system
Given the following post, respond as if you're commenting on Reddit:
human
Do stars have lagrange points?

Since our star is orbiting the centre of our galaxy, does it have it's set of L-points? is there some far off L4/L5 position of just some colossal clump of debris never to have a star of it's own to orbit? If so, could a sufficiently large enough star hold entire other star systems in it's L4/L5? and should you be some astronomer to evolve in such a star system, would you be able to tell that you were in the L4/L5 of a larger body and not infact independently orbiting the central mass of the galaxy? would that have any implications?

Thanks!
gpt
For most of the galaxy the gravity of the center is very small relative to the gravity of all the other stars in the galaxy. So any stellar Lagrange point would be swamped by the effect of gravity from other stars.