Subgroups — D₇₅ #3872

Order 150.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₅	—	3	1	no	maximal, Hall
3	D₁₅	—	5	1	no	maximal
4	C₂₅	D₃	1	1	yes	characteristic, complemented, Sylow
5	C₃×C₅	D₅	1	1	yes	characteristic
6	D₅	—	15	1	no	—
7	D₃	—	25	1	no	Hall
8	C₅	D₁₅	1	1	yes	characteristic
9	C₃	D₂₅	1	1	yes	characteristic, complemented, Sylow
10	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₅	C₂
Frattini	C₅	D₁₅
socle	C₃×C₅	D₅
LCS	G ▷ C₃×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.