6
$\begingroup$

How can one prove that there are no subgroups of $S_5$ with order 40?

Thank you!

  • 2
    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:S52011-12-06
  • 0
    Thanks very much, @Listing!2011-12-06

2 Answers 2