[GAP Forum] Creating all subgroups of SymmetricGroup

Alexander Hulpke hulpke at math.colostate.edu
Wed Nov 4 16:54:35 GMT 2009

Dear GAP forum,

Ivan Jurevitch asked:
> Can I create the set(list/ record) of all subgroups (preferebly
> nonisomorphic) of a Symmetric Group on 9 elements - Sym(9)?
> There is a function IntermediateSubgroup(G,U) which creates all  
> subgroups
> "between"G and U.
`IntermediateSubgroups' is intended for the case that U is nontrivial  
and you don't want to get the full lattice. It likely is very  
inefficient for getting all subgroups.

The command
creates a list of all subgroups. I doubt you would want to have this  
list for S9 (which has 1694723 subgroups in 554 classes) -- you  
probably will be happy with class representatives as obtained from  

Also see questions 7.6 and 7.7 of the FAQ at



    Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288

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