Subgroups — C₅×C₆₃₁⋊C₇ #36348283

Order 22085.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₃₁⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₆₃₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₃₁	C₅×C₇	1	1	yes	characteristic, complemented, Sylow
4	C₅×C₇	—	631	1	no	maximal, Hall
5	C₇	—	631	1	no	Sylow
6	C₅	C₆₃₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₅	C₆₃₁⋊C₇
commutator, cosocle, hypocenter	C₆₃₁	C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₆₃₁	C₇
LCS	G ▷ C₆₃₁
UCS	C₁ ◁ C₅

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.