in the following sentence second clause has conditional mood. but what about first clause (subjunctive or indicative?).
If you loved me you would support me.
It seems to be the subjunctive mood, especially since it's not known as a fact that "you" loves/loved "me". This becomes more clear if you read the sentence instead as:
You would support me if you loved me.
This page has some nice examples that help understand the different verb moods, and this excerpt seems most relevant:
The subjunctive mood can express a doubt or a wish using clauses beginning with "if" or "that"
Here, the first clause seems to be expressing doubt.
The first clause is called the protasis and yours is in the subjunctive mood. "You loved" above is the second-person singular or plural form of the past subjunctive of "to love".