  We introduce the property of having good subgroups for actions of countable
discrete groups on compact metrizable spaces. We show that it implies
comparison for actions of amenable groups and amenable actions of groups
containing the free group on two generators. As a result, free actions on
finite-dimensional spaces of topological full groups of many \'etale groupoids
are almost finite whenever the group is amenable, or have comparison if instead
it contains a free group on two generators and the action is minimal and
amenable. In particular, free minimal actions give rise to classifiable crossed
products in both of the above cases.
