Subgroups — C₅²×D₃ #3879

Order 150.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅²	—	3	1	no	maximal, Hall
3	C₅×D₃	C₅	1	6	yes	maximal, direct product factor
4	C₅²	D₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₃×C₅	C₂×C₅	1	6	yes	complemented
6	C₂×C₅	—	3	6	no	—
7	D₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅	C₅×D₃	1	6	yes	direct product factor
9	C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Sylow
10	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅²

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.