Subgroups — C₁₃×C₁₉²⋊C₅ #37553372

Order 23465.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉²⋊C₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉²	C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
4	C₁₃×C₁₉	—	5	4	no	—
5	C₅×C₁₃	—	361	1	no	maximal, Hall
6	C₁₉	—	5	4	no	—
7	C₁₃	C₁₉²⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
8	C₅	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₁₉²⋊C₅
commutator, cosocle, hypocenter	C₁₉²	C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉²	C₅
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₁₃

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.