Subgroups — C₂×C₃×C₁₁×D₆₅ #22575192

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×D₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×D₁₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×D₆₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented
9	C₃×C₁₁×D₁₃	—	5	2	no	—
10	C₂×C₃×D₆₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×D₅×C₁₁	—	13	1	no	maximal, Hall
13	C₂×C₁₁×D₁₃	—	5	1	no	Hall
14	C₃×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×D₆₅	C₂×C₁₁	1	2	yes	direct product factor
17	C₂×C₃×C₅×C₁₁	D₁₃	1	1	yes	characteristic, complemented
18	C₃×D₅×C₁₁	—	13	2	no	—
19	C₂×C₁₁×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
20	C₁₁×D₁₃	—	5	2	no	—
21	C₂×D₆₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×D₅×C₁₁	—	13	1	no	Hall
23	C₃×C₅×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₃	—	5	1	no	Hall
26	C₁₁×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₁₁	—	65	1	no	Hall
28	C₂×C₅×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
29	D₆₅	C₂×C₃×C₁₁	1	2	yes	direct product factor
30	C₂×C₅×C₁₁	C₃×D₁₃	1	1	yes	characteristic, complemented
31	D₅×C₁₁	—	13	2	no	—
32	C₂×C₃×C₁₃	D₅×C₁₁	1	1	yes	characteristic, complemented
33	C₃×D₁₃	—	5	2	no	—
34	C₂×C₃×C₁₁	—	65	2	no	—
35	C₂×C₃×C₁₁	D₆₅	1	1	yes	characteristic, direct product factor
36	C₅×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×D₅	—	13	1	no	Hall
38	C₅×C₁₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂×D₁₃	—	5	1	no	Hall
40	C₂²×C₁₁	—	65	1	no	Hall
41	C₃×C₁₃	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₁	C₂×D₆₅	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₅	C₁₁×D₁₃	1	1	yes	characteristic, complemented
44	C₃×D₅	—	13	2	no	—
45	C₂×C₁₃	C₃×D₅×C₁₁	1	1	yes	characteristic, complemented
46	D₁₃	—	5	2	no	—
47	C₂×C₁₁	—	65	2	no	—
48	C₂×C₁₁	C₃×D₆₅	1	1	yes	characteristic, direct product factor
49	C₂×D₅	—	13	1	no	Hall
50	C₃×C₅	C₂×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₁₃	C₂×C₃×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	65	1	no	Hall
53	C₁₁	C₂×C₃×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	C₃×C₁₁×D₁₃	1	1	yes	characteristic, complemented
55	D₅	—	13	2	no	—
56	C₂×C₃	—	65	2	no	—
57	C₂×C₃	C₁₁×D₆₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	65	1	no	Sylow
60	C₃	C₂×C₁₁×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	65	2	no	—
62	C₂	C₃×C₁₁×D₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁	D₆₅
commutator, hypocenter	C₅×C₁₃	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×D₆₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₁₃	C₂	semidirect
3. C₂×C₁₁×D₆₅	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
6. C₂×C₅×C₁₁×C₁₃	C₂×C₃	semidirect
7. C₁₁×D₆₅	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₁×C₁₃	D₅	semidirect
10. C₂×C₃×D₆₅	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
14. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
15. C₂×C₃×C₅×C₁₃	C₂×C₁₁	semidirect
16. C₃×D₆₅	C₂×C₁₁	direct (N × H)
17. C₂×C₃×C₅×C₁₁	D₁₃	semidirect
19. C₂×C₁₁×C₁₃	C₃×D₅	semidirect
21. C₂×D₆₅	C₃×C₁₁	direct (N × H)
23. C₃×C₅×C₁₃	C₂²×C₁₁	semidirect
24. C₃×C₅×C₁₁	C₂×D₁₃	semidirect
26. C₁₁×C₁₃	C₂×C₃×D₅	semidirect
28. C₂×C₅×C₁₃	C₂×C₃×C₁₁	semidirect
29. D₆₅	C₂×C₃×C₁₁	direct (N × H)
30. C₂×C₅×C₁₁	C₃×D₁₃	semidirect
32. C₂×C₃×C₁₃	D₅×C₁₁	semidirect
35. C₂×C₃×C₁₁	D₆₅	direct (N × H)
36. C₅×C₁₃	C₂²×C₃×C₁₁	semidirect
38. C₅×C₁₁	C₂×C₃×D₁₃	semidirect
41. C₃×C₁₃	C₂×D₅×C₁₁	semidirect
42. C₃×C₁₁	C₂×D₆₅	direct (N × H)
43. C₂×C₃×C₅	C₁₁×D₁₃	semidirect
45. C₂×C₁₃	C₃×D₅×C₁₁	semidirect
48. C₂×C₁₁	C₃×D₆₅	direct (N × H)
50. C₃×C₅	C₂×C₁₁×D₁₃	semidirect
51. C₁₃	C₂×C₃×D₅×C₁₁	semidirect
53. C₁₁	C₂×C₃×D₆₅	direct (N × H)
54. C₂×C₅	C₃×C₁₁×D₁₃	semidirect
57. C₂×C₃	C₁₁×D₆₅	direct (N × H)
58. C₅	C₂×C₃×C₁₁×D₁₃	semidirect
60. C₃	C₂×C₁₁×D₆₅	direct (N × H)
62. C₂	C₃×C₁₁×D₆₅	direct (N × H)

Subgroups — C2×C3×C11×D65 #22575192

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₁×D₆₅ #22575192