Subgroups — #34091089

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	C₃₄₉⋊C₃	—	19	1	no	maximal, Hall
3	C₃₄₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
4	C₁₉⋊C₃	—	349	1	no	maximal, Hall
5	C₁₉	C₃₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	6631	1	no	Sylow

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

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.