Subgroups — C₁₅₇×D₁₀₃ #44568960

Order 32342.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₅₇	—	103	1	no	maximal, Hall
3	D₁₀₃	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₅₇	D₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₁₀₃	C₂×C₁₅₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	103	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₅₇	D₁₀₃
commutator, cosocle, hypocenter	C₁₀₃	C₂×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₁₀₃×C₁₅₇	C₂
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₁₅₇

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.