The simplest solution is to set the runToBottom flag to true in the subreport tags.
<subreport runToBottom="true">
This causes the subreport to fill out the entire page, so the next report below will start on a new page.
The isTitleNewPage flag isTitleNewPage not do the trick because, as you have noticed, it will split the sub-report title group with the rest of the sub-report content (unless you use an empty title bar).
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