State Government
Subject to the Constitution, a State's executive power extends to matters on which the State Legislature can make laws - provided that where both Parliament and the State Legislature have law-making power on a matter, the State's executive power is subject to and limited by any executive power the Constitution or a Parliamentary law expressly gives to the Union.
This mirrors Article 73 at the state level: a state's executive authority generally matches its own legislative authority, but on subjects where both the Union and states can legislate, the Union's executive authority takes precedence where the Constitution or Parliament's laws specifically say so.
On a subject like education (which both Parliament and state legislatures can legislate on under the Concurrent List), if a central law specifically claims executive authority over some aspect, that overrides the state's own executive power on that specific point.