Subgroups — C₇×C₆₉₁⋊C₅ #37564034

Order 24185.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₆₉₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₉₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₉₁	C₅×C₇	1	1	yes	characteristic, complemented, Sylow
4	C₅×C₇	—	691	1	no	maximal, Hall
5	C₇	C₆₉₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	—	691	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₆₉₁⋊C₅
commutator, cosocle, hypocenter	C₆₉₁	C₅×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₆₉₁	C₅
LCS	G ▷ C₆₉₁
UCS	C₁ ◁ C₇

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.