Subgroups — D₅×C₁₁×C₁₃×D₁₁ #44538263

Order 31460.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₃×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₁²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₃×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₃×D₁₁	—	5	1	no	maximal, Hall
6	C₁₁×C₁₃×D₁₁	—	5	1	no	—
7	C₁₁×C₁₃×D₁₁	D₅	1	1	yes	characteristic, direct product factor
8	C₂×C₁₁²×C₁₃	—	5	1	no	—
9	C₂×D₅×C₁₁×C₁₃	—	11	1	no	maximal
10	D₅×C₁₃×D₁₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
11	D₅×C₁₁×D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₁²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₁₁×C₁₃	—	11	1	no	—
14	C₁₃×D₅₅	C₂×C₁₁	1	1	yes	characteristic, complemented
15	D₅×C₁₁×C₁₃	—	2	5	no	—
16	D₅×C₁₁×C₁₃	—	11	1	no	—
17	D₅×C₁₁×C₁₃	D₁₁	1	1	yes	characteristic, direct product factor
18	D₅×C₁₁×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₅×C₁₃×D₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₁₁×D₅₅	C₂×C₁₃	1	1	yes	characteristic, complemented
21	D₅×C₁₁²	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₅×C₁₁×D₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₅×C₁₁×C₁₃	—	2	5	no	—
24	C₅×C₁₁×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented
25	C₅×C₁₁×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented
26	C₅×C₁₁²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₁₁×C₁₃	—	55	1	no	—
28	C₂×C₁₃×D₁₁	—	5	1	no	—
29	C₂×C₁₁×D₁₁	—	5	1	no	Hall
30	C₂×C₁₁×C₁₃	—	5	1	no	—
31	C₂×C₁₁×C₁₃	—	5	1	no	—
32	C₂×C₁₁×C₁₃	—	10	5	no	—
33	C₂×C₁₁×C₁₃	—	11	1	no	—
34	C₂×C₁₁×C₁₃	—	55	1	no	—
35	C₁₃×D₁₁	—	5	1	no	—
36	C₁₃×D₁₁	D₅×C₁₁	1	1	yes	characteristic, direct product factor
37	C₂×D₅×C₁₃	—	11	1	no	Hall
38	C₂×C₁₁²	—	5	1	no	—
39	C₁₁×D₁₁	—	5	1	no	—
40	C₁₁×D₁₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor
41	C₂×D₅×C₁₁	—	11	1	no	—
42	D₅×D₁₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
43	C₁₁×C₁₃	—	2	5	no	—
44	C₁₁×C₁₃	D₅×D₁₁	1	1	yes	characteristic, direct product factor
45	C₁₁×C₁₃	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
46	C₂×C₅×C₁₃	—	11	1	no	—
47	D₅×C₁₃	—	11	1	no	—
48	D₅×C₁₃	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
49	C₁₁²	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅×C₁₁	—	11	1	no	—
51	D₅₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
52	C₅×D₁₁	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
53	D₅×C₁₁	—	2	5	no	—
54	D₅×C₁₁	—	11	1	no	—
55	D₅×C₁₁	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
56	D₅×C₁₁	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
57	C₅×C₁₃	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
