Subgroups — Dic₁₆₀₈₅ #72299708

Order 64340.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₂₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₂₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₃₂₁₇	—	5	1	no	maximal, Hall
4	C₂×C₃₂₁₇	D₅	1	1	yes	characteristic
5	C₃₂₁₇	Dic₅	1	1	yes	characteristic, complemented, Sylow
6	Dic₅	—	3217	1	no	maximal, Hall
7	C₂×C₅	D₃₂₁₇	1	1	yes	characteristic
8	C₅	Dic₃₂₁₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	16085	1	no	Sylow
10	C₂	D₁₆₀₈₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₆₀₈₅
commutator, hypocenter	C₅×C₃₂₁₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₃₂₁₇	C₂
LCS	G ▷ C₅×C₃₂₁₇
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.