  We study the symmetry properties of autonomous integrating factors from an
algebraic point of view. The symmetries are delineated for the resulting
integrals treated as equations and symmetries of the integrals treated as
functions or configurational invariants. The succession of terms (pattern) is
noted. The general pattern for the solution symmetries for equations in the
simplest form of maximal order is given and the properties of the associated
integrals resulting from this analysis are given.
