We present a molecular-dynamics-based study on certain structural features of disordered two-dimensional lattices of (Formula presented) particles with screened Coulomb interactions which are placed on rigid substrates with (Formula presented) randomly distributed Gaussian pinning centers. We find that over a wide temperature range, for (Formula presented) and for various pinning intensities (Formula presented) the lattice structures are typically described by domains of triangular-lattice-like regions punctuated by domains of clustered topological defects. Our calculations reveal that as (Formula presented) increases, sizable triangular-lattice-like regions coexist with increased topological defect densities. This result suggests that the particles remain correlated even at strong pinning regimes. Its implications are discussed in relation to recent experiments on heavy-ion-irradiated high-temperature superconductors and the assumptions used in various flux pinning theories of type-II superconductors. © 1998 The American Physical Society.