Subgroups — C₂×C₁₃×D₁₆₅ #22575183

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₅₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×D₃₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₁×C₁₃	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₅₅	—	3	2	no	—
8	C₂×C₃×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented
9	C₁₃×D₃₃	—	5	2	no	—
10	C₂×C₁₃×D₁₅	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₆₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃×D₁₁	—	15	1	no	Hall
14	C₃×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₃	D₁₁	1	1	yes	characteristic, complemented
16	C₁₃×D₁₅	—	11	2	no	—
17	C₂×C₃×C₅×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
18	D₁₆₅	C₂×C₁₃	1	2	yes	direct product factor
19	C₂×C₁₁×C₁₃	D₁₅	1	1	yes	characteristic, complemented
20	C₁₃×D₁₁	—	15	2	no	—
21	C₂×D₅×C₁₃	—	33	1	no	Hall
22	C₂×D₅₅	—	3	1	no	Hall
23	C₃×C₅×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃×C₁₃	—	55	1	no	Hall
26	C₁₁×C₁₃	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
27	C₂×D₃₃	—	5	1	no	Hall
28	C₂×C₅×C₁₃	D₃₃	1	1	yes	characteristic, complemented
29	D₅×C₁₃	—	33	2	no	—
30	C₂×C₅×C₁₁	D₃×C₁₃	1	1	yes	characteristic, complemented
31	D₅₅	—	3	2	no	—
32	C₂×C₃×C₁₃	D₅₅	1	1	yes	characteristic, complemented
33	D₃×C₁₃	—	55	2	no	—
34	C₂×C₃×C₁₁	D₅×C₁₃	1	1	yes	characteristic, complemented
35	D₃₃	—	5	2	no	—
36	C₅×C₁₃	C₂×D₃₃	1	1	yes	characteristic, complemented, Hall
37	C₂×D₁₅	—	11	1	no	Hall
38	C₅×C₁₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₃	—	165	1	no	Hall
40	C₂×D₁₁	—	15	1	no	Hall
41	C₃×C₁₃	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₁	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	C₁₃×D₁₁	1	1	yes	characteristic, complemented
44	D₁₅	—	11	2	no	—
45	C₂×C₁₃	—	165	2	no	—
46	C₂×C₁₃	D₁₆₅	1	1	yes	characteristic, direct product factor
47	C₂×C₁₁	C₁₃×D₁₅	1	1	yes	characteristic, complemented
48	D₁₁	—	15	2	no	—
49	C₂×D₅	—	33	1	no	Hall
50	C₃×C₅	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
51	C₁₃	C₂×D₁₆₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×D₃	—	55	1	no	Hall
53	C₁₁	C₂×C₁₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	C₁₃×D₃₃	1	1	yes	characteristic, complemented
55	D₅	—	33	2	no	—
56	C₂×C₃	C₁₃×D₅₅	1	1	yes	characteristic, complemented
57	D₃	—	55	2	no	—
58	C₅	C₂×C₁₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	165	1	no	Sylow
60	C₃	C₂×C₁₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	165	2	no	—
62	C₂	C₁₃×D₁₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₁₆₅
commutator, hypocenter	C₃×C₅×C₁₁	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₆₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₁₃	C₂	semidirect
4. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
6. C₂×C₅×C₁₁×C₁₃	D₃	semidirect
8. C₂×C₃×C₁₁×C₁₃	D₅	semidirect
11. C₅×C₁₁×C₁₃	C₂×D₃	semidirect
12. C₂×D₁₆₅	C₁₃	direct (N × H)
14. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
15. C₂×C₃×C₅×C₁₃	D₁₁	semidirect
17. C₂×C₃×C₅×C₁₁	C₂×C₁₃	semidirect
18. D₁₆₅	C₂×C₁₃	direct (N × H)
19. C₂×C₁₁×C₁₃	D₁₅	semidirect
23. C₃×C₅×C₁₃	C₂×D₁₁	semidirect
24. C₃×C₅×C₁₁	C₂²×C₁₃	semidirect
26. C₁₁×C₁₃	C₂×D₁₅	semidirect
28. C₂×C₅×C₁₃	D₃₃	semidirect
30. C₂×C₅×C₁₁	D₃×C₁₃	semidirect
32. C₂×C₃×C₁₃	D₅₅	semidirect
34. C₂×C₃×C₁₁	D₅×C₁₃	semidirect
36. C₅×C₁₃	C₂×D₃₃	semidirect
38. C₅×C₁₁	C₂×D₃×C₁₃	semidirect
41. C₃×C₁₃	C₂×D₅₅	semidirect
42. C₃×C₁₁	C₂×D₅×C₁₃	semidirect
43. C₂×C₃×C₅	C₁₃×D₁₁	semidirect
46. C₂×C₁₃	D₁₆₅	direct (N × H)
47. C₂×C₁₁	C₁₃×D₁₅	semidirect
50. C₃×C₅	C₂×C₁₃×D₁₁	semidirect
51. C₁₃	C₂×D₁₆₅	direct (N × H)
53. C₁₁	C₂×C₁₃×D₁₅	semidirect
54. C₂×C₅	C₁₃×D₃₃	semidirect
56. C₂×C₃	C₁₃×D₅₅	semidirect
58. C₅	C₂×C₁₃×D₃₃	semidirect
60. C₃	C₂×C₁₃×D₅₅	semidirect
62. C₂	C₁₃×D₁₆₅	direct (N × H)

Subgroups — C2×C13×D165 #22575183

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×D₁₆₅ #22575183