Subgroups — C₁₉⋊C₃×C₃₄₉ #34091086

Order 19893.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃₄₉	—	19	1	no	maximal, Hall
3	C₃₄₉	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₁₉⋊C₃	C₃₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉	C₃×C₃₄₉	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₄₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₃₄₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃₄₉

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.