Subgroups — C₃×C₅⋊D₅ #3878

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	C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅	—	5	6	no	maximal
4	C₅²	C₂×C₃	1	1	yes	characteristic, complemented, Sylow
5	C₃×C₅	D₅	1	6	yes	complemented
6	D₅	—	5	6	no	—
7	C₂×C₃	—	25	1	no	Hall
8	C₅	C₃×D₅	1	6	yes	complemented
9	C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃

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.