You forgot to mention the European horde that invaded America, and swept across the continent. One of the more successful ones, wouldn't you say?
Since the discussion of Israel versus Hamas has resulted in my writing about the Moslem incursions into Europe (the battle of Tours in the middle of France came only 100 years after the death of Mohammed) I thought we should consider the other major shaping force that is even less known or more ignored, the Mongolian invasions from Ghengis Khan forward.
But first, Atilla the Hun was not unrelated to the Mongols and led the Yellow Horde. All subsequent armies of Mongols were named after colours, Ghengis Khan led the Golden Horde, Batu Khan the Blue Horde.
Chin Shih Huang (259-210 BCE) who gave his name to China, was a Mongol warrior whose troops united most of the warring provinces of China, then attempted to close the door on the other Mongol tribes via the Great Wall. This succeeded for roughly a millenium. The next era of expansionism began in 1205. there's a really nice animation of Mongol expansionism
to a patch just north of China all the way east and west including roughly half of the Soviet Union Iran Iraq Afghanistan and Pakistan and Turkey, and all of Poland and Hungary in 90 years. During that time the slaughter of conquered peoples was unprecedented and nearly total. The process including the conquest of China began with Ghengis Khan who also took a shot at Japan while he was at it. His heirs Batu Khan (his grandson) who displaced Ogotai Khan and was succeeded by Berke who spread the empire to Poland and Hungary.
Another unrelated warrior who has come down to us as Tamerlane the Great, or Timur the Lame, was responsible for the conquest of India, Pakistan Afghanistan Iran Irag Syria and Turkey. He was not a Mongol per se in that he was of Turkic stock, and this is how the Indo European language came to enter India, Pakistan, Iran and Turkey.
His grave was excavated during the spring of 1941 and was opened on June 19th despite the curse written on the tomb, "Whoever disturbs my tomb will bring demons of war into his land". The German invasion began on June 22nd. Wikipedia credits him with the death of about 17 million people. Stalin must have studied these people.
Timur is the national hero of Uzbekistan, and has a statue replacing Stalin's in the main square of Tashkent.