By legal definition a moped cannot exceed 50cc. I have a Powerpak ‘cycle moped’ somewhere in the garage. As early teens we used to ride motorcycles around the fields. One was a Mercury Mercette - with a two speed 4 stroke overhead valve engine. Went like stink compared with some mopeds of the day. Only about 2 1/3-3 HP, I believe.
The powerpak: http://www.icenicam.org.uk/articles9/art0150.php
Mercury Mercette engine pic: https://cybermotorcycle.com/gallery/mercury/Mercury-Mercette-06.htm
The Mercette got scrapped over 20 yesrs ago. Wish I had collected it before it was skipped… One would be mega-expensive today
A local Romanian bloke has a modern version of this from wish grafted on the back of his bicycle. It gets a fair lick on and he goes miles on it. Quite how the police have left him alone I don't know. You can here him coming as it's a very distinctive sound somewhat like a woopy cushion