Subgroups — C₅×#87860 #14522793

Order 2000.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1039	C₂	1	1	yes	maximal, characteristic
2	C₅×#6033	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅³	C₄	1	1	yes	characteristic
4	C₅×#1039	C₄	1	1	yes	characteristic
5	C₅×#1039	C₂²	1	1	yes	characteristic
6	#87860	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×#704	—	5	6	no	maximal
8	C₂×C₅³	—	2	1	no	—
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₂×#1039	C₂×C₅	1	1	yes	characteristic
11	C₂×C₅×Dic₅	—	5	6	no	—
12	#6033	C₂×C₅	1	2	yes	complemented
13	C₅×#170	—	5	12	no	—
14	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅²	—	4	6	no	—
16	C₂²×C₅²	C₄×C₅	1	1	yes	characteristic
17	C₂²×C₅²	AGL(1,𝔽₅)	1	6	yes	—
18	#1039	C₄×C₅	1	1	yes	characteristic
19	#1039	C₂²×C₅	1	1	yes	characteristic
20	C₅×Dic₅	—	5	6	no	—
21	C₅×Dic₅	—	5	6	no	—
22	#704	—	5	6	no	—
23	C₅×M₁₆	—	25	1	no	—
24	C₂×C₅²	—	2	1	no	—
25	C₂×C₅²	—	2	6	no	—
26	C₂×C₅²	—	4	12	no	—
27	C₂×C₅²	—	4	6	no	—
28	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
29	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	6	yes	—
30	C₂×C₄×C₅	—	25	1	no	—
31	C₂×Dic₅	—	5	6	no	—
32	#170	—	5	12	no	—
33	C₅×C₈	—	25	2	no	—
34	C₅²	—	4	6	no	—
35	C₅²	C₅×M₁₆	1	1	yes	characteristic, complemented
36	C₅²	#704	1	6	yes	complemented
37	C₂²×C₅	—	4	6	no	—
38	C₂²×C₅	C₅×AGL(1,𝔽₅)	1	6	yes	—
39	C₂²×C₅	#1043	1	1	yes	characteristic
40	C₄×C₅	—	25	1	no	—
41	C₄×C₅	—	25	1	no	—
42	Dic₅	—	5	6	no	—
43	Dic₅	—	5	6	no	—
44	M₁₆	—	25	1	no	Sylow
45	C₂×C₅	—	2	6	no	—
46	C₂×C₅	—	2	1	no	—
47	C₂×C₅	—	4	12	no	—
48	C₂×C₅	—	4	6	no	—
49	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	6	yes	—
50	C₂×C₅	C₂×#1043	1	1	yes	characteristic
51	C₂×C₄	—	25	1	no	—
52	C₈	—	25	2	no	—
53	C₅	—	4	6	no	—
54	C₅	C₅×#704	1	6	yes	complemented
55	C₅	#87860	1	1	yes	characteristic, direct product factor
56	C₂²	C₅×#1043	1	1	yes	characteristic
57	C₄	—	25	1	no	—
58	C₄	—	25	1	no	—
59	C₂	—	2	1	no	—
60	C₂	C₂×C₅×#1043	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#1043
commutator	C₂×C₅²	C₂×C₄×C₅
Frattini	C₂	C₂×C₅×#1043
Fitting, prime radical	C₂²×C₅³	C₄
socle	C₂×C₅³	C₂×C₄
cosocle	#1039	C₂²×C₅
hypercenter	C₂²×C₅	#1043
hypocenter	C₅²	C₅×M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#6033	C₂	semidirect
6. #87860	C₅	direct (N × H)
12. #6033	C₂×C₅	semidirect
14. C₅³	M₁₆	semidirect
35. C₅²	C₅×M₁₆	semidirect
36. C₅²	#704	semidirect
54. C₅	C₅×#704	semidirect
55. C₅	#87860	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#1039	2
C₅×#6033	2
#87860	5
C₅×#704	5

Subgroups — C5×#87860 #14522793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87860 #14522793