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May 12, 2023 at 9:56 comment added userrandrand I am not sure how trustworthy FiniteGroupData is. For example, For $S_4$, FiniteGroupData[{"SymmetricGroup", 4}, "Subgroups"] // Map[FiniteGroupData[#, "Order"] &] does not show a subgroup of order 8. However there are dihedral subgroups of order 8 according to groupprops.subwiki.org/wiki/… and math.stackexchange.com/questions/379841/…
May 11, 2023 at 16:53 comment added Domen I don't see 1455 subgroups listed in your answer. Please, ground your claim that there are not 1455 subgroups.
May 11, 2023 at 16:39 comment added user64494 @Domen: Please, ground your claim. What subgroup of $S_6$ cannot be obtained in such a way?
May 11, 2023 at 14:27 history edited user64494 CC BY-SA 4.0
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May 11, 2023 at 14:21 comment added Domen As it was pointed to you in your previous answer, this does not list all of the subgroups.
May 11, 2023 at 14:20 history answered user64494 CC BY-SA 4.0