Subgroups — D₇₉×C₁₉₇ #44528056

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	C₂×C₁₉₇	—	79	1	no	maximal, Hall
3	C₁₉₇	D₇₉	1	1	yes	characteristic, direct product factor, Sylow
4	D₇₉	C₁₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇₉	C₂×C₁₉₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	79	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉₇	D₇₉
commutator, cosocle, hypocenter	C₇₉	C₂×C₁₉₇
Frattini	C₁	G
Fitting, socle	C₇₉×C₁₉₇	C₂
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₁₉₇

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.