Subgroups — C₅×D₁₃×AGL(1,𝔽₁₁) #28384697

Order 14300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅	D₁₃×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₃	C₂²×C₅
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₃×C₁₁⋊C₅	C₂	semidirect
2. C₅×C₁₃⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₅×C₁₃×AGL(1,𝔽₁₁)	C₂	semidirect
4. C₅×C₁₃×C₁₁⋊C₅	C₂²	semidirect
5. C₅×D₁₁×D₁₃	C₅	semidirect
6. D₁₃×AGL(1,𝔽₁₁)	C₅	direct (N × H)
7. C₅×D₁₄₃	C₂×C₅	semidirect
8. C₅×C₁₃×D₁₁	C₂×C₅	semidirect
9. C₅×C₁₁×D₁₃	C₂×C₅	semidirect
10. C₁₃⋊AGL(1,𝔽₁₁)	C₂×C₅	semidirect
11. C₁₃×AGL(1,𝔽₁₁)	C₂×C₅	semidirect
12. D₁₃×C₁₁⋊C₅	C₂×C₅	semidirect
15. C₅×C₁₁×C₁₃	C₂²×C₅	semidirect
16. C₁₃×C₁₁⋊C₅	C₂²×C₅	semidirect
20. D₁₁×D₁₃	C₅²	semidirect
23. C₅×AGL(1,𝔽₁₁)	D₁₃	direct (N × H)
25. D₁₄₃	C₂×C₅²	semidirect
26. C₁₁×D₁₃	C₂×C₅²	semidirect
27. C₁₃×D₁₁	C₂×C₅²	semidirect
28. C₅×C₁₁⋊C₅	C₂×D₁₃	semidirect
33. C₁₁×C₁₃	C₂²×C₅²	semidirect
39. C₅×D₁₃	AGL(1,𝔽₁₁)	direct (N × H)
42. C₅×D₁₁	C₅×D₁₃	semidirect
45. AGL(1,𝔽₁₁)	C₅×D₁₃	direct (N × H)
48. C₅×C₁₃	C₂×AGL(1,𝔽₁₁)	semidirect
49. C₅×C₁₁	C₂×C₅×D₁₃	semidirect
50. C₁₁⋊C₅	C₂×C₅×D₁₃	semidirect
58. D₁₃	C₅×AGL(1,𝔽₁₁)	direct (N × H)
62. D₁₁	C₅²×D₁₃	semidirect
65. C₁₃	C₂×C₅×AGL(1,𝔽₁₁)	semidirect
66. C₁₁	C₂×C₅²×D₁₃	semidirect
74. C₅	D₁₃×AGL(1,𝔽₁₁)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₃×C₁₁⋊C₅	2
C₅×C₁₃⋊AGL(1,𝔽₁₁)	2
C₅×C₁₃×AGL(1,𝔽₁₁)	2
C₅×D₁₁×D₁₃	5
D₁₃×AGL(1,𝔽₁₁)	5
C₂×C₅²×D₁₃	11
C₂×C₅×AGL(1,𝔽₁₁)	13

Subgroups — C5×D13×AGL(1,𝔽11) #28384697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₃×AGL(1,𝔽₁₁) #28384697