Subgroups — C₅×D₅×D₁₁×C₃₁ #46802178

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₁×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₁₁×C₃₁	—	5	1	no	maximal
6	D₅×D₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₃₁×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
8	D₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₁₁×C₃₁	—	2	2	no	—
10	C₅×D₁₁×C₃₁	—	5	1	no	—
11	C₅×D₁₁×C₃₁	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅×C₁₁×C₃₁	—	5	1	no	—
14	C₂×C₅×D₅×C₃₁	—	11	1	no	maximal, Hall
15	C₅×C₁₁×C₃₁	—	2	2	no	—
16	C₅×C₁₁×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented
17	C₅×C₁₁×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
18	C₂×C₅²×C₃₁	—	11	1	no	—
19	C₅×D₅×C₃₁	—	11	1	no	—
20	C₅×D₅×C₃₁	D₁₁	1	1	yes	characteristic, direct product factor
21	C₂×D₁₁×C₃₁	—	5	1	no	Hall
22	C₅×D₅×D₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅²×C₃₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₁×C₃₁	—	5	1	no	—
25	D₁₁×C₃₁	—	5	1	no	—
26	D₁₁×C₃₁	C₅×D₅	1	1	yes	characteristic, direct product factor
27	C₂²×C₅×C₃₁	—	55	1	no	—
28	C₂×D₅×C₃₁	—	11	1	no	—
29	C₅×D₅₅	C₂×C₃₁	1	1	yes	characteristic, complemented
30	C₅×D₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented
31	C₅²×D₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented
32	C₁₁×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₃₁	—	5	1	no	—
34	C₂×C₅×C₃₁	—	11	1	no	—
35	C₂×C₅×C₃₁	—	11	1	no	—
36	C₂×C₅×C₃₁	—	22	2	no	—
37	C₂×C₅×C₃₁	—	55	1	no	—
38	D₅×C₃₁	—	11	1	no	—
39	D₅×C₃₁	C₅×D₁₁	1	1	yes	characteristic, direct product factor
40	C₅²×C₁₁	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×D₁₁	—	5	1	no	—
42	D₅×D₁₁	C₅×C₃₁	1	1	yes	characteristic, direct product factor
43	C₅×C₃₁	—	2	2	no	—
44	C₅×C₃₁	D₅×D₁₁	1	1	yes	characteristic, direct product factor
45	C₅×C₃₁	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented
46	C₂²×C₃₁	—	55	1	no	Hall
47	C₂×C₅×C₁₁	—	5	1	no	—
48	D₅₅	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
49	C₅×D₁₁	—	2	2	no	—
50	C₅×D₁₁	—	5	1	no	—
51	C₅×D₁₁	D₅×C₃₁	1	1	yes	characteristic, direct product factor
52	C₅×D₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
53	D₅×C₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
54	C₂×C₅×D₅	—	11	1	no	Hall
55	C₂×C₃₁	—	5	1	no	—
56	C₂×C₃₁	—	11	1	no	—
57	C₂×C₃₁	—	55	1	no	—
58	C₅×C₁₁	—	2	2	no	—
59	C₅×C₁₁	C₂×D₅×C₃₁	1	1	yes	characteristic, complemented
60	C₅×C₁₁	C₂²×C₅×C₃₁	1	1	yes	characteristic, complemented
61	C₂×C₅²	—	11	1	no	—
