Arrange these events in the history of the Islamic world, earliest first.

1. The Hijra from Mecca to Medina
2. Arab forces defeat a Roman army at Yarmuk
3. The Umayyads take power and rule from Damascus
4. The Abbasids found Baghdad
5. Abd al-Rahman III claims the caliphal title at Córdoba
6. The Almohad army is destroyed at Las Navas de Tolosa

The compression at the start is the striking part: from a migration in 622 to the destruction of the Sasanian empire and the loss of Roman Syria and Egypt inside thirty years. Everything after 661 happens at an ordinary historical pace by comparison.