Subgroups — D₁₅₆₂₇ #44530413

Order 31254.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₀₉	—	3	1	no	maximal, Hall
3	C₅₂₀₉	D₃	1	1	yes	characteristic, complemented, Sylow
4	D₃	—	5209	1	no	maximal, Hall
5	C₃	D₅₂₀₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	15627	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅₂₀₉	C₂
LCS	G ▷ C₃×C₅₂₀₉
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.