Subgroups — C₅×C₁₁×D₁₆₅ #31827708

Order 18150.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₅₅	—	3	1	no	maximal, Hall
3	C₁₁×D₁₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₁₁×D₃₃	—	5	1	no	maximal
5	C₅²×C₁₁²	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	—	2	2	no	—
7	C₃×C₅×C₁₁²	D₅	1	1	yes	characteristic, complemented
8	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₁₆₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
10	C₅×C₁₁×D₁₅	—	11	1	no	maximal
11	C₁₁×D₅₅	—	3	1	no	—
12	C₅×C₁₁×D₁₁	—	15	1	no	—
13	C₃×C₅²×C₁₁	—	2	5	no	—
14	C₃×C₅²×C₁₁	D₁₁	1	1	yes	characteristic, complemented
15	C₃×C₅²×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₁₁×D₃₃	—	5	1	no	Hall
17	C₅×C₁₁²	—	2	2	no	—
18	C₅×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
19	C₅×C₁₁²	D₁₅	1	1	yes	characteristic, complemented
20	C₅×D₅₅	—	3	1	no	—
21	C₅×D₅×C₁₁	—	33	1	no	—
22	C₃×C₁₁²	C₅×D₅	1	1	yes	characteristic, complemented, Hall
23	D₁₆₅	C₅×C₁₁	1	1	yes	characteristic, direct product factor
24	C₁₁×D₁₅	—	11	1	no	—
25	C₅×D₃₃	—	5	1	no	—
26	C₅×D₃×C₁₁	—	55	1	no	—
27	C₅²×C₁₁	—	2	5	no	—
28	C₅²×C₁₁	D₃×C₁₁	1	1	yes	characteristic, complemented
29	C₅²×C₁₁	D₃₃	1	1	yes	characteristic, complemented
30	C₁₁×D₁₁	—	15	1	no	Hall
31	C₃×C₅×C₁₁	—	2	20	no	—
32	C₃×C₅×C₁₁	—	2	2	no	—
33	C₃×C₅×C₁₁	—	2	2	no	—
34	C₃×C₅×C₁₁	—	2	5	no	—
35	C₃×C₅×C₁₁	—	2	5	no	—
36	C₃×C₅×C₁₁	D₅×C₁₁	1	1	yes	characteristic, complemented
37	C₃×C₅×C₁₁	C₅×D₁₁	1	1	yes	characteristic, complemented
38	C₃×C₅×C₁₁	D₅₅	1	1	yes	characteristic, complemented
39	C₃×C₅×C₁₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
40	C₅×D₁₅	—	11	1	no	Hall
41	C₁₁²	C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅×C₁₁	—	165	1	no	—
43	D₅₅	—	3	1	no	—
44	C₅×D₁₁	—	15	1	no	—
45	D₅×C₁₁	—	33	1	no	—
46	C₃×C₅²	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
47	D₃₃	—	5	1	no	—
48	D₃×C₁₁	—	55	1	no	—
49	C₅×C₁₁	—	2	20	no	—
50	C₅×C₁₁	—	2	2	no	—
51	C₅×C₁₁	—	2	2	no	—
52	C₅×C₁₁	—	2	5	no	—
53	C₅×C₁₁	—	2	5	no	—
54	C₅×C₁₁	C₅×D₃×C₁₁	1	1	yes	characteristic, complemented
55	C₅×C₁₁	C₅×D₃₃	1	1	yes	characteristic, complemented
56	C₅×C₁₁	C₁₁×D₁₅	1	1	yes	characteristic, complemented
57	C₅×C₁₁	D₁₆₅	1	1	yes	characteristic, direct product factor
58	C₅×D₅	—	33	1	no	Hall
59	C₃×C₁₁	—	2	5	no	—
60	C₃×C₁₁	C₅×D₅×C₁₁	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₅×D₅₅	1	1	yes	characteristic, complemented
62	D₁₅	—	11	1	no	—
63	C₅×D₃	—	55	1	no	—
64	C₅²	C₁₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₁₁	—	165	1	no	—
66	D₁₁	—	15	1	no	—
67	C₃×C₅	—	2	2	no	—
68	C₃×C₅	C₅×C₁₁×D₁₁	1	1	yes	characteristic, complemented
69	C₃×C₅	C₁₁×D₅₅	1	1	yes	characteristic, complemented
70	C₁₁	—	2	5	no	—
71	C₁₁	C₅×C₁₁×D₁₅	1	1	yes	characteristic, complemented
72	C₁₁	C₅×D₁₆₅	1	1	yes	characteristic, direct product factor
73	C₂×C₅	—	165	1	no	—
74	D₅	—	33	1	no	—
75	D₃	—	55	1	no	Hall
76	C₅	—	2	2	no	—
77	C₅	C₅×C₁₁×D₃₃	1	1	yes	characteristic, complemented
78	C₅	C₁₁×D₁₆₅	1	1	yes	characteristic, direct product factor
79	C₃	C₅×C₁₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₁₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₂
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁²	C₂	semidirect
3. C₁₁×D₁₆₅	C₅	direct (N × H)
5. C₅²×C₁₁²	D₃	semidirect
7. C₃×C₅×C₁₁²	D₅	semidirect
8. C₃×C₅×C₁₁²	C₂×C₅	semidirect
9. C₅×D₁₆₅	C₁₁	direct (N × H)
14. C₃×C₅²×C₁₁	D₁₁	semidirect
15. C₃×C₅²×C₁₁	C₂×C₁₁	semidirect
18. C₅×C₁₁²	C₅×D₃	semidirect
19. C₅×C₁₁²	D₁₅	semidirect
22. C₃×C₁₁²	C₅×D₅	semidirect
23. D₁₆₅	C₅×C₁₁	direct (N × H)
28. C₅²×C₁₁	D₃×C₁₁	semidirect
29. C₅²×C₁₁	D₃₃	semidirect
36. C₃×C₅×C₁₁	D₅×C₁₁	semidirect
37. C₃×C₅×C₁₁	C₅×D₁₁	semidirect
38. C₃×C₅×C₁₁	D₅₅	semidirect
39. C₃×C₅×C₁₁	C₂×C₅×C₁₁	semidirect
41. C₁₁²	C₅×D₁₅	semidirect
46. C₃×C₅²	C₁₁×D₁₁	semidirect
54. C₅×C₁₁	C₅×D₃×C₁₁	semidirect
55. C₅×C₁₁	C₅×D₃₃	semidirect
56. C₅×C₁₁	C₁₁×D₁₅	semidirect
57. C₅×C₁₁	D₁₆₅	direct (N × H)
60. C₃×C₁₁	C₅×D₅×C₁₁	semidirect
61. C₃×C₁₁	C₅×D₅₅	semidirect
64. C₅²	C₁₁×D₃₃	semidirect
68. C₃×C₅	C₅×C₁₁×D₁₁	semidirect
69. C₃×C₅	C₁₁×D₅₅	semidirect
71. C₁₁	C₅×C₁₁×D₁₅	semidirect
72. C₁₁	C₅×D₁₆₅	direct (N × H)
77. C₅	C₅×C₁₁×D₃₃	semidirect
78. C₅	C₁₁×D₁₆₅	direct (N × H)
79. C₃	C₅×C₁₁×D₅₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅²×C₁₁²	2
C₅×C₁₁×D₅₅	3
C₁₁×D₁₆₅	5
C₅×C₁₁×D₃₃	5
C₅×D₁₆₅	11
C₅×C₁₁×D₁₅	11

Subgroups — C5×C11×D165 #31827708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₁₆₅ #31827708