Here are some of the Dewey call numbers of principal interest to classicists:
182-188 Ancient Philosophy
292 Greek and Roman Religion
470-478 Latin Language
480-488 Greek Language
870-878 Latin Literature
880-888 Classical Greek Literature
913 Ancient Geography and Archaeology
937 Roman History
938 Ancient Greek History
016 is used for subject bibliographies, with the extension after the decimal point representing the subject, so that 016.292 is for bibliographies on Greek and Roman religion.
A special (and unique to Northwestern) scheme is used for literary works, and commentaries on and criticism of those works, under the call numbers 871 (Classical Latin Literature), 879 (Medieval Latin Literature), 881 (Classical Greek Literature), and 888 (Byzantine Literature). It is explained in the document linked below.