Finite Group Databasebeta

← C₃²×C₂₉×C₄₁ #24924168

Subgroups — C₃²×C₂₉×C₄₁ #24924168

Order 10701.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₄₁	C₃	1	4	yes	maximal, direct product factor
2	C₂₉×C₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₄₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₂₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄₁	C₃×C₂₉	1	4	yes	direct product factor
6	C₃×C₂₉	C₃×C₄₁	1	4	yes	direct product factor
7	C₄₁	C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂₉	C₃²×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₂₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₂₉×C₄₁	1	4	yes	direct product factor

	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. C₃×C₂₉×C₄₁	C₃	direct (N × H)
2. C₂₉×C₄₁	C₃²	direct (N × H)
3. C₃²×C₄₁	C₂₉	direct (N × H)
4. C₃²×C₂₉	C₄₁	direct (N × H)
5. C₃×C₄₁	C₃×C₂₉	direct (N × H)
6. C₃×C₂₉	C₃×C₄₁	direct (N × H)
7. C₄₁	C₃²×C₂₉	direct (N × H)
8. C₂₉	C₃²×C₄₁	direct (N × H)
9. C₃²	C₂₉×C₄₁	direct (N × H)
10. C₃	C₃×C₂₉×C₄₁	direct (N × H)