Finite Group Databasebeta

← C₂×C₉×C₅₉₉ #24924803

Subgroups — C₂×C₉×C₅₉₉ #24924803

Order 10782.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅₉₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅₉₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅₉₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₅₉₉	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₅₉₉	C₂×C₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₉	C₅₉₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉	C₂×C₅₉₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₃	C₃×C₅₉₉	1	1	yes	characteristic
9	C₃	C₂×C₃×C₅₉₉	1	1	yes	characteristic
10	C₂	C₉×C₅₉₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅₉₉
socle, prime radical	C₂×C₃×C₅₉₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₅₉₉	C₂	direct (N × H)
4. C₂×C₅₉₉	C₉	direct (N × H)
5. C₅₉₉	C₂×C₉	direct (N × H)
6. C₂×C₉	C₅₉₉	direct (N × H)
7. C₉	C₂×C₅₉₉	direct (N × H)
10. C₂	C₉×C₅₉₉	direct (N × H)