Subgroups — C₁₁×D₁₃×D₁₅ #22575156

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₃×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₁×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₁×D₁₃	—	5	1	no	maximal, Hall
7	C₁₁×D₆₅	—	3	1	no	—
8	D₅×C₁₁×C₁₃	—	3	1	no	—
9	C₅×C₁₁×D₁₃	D₃	1	1	yes	characteristic, complemented
10	C₁₁×D₃₉	—	5	1	no	—
11	D₃×C₁₁×C₁₃	—	5	1	no	—
12	C₃×C₁₁×D₁₃	D₅	1	1	yes	characteristic, complemented
13	D₁₃×D₁₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×D₁₅	—	13	1	no	maximal, Hall
16	C₂×C₁₁×D₁₃	—	15	1	no	Hall
17	C₃×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	D₁₉₅	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₁₃×D₁₅	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₃×C₅×D₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×C₁₁	—	13	1	no	—
22	C₁₁×D₁₅	—	13	1	no	—
23	C₁₁×D₁₅	D₁₃	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁×C₁₃	—	15	1	no	—
25	C₁₁×D₁₃	—	15	1	no	—
26	C₁₁×D₁₃	D₁₅	1	1	yes	characteristic, direct product factor
27	D₅×D₁₃	—	3	1	no	Hall
28	C₂×D₅×C₁₁	—	39	1	no	Hall
29	C₃×C₅×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₃×D₁₃	—	5	1	no	Hall
32	C₁₁×C₁₃	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃×C₁₁	—	65	1	no	Hall
34	D₆₅	—	3	1	no	—
35	C₅×D₁₃	D₃×C₁₁	1	1	yes	characteristic, complemented
36	D₅×C₁₃	—	3	1	no	—
37	C₂×C₅×C₁₁	—	13	1	no	—
38	D₅×C₁₁	—	3	1	no	—
39	D₅×C₁₁	—	39	1	no	—
40	D₃₉	—	5	1	no	—
41	C₃×D₁₃	D₅×C₁₁	1	1	yes	characteristic, complemented
42	D₃×C₁₃	—	5	1	no	—
43	C₂×C₃×C₁₁	—	13	1	no	—
44	D₃×C₁₁	—	5	1	no	—
45	D₃×C₁₁	—	65	1	no	—
46	C₅×C₁₃	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
47	C₂×D₁₅	—	13	1	no	Hall
48	C₅×C₁₁	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
49	C₂×D₁₃	—	15	1	no	Hall
50	C₂²×C₁₁	—	195	1	no	Hall
51	C₃×C₁₃	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
52	C₃×C₁₁	D₅×D₁₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×C₅	—	13	1	no	—
54	D₁₅	—	13	1	no	—
55	D₁₅	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
56	C₂×C₁₃	—	15	1	no	—
57	D₁₃	—	15	1	no	—
58	D₁₃	C₁₁×D₁₅	1	1	yes	characteristic, direct product factor
59	C₂×C₁₁	—	13	1	no	—
60	C₂×C₁₁	—	15	1	no	—
61	C₂×C₁₁	—	195	1	no	—
62	C₂×D₅	—	39	1	no	Hall
63	C₃×C₅	C₂×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
64	C₁₃	C₂×C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
65	C₂×D₃	—	65	1	no	Hall
66	C₁₁	D₁₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₅	—	13	1	no	—
68	D₅	—	3	1	no	—
69	D₅	—	39	1	no	—
70	C₂×C₃	—	13	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	65	1	no	—
73	C₅	D₃×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	195	1	no	Sylow
75	C₃	D₅×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	15	1	no	—
78	C₂	—	195	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₁₃×D₁₅
commutator, hypocenter	C₃×C₅×C₁₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₁₉₅	C₂	semidirect
2. C₁₁×C₁₃×D₁₅	C₂	semidirect
3. C₃×C₅×C₁₁×D₁₃	C₂	semidirect
5. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
9. C₅×C₁₁×D₁₃	D₃	semidirect
12. C₃×C₁₁×D₁₃	D₅	semidirect
13. D₁₃×D₁₅	C₁₁	direct (N × H)
14. C₅×C₁₁×C₁₃	C₂×D₃	semidirect
17. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
18. D₁₉₅	C₂×C₁₁	semidirect
19. C₁₃×D₁₅	C₂×C₁₁	semidirect
20. C₃×C₅×D₁₃	C₂×C₁₁	semidirect
23. C₁₁×D₁₅	D₁₃	direct (N × H)
26. C₁₁×D₁₃	D₁₅	direct (N × H)
29. C₃×C₅×C₁₃	C₂²×C₁₁	semidirect
30. C₃×C₅×C₁₁	C₂×D₁₃	semidirect
32. C₁₁×C₁₃	C₂×D₁₅	semidirect
35. C₅×D₁₃	D₃×C₁₁	semidirect
41. C₃×D₁₃	D₅×C₁₁	semidirect
46. C₅×C₁₃	C₂×D₃×C₁₁	semidirect
48. C₅×C₁₁	D₃×D₁₃	semidirect
51. C₃×C₁₃	C₂×D₅×C₁₁	semidirect
52. C₃×C₁₁	D₅×D₁₃	semidirect
55. D₁₅	C₁₁×D₁₃	direct (N × H)
58. D₁₃	C₁₁×D₁₅	direct (N × H)
63. C₃×C₅	C₂×C₁₁×D₁₃	semidirect
64. C₁₃	C₂×C₁₁×D₁₅	semidirect
66. C₁₁	D₁₃×D₁₅	direct (N × H)
73. C₅	D₃×C₁₁×D₁₃	semidirect
75. C₃	D₅×C₁₁×D₁₃	semidirect

Subgroups — C11×D13×D15 #22575156

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×D₁₃×D₁₅ #22575156