Subgroups — AGL(1,𝔽₁₁)×D₉₅ #35229883

Order 20900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(C₁₉⋊AGL(1,𝔽₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₉₅	C₅	1	1	yes	maximal, characteristic, complemented
6	D₁₉×AGL(1,𝔽₁₁)	—	5	1	no	maximal
7	C₁₉⋊AGL(1,𝔽₁₁)	—	5	1	no	—
8	C₁₉×AGL(1,𝔽₁₁)	—	2	2	no	—
9	C₁₉×AGL(1,𝔽₁₁)	D₅	1	1	yes	characteristic, complemented
10	D₁₉×C₁₁⋊C₅	—	5	1	no	—
11	D₁₀₄₅	C₂×C₅	1	1	yes	characteristic, complemented
12	C₁₁×D₉₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₁₉×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₂×C₅×D₉₅	—	11	1	no	maximal, Hall
15	D₅×AGL(1,𝔽₁₁)	—	19	1	no	maximal, Hall
16	C₅×C₁₁×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
17	C₁₉×C₁₁⋊C₅	—	2	2	no	—
18	C₁₉×C₁₁⋊C₅	C₂×D₅	1	1	yes	characteristic, complemented
19	C₂×C₅²×C₁₉	—	11	1	no	—
20	C₅×D₉₅	—	11	1	no	—
21	C₅×D₉₅	—	22	1	no	—
22	D₁₁×D₁₉	—	5	1	no	Hall
23	C₅⋊AGL(1,𝔽₁₁)	—	19	1	no	—
24	D₅×C₁₁⋊C₅	—	19	1	no	—
25	C₅×AGL(1,𝔽₁₁)	D₁₉	1	1	yes	characteristic, complemented
26	C₅²×C₁₉	—	22	1	no	Hall
27	D₂₀₉	—	5	1	no	—
28	C₁₁×D₁₉	—	5	1	no	—
29	C₁₉×D₁₁	C₅×D₅	1	1	yes	characteristic, complemented
30	C₂×D₉₅	—	11	1	no	—
31	C₂×C₅×D₁₉	—	55	1	no	—
32	C₅×C₁₁⋊C₅	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
33	D₅×D₁₁	—	19	1	no	—
34	C₂×AGL(1,𝔽₁₁)	—	95	1	no	—
35	C₁₁×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₉	—	11	1	no	—
37	C₂×C₅×C₁₉	—	11	1	no	—
38	C₂×C₅×C₁₉	—	22	2	no	—
39	D₉₅	—	11	1	no	—
40	D₉₅	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
41	C₅×D₁₉	—	55	1	no	—
42	C₅×D₁₉	—	110	1	no	—
43	D₅₅	—	19	1	no	—
44	C₅×D₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented
45	D₅×C₁₁	—	19	1	no	—
46	C₂×C₁₁⋊C₅	—	95	1	no	—
47	AGL(1,𝔽₁₁)	—	2	2	no	—
48	AGL(1,𝔽₁₁)	—	95	1	no	—
49	AGL(1,𝔽₁₁)	D₉₅	1	1	yes	characteristic, direct product factor
50	C₂×C₅×D₅	—	209	1	no	Hall
51	C₅×C₁₉	—	22	1	no	—
52	C₅×C₁₉	—	44	2	no	—
53	C₅×C₁₉	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
54	C₂×D₁₉	—	55	1	no	Hall
55	C₅×C₁₁	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
56	C₁₁⋊C₅	—	2	2	no	—
57	C₁₁⋊C₅	C₂×D₉₅	1	1	yes	characteristic, complemented
58	C₂×C₅²	—	11	1	no	—
59	C₅×D₅	—	418	1	no	—
60	C₅×D₅	—	209	1	no	—
61	C₂×D₁₁	—	95	1	no	Hall
62	C₂×C₁₉	—	11	1	no	—
63	D₁₉	—	5	1	no	—
64	D₁₉	—	55	1	no	—
65	C₅²	—	22	1	no	Sylow
66	C₂×C₁₁	—	95	1	no	—
67	D₁₁	—	95	1	no	—
68	D₁₁	C₅×D₉₅	1	1	yes	characteristic, complemented
69	C₂²×C₅	—	1045	1	no	—
70	C₂×D₅	—	209	1	no	—
71	C₁₉	D₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
72	C₁₁	C₂×C₅×D₉₅	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	11	1	no	—
74	C₂×C₅	—	11	1	no	—
75	C₂×C₅	—	1045	1	no	—
76	C₂×C₅	—	22	2	no	—
77	C₂×C₅	—	2090	1	no	—
78	D₅	—	19	1	no	—
79	D₅	—	209	1	no	—
80	C₅	—	22	1	no	—
81	C₅	—	44	2	no	—
82	C₅	D₁₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
83	C₂²	—	1045	1	no	Sylow
84	C₂	—	11	1	no	—
85	C₂	—	1045	1	no	—
86	C₂	—	95	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₁₉	C₂²×C₅
LCS	G ▷ C₅×C₁₁×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×D₉₅	C₂	semidirect
2. C₅⋊(C₁₉⋊AGL(1,𝔽₁₁))	C₂	semidirect
3. C₅×C₁₉×AGL(1,𝔽₁₁)	C₂	semidirect
4. C₅×C₁₉×C₁₁⋊C₅	C₂²	semidirect
5. D₁₁×D₉₅	C₅	semidirect
9. C₁₉×AGL(1,𝔽₁₁)	D₅	semidirect
11. D₁₀₄₅	C₂×C₅	semidirect
12. C₁₁×D₉₅	C₂×C₅	semidirect
13. C₅×C₁₉×D₁₁	C₂×C₅	semidirect
16. C₅×C₁₁×C₁₉	C₂²×C₅	semidirect
18. C₁₉×C₁₁⋊C₅	C₂×D₅	semidirect
25. C₅×AGL(1,𝔽₁₁)	D₁₉	semidirect
29. C₁₉×D₁₁	C₅×D₅	semidirect
32. C₅×C₁₁⋊C₅	C₂×D₁₉	semidirect
35. C₁₁×C₁₉	C₂×C₅×D₅	semidirect
40. D₉₅	AGL(1,𝔽₁₁)	direct (N × H)
44. C₅×D₁₁	C₅×D₁₉	semidirect
49. AGL(1,𝔽₁₁)	D₉₅	direct (N × H)
53. C₅×C₁₉	C₂×AGL(1,𝔽₁₁)	semidirect
55. C₅×C₁₁	C₂×C₅×D₁₉	semidirect
57. C₁₁⋊C₅	C₂×D₉₅	semidirect
68. D₁₁	C₅×D₉₅	semidirect
71. C₁₉	D₅×AGL(1,𝔽₁₁)	semidirect
72. C₁₁	C₂×C₅×D₉₅	semidirect
82. C₅	D₁₉×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
C₁₁⋊C₅×D₉₅	2
C₅⋊(C₁₉⋊AGL(1,𝔽₁₁))	2
C₅×C₁₉×AGL(1,𝔽₁₁)	2
D₁₁×D₉₅	5
D₁₉×AGL(1,𝔽₁₁)	5
C₂×C₅×D₉₅	11
D₅×AGL(1,𝔽₁₁)	19

Subgroups — AGL(1,𝔽11)×D95 #35229883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₁₁)×D₉₅ #35229883