Subgroups — C₄⋊AGL(1,ℤ/25) #14522326

Order 2000.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,ℤ/25)	C₂	1	2	yes	maximal
2	C₄×D₂₅⋊C₅	C₂	1	1	yes	maximal, characteristic
3	C₂×D₂₅⋊C₅	C₂²	1	1	yes	characteristic
4	AGL(1,ℤ/25)	—	2	2	no	—
5	C₄×5₋¹⁺²	C₄	1	1	yes	characteristic, complemented
6	Dic₂₅⋊C₅	C₄	1	1	yes	characteristic, complemented
7	C₅×C₄⋊AGL(1,𝔽₅)	—	5	1	no	maximal
8	C₄⋊#1035	C₅	1	1	yes	maximal, characteristic, complemented
9	C₂×5₋¹⁺²	C₂×C₄	1	1	yes	characteristic
10	D₂₅⋊C₅	D₄	1	1	yes	characteristic
11	D₂₅⋊C₅	Q₈	1	1	yes	characteristic
12	C₂×C₅×AGL(1,𝔽₅)	—	5	2	no	—
13	C₄×C₅×D₅	—	5	1	no	—
14	C₂×#1035	C₂×C₅	1	2	yes	—
15	C₄×D₂₅	C₂×C₅	1	1	yes	characteristic
16	5₋¹⁺²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅×D₅	—	5	1	no	—
18	C₅×AGL(1,𝔽₅)	—	10	2	no	—
19	C₄×C₅²	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₅×Dic₅	—	5	1	no	—
21	C₂×D₂₅	C₂²×C₅	1	1	yes	characteristic
22	#1035	—	2	2	no	—
23	C₄×C₂₅	—	4	1	no	—
24	C₄×C₂₅	C₄×C₅	1	1	yes	characteristic, complemented
25	Dic₂₅	C₄×C₅	1	1	yes	characteristic, complemented
26	C₄⋊AGL(1,𝔽₅)	—	5	1	no	—
27	C₅×C₄⋊C₄	—	25	1	no	—
28	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₅×D₅	—	5	1	no	—
30	C₅×D₅	—	5	1	no	—
31	C₂×C₂₅	—	4	1	no	—
32	C₂×C₂₅	C₂×C₄×C₅	1	1	yes	characteristic
33	D₂₅	C₅×D₄	1	1	yes	characteristic
34	D₂₅	C₅×Q₈	1	1	yes	characteristic
35	C₂×AGL(1,𝔽₅)	—	5	2	no	—
36	C₂×C₄×C₅	—	25	1	no	—
37	C₂×C₄×C₅	—	25	2	no	—
38	C₄×D₅	—	5	1	no	—
39	C₅²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₂₅	—	4	1	no	—
41	C₂₅	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented
42	C₂²×C₅	—	25	1	no	—
43	C₂×D₅	—	5	1	no	—
44	AGL(1,𝔽₅)	—	10	2	no	—
45	C₄×C₅	—	5	1	no	—
46	C₄×C₅	—	25	1	no	—
47	C₄×C₅	—	50	2	no	—
48	C₄×C₅	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
49	Dic₅	—	5	1	no	—
50	C₄⋊C₄	—	25	1	no	Sylow
51	C₂×C₅	—	5	1	no	—
52	C₂×C₅	—	25	1	no	—
53	C₂×C₅	—	25	1	no	—
54	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
55	D₅	—	5	1	no	—
56	D₅	—	5	1	no	—
57	C₂×C₄	—	25	1	no	—
58	C₂×C₄	—	25	2	no	—
59	C₅	—	5	1	no	—
60	C₅	C₅×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
61	C₂²	—	25	1	no	—
62	C₄	—	25	1	no	—
63	C₄	—	50	2	no	—
64	C₄	AGL(1,ℤ/25)	1	1	yes	characteristic, complemented
65	C₂	—	25	1	no	—
66	C₂	—	25	1	no	—
67	C₂	C₂×AGL(1,ℤ/25)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×AGL(1,ℤ/25)
commutator	C₂×C₂₅	C₂×C₄×C₅
Frattini, socle	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)
Fitting	C₄×5₋¹⁺²	C₄
prime radical	C₂×D₂₅⋊C₅	C₂²
cosocle	C₂×D₂₅	C₂²×C₅
hypercenter	C₄	AGL(1,ℤ/25)
hypocenter	C₂₅	C₅×C₄⋊C₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
5. C₄×5₋¹⁺²	C₄	semidirect
6. Dic₂₅⋊C₅	C₄	semidirect
8. C₄⋊#1035	C₅	semidirect
16. 5₋¹⁺²	C₄⋊C₄	semidirect
24. C₄×C₂₅	C₄×C₅	semidirect
25. Dic₂₅	C₄×C₅	semidirect
41. C₂₅	C₅×C₄⋊C₄	semidirect
64. C₄	AGL(1,ℤ/25)	semidirect

Maximal subgroups

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

subgroup	index
C₂×AGL(1,ℤ/25)	2
C₄×D₂₅⋊C₅	2
C₅×C₄⋊AGL(1,𝔽₅)	5
C₄⋊#1035	5

Subgroups — C4⋊AGL(1,ℤ/25) #14522326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊AGL(1,ℤ/25) #14522326