Subgroups — C₁₃₇⋊D₁₃₇ #49176243

Order 37538.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃₇²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₁₃₇	—	137	138	no	maximal
3	C₁₃₇	D₁₃₇	1	138	yes	complemented
4	C₂	—	18769	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃₇²	C₂
LCS	G ▷ C₁₃₇²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃₇²	C₂	semidirect
3. C₁₃₇	D₁₃₇	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃₇²	2
D₁₃₇	137