  We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In
fact, the tangent space to a coadjoint orbit $\mathcal{O}(\alpha)$ at the point
$\alpha$ corresponds to the characteristic space associated to the left
invariant form;$\alpha$ and its dimension is the even part of the Cartan class
of $\alpha$. We apply this remark to determine Lie algebras such that all the
nontrivial orbits (nonreduced to a point) have the same dimension, in
particular when this dimension is 2 or 4. We determine also the Lie algebras of
dimension $2n$ or $2n+1$ having an orbit of dimension $2n$.
