A comprehensive formalization of data-parallel (DP) symmetries in an imperative language paradigm without nesting is presented, which includes translational, affine and access symmetries. A subtyping system which takes these symmetries into account is discussed. A multi-component type is introduced, with type inclusion in each component resecting a diminished symmetry of a supertype compared to any of its subtypes. It is possible to use the proposed type scheme in a DP language compiler to deduce access information from unannotated programs.