Quarles served in the Confederate States Army during the civil war as a Private.
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During the Spanish-American War, Quarles volunteered with the Arkansas Volunteer Infantry (Arkansas State Guard and the Spanish-American War) when called upon by the United States Army as a Major.
While at VMI, James Frank Hopkins, Greenfield Quarles and Riley became close friends and founded Sigma Nu fraternity.
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Sigma Nu (ΣΝ) is an undergraduate college fraternity that was founded by James Frank Hopkins, Greenfield Quarles and James McIlvaine Riley at the Virginia Military Institute in Lexington, Virginia shortly after Hopkins witnessed what he considered a hazing ritual by upperclassmen at the Virginia Military Institute.