Subgroups — D₉×C₂₅₁ #17985271

Order 4518.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₂₅₁	—	3	1	no	maximal
3	C₃×C₂₅₁	D₃	1	1	yes	characteristic
4	C₂×C₂₅₁	—	9	1	no	Hall
5	C₂₅₁	D₉	1	1	yes	characteristic, direct product factor, Sylow
6	D₉	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉	C₂×C₂₅₁	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	3	1	no	—
9	C₃	D₃×C₂₅₁	1	1	yes	characteristic
10	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅₁	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₂₅₁
Frattini	C₃	D₃×C₂₅₁
Fitting	C₉×C₂₅₁	C₂
socle	C₃×C₂₅₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂₅₁

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.