  In 2017 Skabelund constructed two new examples of maximal curves
$\tilde{\mathcal{S}}_q$ and $\tilde{\mathcal{R}}_q$ as covers of the Suzuki and
Ree curves, respectively. The resulting Skabelund curves are analogous to the
Giulietti-Korchm\'aros cover of the Hermitian curve. In this paper a complete
characterization of all Galois subcovers of the Skabelund curves
$\tilde{\mathcal{S}}_q$ and $\tilde{\mathcal{R}}_q$ is given. Calculating the
genera of the corresponding curves, we find new additions to the list of known
genera of maximal curves over finite fields.
