Although it shows aquariums can hold several hundred lbs, this doesn't mean you should pick them up when filled. I've moved 29 gallon aquariums with substrate in them before, but its not the best idea. If you twist it, its easy to crack it.
It's generally not the weight but the stress of movement (shifting/twisting) that causes the failure. Since it is consrtucted of several adjoining parts, each dependant on the other, the structural support is compromised when movement causes the weight to shift (rocks, water,ect). Play it safe, move it M/T!! "T"
Unless this is for a record attempt or a special event, just drain the aquarium.
Otherwise, see if you can get a stiff board under the full aquarium. Lift using the board, the aquarium should sit flat. I take no responsibility for any damage or injury sustained during your attempt.
A 20g full of rocks and water will weigh somewhere in the neighborhood of 200lbs.