Subgroups — C₇₉×D₁₉₇ #44528057

Order 31126.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉₇	C₂×C₇₉	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₇₉	—	197	1	no	maximal, Hall
5	C₇₉	D₁₉₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	197	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₉	D₁₉₇
commutator, cosocle, hypocenter	C₁₉₇	C₂×C₇₉
Frattini	C₁	G
Fitting, socle	C₇₉×C₁₉₇	C₂
LCS	G ▷ C₁₉₇
UCS	C₁ ◁ C₇₉

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.