The word subieran is the imperfect subjunctive form of subir in the third person plural.
See the full subir conjugation

subir

Solía ser parte del continente, antes de que las aguas subieran.
It used to be part of the mainland, before the waters rose.
Debió suceder después de que me subieran de la superficie.
Must have happened right after I came up from the surface.
Me he tomado la libertad de hacer que subieran su equipaje.
I took the liberty of having your luggage brought up.
¿Cómo crees que logré que lo subieran a 25000?
How do you think I got them up to $25,000?
Rémi le pidió que subieran a la pasarela a echar un vistazo.
Rémi asked him to come up on the foot-bridge to have a look.
Le pedí al hotel que subieran una botella de champán a la suite.
I asked the hotel to put a bottle of champagne in your suite.
Mira antes de que mis hombres subieran.
Look before my guys went up the stairs.
Les dije que lo subieran cuando llegases.
I told them to bring it up when you got here.
Hice que te subieran en la lista.
I got you bumped up the list.
Solo quería que subieran las acciones de su empresa.
He wanted our help to drive up the stock in his family business.
Hice que te subieran en la lista.
I got you bumped up the list.
Estarían mejor si subieran a mi departamento a tomar una cerveza.
You'd all be better off coming upstairs to my place for a beer.
Uh, después de que subieran, lo inspeccioné y miré dentro del coche.
After they went up, I went over and looked in the car.
¡Les dijo que subieran después de los brindis!
You told them to come up after the drinks.
Yo ayudé a que los subieran.
I helped get them up there.
Los ayudé a que subieran allá.
I helped get them up there.
¡Les dije que no subieran así!
I told you not to get on!
Te dije que no dejaras que subieran y les dejaste a propósito.
I told you not to give them a lift but you did so on purpose.
No quería que subieran los impuestos.
Didn't want my taxes raised.
No quería exactamente que te subieran los latidos.
Your heart rate's not exactly what I wanted to get a rise out of.
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