Subgroups — C₇₁×D₁₃₇ #34085591

Order 19454.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₇₁	—	137	1	no	maximal, Hall
4	C₁₃₇	C₂×C₇₁	1	1	yes	characteristic, complemented, Sylow
5	C₇₁	D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	137	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	D₁₃₇
commutator, cosocle, hypocenter	C₁₃₇	C₂×C₇₁
Frattini	C₁	G
Fitting, socle	C₇₁×C₁₃₇	C₂
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₇₁

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.