Subgroups — #32913261

Order 18324.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₅₀₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₅₀₉	—	6	2	no	—
4	Dic₅₀₉	—	9	1	no	maximal, Hall
5	C₃×C₅₀₉	—	2	2	no	—
6	C₂×C₅₀₉	—	9	1	no	—
7	C₅₀₉	#157	1	1	yes	characteristic, complemented, Sylow
8	#157	—	509	1	no	maximal, Hall
9	C₃⋊D₃	D₅₀₉	1	1	yes	characteristic
10	C₃²	Dic₅₀₉	1	1	yes	characteristic, complemented, Sylow
11	D₃	—	6	2	no	—
12	C₄	—	4581	1	no	Sylow
13	C₃	—	2	2	no	—
14	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅₀₉	C₄
prime radical, cosocle	C₃⋊D₃×C₅₀₉	C₂
LCS	G ▷ C₃²×C₅₀₉
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.