Subgroups — C₁₉×D₆₁₉ #37555151

Order 23522.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₆₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₁₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₁₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₉	—	619	1	no	maximal, Hall
5	C₁₉	D₆₁₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	619	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₆₁₉
commutator, cosocle, hypocenter	C₆₁₉	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₆₁₉	C₂
LCS	G ▷ C₆₁₉
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.