Subgroups — C₇₃×C₁₀₉⋊C₃ #37558870

Order 23871.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₀₉⋊C₃	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇₃	—	109	1	no	maximal, Hall
4	C₁₀₉	C₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
5	C₇₃	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	109	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃	C₁₀₉⋊C₃
commutator, cosocle, hypocenter	C₁₀₉	C₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₇₃×C₁₀₉	C₃
LCS	G ▷ C₁₀₉
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.