Subgroups — D₈₄₅ #13133021

Order 1690.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₉	—	5	1	no	maximal, Hall
3	C₁₆₉	D₅	1	1	yes	characteristic, complemented, Sylow
4	D₆₅	—	13	1	no	maximal
5	C₅×C₁₃	D₁₃	1	1	yes	characteristic
6	D₁₃	—	65	1	no	—
7	C₁₃	D₆₅	1	1	yes	characteristic
8	D₅	—	169	1	no	Hall
9	C₅	D₁₆₉	1	1	yes	characteristic, complemented, Sylow
10	C₂	—	845	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₁₆₉	C₂
Frattini	C₁₃	D₆₅
socle	C₅×C₁₃	D₁₃
LCS	G ▷ C₅×C₁₆₉
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.