The subordinate is actually the present subjunctive. There's also a past subjunctive (que je fusse, tu fusses, il fût, nous fussions, vous fussiez, ils fussent)

The subordinate is actually the present subjunctive. There's also a past subjunctive (que je fusse, tu fusses, il fût, nous fussions, vous fussiez, ils fussent) and other forms with auxliaries, if I remember my grammar properly, the formsare derived from the simple past, or the other way around, can't remember. The reason it's not subordinate is because I think there are some very rare cases where it can be used without a que, but I can't think over one off the top of my head.