  Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed
field of characteristic 0. If $H$ is not semisimple and $\dim(H)=2n$ for some
odd integer $n$, then $H$ or $H^*$ is not unimodular. Using this result, we
prove that if $\dim(H)=2p$ for some odd prime $p$, then $H$ is semisimple. This
completes the classification of Hopf algebras of dimension $2p$.
