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.
And the challenge with the current learning software is that they treat each one of these forms as a separate flashcard. So, you are learning surface/contextualized forms of the verb rather than understanding how to use the verb itself in various contexts.
Present: Je vais, tu vas, il va, nous allons, vous allez, ils vont
Future: j'irai, tu iras, il ira, nous irons, vous irez, ils iront
Same goes for être (to be):
Present: Je suis, tu es, il est, nous sommes, vous êtes, ils sont
Future: Je serai, tu sera, il sera, nous serons, vous serez, ils seront
Simple past: Je fus, tu fus, il fut, nous fûmes, vous fûtes, ils furent (No one uses simple past, but here it is)
Subordinate (?): Que je sois, que tu sois, qu'il soit, que nous soyons, que vous soyez, qu'ils soient
I guess it's the same in pretty much every language, especially for those 2 common verbs, there are irregular forms everywhere.