Subgroups — C₅×#87802 #14522626

Order 2000.

240 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	C₅³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅³	C₂²	1	1	yes	characteristic
4	C₅×#1039	—	2	2	no	—
5	#87802	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×Dic₂₀	—	5	6	no	maximal
7	C₂×C₅³	D₄	1	1	yes	characteristic
8	#6045	C₂×C₅	1	2	yes	—
9	C₅×Dic₁₀	—	5	12	no	—
10	C₅²×C₈	—	2	12	no	—
11	C₅²×C₈	D₅	1	6	yes	—
12	C₅²×C₈	C₂×C₅	1	1	yes	characteristic
13	C₅³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₅²	—	2	12	no	—
15	C₄×C₅²	C₂×D₅	1	6	yes	—
16	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
17	#1039	—	2	2	no	—
18	C₅×Dic₅	—	10	12	no	—
19	C₅×Q₁₆	—	25	1	no	—
20	Dic₂₀	—	5	6	no	—
21	C₂×C₅²	—	2	12	no	—
22	C₂×C₅²	D₂₀	1	6	yes	—
23	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
24	C₅×Q₈	—	25	2	no	—
25	Dic₁₀	—	5	12	no	—
26	C₅×C₈	—	2	12	no	—
27	C₅×C₈	C₅×D₅	1	6	yes	—
28	C₅×C₈	C₅⋊D₅	1	1	yes	characteristic
29	C₅²	—	2	12	no	—
30	C₅²	Dic₂₀	1	6	yes	complemented
31	C₅²	C₅×Q₁₆	1	1	yes	characteristic, complemented
32	C₄×C₅	—	2	12	no	—
33	C₄×C₅	—	50	2	no	—
34	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
35	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
36	Dic₅	—	10	12	no	—
37	Q₁₆	—	25	1	no	Sylow
38	C₂×C₅	—	2	12	no	—
39	C₂×C₅	C₅×D₂₀	1	6	yes	—
40	C₂×C₅	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
41	Q₈	—	25	2	no	—
42	C₈	C₅×C₅⋊D₅	1	1	yes	characteristic
43	C₅	—	2	12	no	—
44	C₅	C₅×Dic₂₀	1	6	yes	complemented
45	C₅	#87802	1	1	yes	characteristic, direct product factor
46	C₄	—	50	2	no	—
47	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
48	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, prime radical	C₂×C₅³	D₄
hypercenter	C₅×C₈	C₅⋊D₅
hypocenter	C₅²	C₅×Q₁₆
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
5. #87802	C₅	direct (N × H)
13. C₅³	Q₁₆	semidirect
30. C₅²	Dic₂₀	semidirect
31. C₅²	C₅×Q₁₆	semidirect
44. C₅	C₅×Dic₂₀	semidirect
45. C₅	#87802	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×#6045	2
C₅³×C₈	2
#87802	5
C₅×Dic₂₀	5

Subgroups — C5×#87802 #14522626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87802 #14522626