Subgroups — C₅×C₅₉×AGL(1,𝔽₁₁) #44570091

Order 32450.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊C₅×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₉×AGL(1,𝔽₁₁)	C₅	1	5	yes	maximal, direct product factor
3	C₅×D₁₁×C₅₉	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₁⋊C₅×C₅₉	C₂×C₅	1	5	yes	complemented
6	C₂×C₅²×C₅₉	—	11	1	no	maximal, Hall
7	C₅²×C₅₉	—	11	1	no	Hall
8	D₁₁×C₅₉	C₅²	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₅₉	—	11	5	no	—
11	C₂×C₅×C₅₉	—	11	1	no	—
12	C₅×AGL(1,𝔽₁₁)	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₅₉	—	11	5	no	—
14	C₅×C₅₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
15	C₅×C₁₁⋊C₅	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅₉	—	11	1	no	Hall
17	C₅×D₁₁	C₅×C₅₉	1	1	yes	characteristic, complemented
18	AGL(1,𝔽₁₁)	C₅×C₅₉	1	5	yes	direct product factor
19	C₅₉	C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×C₁₁	C₂×C₅×C₅₉	1	1	yes	characteristic, complemented
21	C₁₁⋊C₅	C₂×C₅×C₅₉	1	5	yes	complemented
22	C₂×C₅²	—	11	1	no	Hall
23	C₅²	—	11	1	no	Sylow
24	D₁₁	C₅²×C₅₉	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₂×C₅²×C₅₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	11	5	no	—
27	C₂×C₅	—	11	1	no	—
28	C₅	—	11	5	no	—
29	C₅	C₅₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₅₉	AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁	C₂×C₅²×C₅₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₅₉	C₂×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁⋊C₅×C₅₉	C₂	semidirect
2. C₅₉×AGL(1,𝔽₁₁)	C₅	direct (N × H)
3. C₅×D₁₁×C₅₉	C₅	semidirect
4. C₅×C₁₁×C₅₉	C₂×C₅	semidirect
5. C₁₁⋊C₅×C₅₉	C₂×C₅	semidirect
8. D₁₁×C₅₉	C₅²	semidirect
9. C₁₁×C₅₉	C₂×C₅²	semidirect
12. C₅×AGL(1,𝔽₁₁)	C₅₉	direct (N × H)
14. C₅×C₅₉	AGL(1,𝔽₁₁)	direct (N × H)
15. C₅×C₁₁⋊C₅	C₂×C₅₉	semidirect
17. C₅×D₁₁	C₅×C₅₉	semidirect
18. AGL(1,𝔽₁₁)	C₅×C₅₉	direct (N × H)
19. C₅₉	C₅×AGL(1,𝔽₁₁)	direct (N × H)
20. C₅×C₁₁	C₂×C₅×C₅₉	semidirect
21. C₁₁⋊C₅	C₂×C₅×C₅₉	semidirect
24. D₁₁	C₅²×C₅₉	semidirect
25. C₁₁	C₂×C₅²×C₅₉	semidirect
29. C₅	C₅₉×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×C₅₉	2
C₅₉×AGL(1,𝔽₁₁)	5
C₅×D₁₁×C₅₉	5
C₂×C₅²×C₅₉	11
C₅×AGL(1,𝔽₁₁)	59

Subgroups — C5×C59×AGL(1,𝔽11) #44570091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₅₉×AGL(1,𝔽₁₁) #44570091