Subgroups — C₉₇×C₂₉⋊C₇ #34089012

Order 19691.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₉₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₉₇	—	29	1	no	maximal, Hall
3	C₂₉⋊C₇	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉₇	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
5	C₂₉	C₇×C₉₇	1	1	yes	characteristic, complemented, Sylow
6	C₇	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉₇	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₇×C₉₇
Frattini	C₁	G
Fitting, socle	C₂₉×C₉₇	C₇
LCS	G ▷ C₂₉
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.