Subgroups — C₁₃×D₁₁×AGL(1,𝔽₁₁) #44538166

Order 31460.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×(C₁₁⋊C₅)⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₃×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₁₁²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₁×C₁₃×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₁₁×C₁₃×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×C₁₃×D₁₁	—	11	1	no	maximal
10	C₂×C₁₃×AGL(1,𝔽₁₁)	—	11	1	no	maximal
11	D₁₁×AGL(1,𝔽₁₁)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₁²×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₁₁×C₁₃	—	11	1	no	—
14	C₅×C₁₃×D₁₁	—	11	1	no	—
15	C₅×C₁₃×D₁₁	—	11	1	no	—
16	C₂×C₁₃×C₁₁⋊C₅	—	11	1	no	—
17	C₁₃×AGL(1,𝔽₁₁)	—	11	1	no	—
18	C₁₃×AGL(1,𝔽₁₁)	D₁₁	1	1	yes	characteristic, direct product factor
19	D₁₁×C₁₁⋊C₅	C₂×C₁₃	1	1	yes	characteristic, complemented
20	(C₁₁⋊C₅)⋊D₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₁₁×AGL(1,𝔽₁₁)	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₅×C₁₁×C₁₃	—	11	1	no	—
23	C₁₃×C₁₁⋊C₅	C₂×D₁₁	1	1	yes	characteristic, complemented
24	C₁₁×C₁₁⋊C₅	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₃×D₁₁	—	11	1	no	—
26	C₂×C₁₃×D₁₁	—	11	1	no	—
27	D₁₁²	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₁×C₁₃	—	11	1	no	—
29	C₂×C₁₁×C₁₃	—	11	1	no	—
30	C₁₃×D₁₁	—	11	1	no	—
31	C₁₃×D₁₁	—	11	1	no	—
32	C₁₃×D₁₁	—	110	1	no	—
33	C₁₃×D₁₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
34	C₁₃×D₁₁	C₅×D₁₁	1	1	yes	characteristic, complemented
35	C₂²×C₅×C₁₃	—	121	1	no	Hall
36	C₁₁⋊D₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
37	C₁₁×D₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
38	C₁₁×D₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
39	C₂×C₅×D₁₁	—	11	1	no	—
40	C₂×AGL(1,𝔽₁₁)	—	11	1	no	—
41	C₁₁×C₁₃	—	10	1	no	—
42	C₁₁×C₁₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
43	C₁₁×C₁₃	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented
44	C₂×C₅×C₁₃	—	11	1	no	—
45	C₂×C₅×C₁₃	—	121	1	no	—
46	C₂×C₅×C₁₃	—	121	1	no	—
47	C₁₁²	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅×C₁₁	—	11	1	no	—
49	C₅×D₁₁	—	11	1	no	—
50	C₅×D₁₁	—	11	1	no	—
51	C₂×C₁₁⋊C₅	—	11	1	no	—
52	AGL(1,𝔽₁₁)	—	11	1	no	—
53	AGL(1,𝔽₁₁)	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
54	C₅×C₁₃	—	11	1	no	Hall
55	C₅×C₁₁	—	11	1	no	—
56	C₁₁⋊C₅	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented
