Finite Group Databasebeta

← C₉×C₂₉×C₄₁ #24924167

Subgroups — C₉×C₂₉×C₄₁ #24924167

Order 10701.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₄₁	C₃	1	1	yes	maximal, characteristic
2	C₂₉×C₄₁	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₉×C₄₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉×C₂₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄₁	C₃×C₂₉	1	1	yes	characteristic
6	C₃×C₂₉	C₃×C₄₁	1	1	yes	characteristic
7	C₄₁	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂₉	C₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	C₂₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₂₉×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₂₉×C₄₁
socle, prime radical	C₃×C₂₉×C₄₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×C₄₁	C₉	direct (N × H)
3. C₉×C₄₁	C₂₉	direct (N × H)
4. C₉×C₂₉	C₄₁	direct (N × H)
7. C₄₁	C₉×C₂₉	direct (N × H)
8. C₂₉	C₉×C₄₁	direct (N × H)
9. C₉	C₂₉×C₄₁	direct (N × H)