Subgroups — C₅×C₂₉×C₁₁⋊AGL(1,𝔽₅) #44542075

Order 31900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₉×C₁₁⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₂₉×Dic₁₁	—	5	1	no	maximal
5	D₅×C₁₁×C₂₉	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₁₁×C₂₉	—	5	1	no	—
7	C₅×AGL(1,𝔽₅)×C₂₉	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₂₉	—	4	1	no	—
9	C₅×C₁₁×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
10	C₅×C₁₁×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	C₅×D₅×C₂₉	D₁₁	1	1	yes	characteristic
12	C₂₉×Dic₁₁	—	5	1	no	Hall
13	C₅×C₁₁⋊AGL(1,𝔽₅)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅²×C₂₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₂₉	—	5	1	no	—
16	AGL(1,𝔽₅)×C₂₉	—	11	1	no	—
17	C₄×C₅×C₂₉	—	55	1	no	—
18	C₅×D₅×C₁₁	C₂×C₂₉	1	1	yes	characteristic
19	C₁₁×C₂₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₂₉	—	5	1	no	—
21	D₅×C₂₉	C₅×D₁₁	1	1	yes	characteristic
22	C₅²×C₁₁	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
23	C₁₁⋊AGL(1,𝔽₅)	C₅×C₂₉	1	1	yes	characteristic, direct product factor
24	C₅×Dic₁₁	—	5	1	no	—
25	C₅×C₂₉	—	4	1	no	—
26	C₅×C₂₉	C₅×Dic₁₁	1	1	yes	characteristic, complemented
27	C₅×C₂₉	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
28	C₄×C₂₉	—	55	1	no	Hall
29	C₂×C₅×C₁₁	—	5	1	no	—
30	D₅×C₁₁	C₂×C₅×C₂₉	1	1	yes	characteristic
31	C₅×AGL(1,𝔽₅)	—	11	1	no	Hall
32	C₂×C₂₉	—	5	1	no	—
33	C₅×C₁₁	—	4	1	no	—
34	C₅×C₁₁	C₄×C₅×C₂₉	1	1	yes	characteristic, complemented
35	C₅×C₁₁	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented
36	C₅×D₅	D₁₁×C₂₉	1	1	yes	characteristic
37	Dic₁₁	—	5	1	no	Hall
38	C₂₉	C₅×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
39	C₅²	C₂₉×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₁	—	5	1	no	—
41	AGL(1,𝔽₅)	—	11	1	no	—
42	C₄×C₅	—	55	1	no	—
43	C₁₁	C₅×AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₅	—	5	1	no	—
45	D₅	C₅×D₁₁×C₂₉	1	1	yes	characteristic
46	C₅	—	4	1	no	—
47	C₅	C₅×C₂₉×Dic₁₁	1	1	yes	characteristic, complemented
48	C₅	C₂₉×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
49	C₄	—	55	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₂₉	C₁₁⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₁	C₄×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₉	C₄
prime radical	C₅×D₅×C₁₁×C₂₉	C₂
cosocle	D₅×C₁₁	C₂×C₅×C₂₉
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₅×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₂₉	C₄	semidirect
3. C₂₉×C₁₁⋊AGL(1,𝔽₅)	C₅	direct (N × H)
9. C₅×C₁₁×C₂₉	C₄×C₅	semidirect
10. C₅×C₁₁×C₂₉	AGL(1,𝔽₅)	semidirect
13. C₅×C₁₁⋊AGL(1,𝔽₅)	C₂₉	direct (N × H)
14. C₅²×C₂₉	Dic₁₁	semidirect
19. C₁₁×C₂₉	C₅×AGL(1,𝔽₅)	semidirect
22. C₅²×C₁₁	C₄×C₂₉	semidirect
23. C₁₁⋊AGL(1,𝔽₅)	C₅×C₂₉	direct (N × H)
26. C₅×C₂₉	C₅×Dic₁₁	semidirect
27. C₅×C₂₉	C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
34. C₅×C₁₁	C₄×C₅×C₂₉	semidirect
35. C₅×C₁₁	AGL(1,𝔽₅)×C₂₉	semidirect
38. C₂₉	C₅×C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
39. C₅²	C₂₉×Dic₁₁	semidirect
43. C₁₁	C₅×AGL(1,𝔽₅)×C₂₉	semidirect
47. C₅	C₅×C₂₉×Dic₁₁	semidirect
48. C₅	C₂₉×C₁₁⋊AGL(1,𝔽₅)	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×D₅×C₁₁×C₂₉	2
C₂₉×C₁₁⋊AGL(1,𝔽₅)	5
C₅×C₂₉×Dic₁₁	5
C₅×AGL(1,𝔽₅)×C₂₉	11
C₅×C₁₁⋊AGL(1,𝔽₅)	29

Subgroups — C5×C29×C11⋊AGL(1,𝔽5) #44542075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₉×C₁₁⋊AGL(1,𝔽₅) #44542075