Subgroups — D₁₄₅⋊AGL(1,𝔽₁₁) #44542049

Order 31900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×C₅⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₅⋊D₂₉	C₅	1	1	yes	maximal, characteristic, complemented
6	D₂₉×AGL(1,𝔽₁₁)	—	5	1	no	maximal
7	C₂₉⋊AGL(1,𝔽₁₁)	—	2	2	no	—
8	C₂₉⋊AGL(1,𝔽₁₁)	D₅	1	1	yes	characteristic, complemented
9	C₂₉×AGL(1,𝔽₁₁)	—	5	1	no	—
10	C₁₁⋊C₅×D₂₉	—	5	1	no	—
11	C₂₉×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
12	C₁₁×D₁₄₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₃₁₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₅×D₂₉	—	11	1	no	maximal, Hall
15	C₅×C₁₁×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented
16	C₂₉×C₁₁⋊C₅	—	2	2	no	—
17	C₂₉×C₁₁⋊C₅	C₂×D₅	1	1	yes	characteristic, complemented
18	C₅×D₁₄₅	—	11	1	no	—
19	C₅×D₅×C₂₉	—	11	1	no	—
20	C₅²×D₂₉	—	11	1	no	—
21	D₁₁×D₂₉	—	5	1	no	Hall
22	D₅×AGL(1,𝔽₁₁)	—	29	1	no	maximal, Hall
23	C₅²×C₂₉	—	11	1	no	Hall
24	D₃₁₉	C₅×D₅	1	1	yes	characteristic, complemented
25	C₁₁×D₂₉	—	5	1	no	—
26	D₁₁×C₂₉	—	5	1	no	—
27	C₂×C₅×D₂₉	—	55	1	no	—
28	D₅×D₂₉	—	11	1	no	—
29	C₅⋊AGL(1,𝔽₁₁)	D₂₉	1	1	yes	characteristic, complemented
30	D₅×C₁₁⋊C₅	—	29	1	no	—
31	C₅×AGL(1,𝔽₁₁)	—	29	1	no	—
32	C₁₁×C₂₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₂₉	—	55	1	no	—
34	D₁₄₅	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
35	C₅×D₂₉	—	11	1	no	—
36	C₅×D₂₉	—	11	1	no	—
37	C₅×D₂₉	—	22	2	no	—
38	C₅×D₂₉	—	55	1	no	—
39	D₅×C₂₉	—	11	1	no	—
40	C₅×C₁₁⋊C₅	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	D₅×D₁₁	—	29	1	no	—
42	C₂×AGL(1,𝔽₁₁)	—	145	1	no	—
43	C₅×C₂₉	—	11	1	no	—
44	C₅×C₂₉	—	22	2	no	—
45	C₅×C₂₉	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
46	C₂×D₂₉	—	55	1	no	Hall
47	D₅₅	C₅×D₂₉	1	1	yes	characteristic, complemented
48	C₅×D₁₁	—	29	1	no	—
49	D₅×C₁₁	—	29	1	no	—
50	C₂×C₁₁⋊C₅	—	145	1	no	—
51	AGL(1,𝔽₁₁)	—	5	1	no	—
52	AGL(1,𝔽₁₁)	—	29	1	no	—
53	AGL(1,𝔽₁₁)	—	58	2	no	—
54	C₂×C₅×D₅	—	319	1	no	Hall
55	C₂×C₂₉	—	55	1	no	—
56	D₂₉	—	5	1	no	—
57	D₂₉	—	11	1	no	—
58	C₅×C₁₁	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented
59	C₁₁⋊C₅	—	2	2	no	—
60	C₁₁⋊C₅	D₅×D₂₉	1	1	yes	characteristic, complemented
61	C₂×C₅²	—	319	1	no	—
62	C₅×D₅	—	11	1	no	—
63	C₅×D₅	—	319	1	no	—
64	C₂×D₁₁	—	145	1	no	Hall
65	C₂₉	D₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
66	C₅²	—	11	1	no	Sylow
67	C₂×C₁₁	—	145	1	no	—
68	D₁₁	—	5	1	no	—
69	D₁₁	—	29	1	no	—
70	C₂²×C₅	—	1595	1	no	—
71	C₂×D₅	—	319	1	no	—
72	C₁₁	C₅×D₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	55	1	no	—
74	C₂×C₅	—	1595	1	no	—
75	C₂×C₅	—	319	1	no	—
76	C₂×C₅	—	319	1	no	—
77	C₂×C₅	—	638	2	no	—
78	D₅	—	11	1	no	—
79	D₅	—	29	1	no	—
80	C₅	—	11	1	no	—
81	C₅	—	22	2	no	—
82	C₅	D₂₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
83	C₂²	—	1595	1	no	Sylow
84	C₂	—	55	1	no	—
85	C₂	—	319	1	no	—
86	C₂	—	145	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₂₉	C₂²×C₅
LCS	G ▷ C₅×C₁₁×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×D₁₄₅	C₂	semidirect
2. C₂₉×C₅⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₅×C₂₉⋊AGL(1,𝔽₁₁)	C₂	semidirect
4. C₅×C₂₉×C₁₁⋊C₅	C₂²	semidirect
5. D₅₅⋊D₂₉	C₅	semidirect
8. C₂₉⋊AGL(1,𝔽₁₁)	D₅	semidirect
11. C₂₉×D₅₅	C₂×C₅	semidirect
12. C₁₁×D₁₄₅	C₂×C₅	semidirect
13. C₅×D₃₁₉	C₂×C₅	semidirect
15. C₅×C₁₁×C₂₉	C₂²×C₅	semidirect
17. C₂₉×C₁₁⋊C₅	C₂×D₅	semidirect
24. D₃₁₉	C₅×D₅	semidirect
29. C₅⋊AGL(1,𝔽₁₁)	D₂₉	semidirect
32. C₁₁×C₂₉	C₂×C₅×D₅	semidirect
34. D₁₄₅	AGL(1,𝔽₁₁)	semidirect
40. C₅×C₁₁⋊C₅	C₂×D₂₉	semidirect
45. C₅×C₂₉	C₂×AGL(1,𝔽₁₁)	semidirect
47. D₅₅	C₅×D₂₉	semidirect
58. C₅×C₁₁	C₂×C₅×D₂₉	semidirect
60. C₁₁⋊C₅	D₅×D₂₉	semidirect
65. C₂₉	D₅×AGL(1,𝔽₁₁)	semidirect
72. C₁₁	C₅×D₅×D₂₉	semidirect
82. C₅	D₂₉×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×D₁₄₅	2
C₂₉×C₅⋊AGL(1,𝔽₁₁)	2
C₅×C₂₉⋊AGL(1,𝔽₁₁)	2
D₅₅⋊D₂₉	5
D₂₉×AGL(1,𝔽₁₁)	5
C₅×D₅×D₂₉	11
D₅×AGL(1,𝔽₁₁)	29

Subgroups — D145⋊AGL(1,𝔽11) #44542049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₄₅⋊AGL(1,𝔽₁₁) #44542049