Subgroups — C₁₃₇×D₁₁₃ #44526318

Order 30962.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃₇	—	113	1	no	maximal, Hall
3	D₁₁₃	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃₇	D₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₁₁₃	C₂×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	113	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃₇	D₁₁₃
commutator, cosocle, hypocenter	C₁₁₃	C₂×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₁₁₃×C₁₃₇	C₂
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₁₃₇

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.