Subgroups — #14522602

Order 2000.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#6045	C₂	1	2	yes	maximal
2	C₅×#6029	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅³	C₂²	1	1	yes	characteristic
4	C₅×#1039	—	2	2	no	—
5	#87776	—	5	2	no	maximal
6	#87775	—	5	1	no	maximal
7	C₂×C₅³	D₄	1	1	yes	characteristic
8	#6045	D₅	1	2	yes	—
9	C₅×Dic₁₀	—	5	2	no	—
10	C₅×Dic₁₀	—	5	2	no	—
11	C₅×Dic₁₀	—	10	4	no	—
12	#6029	D₅	1	1	yes	characteristic
13	C₅×#168	—	5	2	no	—
14	C₅×#168	—	10	2	no	—
15	C₅³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₅²	—	2	2	no	—
17	C₄×C₅²	—	2	4	no	—
18	C₄×C₅²	—	4	4	no	—
19	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
20	C₄×C₅²	C₂×D₅	1	2	yes	—
21	#1039	—	2	2	no	—
22	C₅×Dic₅	—	10	8	no	—
23	C₅×Dic₅	—	10	2	no	—
24	C₅×Dic₅	—	10	2	no	—
25	#689	—	25	2	no	—
26	Dic₂₀	—	25	1	no	—
27	C₂×C₅²	—	2	2	no	—
28	C₂×C₅²	—	2	4	no	—
29	C₂×C₅²	—	4	4	no	—
30	C₂×C₅²	D₂₀	1	1	yes	characteristic
31	C₂×C₅²	C₂²⋊D₅	1	2	yes	—
32	C₅×Q₈	—	25	2	no	—
33	Dic₁₀	—	5	2	no	—
34	Dic₁₀	—	5	2	no	—
35	Dic₁₀	—	10	4	no	—
36	C₅×C₈	—	25	1	no	—
37	#168	—	5	2	no	—
38	#168	—	10	2	no	—
39	C₅²	—	2	2	no	—
40	C₅²	—	2	4	no	—
41	C₅²	—	4	4	no	—
42	C₅²	Dic₂₀	1	1	yes	characteristic, complemented
43	C₅²	#689	1	2	yes	complemented
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	—	2	4	no	—
46	C₄×C₅	—	4	4	no	—
47	C₄×C₅	—	50	2	no	—
48	C₄×C₅	D₅²	1	1	yes	characteristic
49	C₄×C₅	D₅²	1	2	yes	—
50	Dic₅	—	10	8	no	—
51	Dic₅	—	10	2	no	—
52	Dic₅	—	10	2	no	—
53	Q₁₆	—	125	1	no	Sylow
54	C₂×C₅	—	2	2	no	—
55	C₂×C₅	—	2	4	no	—
56	C₂×C₅	—	4	4	no	—
57	C₂×C₅	#6037	1	1	yes	characteristic
58	C₂×C₅	#6038	1	2	yes	—
59	Q₈	—	25	2	no	—
60	C₈	—	25	1	no	—
61	C₅	—	2	2	no	—
62	C₅	—	2	4	no	—
63	C₅	—	4	4	no	—
64	C₅	#87775	1	1	yes	characteristic, complemented
65	C₅	#87776	1	2	yes	complemented
66	C₄	—	50	2	no	—
67	C₄	#92566	1	1	yes	characteristic
68	C₂	#11758757	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758757
commutator, Fitting, cosocle	C₄×C₅³	C₂²
Frattini, hypercenter	C₄	#92566
socle, prime radical	C₂×C₅³	D₄
hypocenter	C₅³	Q₁₆
LCS	G ▷ C₄×C₅³ ▷ C₂×C₅³ ▷ C₅³
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
15. C₅³	Q₁₆	semidirect
42. C₅²	Dic₂₀	semidirect
43. C₅²	#689	semidirect
64. C₅	#87775	semidirect
65. C₅	#87776	semidirect

Maximal subgroups

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

subgroup	index
C₅×#6045	2
C₅×#6029	2
#87776	5
#87775	5