I have done some research and found out that pushmatic can be Square D or ITE. The following link to Connecticut Electric lists original pushmatic and the ITE replacement. The original type breakers are 10 bucks more than the replacement. I made up a diagram showing a sub panel attached to your main. The graphic representation of the existing panel may not even look close to yours but I tried. I'm figuring on a 40 amp feeder for the sub panel. You'll use #8-3 with ground romex. You can go to Home Depot or Lowes for the sub. Go with any manufacturer you are comfortable with. GE, Cutler-Hammer, Westinghouse, Challenger are all good brands. Get something you don't have to use mail order for breakers. Any questions write back.
Pushmatic Circuit Breakers Shipped Fast
Stock No for the interchangeable breaker is PUSH-240