Subgroups — D₁₅₇₀₇ #44536144

Order 31414.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃₉	—	113	1	no	maximal, Hall
3	D₁₁₃	—	139	1	no	maximal, Hall
4	C₁₃₉	D₁₁₃	1	1	yes	characteristic, complemented, Sylow
5	C₁₁₃	D₁₃₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	15707	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁₃×C₁₃₉	C₂
LCS	G ▷ C₁₁₃×C₁₃₉
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.