Subgroups — C₁₂₇×D₁₃₁ #45685398

Order 33274.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃₁	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₂₇	—	131	1	no	maximal, Hall
4	C₁₃₁	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
5	C₁₂₇	D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	131	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₂₇	D₁₃₁
commutator, cosocle, hypocenter	C₁₃₁	C₂×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₁₂₇×C₁₃₁	C₂
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₁₂₇

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.