Subgroups — C₅×D₃₁×AGL(1,𝔽₁₁) #46802065

Order 34100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊C₅×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×(C₁₁⋊C₅)⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₁×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₁×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×D₁₁×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented
6	D₃₁×AGL(1,𝔽₁₁)	C₅	1	5	yes	maximal, direct product factor
7	(C₁₁⋊C₅)⋊D₃₁	C₂×C₅	1	5	yes	complemented
8	C₃₁×AGL(1,𝔽₁₁)	C₂×C₅	1	5	yes	complemented
9	C₁₁⋊C₅×D₃₁	C₂×C₅	1	5	yes	complemented
10	C₅×D₃₄₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×D₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×C₁₁×D₃₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅²×D₃₁	—	11	1	no	maximal, Hall
14	C₅×C₁₁×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
15	C₃₁×C₁₁⋊C₅	C₂²×C₅	1	5	yes	complemented
16	C₂×C₅²×C₃₁	—	11	1	no	—
17	C₅²×D₃₁	—	11	1	no	—
18	C₅²×D₃₁	—	11	1	no	—
19	D₁₁×D₃₁	C₅²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
21	C₅²×C₃₁	—	11	1	no	Hall
22	D₃₄₁	C₂×C₅²	1	1	yes	characteristic, complemented
23	C₁₁×D₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
24	D₁₁×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
25	C₂×C₅×D₃₁	—	11	5	no	—
26	C₂×C₅×D₃₁	—	11	1	no	—
27	C₂×C₅×C₁₁⋊C₅	—	31	1	no	—
28	C₅×AGL(1,𝔽₁₁)	—	31	1	no	—
29	C₅×AGL(1,𝔽₁₁)	D₃₁	1	1	yes	characteristic, direct product factor
30	C₁₁×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₃₁	—	11	5	no	—
32	C₂×C₅×C₃₁	—	11	1	no	—
33	C₅×D₃₁	—	11	5	no	—
34	C₅×D₃₁	—	11	1	no	—
35	C₅×D₃₁	—	11	5	no	—
36	C₅×D₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
37	C₅×C₁₁⋊C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅×D₁₁	—	31	1	no	—
39	C₂×AGL(1,𝔽₁₁)	—	31	5	no	—
40	C₅×C₃₁	—	11	5	no	—
41	C₅×C₃₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
42	C₂×D₃₁	—	11	1	no	Hall
43	C₂×C₅×C₁₁	—	31	1	no	—
44	C₅×D₁₁	—	31	1	no	—
45	C₅×D₁₁	C₅×D₃₁	1	1	yes	characteristic, complemented
46	C₂×C₁₁⋊C₅	—	31	5	no	—
47	AGL(1,𝔽₁₁)	—	31	5	no	—
48	AGL(1,𝔽₁₁)	C₅×D₃₁	1	5	yes	direct product factor
49	C₂²×C₅²	—	341	1	no	Hall
50	C₂×C₃₁	—	11	1	no	—
51	D₃₁	—	11	1	no	—
52	D₃₁	C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
53	C₅×C₁₁	C₂×C₅×D₃₁	1	1	yes	characteristic, complemented
54	C₁₁⋊C₅	C₂×C₅×D₃₁	1	5	yes	complemented
55	C₂×C₅²	—	11	1	no	—
56	C₂×C₅²	—	341	1	no	—
57	C₂×C₅²	—	341	1	no	—
58	C₂×D₁₁	—	31	1	no	Hall
59	C₃₁	C₂×C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
60	C₅²	—	11	1	no	Sylow
61	C₂×C₁₁	—	31	1	no	—
62	D₁₁	—	31	1	no	—
63	D₁₁	C₅²×D₃₁	1	1	yes	characteristic, complemented
64	C₂²×C₅	—	341	1	no	—
65	C₂²×C₅	—	341	5	no	—
66	C₁₁	C₂×C₅²×D₃₁	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	11	5	no	—
68	C₂×C₅	—	11	1	no	—
69	C₂×C₅	—	31	1	no	—
70	C₂×C₅	—	341	5	no	—
71	C₂×C₅	—	341	5	no	—
72	C₂×C₅	—	341	1	no	—
73	C₅	—	11	5	no	—
74	C₅	D₃₁×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
75	C₂²	—	341	1	no	Sylow
76	C₂	—	11	1	no	—
77	C₂	—	31	1	no	—
78	C₂	—	341	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃₁×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁×C₃₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₃₁	C₂²×C₅
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁⋊C₅×D₃₁	C₂	semidirect
2. C₅×(C₁₁⋊C₅)⋊D₃₁	C₂	semidirect
3. C₅×C₃₁×AGL(1,𝔽₁₁)	C₂	semidirect
4. C₅×C₃₁×C₁₁⋊C₅	C₂²	semidirect
5. C₅×D₁₁×D₃₁	C₅	semidirect
6. D₃₁×AGL(1,𝔽₁₁)	C₅	direct (N × H)
7. (C₁₁⋊C₅)⋊D₃₁	C₂×C₅	semidirect
8. C₃₁×AGL(1,𝔽₁₁)	C₂×C₅	semidirect
9. C₁₁⋊C₅×D₃₁	C₂×C₅	semidirect
10. C₅×D₃₄₁	C₂×C₅	semidirect
11. C₅×D₁₁×C₃₁	C₂×C₅	semidirect
12. C₅×C₁₁×D₃₁	C₂×C₅	semidirect
14. C₅×C₁₁×C₃₁	C₂²×C₅	semidirect
15. C₃₁×C₁₁⋊C₅	C₂²×C₅	semidirect
19. D₁₁×D₃₁	C₅²	semidirect
22. D₃₄₁	C₂×C₅²	semidirect
23. C₁₁×D₃₁	C₂×C₅²	semidirect
24. D₁₁×C₃₁	C₂×C₅²	semidirect
29. C₅×AGL(1,𝔽₁₁)	D₃₁	direct (N × H)
30. C₁₁×C₃₁	C₂²×C₅²	semidirect
36. C₅×D₃₁	AGL(1,𝔽₁₁)	direct (N × H)
37. C₅×C₁₁⋊C₅	C₂×D₃₁	semidirect
41. C₅×C₃₁	C₂×AGL(1,𝔽₁₁)	semidirect
45. C₅×D₁₁	C₅×D₃₁	semidirect
48. AGL(1,𝔽₁₁)	C₅×D₃₁	direct (N × H)
52. D₃₁	C₅×AGL(1,𝔽₁₁)	direct (N × H)
53. C₅×C₁₁	C₂×C₅×D₃₁	semidirect
54. C₁₁⋊C₅	C₂×C₅×D₃₁	semidirect
59. C₃₁	C₂×C₅×AGL(1,𝔽₁₁)	semidirect
63. D₁₁	C₅²×D₃₁	semidirect
66. C₁₁	C₂×C₅²×D₃₁	semidirect
74. C₅	D₃₁×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×C₁₁⋊C₅×D₃₁	2
C₅×(C₁₁⋊C₅)⋊D₃₁	2
C₅×C₃₁×AGL(1,𝔽₁₁)	2
C₅×D₁₁×D₃₁	5
D₃₁×AGL(1,𝔽₁₁)	5
C₂×C₅²×D₃₁	11
C₂×C₅×AGL(1,𝔽₁₁)	31

Subgroups — C5×D31×AGL(1,𝔽11) #46802065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₁×AGL(1,𝔽₁₁) #46802065