Subgroups — C₉₇×C₄₁⋊C₅ #34091007

Order 19885.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₉₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₉₇	—	41	1	no	maximal, Hall
3	C₄₁⋊C₅	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉₇	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
5	C₄₁	C₅×C₉₇	1	1	yes	characteristic, complemented, Sylow
6	C₅	—	41	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉₇	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₅×C₉₇
Frattini	C₁	G
Fitting, socle	C₄₁×C₉₇	C₅
LCS	G ▷ C₄₁
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.