Subgroups — C₁₃×D₁₁×D₁₅ #22575159

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₃	D₁₁×D₁₅
commutator, hypocenter	C₃×C₅×C₁₁	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₆₅	C₂	semidirect
2. C₁₁×C₁₃×D₁₅	C₂	semidirect
3. C₃×C₅×C₁₃×D₁₁	C₂	semidirect
5. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
9. C₅×C₁₃×D₁₁	D₃	semidirect
12. C₃×C₁₃×D₁₁	D₅	semidirect
14. C₅×C₁₁×C₁₃	C₂×D₃	semidirect
15. D₁₁×D₁₅	C₁₃	direct (N × H)
17. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
20. C₁₃×D₁₅	D₁₁	direct (N × H)
21. D₁₆₅	C₂×C₁₃	semidirect
22. C₁₁×D₁₅	C₂×C₁₃	semidirect
23. C₃×C₅×D₁₁	C₂×C₁₃	semidirect
26. C₁₃×D₁₁	D₁₅	direct (N × H)
29. C₃×C₅×C₁₃	C₂×D₁₁	semidirect
30. C₃×C₅×C₁₁	C₂²×C₁₃	semidirect
32. C₁₁×C₁₃	C₂×D₁₅	semidirect
38. C₅×D₁₁	D₃×C₁₃	semidirect
44. C₃×D₁₁	D₅×C₁₃	semidirect
46. C₅×C₁₃	D₃×D₁₁	semidirect
48. C₅×C₁₁	C₂×D₃×C₁₃	semidirect
51. C₃×C₁₃	D₅×D₁₁	semidirect
52. C₃×C₁₁	C₂×D₅×C₁₃	semidirect
55. D₁₅	C₁₃×D₁₁	direct (N × H)
61. D₁₁	C₁₃×D₁₅	direct (N × H)
63. C₃×C₅	C₂×C₁₃×D₁₁	semidirect
64. C₁₃	D₁₁×D₁₅	direct (N × H)
66. C₁₁	C₂×C₁₃×D₁₅	semidirect
73. C₅	D₃×C₁₃×D₁₁	semidirect
75. C₃	D₅×C₁₃×D₁₁	semidirect

Subgroups — C13×D11×D15 #22575159

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×D₁₁×D₁₅ #22575159