Going by your last edit's numbers you have at most 8x15 year olds and 16 of each of the years 12-14 who can do any serious labor and would be able to care for the other kids in a leadership role. That's 40 kids, let's say 60, who can "run" things.
The rest of the kids consist of 0-5 year olds who can provide no useful labor or generate no resources, but do consume resources and require constant care. Large families with adults might manage with one adult caring for and one working all the hours of the day and night to support maybe 7 kids. But these aren't grown adults, they're teens. The best they'll manage will be half that - maybe one older teen to care for three young kids and probably two older teens to generate resources for the "family" of six (and even that sounds optimistic). It's a dubious maybe with the support of middle year kids, who you'd need to generate enough resources to equate to feeding themselves doing chores that release the older kids for more work.
Even with these optimistic numbers you're looking at something skewed heavily to teens with minimal younger kids.
So I'd pitch this at fully loading the 11-15 year old "slots".
Maybe 1-2 kids in each of the 0-5 year old slots.
Maybe 1-3 kids in each of the 6-8 year old slots.
Maybe 1-4 kids in the 9-10 year old slots.
Given that distribution you're maybe talking about a party of teens in one location "surviving" the apocalypse and picking up odd one or twos of survivors of younger kids as they "search the ruins" or whatever approach you want to take.
Note that the problem with this scenario remains simply that even if they could survive that's all they could do. There's no scope here for building a civilization - they'd be barely able to subsist. Think of it this way : I'm a well educated science grad in his mid fifties. I survive the apocalypse and I'm reduced to farming. Which means I'm dead because as well educated as I am I know nothing about farming really. Your kids need to be farmers and that's what they need to know. Forget science - your science can't save you now !
But even with a bunch of farmer's kids, be aware that farming in a modern setting is not remotely like farming in a post-apocalyptic world would be. No bags of seed or fertilizer to hand, things like that have gone.
Your other issue is health. Again few adults could provide health care of a useful kind in a post-apocalyptic world. Do you know how to treat a wound ? Fix a broken bone ? Diagnose an infection and cure it ! Walk into a fully stocked pharmacy (as an educated adult) and work out which pills will help and which will make things worse. What if someone needs an appendix taken out (as I did in my teens) ? What if someone gets bitten by a rat ? Is a mark on the skin a serious infection that will kill or just a rash that will go away ? What's good blood pressure and heart rate in children of different ages and sexes ? What's bad ? Can you do anything about it or do you even need to if these basic things are out of expected ranges ?
So health could be a killer here.
When is the food safe to eat ? When is it not ? I'd have trouble with that one (remember - post apocalyptic !). If e.g. I plant a potato and it looks green is is safe to eat or not ? What if the whole crop looks that way and there doesn't seem to be an alternative ? One thing kids are not good at (and many adults) is contingency planning - they're unlikely to have a backup plan for problems. And can you bake bread starting from a field full of wheat ?
I'm dubious that sufficient numbers can survive to produce a decent sized second generation. The entire society would be on subsistence levels of existence for a very, very long time (many generations).