Subgroups — C₃⋊D₅₂₅₉ #44538816

Order 31554.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₅₉	—	3	4	no	maximal
3	C₃×C₁₇₅₃	D₃	1	4	yes	complemented
4	D₁₇₅₃	—	9	1	no	Hall
5	C₁₇₅₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
6	C₃⋊D₃	—	1753	1	no	maximal, Hall
7	C₃²	D₁₇₅₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	5259	4	no	—
9	C₃	D₅₂₅₉	1	4	yes	complemented
10	C₂	—	15777	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇₅₃	C₂
LCS	G ▷ C₃²×C₁₇₅₃
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.