Subgroups — C₃⋊D₇₅ #90644

Order 450.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₅	—	3	4	no	maximal
3	C₃⋊D₁₅	—	5	1	no	maximal
4	C₃×C₂₅	D₃	1	4	yes	complemented
5	D₂₅	—	9	1	no	Hall
6	C₃²×C₅	D₅	1	1	yes	characteristic
7	D₁₅	—	15	4	no	—
8	C₂₅	C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
9	C₃⋊D₃	—	25	1	no	Hall
10	C₃×C₅	D₁₅	1	4	yes	—
11	D₅	—	45	1	no	—
12	C₃²	D₂₅	1	1	yes	characteristic, complemented, Sylow
13	D₃	—	75	4	no	—
14	C₅	C₃⋊D₁₅	1	1	yes	characteristic
15	C₃	D₇₅	1	4	yes	complemented
16	C₂	—	225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₂₅	C₂
Frattini	C₅	C₃⋊D₁₅
socle	C₃²×C₅	D₅
LCS	G ▷ C₃²×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.