Using an extension of Pirogov Sinai theory, we prove phase transitions, corresponding to sublattice orderings, for a general class of hard-core lattice particle systems with a finite number of perfect coverings. These include many cases for which such transitions have been proven. The proof also shows that for these systems the Gaunt Fisher expansion of the pressure in powers of the inverse fugacity (aside from an explicit logarithmic term) has a nonzero radius of convergence.