The Society of Jesus was designed as a deliberate departure from everything monastic, and that design is what made it the foremost order of the Counter-Reformation.
No choir, no habit, long formation
Approved in 1540, the Jesuits abandoned the choral office, the distinctive habit and the enclosure that defined the older orders. In their place they put a long and selective formation, a centralised command under a Superior General, and a special fourth vow of obedience to the pope regarding mission, so that the order could be deployed rapidly and globally rather than rooted to a house. Shaped by the Spiritual Exercises of Ignatius of Loyola, the members were preachers, teachers and missionaries first.
Suppression and restoration
The order became the leading force of the Counter-Reformation in education, scholarship and mission from Brazil to Japan, and it made enemies in proportion. It was suppressed outright by papal decree in 1773, under pressure from the Catholic monarchies, and restored in 1814, a near-total dissolution and revival that no other major order has undergone. It remains the largest male religious order, and the tension between its central obedience and its intellectual independence has run through its whole history.