The Subjunctive mood can be used in adverbial clauses of purpose introduced by the conjunctions: that, so that, in order that.

Adverbial clauses of purpose answer the questions: for what?, for what purpose?.

The Analytical Subjunctive with the mood auxiliaries may or might is used here when the action refers to the present or future and with might only when the action refers to the past.

She made him put his coat on so that he might not catch cold.
Она заставила его надеть пальто, чтобы он не простудился.

The Analytical Subjunctive with the mood auxiliary should also occurs here.

She made a shopping list so that he should forget nothing.
Она составили список того, что нужно купить, чтобы он ничего не забыл.

The Subjunctive mood can be also used in adverbial clauses of purpose introduced by the conjunction lest.

He put down all she said lest there should be any mistake.
Он записывал все, что она говорила так, чтобы не было никакой ошибки.