Subgroups — D₃₆₁ #10624373

Order 722.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₁₉	—	19	1	no	maximal
3	C₁₉	D₁₉	1	1	yes	characteristic
4	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃₆₁	C₂
Frattini, socle	C₁₉	D₁₉
LCS	G ▷ C₃₆₁
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₆₁	C₂	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₆₁	2
D₁₉	19