direct product factor
18	C₅×C₇×C₁₁	C₂×D₇	1	8	yes	complemented
19	D₇×D₁₁	—	7	8	no	—
20	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×D₁₁	—	49	1	no	Hall
22	C₂×C₇⋊D₇	—	11	1	no	Hall
23	D₇₇	—	7	8	no	—
24	C₇×D₁₁	C₅×D₇	1	8	yes	complemented
25	C₁₁×D₇	—	7	8	no	—
26	C₂×C₅×D₇	—	77	8	no	—
27	C₂×C₅×C₁₁	—	49	1	no	—
28	C₅×D₁₁	—	49	1	no	—
29	C₅×D₁₁	C₇⋊D₇	1	1	yes	characteristic, direct product factor
30	C₂×C₇²	—	11	1	no	—
31	C₇⋊D₇	—	11	1	no	—
32	C₇⋊D₇	C₅×D₁₁	1	1	yes	characteristic, direct product factor
33	C₇×C₁₁	C₂×C₅×D₇	1	8	yes	complemented
34	C₂×C₅×C₇	—	11	8	no	—
35	C₅×D₇	—	7	8	no	—
36	C₅×D₇	—	77	8	no	—
37	C₅×C₁₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
38	C₇²	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₁	—	49	1	no	Hall
40	C₅×C₇	D₇×D₁₁	1	8	yes	complemented
41	C₂×D₇	—	77	8	no	—
42	C₂×C₁₁	—	49	1	no	—
43	D₁₁	—	49	1	no	—
44	D₁₁	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor
45	C₂²×C₅	—	539	1	no	Hall
46	C₂×C₇	—	11	8	no	—
47	D₇	—	7	8	no	—
48	D₇	—	77	8	no	—
49	C₁₁	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	11	1	no	—
51	C₂×C₅	—	539	1	no	—
52	C₂×C₅	—	49	1	no	—
53	C₇	C₅×D₇×D₁₁	1	8	yes	complemented
54	C₅	D₁₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²	—	539	1	no	Sylow
56	C₂	—	11	1	no	—
57	C₂	—	539	1	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₁×C₇⋊D₇
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×C₁₁×C₇⋊D₇	C₂	semidirect
3. C₅×C₇²×D₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
5. D₁₁×C₇⋊D₇	C₅	direct (N × H)
7. C₇⋊D₇₇	C₂×C₅	semidirect
8. C₁₁×C₇⋊D₇	C₂×C₅	semidirect
9. C₇²×D₁₁	C₂×C₅	semidirect
13. C₅×C₇×D₁₁	D₇	semidirect
14. C₇²×C₁₁	C₂²×C₅	semidirect
17. C₅×C₇⋊D₇	D₁₁	direct (N × H)
18. C₅×C₇×C₁₁	C₂×D₇	semidirect
20. C₅×C₇²	C₂×D₁₁	semidirect
24. C₇×D₁₁	C₅×D₇	semidirect
29. C₅×D₁₁	C₇⋊D₇	direct (N × H)
32. C₇⋊D₇	C₅×D₁₁	direct (N × H)
33. C₇×C₁₁	C₂×C₅×D₇	semidirect
37. C₅×C₁₁	C₂×C₇⋊D₇	semidirect
38. C₇²	C₂×C₅×D₁₁	semidirect
40. C₅×C₇	D₇×D₁₁	semidirect
44. D₁₁	C₅×C₇⋊D₇	direct (N × H)
49. C₁₁	C₂×C₅×C₇⋊D₇	semidirect
53. C₇	C₅×D₇×D₁₁	semidirect
54. C₅	D₁₁×C₇⋊D₇	direct (N × H)

Subgroups — C5×D11×C7⋊D7 #24924757

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₁₁×C₇⋊D₇ #24924757