Subgroups — D₁₁₉₀₅ #37558374

Order 23810.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃₈₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₃₈₁	—	5	1	no	maximal, Hall
3	C₂₃₈₁	D₅	1	1	yes	characteristic, complemented, Sylow
4	D₅	—	2381	1	no	maximal, Hall
5	C₅	D₂₃₈₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	11905	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₂₃₈₁	C₂
LCS	G ▷ C₅×C₂₃₈₁
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.