Complex sentence: For the rest of the 1920s UCD and QUB established themselves as the two strongest teams in the competition with UCD winning it outright on five occasions while QUB achieved the same feat twice.
Split into simpler sentences: For the rest of the 1920s, UCD and QUB established themselves as the two strongest teams in the competition. UCD won the cup outright on five occasions while QUB achieved the same feat twice.