követhették
"követhették" is the third-person plural conditional past form of the Hungarian verb "követ". "Követ" translates to "to follow" in English. Therefore, "követhették" expresses a hypothetical or potential action of following that could have happened in the past, but did not necessarily occur. It implies that the subjects were in a position to follow, or it was possible for them to follow, but the decision or outcome is uncertain or contrary to fact.
The conditional mood in Hungarian, especially the past conditional, is used to express unfulfilled conditions, possibilities,