500/20=41 Amps.

If the vehicle came with an actual cigarette lighter then the outlet will have to be at least 20 Amps, otherwise the element won't heat-up or the fuse would blow. So ignoring inverter inefficiency, the biggest unit you could safely run off 20A is 240W. Older vehicles were 30 Amps, so could handle up to 360W.

You can't just stick a bigger fuse in; the wiring itself has to support the load.

If you want to run new wire to the battery to support a larger inverter you need to choose the right gauge wire. This chart will tell you what size wire is needed, based on current draw and loop distance.

http://www.engineeringtoolbox.com/amps-wire-gauge-d_730.html

Note that for DC, the frame is the same as the battery. So instead of running ground all the way back to the battery, just connect it to a nearby frame point to save wire distance and, possibly, going up to a heavier-gauge wire.

To convert watts to amps divide by 12.