Subgroups — C₉₇×D₁₅₇ #44478641

Order 30458.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₇×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅₇	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₉₇	—	157	1	no	maximal, Hall
4	C₁₅₇	C₂×C₉₇	1	1	yes	characteristic, complemented, Sylow
5	C₉₇	D₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	157	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉₇	D₁₅₇
commutator, cosocle, hypocenter	C₁₅₇	C₂×C₉₇
Frattini	C₁	G
Fitting, socle	C₉₇×C₁₅₇	C₂
LCS	G ▷ C₁₅₇
UCS	C₁ ◁ C₉₇

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.