  A Hopf Galois structure on a finite field extension $L/K$ is a pair
$(H,\mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a
Hopf action. In this paper we present a program written in the computational
algebra system Magma which gives all Hopf Galois structures on separable field
extensions of a given degree and several properties of those. We show a table
which summarizes the program results. Besides, for separable field extensions
of degree $2p^n$, with $p$ an odd prime number, we prove that the occurrence of
some type of Hopf Galois structure may either imply or exclude the occurrence
of some other type. In particular, for separable field extensions of degree
$2p^2$, we determine exactly the possible sets of Hopf Galois structure types.
