First, there are the numbered fleets. 2nd Fleet is the Atlantic, 6th is the Med, 5th is the Persian Gulf area, 3rd is the eastern Pacific and 7th is the western Pacific.
Then there were task forces, which reported to the fleet commander. TF 60 was the carrier force and their escorts. TF 61 was the amphib ships, TF 62 was the Marines on those ships, TF 63 was the logistics fleet. I've forgotten what TF the subs were (other than "sonar contact = enemy").
There were normally two carriers in the Med. Each carrier made up a task group, 60.1 and 60.2. The embarked destroyer commodore was head of the task unit for the their task group, making them 60.1.1, etc. Ships that were split off for independent assignments (which happened to the ASW 1052s frequently) were designated as task elements.
The commander of any of those forces was designated with a C, so the commander of TG 60.1 was known as CTG 60.1. That was a valid naval message address. So if the staff of Cruiser and Destroyer Group 2 was in the Med as the boss of TG 60.1 and you needed to send a message to the admiral, you addressed it to either COMCRUDESGRU TWO or CTG 60.1, depending on whether or not the subject matter was administrative or operational.
This is background for an upcoming post.