Finite Group Databasebeta

← C₅×C₂₃×C₄₉ #19150660

Subgroups — C₅×C₂₃×C₄₉ #19150660

Order 5635.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₇×C₂₃	C₇	1	1	yes	maximal, characteristic
3	C₅×C₄₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₂₃	C₅×C₇	1	1	yes	characteristic
5	C₅×C₂₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
6	C₄₉	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₅×C₇	C₇×C₂₃	1	1	yes	characteristic
8	C₂₃	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₇	C₅×C₇×C₂₃	1	1	yes	characteristic
10	C₅	C₂₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₇	C₅×C₇×C₂₃
socle	C₅×C₇×C₂₃	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₄₉	C₅	direct (N × H)
3. C₅×C₄₉	C₂₃	direct (N × H)
5. C₅×C₂₃	C₄₉	direct (N × H)
6. C₄₉	C₅×C₂₃	direct (N × H)
8. C₂₃	C₅×C₄₉	direct (N × H)
10. C₅	C₂₃×C₄₉	direct (N × H)