Originally Posted by Skyehmm

You don't have to actually start any mission to see which helper squads you can choose from. Just looking at the "Choose Helper Squad" screen will help you with that if you really need to look for a specific squad.

To get out of that window you can click on any of the buttons on the left side in the game.

Yes, but I suspect there's something more involved as well, probably last login time (I have one person on my friendslist who hasn't logged in for more than a week, his squad just occasionally shows up after I do a lot of runs in a short period of time). So, if you want to use the squad of someone who hasn't logged in for a while (could be hours, could be days, depends on how often everybody else on your list logs in as well), you'd have to "clean up" the more recent logins by actually using them.