58	C₅×C₁₁	—	2	5	no	—
59	C₅×C₁₁	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented
60	C₅×C₁₁	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented
61	C₂²×C₁₃	—	55	1	no	Hall
62	C₂²×C₁₁	—	55	1	no	—
63	C₂×D₁₁	—	5	1	no	—
64	C₂×C₁₃	—	5	1	no	—
65	C₂×C₁₃	—	11	1	no	—
66	C₂×C₁₃	—	55	1	no	—
67	C₂×C₁₁	—	5	1	no	—
68	C₂×C₁₁	—	5	1	no	—
69	C₂×C₁₁	—	10	5	no	—
70	C₂×C₁₁	—	11	1	no	—
71	C₂×C₁₁	—	55	1	no	—
72	D₁₁	—	5	1	no	—
73	D₁₁	D₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
74	C₂×D₅	—	11	1	no	Hall
75	C₁₃	D₅×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
76	C₁₁	—	2	5	no	—
77	C₁₁	D₅×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
78	C₁₁	C₂×D₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented
79	C₂×C₅	—	11	1	no	—
80	D₅	—	11	1	no	—
81	D₅	C₁₁×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
82	C₅	C₂×C₁₁×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	55	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	11	1	no	—
86	C₂	—	55	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₃	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₃×D₁₁	C₂	semidirect
2. D₅×C₁₁²×C₁₃	C₂	semidirect
3. C₁₁×C₁₃×D₅₅	C₂	semidirect
4. C₅×C₁₁²×C₁₃	C₂²	semidirect
7. C₁₁×C₁₃×D₁₁	D₅	direct (N × H)
10. D₅×C₁₃×D₁₁	C₁₁	direct (N × H)
11. D₅×C₁₁×D₁₁	C₁₃	direct (N × H)
12. C₁₁²×C₁₃	C₂×D₅	semidirect
14. C₁₃×D₅₅	C₂×C₁₁	semidirect
17. D₅×C₁₁×C₁₃	D₁₁	direct (N × H)
18. D₅×C₁₁×C₁₃	C₂×C₁₁	semidirect
19. C₅×C₁₃×D₁₁	C₂×C₁₁	semidirect
20. C₁₁×D₅₅	C₂×C₁₃	semidirect
21. D₅×C₁₁²	C₂×C₁₃	semidirect
22. C₅×C₁₁×D₁₁	C₂×C₁₃	semidirect
24. C₅×C₁₁×C₁₃	C₂×D₁₁	semidirect
25. C₅×C₁₁×C₁₃	C₂²×C₁₁	semidirect
26. C₅×C₁₁²	C₂²×C₁₃	semidirect
36. C₁₃×D₁₁	D₅×C₁₁	direct (N × H)
40. C₁₁×D₁₁	D₅×C₁₃	direct (N × H)
42. D₅×D₁₁	C₁₁×C₁₃	direct (N × H)
44. C₁₁×C₁₃	D₅×D₁₁	direct (N × H)
45. C₁₁×C₁₃	C₂×D₅×C₁₁	semidirect
48. D₅×C₁₃	C₁₁×D₁₁	direct (N × H)
49. C₁₁²	C₂×D₅×C₁₃	semidirect
51. D₅₅	C₂×C₁₁×C₁₃	semidirect
52. C₅×D₁₁	C₂×C₁₁×C₁₃	semidirect
55. D₅×C₁₁	C₁₃×D₁₁	direct (N × H)
56. D₅×C₁₁	C₂×C₁₁×C₁₃	semidirect
57. C₅×C₁₃	C₂×C₁₁×D₁₁	semidirect
59. C₅×C₁₁	C₂×C₁₃×D₁₁	semidirect
60. C₅×C₁₁	C₂²×C₁₁×C₁₃	semidirect
73. D₁₁	D₅×C₁₁×C₁₃	direct (N × H)
75. C₁₃	D₅×C₁₁×D₁₁	direct (N × H)
77. C₁₁	D₅×C₁₃×D₁₁	direct (N × H)
78. C₁₁	C₂×D₅×C₁₁×C₁₃	semidirect
81. D₅	C₁₁×C₁₃×D₁₁	direct (N × H)
82. C₅	C₂×C₁₁×C₁₃×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×C₁₃×D₁₁	2
D₅×C₁₁²×C₁₃	2
C₁₁×C₁₃×D₅₅	2
C₂×C₁₁×C₁₃×D₁₁	5
C₂×D₅×C₁₁×C₁₃	11
D₅×C₁₃×D₁₁	11
D₅×C₁₁×D₁₁	13

Subgroups — D5×C11×C13×D11 #44538263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×C₁₃×D₁₁ #44538263