I know of 5.. Boston College, Georgia Tech, Army, Navy, Air Force
You are forgetting MIT (Massachusetts Institute of Technology).
MIT is an Ivy League school and they only compete in Division 1A Basketball which includes 1AA (which has quite a few schools without University in their official school name) as well.
MIT is NOT an Ivy League school - it is a Division III school
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Division 1 College Football is one of the largest in the country. The Division 1 schools that do not have university in their name are MIT, Georgia Tech, Boston College, Army, Navy, and Air Force.
United States Naval Academy (Navy)
United States Military Academy (Army)
United States Air Force Academy (Air Force)
Boston College
These immediately come to mind. There may be one or two others.