We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface
X
X
that guarantee the surface
X
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
X
. When the surface
X
X
is end symmetric, we prove that
X
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
X
such that
X
X
is parabolic. As an application, we solve an open question from the prior work of Basmajian, Hakobyan and the second author [Proc. Lond. Math. Soc. (3) 125 (2022), pp. 568–625].