Subgroups — C₂×C₅×D₇×C₁₁⋊C₅ #21440407

Order 7700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₇×C₁₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₅×C₇×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₁×D₇	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×D₇×C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
6	C₂²×C₅×C₁₁⋊C₅	—	7	1	no	maximal, Hall
7	C₂×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅×C₁₁×D₇	C₂×C₅	1	2	yes	complemented
9	C₂×C₇×C₁₁⋊C₅	C₂×C₅	1	5	yes	complemented
10	D₇×C₁₁⋊C₅	C₂×C₅	1	10	yes	direct product factor
11	C₂×C₅²×D₇	—	11	1	no	maximal, Hall
12	C₂×C₅×C₁₁⋊C₅	—	7	2	no	—
13	C₂×C₅×C₁₁⋊C₅	D₇	1	1	yes	characteristic, direct product factor
14	C₅×C₇×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
15	C₇×C₁₁⋊C₅	C₂²×C₅	1	5	yes	complemented
16	C₂×C₅²×C₇	—	11	1	no	—
17	C₅²×D₇	—	11	2	no	—
18	C₂×C₁₁×D₇	C₅²	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₁⋊C₅	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₅×C₁₁	—	7	1	no	—
21	C₂²×C₁₁⋊C₅	—	7	5	no	—
22	C₅²×C₇	—	11	1	no	Hall
23	C₂×C₇×C₁₁	C₂×C₅²	1	1	yes	characteristic, complemented
24	C₁₁×D₇	C₂×C₅²	1	2	yes	complemented
25	C₂×C₅×D₇	—	11	5	no	—
26	C₂×C₅×D₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
27	C₂×C₅×C₁₁	—	7	2	no	—
28	C₂×C₅×C₁₁	C₅×D₇	1	1	yes	characteristic, complemented
29	C₂×C₁₁⋊C₅	—	7	10	no	—
30	C₂×C₁₁⋊C₅	C₅×D₇	1	5	yes	direct product factor
31	C₂²×C₅²	—	77	1	no	Hall
32	C₇×C₁₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₇	—	11	5	no	—
34	C₂×C₅×C₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
35	C₅×D₇	—	11	10	no	—
36	C₅×D₇	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
37	C₅×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented
38	C₁₁⋊C₅	C₂×C₅×D₇	1	5	yes	direct product factor
39	C₂×C₅²	—	11	1	no	—
40	C₂×C₅²	—	77	2	no	—
41	C₂²×C₁₁	—	7	1	no	Hall
42	C₅×C₇	—	11	5	no	—
43	C₅×C₇	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented
44	C₂×D₇	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
45	C₅²	—	11	1	no	Sylow
46	C₂×C₁₁	—	7	2	no	—
47	C₂×C₁₁	C₅²×D₇	1	1	yes	characteristic, complemented
48	C₂²×C₅	—	7	1	no	—
49	C₂²×C₅	—	77	5	no	—
50	C₂×C₇	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented
51	D₇	C₂×C₅×C₁₁⋊C₅	1	2	yes	direct product factor
52	C₁₁	C₂×C₅²×D₇	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₅	—	7	2	no	—
54	C₂×C₅	—	11	5	no	—
55	C₂×C₅	—	77	10	no	—
56	C₂×C₅	D₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
57	C₇	C₂²×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
58	C₅	—	11	5	no	—
59	C₅	C₂×D₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
60	C₂²	—	7	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	C₅×D₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇×C₁₁⋊C₅
commutator, hypocenter	C₇×C₁₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₁	C₂×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇×C₁₁⋊C₅	C₂	semidirect
2. C₅×D₇×C₁₁⋊C₅	C₂	direct (N × H)
3. C₅×C₇×C₁₁⋊C₅	C₂²	semidirect
4. C₂×C₅×C₁₁×D₇	C₅	semidirect
5. C₂×D₇×C₁₁⋊C₅	C₅	direct (N × H)
7. C₂×C₅×C₇×C₁₁	C₂×C₅	semidirect
8. C₅×C₁₁×D₇	C₂×C₅	semidirect
9. C₂×C₇×C₁₁⋊C₅	C₂×C₅	semidirect
10. D₇×C₁₁⋊C₅	C₂×C₅	direct (N × H)
13. C₂×C₅×C₁₁⋊C₅	D₇	direct (N × H)
14. C₅×C₇×C₁₁	C₂²×C₅	semidirect
15. C₇×C₁₁⋊C₅	C₂²×C₅	semidirect
18. C₂×C₁₁×D₇	C₅²	semidirect
19. C₅×C₁₁⋊C₅	C₂×D₇	direct (N × H)
23. C₂×C₇×C₁₁	C₂×C₅²	semidirect
24. C₁₁×D₇	C₂×C₅²	semidirect
26. C₂×C₅×D₇	C₁₁⋊C₅	direct (N × H)
28. C₂×C₅×C₁₁	C₅×D₇	semidirect
30. C₂×C₁₁⋊C₅	C₅×D₇	direct (N × H)
32. C₇×C₁₁	C₂²×C₅²	semidirect
34. C₂×C₅×C₇	C₂×C₁₁⋊C₅	semidirect
36. C₅×D₇	C₂×C₁₁⋊C₅	direct (N × H)
37. C₅×C₁₁	C₂×C₅×D₇	semidirect
38. C₁₁⋊C₅	C₂×C₅×D₇	direct (N × H)
43. C₅×C₇	C₂²×C₁₁⋊C₅	semidirect
44. C₂×D₇	C₅×C₁₁⋊C₅	direct (N × H)
47. C₂×C₁₁	C₅²×D₇	semidirect
50. C₂×C₇	C₂×C₅×C₁₁⋊C₅	semidirect
51. D₇	C₂×C₅×C₁₁⋊C₅	direct (N × H)
52. C₁₁	C₂×C₅²×D₇	semidirect
56. C₂×C₅	D₇×C₁₁⋊C₅	direct (N × H)
57. C₇	C₂²×C₅×C₁₁⋊C₅	semidirect
59. C₅	C₂×D₇×C₁₁⋊C₅	direct (N × H)
62. C₂	C₅×D₇×C₁₁⋊C₅	direct (N × H)

Subgroups — C2×C5×D7×C11⋊C5 #21440407

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₇×C₁₁⋊C₅ #21440407