Finite Group Databasebeta

← C₅×C₂₃×C₆₇ #21440468

Subgroups — C₅×C₂₃×C₆₇ #21440468

Order 7705.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₆₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₂₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₆₇	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₂₃	C₅×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	C₂₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×C₆₇	C₅	direct (N × H)
2. C₅×C₆₇	C₂₃	direct (N × H)
3. C₅×C₂₃	C₆₇	direct (N × H)
4. C₆₇	C₅×C₂₃	direct (N × H)
5. C₂₃	C₅×C₆₇	direct (N × H)
6. C₅	C₂₃×C₆₇	direct (N × H)