Subgroups — C₅×#87800 #14522624

Order 2000.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic
2	C₅×#6045	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₅⋊D₅	—	2	1	no	—
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	C₅×#1039	—	2	1	no	—
7	#87800	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×#677	—	5	6	no	maximal
9	C₂×C₅³	D₄	1	1	yes	characteristic
10	C₅×C₅⋊D₅	—	4	1	no	—
11	C₄⋊(C₅⋊D₅)	C₂×C₅	1	1	yes	characteristic
12	#6045	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₂₀	—	5	6	no	—
14	C₅×Dic₁₀	—	5	6	no	—
15	C₅²×C₈	—	2	12	no	—
16	C₅²×C₈	D₅	1	6	yes	complemented
17	C₅²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅⋊D₅	—	2	1	no	—
20	C₂×C₅×D₅	—	10	6	no	—
21	C₄×C₅²	—	2	12	no	—
22	C₄×C₅²	C₂×D₅	1	6	yes	—
23	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
24	#1039	—	2	1	no	—
25	C₅×Dic₅	—	10	6	no	—
26	C₅×SD₁₆	—	25	1	no	—
27	#677	—	5	6	no	—
28	C₂×C₅²	—	2	12	no	—
29	C₂×C₅²	D₂₀	1	6	yes	—
30	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
31	C₅⋊D₅	—	4	1	no	—
32	C₅×D₅	—	20	6	no	—
33	C₅×Q₈	—	25	1	no	—
34	C₅×D₄	—	25	1	no	—
35	D₂₀	—	5	6	no	—
36	Dic₁₀	—	5	6	no	—
37	C₅×C₈	—	2	12	no	—
38	C₅×C₈	C₅×D₅	1	6	yes	complemented
39	C₅×C₈	C₅⋊D₅	1	1	yes	characteristic, complemented
40	C₅²	—	2	12	no	—
41	C₅²	#677	1	6	yes	complemented
42	C₅²	C₅×SD₁₆	1	1	yes	characteristic, complemented
43	C₂²×C₅	—	50	1	no	—
44	C₂×D₅	—	10	6	no	—
45	C₄×C₅	—	2	12	no	—
46	C₄×C₅	—	50	1	no	—
47	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
48	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
49	Dic₅	—	10	6	no	—
50	SD₁₆	—	25	1	no	Sylow
51	C₂×C₅	—	2	12	no	—
52	C₂×C₅	—	100	1	no	—
53	C₂×C₅	C₅×D₂₀	1	6	yes	—
54	C₂×C₅	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
55	D₅	—	20	6	no	—
56	Q₈	—	25	1	no	—
57	D₄	—	25	1	no	—
58	C₈	C₅×C₅⋊D₅	1	1	yes	characteristic, complemented
59	C₅	—	2	12	no	—
60	C₅	C₅×#677	1	6	yes	complemented
61	C₅	#87800	1	1	yes	characteristic, direct product factor
62	C₂²	—	50	1	no	—
63	C₄	—	50	1	no	—
64	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
65	C₂	—	100	1	no	—
66	C₂	C₅×C₄⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₄⋊(C₅⋊D₅)
commutator, cosocle	C₄×C₅²	C₂²×C₅
Frattini	C₄	C₂×C₅×C₅⋊D₅
Fitting	C₅³×C₈	C₂
socle	C₂×C₅³	D₄
prime radical	C₅×C₄⋊(C₅⋊D₅)	C₂
hypercenter	C₅×C₈	C₅⋊D₅
hypocenter	C₅²	C₅×SD₁₆
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#6045	C₂	semidirect
3. C₅³×C₈	C₂	semidirect
7. #87800	C₅	direct (N × H)
12. #6045	C₂×C₅	semidirect
16. C₅²×C₈	D₅	semidirect
17. C₅²×C₈	C₂×C₅	semidirect
18. C₅³	SD₁₆	semidirect
38. C₅×C₈	C₅×D₅	semidirect
39. C₅×C₈	C₅⋊D₅	semidirect
41. C₅²	#677	semidirect
42. C₅²	C₅×SD₁₆	semidirect
58. C₈	C₅×C₅⋊D₅	semidirect
60. C₅	C₅×#677	semidirect
61. C₅	#87800	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×C₄⋊(C₅⋊D₅)	2
C₅×#6045	2
C₅³×C₈	2
#87800	5
C₅×#677	5

Subgroups — C5×#87800 #14522624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87800 #14522624