Subgroups — #92524

Order 500.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₅	C₄	1	1	yes	characteristic, complemented, Sylow
3	#1039	—	5	1	no	maximal
4	Dic₂₅	—	5	5	no	maximal
5	C₂×C₅²	D₅	1	1	yes	characteristic
6	C₂×C₂₅	D₅	1	5	yes	—
7	C₅²	Dic₅	1	1	yes	characteristic
8	C₂₅	Dic₅	1	5	yes	complemented
9	Dic₅	—	25	1	no	—
10	Dic₅	—	25	5	no	—
11	C₂×C₅	D₂₅	1	5	yes	—
12	C₂×C₅	C₅⋊D₅	1	1	yes	characteristic
13	C₅	Dic₂₅	1	5	yes	complemented
14	C₅	#1039	1	1	yes	characteristic
15	C₄	—	125	1	no	Sylow
16	C₂	C₅⋊D₂₅	1	1	yes	characteristic

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.