Finite Group Databasebeta

← C₃₇×C₂₈₉ #24924115

Subgroups — C₃₇×C₂₈₉ #24924115

Order 10693.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃₇	C₁₇	1	1	yes	maximal, characteristic
2	C₂₈₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₃₇	C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
4	C₁₇	C₁₇×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₇	C₁₇×C₃₇
socle, prime radical	C₁₇×C₃₇	C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₈₉	C₃₇	direct (N × H)
3. C₃₇	C₂₈₉	direct (N × H)