Subgroups — D₆₁×C₁₃₁ #30630487

Order 15982.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃₁	—	61	1	no	maximal, Hall
3	C₁₃₁	D₆₁	1	1	yes	characteristic, direct product factor, Sylow
4	D₆₁	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₆₁	C₂×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃₁	D₆₁
commutator, cosocle, hypocenter	C₆₁	C₂×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₆₁×C₁₃₁	C₂
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₁₃₁

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.