The best way to get a completely up-to-date list of active sororities and fraternities at UCLA is to visit the UCLA's official website for Greek Life. They usually have a directory or list of recognized organizations. Look for a section dedicated to student organizations or Greek life.
Searching for "UCLA Greek Life" on Google will also likely bring up the relevant page quickly.
Keep in mind that membership in these organizations can fluctuate, so an official university source is always the most reliable.