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The discrete cocompact subgroups of the five-dimensional connected, simplyconnected nilpotent Lie groups are determined up to isomorphism. Moreover, weprove if $G=N\times A$ is a connected, simply connected, nilpotent Lie groupwith an Abelian factor $A$, then every uniform subgroup of $G$ is the directproduct of a uniform subgroup of $N$ and ${\mathbb Z}^r$ where $r=\dim A$.

Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups