Subgroups — D₁₆₅₈₉ #45684367

Order 33178.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₃	—	53	1	no	maximal, Hall
3	C₃₁₃	D₅₃	1	1	yes	characteristic, complemented, Sylow
4	D₅₃	—	313	1	no	maximal, Hall
5	C₅₃	D₃₁₃	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	16589	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅₃×C₃₁₃	C₂
LCS	G ▷ C₅₃×C₃₁₃
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.