Subgroups — C₅×#87837 #14522744

Order 2000.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#6037	C₂	1	2	yes	maximal, complemented
2	C₅×#6034	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₅	—	2	2	no	—
4	C₅×#1039	C₂²	1	1	yes	characteristic
5	#87837	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅³	D₄	1	1	yes	characteristic
7	C₅²×D₅	—	4	2	no	—
8	C₅×C₂²⋊D₅	—	10	2	no	—
9	#6037	C₂×C₅	1	2	yes	complemented
10	#6034	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×#170	—	10	1	no	—
12	C₅³	D₈	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₅²	—	10	2	no	—
14	C₂×C₅×D₅	—	2	2	no	—
15	C₂×C₅×D₅	—	2	2	no	—
16	C₂×C₅×D₅	—	4	4	no	—
17	#1039	C₂²×C₅	1	1	yes	characteristic
18	C₅×Dic₅	—	10	1	no	—
19	C₅×Dic₅	—	10	2	no	—
20	C₅×D₈	—	25	1	no	maximal
21	C₂×C₅²	—	2	2	no	—
22	C₂×C₅²	—	2	1	no	—
23	C₂×C₅²	—	4	4	no	—
24	C₂×C₅²	—	8	1	no	—
25	C₂×C₅²	—	20	2	no	—
26	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
27	C₅×D₅	—	4	2	no	—
28	C₅×D₅	—	4	8	no	—
29	C₅×D₅	—	4	2	no	—
30	C₅×D₄	—	25	2	no	—
31	C₂²⋊D₅	—	10	2	no	—
32	#170	—	10	1	no	—
33	C₅×C₈	—	25	1	no	—
34	C₅²	—	2	2	no	—
35	C₅²	—	2	1	no	—
36	C₅²	—	4	4	no	—
37	C₅²	—	8	1	no	—
38	C₅²	C₅×D₈	1	1	yes	characteristic, complemented
39	C₂²×C₅	—	10	2	no	—
40	C₂²×C₅	—	10	2	no	—
41	C₂²×C₅	—	20	4	no	—
42	C₂×D₅	—	2	2	no	—
43	C₄×C₅	—	25	1	no	—
44	Dic₅	—	10	1	no	—
45	Dic₅	—	10	2	no	—
46	D₈	—	25	1	no	Sylow
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	—	2	1	no	—
49	C₂×C₅	—	4	4	no	—
50	C₂×C₅	—	8	1	no	—
51	C₂×C₅	—	20	2	no	—
52	C₂×C₅	—	20	8	no	—
53	C₂×C₅	—	20	2	no	—
54	C₂×C₅	D₅²⋊C₂	1	1	yes	characteristic
55	D₅	—	4	2	no	—
56	D₄	—	25	2	no	—
57	C₈	—	25	1	no	—
58	C₅	—	2	2	no	—
59	C₅	—	2	1	no	—
60	C₅	—	4	4	no	—
61	C₅	—	8	1	no	—
62	C₅	#87837	1	1	yes	characteristic, direct product factor
63	C₂²	—	10	2	no	—
64	C₄	—	25	1	no	—
65	C₂	—	20	2	no	—
66	C₂	C₅×D₅²⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₅²⋊C₂
commutator, cosocle	#1039	C₂²×C₅
Frattini	C₂	C₅×D₅²⋊C₂
Fitting, socle	C₂×C₅³	D₄
hypocenter	C₅²	C₅×D₈
LCS	G ▷ #1039 ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#6037	C₂	semidirect
2. C₅×#6034	C₂	semidirect
5. #87837	C₅	direct (N × H)
9. #6037	C₂×C₅	semidirect
10. #6034	C₂×C₅	semidirect
12. C₅³	D₈	semidirect
38. C₅²	C₅×D₈	semidirect
62. C₅	#87837	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×#6037	2
C₅×#6034	2
#87837	5
C₅×D₈	25

Subgroups — C5×#87837 #14522744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87837 #14522744