Subgroups — D₃×D₅×C₁₁×C₁₃ #22575163

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂²×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×D₁₅	C₂	semidirect
2. C₅×D₃×C₁₁×C₁₃	C₂	semidirect
3. C₃×D₅×C₁₁×C₁₃	C₂	semidirect
5. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
9. D₅×C₁₁×C₁₃	D₃	direct (N × H)
12. D₃×C₁₁×C₁₃	D₅	direct (N × H)
13. D₃×D₅×C₁₃	C₁₁	direct (N × H)
14. C₅×C₁₁×C₁₃	C₂×D₃	semidirect
15. D₃×D₅×C₁₁	C₁₃	direct (N × H)
17. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
18. C₁₃×D₁₅	C₂×C₁₁	semidirect
19. C₅×D₃×C₁₃	C₂×C₁₁	semidirect
20. C₃×D₅×C₁₃	C₂×C₁₁	semidirect
21. C₁₁×D₁₅	C₂×C₁₃	semidirect
22. C₅×D₃×C₁₁	C₂×C₁₃	semidirect
23. C₃×D₅×C₁₁	C₂×C₁₃	semidirect
29. C₃×C₅×C₁₃	C₂²×C₁₁	semidirect
30. C₃×C₅×C₁₁	C₂²×C₁₃	semidirect
32. C₁₁×C₁₃	D₃×D₅	direct (N × H)
36. D₅×C₁₃	D₃×C₁₁	direct (N × H)
39. D₅×C₁₁	D₃×C₁₃	direct (N × H)
42. D₃×C₁₃	D₅×C₁₁	direct (N × H)
45. D₃×C₁₁	D₅×C₁₃	direct (N × H)
46. C₅×C₁₃	C₂×D₃×C₁₁	semidirect
47. D₃×D₅	C₁₁×C₁₃	direct (N × H)
48. C₅×C₁₁	C₂×D₃×C₁₃	semidirect
51. C₃×C₁₃	C₂×D₅×C₁₁	semidirect
52. C₃×C₁₁	C₂×D₅×C₁₃	semidirect
53. D₁₅	C₂×C₁₁×C₁₃	semidirect
54. C₃×D₅	C₂×C₁₁×C₁₃	semidirect
55. C₅×D₃	C₂×C₁₁×C₁₃	semidirect
63. C₃×C₅	C₂²×C₁₁×C₁₃	semidirect
64. C₁₃	D₃×D₅×C₁₁	direct (N × H)
66. C₁₁	D₃×D₅×C₁₃	direct (N × H)
69. D₅	D₃×C₁₁×C₁₃	direct (N × H)
72. D₃	D₅×C₁₁×C₁₃	direct (N × H)
73. C₅	C₂×D₃×C₁₁×C₁₃	semidirect
75. C₃	C₂×D₅×C₁₁×C₁₃	semidirect

Subgroups — D3×D5×C11×C13 #22575163

Conjugacy classes of subgroups

Complements

Subgroups — D₃×D₅×C₁₁×C₁₃ #22575163