Monolayers of cobalt phthalocyanine (CoPc) and fluorinated cobalt phthalocyanine (F16CoPc) on silver (111) and on highly (0001) oriented pyrolytic graphite (HOPG) were imaged with a scanning tunneling microscope (STM) at cryogenic temperatures (around 30 K) at Chemnitz University of Technology. Domains of regular arrays with periodicity in two dimensions (2D) and a variety of plane symmetries were observed. Crystallographic image processing (CIP) was used to quantify deviations from the plane symmetry groups and to obtain symmetrized versions of the content of the average unit cells of some of these arrays. Conclusions on the point symmetry of the CoPc and F16CoPc molecules within the arrays were drawn.