Subgroups — C₃×D₆₁ #67255

Order 366.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₃	—	61	1	no	maximal, Hall
5	C₃	D₆₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₆₁
commutator, cosocle, hypocenter	C₆₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₆₁	C₂
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₃

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.