Make, let and allow all talk about getting someone to do something, or letting them do it. They are close in meaning, but they do not use the same structure after them.
Use make when someone forces another person to do something, or when something causes a reaction. There is no "to" before the verb.
Structure: make + person + verb
Use let to say that someone gives permission. There is no "to" before the verb either.
Structure: let + person + verb
Allow means the same as let, but it is a little more formal, and it needs "to" before the verb.
Structure: allow + person + to + verb
If there is no person after allow, use a noun or an -ing form. "Allow to do" on its own is not correct.
In the passive, make takes "to" again. Let has no passive form: use be allowed to instead.
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