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.