HC3 typically sends two or more teams to the International Collegiate Programming Competition (ICPC) every year.
(might be reactivated some time in some form)
HC3 used to run a prize contest for Harvard students.
In 2008 HC3 sent a 10 person team to the CS Games in Canada.
In 2009 HC3 organized an ICFP team, but the team decided not to compete in the actual contest.
From 2000 to 2019 HC3 participated in and helped run the Boston Preliminary ICPC Contest (BOSPRE).