Subgroups — D₅×C₃₁×AGL(1,𝔽₁₁) #46802097

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×C₅⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₁×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₁×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×AGL(1,𝔽₁₁)	—	5	1	no	maximal
7	C₃₁×AGL(1,𝔽₁₁)	—	2	2	no	—
8	C₃₁×AGL(1,𝔽₁₁)	—	5	1	no	—
9	C₃₁×AGL(1,𝔽₁₁)	D₅	1	1	yes	characteristic, direct product factor
10	C₃₁×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
11	D₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×D₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₃₁×C₁₁⋊C₅	—	5	1	no	—
14	C₂×C₅×D₅×C₃₁	—	11	1	no	maximal, Hall
15	C₅×C₁₁×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
16	C₃₁×C₁₁⋊C₅	—	2	2	no	—
17	C₃₁×C₁₁⋊C₅	C₂×D₅	1	1	yes	characteristic, complemented
18	C₂×C₅²×C₃₁	—	11	1	no	—
19	C₅×D₅×C₃₁	—	11	1	no	—
20	C₅×D₅×C₃₁	—	11	1	no	—
21	C₂×D₁₁×C₃₁	—	5	1	no	Hall
22	D₅×AGL(1,𝔽₁₁)	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅²×C₃₁	—	11	1	no	Hall
24	C₂×C₁₁×C₃₁	—	5	1	no	—
25	D₁₁×C₃₁	—	5	1	no	—
26	D₁₁×C₃₁	C₅×D₅	1	1	yes	characteristic, complemented
27	C₂²×C₅×C₃₁	—	55	1	no	—
28	C₂×D₅×C₃₁	—	11	1	no	—
29	C₅⋊AGL(1,𝔽₁₁)	C₂×C₃₁	1	1	yes	characteristic, complemented
30	D₅×C₁₁⋊C₅	C₂×C₃₁	1	1	yes	characteristic, complemented
31	C₅×AGL(1,𝔽₁₁)	C₂×C₃₁	1	1	yes	characteristic, complemented
32	C₁₁×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₃₁	—	11	1	no	—
34	C₂×C₅×C₃₁	—	11	1	no	—
35	C₂×C₅×C₃₁	—	22	2	no	—
36	C₂×C₅×C₃₁	—	55	1	no	—
37	C₂×C₅×C₃₁	—	55	1	no	—
38	D₅×C₃₁	—	11	1	no	—
39	D₅×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
40	C₅×C₁₁⋊C₅	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
41	D₅×D₁₁	C₅×C₃₁	1	1	yes	characteristic, complemented
42	C₂×AGL(1,𝔽₁₁)	—	5	1	no	—
43	C₅×C₃₁	—	11	1	no	—
44	C₅×C₃₁	—	22	2	no	—
45	C₅×C₃₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
46	C₂²×C₃₁	—	55	1	no	Hall
47	D₅₅	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
48	C₅×D₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
49	D₅×C₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
50	C₂×C₁₁⋊C₅	—	5	1	no	—
51	AGL(1,𝔽₁₁)	—	2	2	no	—
52	AGL(1,𝔽₁₁)	—	5	1	no	—
53	AGL(1,𝔽₁₁)	D₅×C₃₁	1	1	yes	characteristic, direct product factor
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	C₂²×C₅×C₃₁	1	1	yes	characteristic, complemented
59	C₁₁⋊C₅	—	2	2	no	—
60	C₁₁⋊C₅	C₂×D₅×C₃₁	1	1	yes	characteristic, complemented
61	C₂×C₅²	—	11	1	no	—
62	C₅×D₅	—	11	1	no	—
63	C₅×D₅	—	11	1	no	—
64	C₂×D₁₁	—	5	1	no	Hall
65	C₃₁	D₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
66	C₅²	—	11	1	no	Sylow
67	C₂×C₁₁	—	5	1	no	—
68	D₁₁	—	5	1	no	—
69	D₁₁	C₅×D₅×C₃₁	1	1	yes	characteristic, complemented
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	—	11	1	no	—
74	C₂×C₅	—	11	1	no	—
75	C₂×C₅	—	22	2	no	—
76	C₂×C₅	—	55	1	no	—
77	C₂×C₅	—	55	1	no	—
78	D₅	—	11	1	no	—
79	D₅	C₃₁×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
80	C₅	—	11	1	no	—
81	C₅	—	22	2	no	—
82	C₅	C₂×C₃₁×AGL(1,𝔽₁₁)	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	C₃₁	D₅×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₃₁	C₂²×C₅
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. D₅×C₃₁×C₁₁⋊C₅	C₂	semidirect
2. C₃₁×C₅⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₅×C₃₁×AGL(1,𝔽₁₁)	C₂	semidirect
4. C₅×C₃₁×C₁₁⋊C₅	C₂²	semidirect
5. D₅×D₁₁×C₃₁	C₅	semidirect
9. C₃₁×AGL(1,𝔽₁₁)	D₅	direct (N × H)
10. C₃₁×D₅₅	C₂×C₅	semidirect
11. D₅×C₁₁×C₃₁	C₂×C₅	semidirect
12. C₅×D₁₁×C₃₁	C₂×C₅	semidirect
15. C₅×C₁₁×C₃₁	C₂²×C₅	semidirect
17. C₃₁×C₁₁⋊C₅	C₂×D₅	semidirect
22. D₅×AGL(1,𝔽₁₁)	C₃₁	direct (N × H)
26. D₁₁×C₃₁	C₅×D₅	semidirect
29. C₅⋊AGL(1,𝔽₁₁)	C₂×C₃₁	semidirect
30. D₅×C₁₁⋊C₅	C₂×C₃₁	semidirect
31. C₅×AGL(1,𝔽₁₁)	C₂×C₃₁	semidirect
32. C₁₁×C₃₁	C₂×C₅×D₅	semidirect
39. D₅×C₃₁	AGL(1,𝔽₁₁)	direct (N × H)
40. C₅×C₁₁⋊C₅	C₂²×C₃₁	semidirect
41. D₅×D₁₁	C₅×C₃₁	semidirect
45. C₅×C₃₁	C₂×AGL(1,𝔽₁₁)	semidirect
47. D₅₅	C₂×C₅×C₃₁	semidirect
48. C₅×D₁₁	C₂×C₅×C₃₁	semidirect
49. D₅×C₁₁	C₂×C₅×C₃₁	semidirect
53. AGL(1,𝔽₁₁)	D₅×C₃₁	direct (N × H)
58. C₅×C₁₁	C₂²×C₅×C₃₁	semidirect
60. C₁₁⋊C₅	C₂×D₅×C₃₁	semidirect
65. C₃₁	D₅×AGL(1,𝔽₁₁)	direct (N × H)
69. D₁₁	C₅×D₅×C₃₁	semidirect
72. C₁₁	C₂×C₅×D₅×C₃₁	semidirect
79. D₅	C₃₁×AGL(1,𝔽₁₁)	direct (N × H)
82. C₅	C₂×C₃₁×AGL(1,𝔽₁₁)	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃₁×C₁₁⋊C₅	2
C₃₁×C₅⋊AGL(1,𝔽₁₁)	2
C₅×C₃₁×AGL(1,𝔽₁₁)	2
D₅×D₁₁×C₃₁	5
C₂×C₃₁×AGL(1,𝔽₁₁)	5
C₂×C₅×D₅×C₃₁	11
D₅×AGL(1,𝔽₁₁)	31

Subgroups — D5×C31×AGL(1,𝔽11) #46802097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃₁×AGL(1,𝔽₁₁) #46802097