During the peak years of activity on the Apollo program NASA's prime contractors for the construction of the Apollo Command Modules (North American Rockwell) and Lunar Modules (Grumman) employed thousands of people to work on these projects, but many other companies were involved in this immense project.
Below I identify a few patches produced by some of these companies that were used by employees working on their space projects.
ILC Industries were the prime contractor for the space suits used on the Apollo missions. ILC suit technicians worked directly with the Apollo astronauts during the pre-flight suiting-up and were present in the white room during spacecraft ingress. The embroidered patches they wore on their overalls at this time are described below.
This patch was used on the coveralls of ILC suit techs working at the KSC during the Apollo program, as show in these photos.
This patch was used on the back of coveralls of ILC suit techs working as the KSC during the Apollo program, as show in these photos.
Chrysler were the prime contractor for the Saturn IB booster.
This oversize patch was presumably for use on the back of coveralls of the Chrysler technicians working on the Saturn 1B booster.
This patch was used on the coveralls of the Chrysler technicians working on the Saturn 1B booster.
McDonnell Aviation were the prime contractor for the Mercury and Gemini spacecraft.
This patch was likely used on the coveralls of McDonnell employees working on the Mercury and Gemini programs.
The Martin Company were the prime contractor for the Titan boosters used to launch the Gemini spacecraft.
This patch was used on the coveralls of Martin Company employees working on the Titan boosters for the Gemini program.
The Aerospace Systems Division of Bendix Corp were the prime contractor for the experiments packages deployed on the lunar surface during the Apollo program, including the EASAP and ALSEP. They were also involved in other technology used in the space program including communications equipment, and apparently life support equipment.
This 5" patch was apparently produced by Bendix to highlight their role in providing life support technology for the Apollo program.
[1] Examples of Chrysler Saturn 1B patch sales:
Lunar Legacies Space Auction lot 101 May 21, 2011 sold at $149.50
231160210794 Feb 21, 2014 sold at $228.30 [with condition issues]
eBay item no. 231289955842 Jul 28, 2014 sold at $70
[2] Examples of Chrysler Corporation Space Division patch sales:
eBay item no. 231160227813 Feb 21, 2014 sold at $150 [with condition issues]
[3] Examples of McDonnell text patch sales:
Lunar Legacies Space Auction lot 58 Feb 19, 2011 sold at $86.25
[4] Examples of Martin logo patch sales:
Lunar Legacies Space Auction lot 102 Feb 19, 2011 - jacket with Gemini 11 crew patch