Finite Group Databasebeta

← C₇×C₂₃×C₅₉ #23748841

Subgroups — C₇×C₂₃×C₅₉ #23748841

Order 9499.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₇×C₅₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₂₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅₉	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₂₃	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₇	C₂₃×C₅₉	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×C₅₉	C₇	direct (N × H)
2. C₇×C₅₉	C₂₃	direct (N × H)
3. C₇×C₂₃	C₅₉	direct (N × H)
4. C₅₉	C₇×C₂₃	direct (N × H)
5. C₂₃	C₇×C₅₉	direct (N × H)
6. C₇	C₂₃×C₅₉	direct (N × H)