Your query has some group by problems (actually, you should not have any group by clauses), and you should convert it to a join:
SELECT
c.id,
c.name,
c.securityid
FROM c_contact c
LEFT JOIN c_monitoring m ON m.securityid = c.securityid
AND m.ended is null
WHERE c.securityid != ''
AND m.securityid IS NULL
See SQLFiddle
I also tidied up the query a little with aliases.