How can one prove that there are no subgroups of $S_5$ with order 40?
Thank you!
abstract-algebragroup-theoryfinite-groups
asked 2011-12-06
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http://www.maths.qmul.ac.uk/~rab/MAS305/algnotes5.pdf page 5 shows what you want. Note also that all subgroups of $S_5$ have been classified: http://groupprops.subwiki.org/wiki/Subgroup_structure_of_symmetric_group:S5 – 2011-12-06