'Is it okay to add a headline inside an HTML button?

I was wondering if it is semantically correct or OK to add a headline such as h1, h2, h3, h4 inside an HTML button.

Example

<button type="button">
   <h3>Button headline text</h3>
</button>

html semantic-markup

Solution 1:^[1]

Semantically? Maybe. You could make arguments either way and it would depend on context.

However, syntactically, it is invalid. HTML does not allow h3 elements to be descendants of button elements.

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Solution	Source
Solution 1	Quentin