Subgroups — C₁₃₁⋊#6923 #44544201

Order 31964.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃₁	—	61	1	no	maximal, Hall
4	C₂×C₁₃₁	—	61	1	no	—
5	#6923	—	131	1	no	maximal, Hall
6	C₁₃₁	#6923	1	1	yes	characteristic, complemented, Sylow
7	D₆₁	D₁₃₁	1	1	yes	characteristic
8	C₆₁	Dic₁₃₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	7991	1	no	Sylow
10	C₂	—	61	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₆₁×C₁₃₁	C₄
prime radical, cosocle	D₆₁×C₁₃₁	C₂
LCS	G ▷ C₆₁×C₁₃₁
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.