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It can be done, but not easily.
The problem is that the normal way a Canon Master triggers a Canon Slave is by sending optical pulses from the Master, the first ones being command and control signals and the last one being the "fire now!" signal.
If you try to trigger a strobe with that system, the strobe will fire out of sync upon seeing the first preflash.
The way to do it is to set the on-camera Speedlite to Manual mode with Wireless set to "Off" so it doesn't send any ETTL metering preflashes or Wireless C&C preflashes, and then use the built-in optical sensor on the ABs and a Canon-compatible optical sensor plugged into a hot-shoe adapter on which the 420EX is mounted.
It's a lot easier to fire all of them with radio triggers. I am currently using the Yongnuo YN-622C system, which can fire Speedlites in ETTL or Manual mode, and trigger strobes through their PC jack.