What are the parental/child supports available in Japan?

We got the lump sum 500k payment for our first child, which basically all went to the cost of birthing her. There's the 15k/month payment (which seems rather low).

Is there anything else?

Daycare isn't free. My wife said high school isn't even free (unless your kid scores high enough to get into a free one).

Am I missing something? Is that really it?

(Before you say it's better than the USA, I'm not American and I'm not interested in comparing anything to the USA, which is what people do every time I post here).

Edit: I already have a child and assumed zero support for them, but my wife and I want to have more kids and are thinking about financial matters, for those of you trying to shame me. I'm thinking about future children, not my current one, thanks.

by kinokogadaisuki