Similarly - as full moon must be opposite to the sun, full moon moonrise happens around sunset and moonset happens around sunrise.

Also full moon rises the highest in winter, contrary to the sun - when it’s at it’s lowest[1].

Funny things happen at the poles where sun is above/below horizon for half a year: https://astronomy.stackexchange.com/a/27750

[1] the further from equator you are the more pronounced it is.