  We classify the constraints on a stationary point of the potential invariant
under a finite group into intrinsic and extrinsic based on whether they are
independent of the coefficients in the potential or not. We find that the
symmetry group of a set of stationary points can be larger than that of the
potential and the stabilizer under this group generates intrinsic constraints.
By applying these findings in the framework of the auxiliary group, we show
that the constraints that can only be obtained extrinsically in an elementary
theory can be generated intrinsically in an effective theory.
