Subgroups — C₇₃×C₆₁⋊C₅ #36373003

Order 22265.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₇₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇₃	—	61	1	no	maximal, Hall
3	C₆₁⋊C₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇₃	C₆₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
5	C₆₁	C₅×C₇₃	1	1	yes	characteristic, complemented, Sylow
6	C₅	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃	C₆₁⋊C₅
commutator, cosocle, hypocenter	C₆₁	C₅×C₇₃
Frattini	C₁	G
Fitting, socle	C₆₁×C₇₃	C₅
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₇₃

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.