Joseph,
Yes, but most presidents don’t appoint political opponents to their cabinets, especially to prominent/ powerful positions like Sec of State. Generally speaking, the vice-president is not a politically powerful position, though it can be a springboard for a future presidential run. In recent years, a presidential candidate’s selection of a running mate has become opportunity to broaden one’s demographic/ political appeal (see John McCain & Sarah Palin). Thus choosing one’s former political rival as a running mate is a practical move that can help a candidate achieve a win that otherwise wouldn’t have been possible. There is no similar political advantage to appointing a competitor to a Cabinet position.
How many presidents since Lincoln have appointed a bitter political oppponent to an important Cabinet position, as President Obama appointed Ms. Clinton?