Subgroups — D₃₁×C₅⋊AGL(1,𝔽₁₁) #46802096

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊((C₁₁⋊C₅)⋊D₃₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×C₅⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁⋊C₅×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₁×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₁×D₅₅	C₅	1	1	yes	maximal, characteristic, complemented
6	D₃₁×AGL(1,𝔽₁₁)	—	5	1	no	maximal
7	(C₁₁⋊C₅)⋊D₃₁	—	5	1	no	—
8	C₃₁×AGL(1,𝔽₁₁)	—	5	1	no	—
9	C₁₁⋊C₅×D₃₁	—	2	2	no	—
10	C₁₁⋊C₅×D₃₁	D₅	1	1	yes	characteristic, complemented
11	D₁₇₀₅	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃₁×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₁₁×D₃₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₅×D₃₁	—	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	C₅×D₁₅₅	—	11	1	no	—
19	C₅×D₅×C₃₁	—	11	1	no	—
20	C₅²×D₃₁	—	11	1	no	—
21	D₁₁×D₃₁	—	5	1	no	Hall
22	C₂×C₅⋊AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
23	C₅²×C₃₁	—	11	1	no	Hall
24	D₃₄₁	—	5	1	no	—
25	C₁₁×D₃₁	C₅×D₅	1	1	yes	characteristic, complemented
26	D₁₁×C₃₁	—	5	1	no	—
27	C₂×C₅×D₃₁	—	55	1	no	—
28	D₅×D₃₁	—	11	1	no	—
29	C₂×C₅×C₁₁⋊C₅	—	31	1	no	—
30	C₅⋊AGL(1,𝔽₁₁)	—	31	1	no	—
31	C₅⋊AGL(1,𝔽₁₁)	D₃₁	1	1	yes	characteristic, direct product factor
32	C₁₁×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₃₁	—	55	1	no	—
34	D₁₅₅	—	11	1	no	—
35	C₅×D₃₁	—	11	1	no	—
36	C₅×D₃₁	—	22	2	no	—
37	C₅×D₃₁	—	55	1	no	—
38	C₅×D₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
39	D₅×C₃₁	—	11	1	no	—
40	C₅×C₁₁⋊C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
41	C₂×D₅₅	—	31	1	no	—
42	C₂×AGL(1,𝔽₁₁)	—	155	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	C₂×D₃₁	—	55	1	no	Hall
47	C₂×C₅×C₁₁	—	31	1	no	—
48	D₅₅	—	31	1	no	—
49	D₅₅	C₅×D₃₁	1	1	yes	characteristic, complemented
50	C₂×C₁₁⋊C₅	—	31	1	no	—
51	C₂×C₁₁⋊C₅	—	62	2	no	—
52	AGL(1,𝔽₁₁)	—	5	1	no	—
53	AGL(1,𝔽₁₁)	—	155	1	no	—
54	C₂×C₅×D₅	—	341	1	no	Hall
55	C₂×C₃₁	—	55	1	no	—
56	D₃₁	—	55	1	no	—
57	D₃₁	C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
58	C₅×C₁₁	C₂×C₅×D₃₁	1	1	yes	characteristic, complemented
59	C₁₁⋊C₅	—	2	2	no	—
60	C₁₁⋊C₅	D₅×D₃₁	1	1	yes	characteristic, complemented
61	C₂×C₅²	—	341	1	no	—
62	C₅×D₅	—	11	1	no	—
63	C₅×D₅	—	341	1	no	—
64	C₂×D₁₁	—	155	1	no	Hall
65	C₃₁	C₂×C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
66	C₅²	—	11	1	no	Sylow
67	C₂×C₁₁	—	31	1	no	—
68	D₁₁	—	5	1	no	—
69	D₁₁	—	155	1	no	—
70	C₂²×C₅	—	1705	1	no	—
71	C₂×D₅	—	341	1	no	—
72	C₁₁	C₅×D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	31	1	no	—
74	C₂×C₅	—	55	1	no	—
75	C₂×C₅	—	341	1	no	—
76	C₂×C₅	—	1705	1	no	—
77	C₂×C₅	—	682	2	no	—
78	D₅	—	11	1	no	—
79	D₅	—	341	1	no	—
80	C₅	—	11	1	no	—
81	C₅	—	22	2	no	—
82	C₅	D₃₁×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
83	C₂²	—	1705	1	no	Sylow
84	C₂	—	31	1	no	—
85	C₂	—	55	1	no	—
86	C₂	—	1705	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₃₁	C₂²×C₅
LCS	G ▷ C₅×C₁₁×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊((C₁₁⋊C₅)⋊D₃₁)	C₂	semidirect
2. C₃₁×C₅⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₅×C₁₁⋊C₅×D₃₁	C₂	semidirect
4. C₅×C₃₁×C₁₁⋊C₅	C₂²	semidirect
5. D₃₁×D₅₅	C₅	semidirect
10. C₁₁⋊C₅×D₃₁	D₅	semidirect
11. D₁₇₀₅	C₂×C₅	semidirect
12. C₃₁×D₅₅	C₂×C₅	semidirect
13. C₅×C₁₁×D₃₁	C₂×C₅	semidirect
15. C₅×C₁₁×C₃₁	C₂²×C₅	semidirect
17. C₃₁×C₁₁⋊C₅	C₂×D₅	semidirect
25. C₁₁×D₃₁	C₅×D₅	semidirect
31. C₅⋊AGL(1,𝔽₁₁)	D₃₁	direct (N × H)
32. C₁₁×C₃₁	C₂×C₅×D₅	semidirect
38. C₅×D₃₁	AGL(1,𝔽₁₁)	semidirect
40. C₅×C₁₁⋊C₅	C₂×D₃₁	semidirect
45. C₅×C₃₁	C₂×AGL(1,𝔽₁₁)	semidirect
49. D₅₅	C₅×D₃₁	semidirect
57. D₃₁	C₅⋊AGL(1,𝔽₁₁)	direct (N × H)
58. C₅×C₁₁	C₂×C₅×D₃₁	semidirect
60. C₁₁⋊C₅	D₅×D₃₁	semidirect
65. C₃₁	C₂×C₅⋊AGL(1,𝔽₁₁)	semidirect
72. C₁₁	C₅×D₅×D₃₁	semidirect
82. C₅	D₃₁×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
C₅⋊((C₁₁⋊C₅)⋊D₃₁)	2
C₃₁×C₅⋊AGL(1,𝔽₁₁)	2
C₅×C₁₁⋊C₅×D₃₁	2
D₃₁×D₅₅	5
D₃₁×AGL(1,𝔽₁₁)	5
C₅×D₅×D₃₁	11
C₂×C₅⋊AGL(1,𝔽₁₁)	31

Subgroups — D31×C5⋊AGL(1,𝔽11) #46802096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×C₅⋊AGL(1,𝔽₁₁) #46802096