Subgroups — #92560

Order 500.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅³	C₄	1	1	yes	characteristic, complemented, Sylow
3	#1044	—	5	1	no	maximal
4	#1042	—	5	2	no	maximal
5	C₅⋊D₅	D₅	1	1	yes	characteristic
6	C₅×D₅	—	5	2	no	—
7	C₅×D₅	—	10	2	no	—
8	C₅²	—	2	2	no	—
9	C₅²	—	4	4	no	—
10	C₅²	—	4	2	no	—
11	C₅²	Dic₅	1	1	yes	characteristic, complemented
12	C₅²	AGL(1,𝔽₅)	1	2	yes	complemented
13	AGL(1,𝔽₅)	—	25	2	no	—
14	Dic₅	—	25	1	no	—
15	C₂×C₅	—	25	1	no	—
16	D₅	—	5	2	no	—
17	D₅	—	10	2	no	—
18	C₅	—	2	2	no	—
19	C₅	—	4	4	no	—
20	C₅	—	4	2	no	—
21	C₅	#1042	1	2	yes	complemented
22	C₅	#1044	1	1	yes	characteristic, complemented
23	C₄	—	125	1	no	Sylow
24	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅³	C₄
prime radical, cosocle	C₅×C₅⋊D₅	C₂
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.