Subgroups — Dic₈₅ #66769

Order 340.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₇	—	5	1	no	maximal, Hall
4	C₂×C₁₇	D₅	1	1	yes	characteristic
5	Dic₅	—	17	1	no	maximal, Hall
6	C₁₇	Dic₅	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₅	D₁₇	1	1	yes	characteristic
8	C₅	Dic₁₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	85	1	no	Sylow
10	C₂	D₈₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₅
commutator, hypocenter	C₅×C₁₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂

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.