Subgroups — C₁₉×D₇₀₉ #41002287

Order 26942.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₇₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₀₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇₀₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₉	—	709	1	no	maximal, Hall
5	C₁₉	D₇₀₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	709	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₇₀₉
commutator, cosocle, hypocenter	C₇₀₉	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₇₀₉	C₂
LCS	G ▷ C₇₀₉
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.