Subgroups — #14522360

Order 2000.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅⋊D₂₅	C₂	1	1	yes	maximal, characteristic
2	#11758646	C₂	1	2	yes	maximal, complemented
3	C₂×C₅⋊D₂₅	C₄	1	1	yes	characteristic
4	C₄×C₅×C₂₅	C₄	1	1	yes	characteristic
5	#92524	C₂²	1	1	yes	characteristic
6	#87855	—	5	1	no	maximal
7	D₂₅⋊C₈	—	5	5	no	maximal
8	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₅⋊D₂₅	C₈	1	2	yes	complemented
10	C₄×C₅⋊D₅	—	5	1	no	—
11	#6033	—	5	2	no	—
12	C₄×D₂₅	—	5	5	no	—
13	#6016	—	5	10	no	—
14	C₅×C₂₅	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅⋊D₅	—	5	1	no	—
16	C₄×C₅²	AGL(1,𝔽₅)	1	1	yes	characteristic
17	#1039	—	5	1	no	—
18	C₂×D₂₅	—	5	5	no	—
19	C₄×C₂₅	AGL(1,𝔽₅)	1	5	yes	—
20	Dic₂₅	—	5	5	no	—
21	D₅⋊C₈	—	25	5	no	—
22	D₅⋊C₈	—	25	1	no	—
23	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₅⋊D₅	—	5	2	no	—
25	C₂×C₂₅	C₂×AGL(1,𝔽₅)	1	5	yes	—
26	D₂₅	—	5	10	no	—
27	C₄×D₅	—	25	5	no	—
28	C₄×D₅	—	25	1	no	—
29	#170	—	25	2	no	—
30	#170	—	25	10	no	—
31	C₅²	D₅⋊C₈	1	1	yes	characteristic
32	C₂₅	D₅⋊C₈	1	5	yes	complemented
33	C₂×D₅	—	25	5	no	—
34	C₂×D₅	—	25	1	no	—
35	C₄×C₅	#1035	1	5	yes	—
36	C₄×C₅	#1043	1	1	yes	characteristic
37	Dic₅	—	25	5	no	—
38	Dic₅	—	25	1	no	—
39	C₂×C₈	—	125	1	no	Sylow
40	C₂×C₅	C₂×#1035	1	5	yes	—
41	C₂×C₅	C₂×#1043	1	1	yes	characteristic
42	D₅	—	25	2	no	—
43	D₅	—	25	10	no	—
44	C₂×C₄	—	125	1	no	—
45	C₈	—	125	2	no	—
46	C₅	D₂₅⋊C₈	1	5	yes	complemented
47	C₅	#87855	1	1	yes	characteristic
48	C₂²	—	125	1	no	—
49	C₄	—	125	1	no	—
50	C₄	#92536	1	1	yes	characteristic
51	C₂	—	125	2	no	—
52	C₂	C₂×#92536	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#92536
commutator, hypocenter	C₅×C₂₅	C₂×C₈
Frattini	C₂×C₅	C₂×#1043
Fitting	C₄×C₅×C₂₅	C₄
socle	C₂×C₅²	C₂×AGL(1,𝔽₅)
prime radical	C₂×C₅⋊D₂₅	C₄
cosocle	#92524	C₂²
LCS	G ▷ C₅×C₂₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. #11758646	C₂	semidirect
9. C₅⋊D₂₅	C₈	semidirect
14. C₅×C₂₅	C₂×C₈	semidirect
32. C₂₅	D₅⋊C₈	semidirect
46. C₅	D₂₅⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅⋊D₂₅	2
#11758646	2
#87855	5
D₂₅⋊C₈	5