Thread: Subgrounds of Symmetric Groups

I'm trying to find all of the subgroups of the symmetric . But am not sure how to generate these groups as all of the properties of groups must be satisfied.

I am thinking it is something along the lines of:
{(123)->(123)} (no change)
{(123)->(123), (312), (231)}
{(123)->(123),(132), (213), (321)}

Is this the right track? Or am out out in left field?

Originally Posted by apsis

I'm trying to find all of the subgroups of the symmetric . But am not sure how to generate these groups as all of the properties of groups must be satisfied.

I am thinking it is something along the lines of:
{(123)->(123)} (no change)
{(123)->(123), (312), (231)}
{(123)->(123),(132), (213), (321)}

Is this the right track? Or am out out in left field?

The subgroups are .