  A class of nongraded Hamiltonian Lie algebras was earlier introduced by Xu.
These Lie algebras have a Poisson bracket structure. In this paper, the
isomorphism classes of these Lie algebras are determined by employing a
``sandwich'' method and by studying some features of these Lie algebras. It is
obtained that two Hamiltonian Lie algebras are isomorphic if and only if their
corresponding Poisson algebras are isomorphic. Furthermore, the derivation
algebras and the second cohomology groups are determined.
