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OPEN This is open, and cannot be resolved with a finite computation.
Describe (by statistical means) the arithmetic structure of the orders of subgroups of $S_n$.
Disclaimer: The open status of this problem reflects the current belief of the owner of this website. There may be literature on this problem that I am unaware of, which may partially or completely solve the stated problem. Please do your own literature search before expending significant effort on solving this problem. If you find any relevant literature not mentioned here, please add this in a comment.
This is given in [Va99] as a problem of Erdős and Turán. I have reproduced the problem verbatim; I am not entirely sure what it is asking for.

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The original source is ambiguous as to what the problem is - please add a comment if you have an opinion.
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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #1163, https://www.erdosproblems.com/1163, accessed 2026-03-01