62	C₅×D₅	—	11	1	no	—
63	C₅×D₅	D₁₁×C₃₁	1	1	yes	characteristic, direct product factor
64	C₂×D₁₁	—	5	1	no	Hall
65	C₃₁	C₅×D₅×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
66	C₅²	C₂×D₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₁₁	—	5	1	no	—
68	D₁₁	—	5	1	no	—
69	D₁₁	C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor
70	C₂²×C₅	—	55	1	no	—
71	C₂×D₅	—	11	1	no	—
72	C₁₁	C₂×C₅×D₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	5	1	no	—
74	C₂×C₅	—	11	1	no	—
75	C₂×C₅	—	11	1	no	—
76	C₂×C₅	—	22	2	no	—
77	C₂×C₅	—	55	1	no	—
78	D₅	—	11	1	no	—
79	D₅	C₅×D₁₁×C₃₁	1	1	yes	characteristic, direct product factor
80	C₅	—	2	2	no	—
81	C₅	D₅×D₁₁×C₃₁	1	1	yes	characteristic, direct product factor
82	C₅	C₂×C₅×D₁₁×C₃₁	1	1	yes	characteristic, complemented
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	C₅×C₃₁	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₃₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₅×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅²×D₁₁×C₃₁	C₂	semidirect
2. C₅×D₅×C₁₁×C₃₁	C₂	semidirect
3. C₅×C₃₁×D₅₅	C₂	semidirect
4. C₅²×C₁₁×C₃₁	C₂²	semidirect
6. D₅×D₁₁×C₃₁	C₅	direct (N × H)
7. C₃₁×D₅₅	C₂×C₅	semidirect
8. D₅×C₁₁×C₃₁	C₂×C₅	semidirect
11. C₅×D₁₁×C₃₁	D₅	direct (N × H)
12. C₅×D₁₁×C₃₁	C₂×C₅	semidirect
16. C₅×C₁₁×C₃₁	C₂×D₅	semidirect
17. C₅×C₁₁×C₃₁	C₂²×C₅	semidirect
20. C₅×D₅×C₃₁	D₁₁	direct (N × H)
22. C₅×D₅×D₁₁	C₃₁	direct (N × H)
23. C₅²×C₃₁	C₂×D₁₁	semidirect
26. D₁₁×C₃₁	C₅×D₅	direct (N × H)
29. C₅×D₅₅	C₂×C₃₁	semidirect
30. C₅×D₅×C₁₁	C₂×C₃₁	semidirect
31. C₅²×D₁₁	C₂×C₃₁	semidirect
32. C₁₁×C₃₁	C₂×C₅×D₅	semidirect
39. D₅×C₃₁	C₅×D₁₁	direct (N × H)
40. C₅²×C₁₁	C₂²×C₃₁	semidirect
42. D₅×D₁₁	C₅×C₃₁	direct (N × H)
44. C₅×C₃₁	D₅×D₁₁	direct (N × H)
45. C₅×C₃₁	C₂×C₅×D₁₁	semidirect
48. D₅₅	C₂×C₅×C₃₁	semidirect
51. C₅×D₁₁	D₅×C₃₁	direct (N × H)
52. C₅×D₁₁	C₂×C₅×C₃₁	semidirect
53. D₅×C₁₁	C₂×C₅×C₃₁	semidirect
59. C₅×C₁₁	C₂×D₅×C₃₁	semidirect
60. C₅×C₁₁	C₂²×C₅×C₃₁	semidirect
63. C₅×D₅	D₁₁×C₃₁	direct (N × H)
65. C₃₁	C₅×D₅×D₁₁	direct (N × H)
66. C₅²	C₂×D₁₁×C₃₁	semidirect
69. D₁₁	C₅×D₅×C₃₁	direct (N × H)
72. C₁₁	C₂×C₅×D₅×C₃₁	semidirect
79. D₅	C₅×D₁₁×C₃₁	direct (N × H)
81. C₅	D₅×D₁₁×C₃₁	direct (N × H)
82. C₅	C₂×C₅×D₁₁×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₁₁×C₃₁	2
C₅×D₅×C₁₁×C₃₁	2
C₅×C₃₁×D₅₅	2
C₂×C₅×D₁₁×C₃₁	5
D₅×D₁₁×C₃₁	5
C₂×C₅×D₅×C₃₁	11
C₅×D₅×D₁₁	31

Subgroups — C5×D5×D11×C31 #46802178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×D₁₁×C₃₁ #46802178