Your 2nd-half-of-the-1800s brass button is known as a Livery button. That type shows the coat-of-arms of a family in the Nobility, or just quite wealthy. Livery buttons were worn on the uniforms of household staff, from butlers to doormen to coachmen. Your button shows a coronet (which is not a crown worn by Royalty) representing a particular rank of Nobility. Having 5 knobs on the coronet's top is for a Viscount, if I recall correctly. But 5 might be for a Baron.
To learn more, and perhaps find a match for yours, do a googlesearch for Livery buttons.