That part I dont know. They are all pretty similar for each branch of the military if not exactly alike , but I would guess that if the color of it now is close to what it was when it was lost , then its probably army or marine , but thats just guessing based on its subdued color. If it has darkened over time from the ground and elements then who knows. You could probably do a google search for something like " military hat insignia" or any variation of words to get you started tracking it down. I forgot if there is any technical term for the piece or not. I was in the airforce and ours were bright and shiny almost chrome. I think some older style army and marine uniforms had a subdued one on their tan/green colored hat.