This morning, as I was listening to an mp3 of the other day's news in German on my way to work to see if I could understand anything, this sentence sprang out:
Die Polizei nahm rund 400 Personen fest. (Police arrested about 400 people.)
The verb is "festnehmen", but if I think of it as "nehmen" plus a word that modifies it, the placement of the prefix is perfectly intuitive in English:
The police took about 400 people firmly.
I take back all the bad things I've said about German grammar.