The matching buttons shown left and right in the top row depict the Roman goddess of war, Minerva, who is often shown wearing a helmet. Usually, there is a dragon atop the helmet, as in this case, although some are so stylized that you really can't tell what they are. Here's a link to a page of other Minerva buttons:
http://www.iwantbuttons.com/trays/WRBA/2003/image40.htmA button bearing the same central design as the mesh one, but with a different border and struck in solid brass, is listed in Hughes & Lester's buttons book, and the pattern is described as, "Shield, Battle Trophies and Crown."