College or university means, unless defined in a separate subpart, an educational institution in any State which:
(1) Admits as regular students only persons having a certificate of graduation from a school providing secondary education, or the recognized equivalent of such a certificate;
(2) Is legally authorized within such State to provide a program of education beyond secondary education;
(3) Provides an educational program for which a bachelor's degree or any other higher degree is awarded;
(4) Is a public or other nonprofit institution; and
(5) Is accredited by a nationally recognized accrediting agency or association. Unless otherwise stated for a specific program, this term includes a research foundation maintained by such an institution.