This is a great article summarising the major countries and their space agencies. I now you wanted to only touch on the major players but I have a couple of additions, that are worth a mention

China - They are only the 3rd country that has launched humans into space, which are aptly names Taikonauts.
Their space program is run by CNSA - China National space Administration.

India - India is famous for their PLSV launch vehicle which has launched a probe to mars. The agency is called ISRO Indian space Research Organisation.

Australia - This is my home country that's why I am mentioning it, but Australia was the 4th country to launch a satellite to orbit in 1968 behind, Russia, USA, and France, unfortunately there has been a massive lack of interest and investment since, and only recently on 1st of July 2018 the Australian space agency was formed. At this stage there is currently no local launch capacity but that's likely to change in a few years.