  We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface
$X$ that guarantee the surface $X$ is of parabolic type. An interesting class
of Riemann surfaces for this problem is the one with finitely many topological
ends. In this case the length part of the Fenchel-Nielsen coordinates can go to
infinity for {parabolic $X$}. When the surface $X$ is end symmetric, we prove
that {$X$ being parabolic} is equivalent to the covering group being of the
first kind. Then we give necessary and sufficient conditions on the
Fenchel-Nielsen coordinates of a half-twist symmetric surface $X$ such that
{$X$ is parabolic}. As an application, we solve an open question from the prior
work of Basmajian, Hakobyan and the second author.
