  An $H$-closed quasitopological group is a Hausdorff quasitopological group
which is contained in each Hausdorff quasitopological group as a closed
subspace. We obtained a sufficient condition for a quasitopological group to be
$H$-closed, which allowed us to solve a problem by Arhangel'skii and Choban and
to show that a topological group $G$ is $H$-closed in the class of
quasitopological groups if and only if $G$ is Ra\v\i kov-complete. Also we
present examples of non-compact quasitopological groups whose topological
spaces are $H$-closed.