57	C₂²×C₁₃	—	121	1	no	Hall
58	C₂×D₁₁	—	11	1	no	—
59	C₂×D₁₁	—	11	1	no	—
60	C₂×C₁₃	—	11	1	no	—
61	C₂×C₁₃	—	11	1	no	—
62	C₂×C₁₃	—	121	1	no	—
63	C₂×C₁₁	—	11	1	no	—
64	C₂×C₁₁	—	11	1	no	—
65	D₁₁	—	11	1	no	—
66	D₁₁	—	11	1	no	—
67	D₁₁	—	110	1	no	—
68	D₁₁	C₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
69	D₁₁	C₅×C₁₃×D₁₁	1	1	yes	characteristic, complemented
70	C₂²×C₅	—	121	1	no	Hall
71	C₁₃	D₁₁×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
72	C₁₁	—	10	1	no	—
73	C₁₁	C₂×C₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
74	C₁₁	C₂×C₅×C₁₃×D₁₁	1	1	yes	characteristic, complemented
75	C₂×C₅	—	11	1	no	—
76	C₂×C₅	—	121	1	no	—
77	C₂×C₅	—	121	1	no	—
78	C₅	—	11	1	no	Sylow
79	C₂²	—	121	1	no	Sylow
80	C₂	—	11	1	no	—
81	C₂	—	11	1	no	—
82	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₁₁×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁²	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁²×C₁₃	C₂²×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₁×C₁₁⋊C₅	C₂	semidirect
2. C₁₃×(C₁₁⋊C₅)⋊D₁₁	C₂	semidirect
3. C₁₁×C₁₃×AGL(1,𝔽₁₁)	C₂	semidirect
4. C₁₁×C₁₃×C₁₁⋊C₅	C₂²	semidirect
5. C₁₃×D₁₁²	C₅	semidirect
6. C₁₃×C₁₁⋊D₁₁	C₂×C₅	semidirect
7. C₁₁×C₁₃×D₁₁	C₂×C₅	semidirect
8. C₁₁×C₁₃×D₁₁	C₂×C₅	semidirect
11. D₁₁×AGL(1,𝔽₁₁)	C₁₃	direct (N × H)
12. C₁₁²×C₁₃	C₂²×C₅	semidirect
18. C₁₃×AGL(1,𝔽₁₁)	D₁₁	direct (N × H)
19. D₁₁×C₁₁⋊C₅	C₂×C₁₃	semidirect
20. (C₁₁⋊C₅)⋊D₁₁	C₂×C₁₃	semidirect
21. C₁₁×AGL(1,𝔽₁₁)	C₂×C₁₃	semidirect
23. C₁₃×C₁₁⋊C₅	C₂×D₁₁	semidirect
24. C₁₁×C₁₁⋊C₅	C₂²×C₁₃	semidirect
27. D₁₁²	C₅×C₁₃	semidirect
33. C₁₃×D₁₁	AGL(1,𝔽₁₁)	direct (N × H)
34. C₁₃×D₁₁	C₅×D₁₁	semidirect
36. C₁₁⋊D₁₁	C₂×C₅×C₁₃	semidirect
37. C₁₁×D₁₁	C₂×C₅×C₁₃	semidirect
38. C₁₁×D₁₁	C₂×C₅×C₁₃	semidirect
42. C₁₁×C₁₃	C₂×AGL(1,𝔽₁₁)	semidirect
43. C₁₁×C₁₃	C₂×C₅×D₁₁	semidirect
47. C₁₁²	C₂²×C₅×C₁₃	semidirect
53. AGL(1,𝔽₁₁)	C₁₃×D₁₁	direct (N × H)
56. C₁₁⋊C₅	C₂×C₁₃×D₁₁	semidirect
68. D₁₁	C₁₃×AGL(1,𝔽₁₁)	direct (N × H)
69. D₁₁	C₅×C₁₃×D₁₁	semidirect
71. C₁₃	D₁₁×AGL(1,𝔽₁₁)	direct (N × H)
73. C₁₁	C₂×C₁₃×AGL(1,𝔽₁₁)	semidirect
74. C₁₁	C₂×C₅×C₁₃×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₁₁×C₁₁⋊C₅	2
C₁₃×(C₁₁⋊C₅)⋊D₁₁	2
C₁₁×C₁₃×AGL(1,𝔽₁₁)	2
C₁₃×D₁₁²	5
C₂×C₅×C₁₃×D₁₁	11
C₂×C₁₃×AGL(1,𝔽₁₁)	11
D₁₁×AGL(1,𝔽₁₁)	13

Subgroups — C13×D11×AGL(1,𝔽11) #44538166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₁₁×AGL(1,𝔽₁₁) #44538166