Hi,
1. Let us play together.
2. Let them play together.
What is subject of both the sentences?
These are imperatives, which means they are orders. There is no explicit subject. However, a subject is implied. In other words, we understand who is being 'ordered' to do the action.
In #1, it's the group, of which the person speaking is a member.
In #2, it's 'you', the person being spoken to.
Let us is usually, but not always, abbreviated to Let's
Best wishes, Clive.