Subgroups — D₁₅₈₅₇ #44540508

Order 31714.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅₇	—	101	1	no	maximal, Hall
3	D₁₀₁	—	157	1	no	maximal, Hall
4	C₁₅₇	D₁₀₁	1	1	yes	characteristic, complemented, Sylow
5	C₁₀₁	D₁₅₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	15857	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₀₁×C₁₅₇	C₂
LCS	G ▷ C₁₀₁×C₁₅₇
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.