Subgroups — #87802⋊C₅ #14522161

Order 2000.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6045⋊C₅	C₂	1	2	yes	maximal
2	C₈×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic
3	C₄×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
4	#1039⋊C₅	—	2	2	no	—
5	#87802	C₅	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₂₀	—	5	1	no	maximal
7	C₂×H(3,𝔽₅)	D₄	1	1	yes	characteristic
8	#6045	C₂×C₅	1	2	yes	—
9	C₅×Dic₁₀	—	5	2	no	—
10	C₅²×C₈	—	2	2	no	—
11	C₅²×C₈	D₅	1	1	yes	characteristic
12	C₅²×C₈	C₂×C₅	1	1	yes	characteristic
13	H(3,𝔽₅)	Q₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₅²	—	2	2	no	—
15	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
16	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
17	#1039	—	2	2	no	—
18	C₅×Dic₅	—	10	2	no	—
19	C₅×Q₁₆	—	25	1	no	—
20	Dic₂₀	—	5	1	no	—
21	Dic₂₀	—	25	1	no	—
22	C₂×C₅²	—	2	2	no	—
23	C₂×C₅²	D₂₀	1	1	yes	characteristic
24	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
25	C₅×Q₈	—	25	2	no	—
26	Dic₁₀	—	5	2	no	—
27	Dic₁₀	—	25	2	no	—
28	C₅×C₈	—	5	1	no	—
29	C₅×C₈	—	5	1	no	—
30	C₅×C₈	—	10	2	no	—
31	C₅×C₈	C₅×D₅	1	1	yes	characteristic
32	C₅²	—	2	2	no	—
33	C₅²	Dic₂₀	1	1	yes	characteristic, complemented
34	C₅²	C₅×Q₁₆	1	1	yes	characteristic, complemented
35	C₄×C₅	—	5	1	no	—
36	C₄×C₅	—	5	1	no	—
37	C₄×C₅	—	10	2	no	—
38	C₄×C₅	—	50	2	no	—
39	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
40	Dic₅	—	10	2	no	—
41	Dic₅	—	50	2	no	—
42	Q₁₆	—	25	1	no	Sylow
43	C₂×C₅	—	5	1	no	—
44	C₂×C₅	—	5	1	no	—
45	C₂×C₅	—	10	2	no	—
46	C₂×C₅	C₅×D₂₀	1	1	yes	characteristic
47	Q₈	—	25	2	no	—
48	C₈	(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
49	C₅	—	5	1	no	—
50	C₅	—	5	1	no	—
51	C₅	—	10	2	no	—
52	C₅	C₅×Dic₂₀	1	1	yes	characteristic
53	C₄	—	50	2	no	—
54	C₄	C₂×(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
55	C₂	C₄⋊((C₅⋊D₅)⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊((C₅⋊D₅)⋊C₅)
commutator, cosocle	C₄×C₅²	C₂²×C₅
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₈×H(3,𝔽₅)	C₂
socle	C₂×C₅	C₅×D₂₀
prime radical	C₂×H(3,𝔽₅)	D₄
hypercenter	C₈	(C₅⋊D₅)⋊C₅
hypocenter	C₅²	C₅×Q₁₆
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
5. #87802	C₅	semidirect
13. H(3,𝔽₅)	Q₁₆	semidirect
33. C₅²	Dic₂₀	semidirect
34. C₅²	C₅×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
#6045⋊C₅	2
C₈×H(3,𝔽₅)	2
#87802	5
C₅×Dic₂₀	5

Subgroups — #87802⋊C5 #14522161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #87802⋊C₅ #14522161