Subgroups — C₁₉×C₁₀₃⋊C₁₇ #45685366

Order 33269.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₁₀₃	C₁₇	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₀₃⋊C₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₁₉	—	103	1	no	maximal, Hall
4	C₁₀₃	C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
5	C₁₉	C₁₀₃⋊C₁₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₁₇	—	103	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₁₀₃⋊C₁₇
commutator, cosocle, hypocenter	C₁₀₃	C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₁₀₃	C₁₇
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₁₉

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.