Subgroups — D₂₂₅ #90638

Order 450.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₅	—	3	1	no	maximal
3	D₄₅	—	5	1	no	maximal
4	C₃×C₂₅	D₃	1	1	yes	characteristic
5	D₂₅	—	9	1	no	Hall
6	C₅×C₉	D₅	1	1	yes	characteristic
7	D₁₅	—	15	1	no	—
8	C₂₅	D₉	1	1	yes	characteristic, complemented, Sylow
9	D₉	—	25	1	no	Hall
10	C₃×C₅	D₁₅	1	1	yes	characteristic
11	D₅	—	45	1	no	—
12	C₉	D₂₅	1	1	yes	characteristic, complemented, Sylow
13	D₃	—	75	1	no	—
14	C₅	D₄₅	1	1	yes	characteristic
15	C₃	D₇₅	1	1	yes	characteristic
16	C₂	—	225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₅	C₂
Frattini, socle	C₃×C₅	D₁₅
LCS	G ▷ C₉×C₂₅
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.