Subgroups — D₅² #1045

Order 100.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅	C₂	1	2	yes	maximal, complemented
3	C₅²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×D₅	—	5	2	no	maximal
5	C₂×C₅	—	5	2	no	—
6	D₅	—	5	2	no	—
7	D₅	—	10	2	no	—
8	D₅	D₅	1	2	yes	direct product factor
9	C₅	—	2	2	no	—
10	C₅	C₂×D₅	1	2	yes	complemented
11	C₂²	—	25	1	no	Sylow
12	C₂	—	5	2	no	—
13	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²	C₂²
LCS	G ▷ C₅²
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.