These words look similar, but they’re not always interchangeable.

Administer often means organising or managing a system, programme or process.
„She administers the company’s pension scheme.“

Manage is often the more natural choice when talking about people, teams or projects.
„He manages a team of twelve.“

And what about administrate?
It exists, but administer is usually the more familiar choice.

💡 Quick tip:
Don’t automatically translate the German administrieren as administrate.
Depending on the context, manage, administer or handle may be more natural.