The Allen and Greenough is still under construction;
so some links may not work quite the way you would expect.
593. A clause depending upon a Subjunctive clause or
an equivalent Infinitive will itself take the Subjunctive if regarded
as an integral part of that clause: - [The subjunctive in this
use is of the same nature as the subjunctive in the main clause. A
dependent clause in a clause of purpose is really a part of the purpose,
as is seen from the use of should and other auxiliaries in English.
In a result clause this is less clear, but the result construction is a
branch of the characteristic (§ 534), to which category the dependent
clause in this case evidently belongs when it takes the subjunctive.]