Watches got more complicated in the 1950s, literally and figuratively. A basic watch had two hands, an hour and a minute hand and this first complication is a second hand. From there you can add a lot of complications like an alarm, a chime, a calendar, a day of the week, a selfwinding mechanism, a stopwatch, etc. etc..
Watches with lots of complications are very common today but early in the 20th century just telling the correct time was the mark of a fine watch.
In 1953 Hamilton introduced it's first automatic and it did so by reintroducing the lllinois brand name. In 1954 the first Hamilton-branded automatics hit the scene. Hamilton also introduced date complications around the same time period.
By the 1960s calendar models and automatics were staples of the Hamilton lineup. Chronographs came later in the 1960s and by the 1970s watches could also keep track of the day of the week.
One of the first Thin-o-matic models to feature a calendar complication was the T-575. It was only made for two years.