Can I put jar lids in the dishwasher?

I’ve recently had this idea to decoupage bright bits of paper onto jars to use as containers for odds n’ ends, candles or whatever I feel like. I was going to buy a bunch of jars until I realized that I buy food in jars all the time so it would be easier and cheaper to clean these out, remove the labels and just use them. Well, I’ve discovered that the easiest way to clean out the food, remove the labels and remove the glue from the jars is to just stick them in the dishwasher.

Can I do the same with the jar lids? I feel like I can’t clean them as thoroughly with just a sponge and dish soap so I’m wondering, can I put them in the dishwasher without damaging them?