Were Austria, Czech Republic, Germany and Poland part of the Austrian-Hungarian Empire that ruled Mexico?

um problem is here spain ruled mexico, which was later granted independece as the mexican empire-which was what fought the U.S not the austo-hungarian empire. and to the other part, yes and no you see the germans had their own empire which had about half of modern poland in it, the other half was part of the russian empire-which was later over thrown in the russian civil war by the soviet union...which was when poland and several other countrys were created, do to the allies deciding to split up eastern europe. and yes because the czech republic (then called czechoslovia) was part of it. after World War One these empires ceased to exist being replaced with indepentant countries and other powers such as the germany to- weimar rebublic (later transformed into the third reich under hitler) and russia to-the soviet union.