Subgroups — C₂₃×D₃₅₉ #30658251

Order 16514.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₅₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₅₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₂₃	—	359	1	no	maximal, Hall
5	C₂₃	D₃₅₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	359	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	D₃₅₉
commutator, cosocle, hypocenter	C₃₅₉	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₂₃×C₃₅₉	C₂
LCS	G ▷ C₃₅₉
UCS	C₁ ◁ C₂₃

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.