Given a group action on a vector space, and we study the problem of effectively separating the orbits under this action. After briefly discussing the history of this problem, we introduce a family of invariant functions that we call max filters. When the group is a finite subgroup of the orthogonal group, a sufficiently large max filter bank can separate the orbits, and even be bilipschitz in the quotient metric. We conclude by applying max filters to various machine learning tasks.