とりあえずたたき台

SELECT b.*, a.image_filename, a.name AS com_name, MAX(c.r_datetime) AS mtime
FROM c_commu a LEFT JOIN c_commu_topic b USING(c_commu_id) LEFT JOIN c_commu_topic_comment c USING(c_commu_topic_id)
WHERE b.name != 'NULL' AND a.public_flag IN ('public', 'auth_sns')
GROUP BY b.c_commu_topic_id ORDER BY mtime DESC LIMIT 20;