By tradition, and because they are priests of a religious order and not of a specific diocese, Jesuit priests are rarely elevated to bishop, archbishop, or cardinal. In fact, the Superior General of the Society of Jesus, who holds a very powerful position in the Church, is referred to as “The Black Pope” because he wears the black cassock of an ordinary priest, not the purple or scarlet robes of bishops and cardinals.
Although technically an ordinary priest can be elected pope(he is made a bishop before installed as pope), this does not occur much, and not in modern times.
So, Pope Francis is the rare Jesuit who has been made a cardinal and also been the head of an archdiocese (the only other one I know offhand was Cardinal Martini, previous Archbishop of Milan).
Pope JP II elevated a Jesuit theologian to Cardinal as an essentially honorary office (he was older than 80 and ineligible to vote when elevated)- that was Avery Cardinal Dulles, who was a professor at Fordham University.
How many orders are there? do they differ greatly?