Subgroups — D₁₃×C₅⋊AGL(1,𝔽₁₁) #28384708

Order 14300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₁₃⋊AGL(1,𝔽₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₅⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₅₅	C₅	1	1	yes	maximal, characteristic, complemented
6	D₁₃×AGL(1,𝔽₁₁)	—	5	1	no	maximal
7	D₇₁₅	C₂×C₅	1	1	yes	characteristic, complemented
8	C₁₃×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×C₁₁×D₁₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₁₃⋊AGL(1,𝔽₁₁)	—	5	1	no	—
11	C₁₃×AGL(1,𝔽₁₁)	—	5	1	no	—
12	D₁₃×C₁₁⋊C₅	—	2	2	no	—
13	D₁₃×C₁₁⋊C₅	D₅	1	1	yes	characteristic, complemented
14	C₅×D₅×D₁₃	—	11	1	no	maximal, Hall
15	C₂×C₅⋊AGL(1,𝔽₁₁)	—	13	1	no	maximal, Hall
16	C₅×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented
17	C₁₃×C₁₁⋊C₅	—	2	2	no	—
18	C₁₃×C₁₁⋊C₅	C₂×D₅	1	1	yes	characteristic, complemented
19	C₅×D₆₅	—	11	1	no	—
20	C₅×D₅×C₁₃	—	11	1	no	—
21	C₅²×D₁₃	—	22	1	no	—
22	D₁₁×D₁₃	—	5	1	no	Hall
23	C₂×C₅×C₁₁⋊C₅	—	13	1	no	—
24	C₅⋊AGL(1,𝔽₁₁)	—	13	1	no	—
25	C₅⋊AGL(1,𝔽₁₁)	D₁₃	1	1	yes	characteristic, direct product factor
26	C₅²×C₁₃	—	22	1	no	Hall
27	D₁₄₃	—	5	1	no	—
28	C₁₁×D₁₃	C₅×D₅	1	1	yes	characteristic, complemented
29	C₁₃×D₁₁	—	5	1	no	—
30	C₅×C₁₁⋊C₅	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×D₁₃	—	55	1	no	—
32	D₅×D₁₃	—	11	1	no	—
33	C₂×D₅₅	—	13	1	no	—
34	C₂×AGL(1,𝔽₁₁)	—	65	1	no	—
35	C₁₁×C₁₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₃	—	55	1	no	—
37	D₆₅	—	11	1	no	—
38	C₅×D₁₃	—	11	1	no	—
39	C₅×D₁₃	—	22	2	no	—
40	C₅×D₁₃	—	55	1	no	—
41	C₅×D₁₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
42	D₅×C₁₃	—	11	1	no	—
43	C₂×C₅×C₁₁	—	13	1	no	—
44	D₅₅	—	13	1	no	—
45	D₅₅	C₅×D₁₃	1	1	yes	characteristic, complemented
46	C₂×C₁₁⋊C₅	—	13	1	no	—
47	C₂×C₁₁⋊C₅	—	26	2	no	—
48	AGL(1,𝔽₁₁)	—	5	1	no	—
49	AGL(1,𝔽₁₁)	—	65	1	no	—
50	C₂×C₅×D₅	—	143	1	no	Hall
51	C₅×C₁₃	—	11	1	no	—
52	C₅×C₁₃	—	22	2	no	—
53	C₅×C₁₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
54	C₅×C₁₁	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented
55	C₁₁⋊C₅	—	2	2	no	—
56	C₁₁⋊C₅	D₅×D₁₃	1	1	yes	characteristic, complemented
57	C₂×D₁₃	—	55	1	no	Hall
58	C₂×C₅²	—	286	1	no	—
59	C₅×D₅	—	11	1	no	—
60	C₅×D₅	—	143	1	no	—
61	C₂×D₁₁	—	65	1	no	Hall
62	C₂×C₁₃	—	55	1	no	—
63	D₁₃	—	55	1	no	—
64	D₁₃	C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
65	C₅²	—	22	1	no	Sylow
66	C₂×C₁₁	—	13	1	no	—
67	D₁₁	—	5	1	no	—
68	D₁₁	—	65	1	no	—
69	C₂²×C₅	—	715	1	no	—
70	C₂×D₅	—	143	1	no	—
71	C₁₃	C₂×C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
72	C₁₁	C₅×D₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	13	1	no	—
74	C₂×C₅	—	286	1	no	—
75	C₂×C₅	—	286	2	no	—
76	C₂×C₅	—	55	1	no	—
77	C₂×C₅	—	715	1	no	—
78	D₅	—	11	1	no	—
79	D₅	—	143	1	no	—
80	C₅	—	22	1	no	—
81	C₅	—	22	2	no	—
82	C₅	D₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
83	C₂²	—	715	1	no	Sylow
84	C₂	—	13	1	no	—
85	C₂	—	55	1	no	—
86	C₂	—	715	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₁₃	C₂²×C₅
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₁₃⋊AGL(1,𝔽₁₁))	C₂	semidirect
2. C₁₃×C₅⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₅×D₁₃×C₁₁⋊C₅	C₂	semidirect
4. C₅×C₁₃×C₁₁⋊C₅	C₂²	semidirect
5. D₁₃×D₅₅	C₅	semidirect
7. D₇₁₅	C₂×C₅	semidirect
8. C₁₃×D₅₅	C₂×C₅	semidirect
9. C₅×C₁₁×D₁₃	C₂×C₅	semidirect
13. D₁₃×C₁₁⋊C₅	D₅	semidirect
16. C₅×C₁₁×C₁₃	C₂²×C₅	semidirect
18. C₁₃×C₁₁⋊C₅	C₂×D₅	semidirect
25. C₅⋊AGL(1,𝔽₁₁)	D₁₃	direct (N × H)
28. C₁₁×D₁₃	C₅×D₅	semidirect
30. C₅×C₁₁⋊C₅	C₂×D₁₃	semidirect
35. C₁₁×C₁₃	C₂×C₅×D₅	semidirect
41. C₅×D₁₃	AGL(1,𝔽₁₁)	semidirect
45. D₅₅	C₅×D₁₃	semidirect
53. C₅×C₁₃	C₂×AGL(1,𝔽₁₁)	semidirect
54. C₅×C₁₁	C₂×C₅×D₁₃	semidirect
56. C₁₁⋊C₅	D₅×D₁₃	semidirect
64. D₁₃	C₅⋊AGL(1,𝔽₁₁)	direct (N × H)
71. C₁₃	C₂×C₅⋊AGL(1,𝔽₁₁)	semidirect
72. C₁₁	C₅×D₅×D₁₃	semidirect
82. C₅	D₁₃×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⋊(C₁₃⋊AGL(1,𝔽₁₁))	2
C₁₃×C₅⋊AGL(1,𝔽₁₁)	2
C₅×D₁₃×C₁₁⋊C₅	2
D₁₃×D₅₅	5
D₁₃×AGL(1,𝔽₁₁)	5
C₅×D₅×D₁₃	11
C₂×C₅⋊AGL(1,𝔽₁₁)	13

Subgroups — D13×C5⋊AGL(1,𝔽11) #28384708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×C₅⋊AGL(1,𝔽₁₁) #28384708