Morning Musume (1997-Present)
Morning Musume were formed when Tsunku, their producer, took the five running up members of his talent search and decided to make them into a girl group. They were an instant success and a tabloid staple due to their constant changing line up of members. They suffered a large sales drop during the latter half of the 2000's but recently have improved their sales with their new EDM based music.
Mini Moni (2000-2004)
Mini Moni, a Morning Musume sub-unit, was one of the most popular girl group sub units of all time. They were notorious for their outlandish music videos and crazy songs. They suffered a sales drop along with Morning Musume and later disbanded in 2004.
MAX was originally a girl group called "Super Monkey's" that was fronted by superstar Amuro Namie. After Namie's departure the remaining members of Super Monkey's formed MAX. They were very popular in the late 90's for their dance songs and gained similar sucess in the early 2000's for their more matured sound. They still make music today despite the fact that they're no longer popular.
AKB48 is notorious for being one of the biggest pop groups of all time. There is a lot I could say about them but I really don't have the time. They used to be really cool around 2010 but most people I know have jumped ship. They also have a long record of only 1 million selling singles since 2010.
°C-ute were formed in 2005 as a sister group to Morning Musume. They had songs good songs around 2010-ish but now they really only release outdated EDM songs.
Buono! was formed in 2007 to sing the opening and ending songs for the Shugo Chara anime. They consist of members of the girl groups °C-ute and Berryz Kobo. I used to listen to them in middle school so their music is kind of nostalgic to me.
E-Girls were formed in 2011 as a combination of the girl groups Flower, Dream and Happiness. They have immense popularity and are the sister group to the boy band EXILE.
Sources: Google Images, Youtube, Me