Using a submenu to filter content

I have a page that loads 20 posts. 5 are type “a,” 5 are type “b,” 5 are type “c” and 5 are type “d.” I’d like to assign each one of them a second category and the create a sub-menu where users can “filter” by type. By default, the page loads all of them, which is what I want. But, I’d like them to then be able to narrow them down by type if they want. So the submenu would be “All | Type A | Type B | Type C | Type D.”

I can create a link on each of these submenu items that reloads the page and runs the proper loop for just that type. But, since all the posts are already loaded to start with this seems like a waste to reload the page and run another loop. Is there a way to simply click on a submenu link and have certain items on the page remain and others disappear? Without reloading the page? Thanks for any help or guidance.