b.subordinate clause.
A subordinate clause is essentially a sentence fragment. It can't stand by itself and make sense. That means it is dependent on an independent clause for meaning. It can be connected to that independent clause either before or after it.
Ex.
Dependent (subordinate) clause: when you get home
Independent clause: We will watch TV.
Combined: We will watch TV when you get home.
Combined: When you get home, we will watch TV.
A subordinate idea in the sentence is the part of the sentence that does not convey a complete idea or thought and needs the main sentence to complete its message. The subordinate idea in the given sentence above is "After we found the classroom". This is introduced by the subordinating conjunction "after".