Subgroups — #14522939

Order 2000.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758789	C₂	1	3	yes	maximal
2	#92566	C₂²	1	1	yes	characteristic
3	#92561	C₄	1	3	yes	complemented
4	C₅×#1044	C₄	1	3	yes	complemented
5	AGL(1,𝔽₅)²	—	5	3	no	maximal
6	C₅×C₅⋊D₅	C₂×C₄	1	3	yes	—
7	D₅⋊AGL(1,𝔽₅)	—	5	3	no	—
8	D₅×AGL(1,𝔽₅)	—	5	6	no	—
9	C₅³	C₄²	1	1	yes	characteristic, complemented, Sylow
10	D₅²	—	5	3	no	—
11	#1044	AGL(1,𝔽₅)	1	3	yes	complemented
12	#1043	—	5	3	no	—
13	#1042	—	5	6	no	—
14	#1042	—	20	3	no	—
15	C₅×AGL(1,𝔽₅)	—	5	6	no	—
16	C₄×AGL(1,𝔽₅)	—	25	3	no	—
17	C₅⋊D₅	C₂×AGL(1,𝔽₅)	1	3	yes	—
18	C₅×D₅	—	5	6	no	—
19	C₅×D₅	—	20	3	no	—
20	C₂×AGL(1,𝔽₅)	—	25	6	no	—
21	C₄×D₅	—	25	3	no	—
22	C₅²	—	4	3	no	—
23	C₅²	—	16	1	no	—
24	C₅²	C₄×AGL(1,𝔽₅)	1	3	yes	complemented
25	C₂×D₅	—	25	3	no	—
26	AGL(1,𝔽₅)	—	5	6	no	—
27	AGL(1,𝔽₅)	—	25	6	no	—
28	AGL(1,𝔽₅)	—	100	3	no	—
29	C₄×C₅	—	25	3	no	—
30	Dic₅	—	25	3	no	—
31	C₄²	—	125	1	no	Sylow
32	C₂×C₅	—	25	3	no	—
33	D₅	—	5	6	no	—
34	D₅	—	20	3	no	—
35	C₂×C₄	—	125	3	no	—
36	C₅	—	4	3	no	—
37	C₅	—	16	1	no	—
38	C₅	AGL(1,𝔽₅)²	1	3	yes	complemented
39	C₂²	—	125	1	no	—
40	C₄	—	25	3	no	—
41	C₄	—	125	3	no	—
42	C₂	—	25	3	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅³	C₄²
prime radical, cosocle	#92566	C₂²
LCS	G ▷ C₅³
UCS	C₁

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

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

subgroup	index
#11758789	2
AGL(1,𝔽₅)²	5