Subgroups — C₅×C₁₁×D₇² #24924758

Order 10780.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×C₁₁×D₇	C₂	1	2	yes	maximal, complemented
3	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₇²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×D₇	—	7	2	no	maximal
6	C₁₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×C₁₁×D₇	C₂×C₅	1	2	yes	complemented
8	C₅×D₇²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇×C₁₁	—	7	2	no	—
10	C₅×C₁₁×D₇	—	7	2	no	—
11	C₅×C₁₁×D₇	—	14	3	no	—
12	C₅×C₁₁×D₇	D₇	1	2	yes	direct product factor
13	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇⋊D₇	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₅×C₇×D₇	C₂×C₁₁	1	2	yes	complemented
16	C₅×C₇×C₁₁	—	2	3	no	—
17	C₅×C₇×C₁₁	C₂×D₇	1	2	yes	complemented
18	C₂×C₁₁×D₇	—	7	2	no	—
19	C₅×C₇²	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₅×C₁₁	—	49	1	no	Hall
21	D₇²	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₇×C₁₁	—	7	2	no	—
23	C₁₁×D₇	—	7	2	no	—
24	C₁₁×D₇	—	14	3	no	—
25	C₁₁×D₇	C₅×D₇	1	2	yes	direct product factor
26	C₂×C₅×D₇	—	7	2	no	—
27	C₂×C₅×C₁₁	—	7	2	no	—
28	C₂×C₅×C₁₁	—	49	1	no	—
29	C₇⋊D₇	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
30	C₇×D₇	C₂×C₅×C₁₁	1	2	yes	complemented
31	C₇×C₁₁	—	2	3	no	—
32	C₇×C₁₁	C₂×C₅×D₇	1	2	yes	complemented
33	C₂×C₅×C₇	—	7	2	no	—
34	C₅×D₇	—	7	2	no	—
35	C₅×D₇	—	14	3	no	—
36	C₅×D₇	C₁₁×D₇	1	2	yes	direct product factor
37	C₅×C₁₁	D₇²	1	1	yes	characteristic, direct product factor, Hall
38	C₇²	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₁₁	—	49	1	no	Hall
40	C₅×C₇	—	2	3	no	—
41	C₅×C₇	C₂×C₁₁×D₇	1	2	yes	complemented
42	C₂×D₇	—	7	2	no	—
43	C₂×C₁₁	—	7	2	no	—
44	C₂×C₁₁	—	49	1	no	—
45	C₂²×C₅	—	49	1	no	Hall
46	C₂×C₇	—	7	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	D₇	C₅×C₁₁×D₇	1	2	yes	direct product factor
50	C₁₁	C₅×D₇²	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₅	—	7	2	no	—
52	C₂×C₅	—	49	1	no	—
53	C₇	—	2	3	no	—
54	C₇	C₂×C₅×C₁₁×D₇	1	2	yes	complemented
55	C₅	C₁₁×D₇²	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	—	49	1	no	Sylow
57	C₂	—	7	2	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₇²
commutator, cosocle, hypocenter	C₇²	C₂²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₇⋊D₇	C₂	semidirect
2. C₅×C₇×C₁₁×D₇	C₂	semidirect
3. C₅×C₇²×C₁₁	C₂²	semidirect
4. C₁₁×D₇²	C₅	direct (N × H)
6. C₁₁×C₇⋊D₇	C₂×C₅	semidirect
7. C₇×C₁₁×D₇	C₂×C₅	semidirect
8. C₅×D₇²	C₁₁	direct (N × H)
12. C₅×C₁₁×D₇	D₇	direct (N × H)
13. C₇²×C₁₁	C₂²×C₅	semidirect
14. C₅×C₇⋊D₇	C₂×C₁₁	semidirect
15. C₅×C₇×D₇	C₂×C₁₁	semidirect
17. C₅×C₇×C₁₁	C₂×D₇	semidirect
19. C₅×C₇²	C₂²×C₁₁	semidirect
21. D₇²	C₅×C₁₁	direct (N × H)
25. C₁₁×D₇	C₅×D₇	direct (N × H)
29. C₇⋊D₇	C₂×C₅×C₁₁	semidirect
30. C₇×D₇	C₂×C₅×C₁₁	semidirect
32. C₇×C₁₁	C₂×C₅×D₇	semidirect
36. C₅×D₇	C₁₁×D₇	direct (N × H)
37. C₅×C₁₁	D₇²	direct (N × H)
38. C₇²	C₂²×C₅×C₁₁	semidirect
41. C₅×C₇	C₂×C₁₁×D₇	semidirect
49. D₇	C₅×C₁₁×D₇	direct (N × H)
50. C₁₁	C₅×D₇²	direct (N × H)
54. C₇	C₂×C₅×C₁₁×D₇	semidirect
55. C₅	C₁₁×D₇²	direct (N × H)

Subgroups — C5×C11×D72 #24924758

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₁₁×D₇² #24924758