Subgroups — #14522600

Order 2000.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊(C₅⋊D₅)	C₂	1	2	yes	maximal, complemented
2	C₅×#6029	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₅⋊D₅	—	2	2	no	—
4	C₄×C₅³	C₂²	1	1	yes	characteristic
5	#87771	—	5	2	no	maximal
6	#87770	—	5	1	no	maximal
7	C₂×C₅³	D₄	1	1	yes	characteristic
8	C₅×C₅⋊D₅	—	4	2	no	—
9	C₄⋊(C₅⋊D₅)	D₅	1	2	yes	complemented
10	C₅×D₂₀	—	5	2	no	—
11	C₅×D₂₀	—	5	2	no	—
12	C₅×D₂₀	—	10	4	no	—
13	#6029	D₅	1	1	yes	characteristic, complemented
14	C₅×#168	—	5	2	no	—
15	C₅×#168	—	10	2	no	—
16	C₅³	D₈	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅⋊D₅	—	2	2	no	—
18	C₂×C₅×D₅	—	10	8	no	—
19	C₂×C₅×D₅	—	10	2	no	—
20	C₂×C₅×D₅	—	10	2	no	—
21	C₄×C₅²	—	2	2	no	—
22	C₄×C₅²	—	2	4	no	—
23	C₄×C₅²	—	4	4	no	—
24	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
25	C₄×C₅²	C₂×D₅	1	2	yes	—
26	#686	—	25	2	no	—
27	D₄₀	—	25	1	no	—
28	C₂×C₅²	—	2	2	no	—
29	C₂×C₅²	—	2	4	no	—
30	C₂×C₅²	—	4	4	no	—
31	C₂×C₅²	D₂₀	1	1	yes	characteristic
32	C₂×C₅²	C₂²⋊D₅	1	2	yes	—
33	C₅⋊D₅	—	4	2	no	—
34	C₅×D₅	—	20	8	no	—
35	C₅×D₅	—	20	2	no	—
36	C₅×D₅	—	20	2	no	—
37	C₅×D₄	—	25	2	no	—
38	D₂₀	—	5	2	no	—
39	D₂₀	—	5	2	no	—
40	D₂₀	—	10	4	no	—
41	C₅×C₈	—	25	1	no	—
42	#168	—	5	2	no	—
43	#168	—	10	2	no	—
44	C₅²	—	2	2	no	—
45	C₅²	—	2	4	no	—
46	C₅²	—	4	4	no	—
47	C₅²	D₄₀	1	1	yes	characteristic, complemented
48	C₅²	#686	1	2	yes	complemented
49	C₂²×C₅	—	50	2	no	—
50	C₂×D₅	—	10	8	no	—
51	C₂×D₅	—	10	2	no	—
52	C₂×D₅	—	10	2	no	—
53	C₄×C₅	—	2	2	no	—
54	C₄×C₅	—	2	4	no	—
55	C₄×C₅	—	4	4	no	—
56	C₄×C₅	D₅²	1	1	yes	characteristic
57	C₄×C₅	D₅²	1	2	yes	—
58	D₈	—	125	1	no	Sylow
59	C₂×C₅	—	2	2	no	—
60	C₂×C₅	—	2	4	no	—
61	C₂×C₅	—	4	4	no	—
62	C₂×C₅	—	100	2	no	—
63	C₂×C₅	#6037	1	1	yes	characteristic
64	C₂×C₅	#6038	1	2	yes	—
65	D₅	—	20	8	no	—
66	D₅	—	20	2	no	—
67	D₅	—	20	2	no	—
68	D₄	—	25	2	no	—
69	C₈	—	25	1	no	—
70	C₅	—	2	4	no	—
71	C₅	—	2	2	no	—
72	C₅	—	4	4	no	—
73	C₅	#87770	1	1	yes	characteristic, complemented
74	C₅	#87771	1	2	yes	complemented
75	C₂²	—	50	2	no	—
76	C₄	#92566	1	1	yes	characteristic
77	C₂	—	100	2	no	—
78	C₂	#11758757	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758757
commutator, Fitting, cosocle	C₄×C₅³	C₂²
Frattini, hypercenter	C₄	#92566
socle	C₂×C₅³	D₄
hypocenter	C₅³	D₈
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
1. C₅×C₄⋊(C₅⋊D₅)	C₂	semidirect
2. C₅×#6029	C₂	semidirect
9. C₄⋊(C₅⋊D₅)	D₅	semidirect
13. #6029	D₅	semidirect
16. C₅³	D₈	semidirect
47. C₅²	D₄₀	semidirect
48. C₅²	#686	semidirect
73. C₅	#87770	semidirect
74. C₅	#87771	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₄⋊(C₅⋊D₅)	2
C₅×#6029	2
#87771	5
#87770	5