You can have considerably more than 15 points and still not meet the support group criteria. However, in most cases, scoring 15 points for any single descriptor
will qualify you for the support group.
You can find out more here
Qualifying for support group As an aside, if you have no income other than ESA and you are single (or your partner earns less than aprox £150 per week) with less than £16,000 savings, you should be able to get income related ESA once your contributary benefit has stopped.