Union Triad 
The Union Triad is a group of three early fraternities founded at Union College in Schenectady, New York: the Kappa Alpha Society (established 1825), Sigma Phi (1827) and Delta Phi (1827). No formal organization exists.
These three organizations are the oldest existing Greek-letter social fraternities in North America.
Other fraternities which owe their birth to Union College include Psi Upsilon (1833), Chi Psi (1841) and Theta Delta Chi (1847). Collectively, these many foundings earned Union College the title Mother of Fraternities.
Miami Triad 
The Miami Triad refers to three fraternities founded at Miami University in Oxford, Ohio in the 19th century: Beta Theta Pi (1839), Phi Delta Theta (1848), and Sigma Chi (1855). Historians of fraternities often compare the significance of the Miami Triad to that of the earlier Union Triad.
Delta Zeta sorority was founded at Miami University in 1902, and Phi Kappa Tau fraternity in 1906. Delta Sigma Epsilon sorority began there in 1914, merging in 1956 with Delta Zeta. These numerous Greek organization foundings cause some to refer to the school also as the Mother of Fraternities.
It has been tradition at some campuses that have chapters of each of the Miami Triad, such as the University of Kansas, and the University of Mississippi, to hold an annual party, formal, or ball, often referred to as "Miami Triad" or simply "Triad", to commemorate their tie to each other and the Miami Triad's place in Greek history. This tradition has waned in recent years and some schools have transformed the celebration into new events, such as the University of Kansas' Miami Triad Concert.
Lexington Triad 
Members of the triad include Alpha Tau Omega (founded in Richmond, Virginia in 1865 by students from Virginia Military Institute (VMI) in Lexington), Kappa Alpha Order (founded in 1865 at Washington and Lee University (not to be confused with the Kappa Alpha Society), and Sigma Nu (founded in 1869 at VMI). The national headquarters of both the Kappa Alpha Order and Sigma Nu are located in Lexington.
The members of the Triad are sometimes also grouped as part of the Virginia Circle, which includes several other fraternities founded in Virginia roughly during the period of the Lexington Triad: Kappa Sigma and Pi Kappa Alpha at the University of Virginia, and sometimes Sigma Phi Epsilon at Richmond College.
Jefferson Duo 
The Jefferson Duo includes the fraternities Phi Gamma Delta and Phi Kappa Psi, founded in 1848 and 1852, respectively, at Jefferson College in Canonsburg, Pennsylvania. A third, Kappa Phi Lambda, was also founded there but dissolved in 1874. In 1865, Jefferson College combined with Washington College to become Washington & Jefferson College.
See also 
- Order, Kappa Alpha (October, 1907). "Greek Notes and Clippings". The Kappa Alpha Journal XXV (1) (Richmond, Va)
- The History of College Fraternities
- Complete History of the Fraternal Values Society
- The Jayhawker Yearkbook (1937 ed.). Lawrence, KS: University of Kansas. p. 153.
- Ole Miss Yearkbook (1957 ed.). Oxford, MS: University of Mississippi. p. 155.
- "Kansan.com: Students remember friend with 2nd annual concert". Retrieved 2008-06-03.
- "The Miami Triad In Extension". The Scroll of Phi Delta Theta X. New York: Phi Delta Theta. 1886. p. 169. "...together with the Jefferson Triad, went beyond it in the direction most natural—South, where..."
- "Phi Psi Scholarship". The Phi gamma delta, Volume 45. Board of Trustees of the Fraternity of Phi Gamma Delta. October 1922. p. 807. "...PHI GAMMA DELTA'S fellow member of the "Jefferson Duo" — Phi Kappa Psi — has taken an unusually courageous stand in the matter of..."
- "History of Greek Letter Organizations". Phi Gamma Delta. Retrieved 2010-04-26. "These two-Phi Gamma Delta and Phi Kappa Psi- comprise the famed “Jefferson Duo.” A third fraternity, Kappa Phi Lambda, also had its genesis at old Jefferson College, where it was established in 1862, spreading to nine other colleges."