I've recently built a HQ for my third trading company, but it's not creating any trade routes.

Interstar Group has its new HQ on Maial, just one star lane away from Gemini, the HQ of Andromeda Company.  Andromeda is able to form trade routes, so I can't imagine what could be interfering with Interstar unless there is something on Maial itself.  But Maial is deep in the heart of my territory, with no enemy fleets anywhere nearby.

The map doesn't show any blockades, either.

Any ideas what's stopping them?

Also, I've just built my third trading subsidiary on Adana (middle of the picture), finished on the turn this screenshot was taken, but none of my trading companies have formed a route to it.

This is stopping me from completing my main quest line, which requires me to have 6 trade routes.

AutoSave 119.sav

Verta looks like an enemy system. Do the routes go through that? 

Out of interest - were your other companies built before you got wormhole tech? Maybe they take a longer route that isn't blocked, unlike the shorter route that is?

(I actually preferred Endless Legend's system of producing the maximally profitable routes dynamically each turn, compared to ES2's handling which is much more static. But I think there were development reasons for this approach.)