List of Organizations

Group Name: HARMONY (aka Team Discord)
Objective: Protect the environment
Alignment: Chaotic Good (in their eyes), Chaotic Evil (in the eyes of big business and the media)
History: Formed over an internet chat room by an eccentric former pop singer and other like minded people, they came together in order to wage war against big businesses that use the world as their dumping ground and fight for the creatures and plants that can't stand up for themselves.

They mainly communicate/coordinate via the internet and will sometimes meet in abandoned wax museum in Los Angelous or other unusual locations across the globe. Fate enjoys wearing outlandish costumes and forces her underlings to dress in a similar fashion whenever they have an offline meeting or go on a mission. Of course because of this their threats and ideals are rarely taken seriously.
Member List:
Fate Testarossa

Group Name: Live Corp 
Objective:  Secretly Conquer the World. Publicly: Advance Technology. 
Alignment: Good publicly, evil privately. 
History: Nek when he came to this time realized that the number of 'legends' outweighed his ability to combat them and so he was going to need some help. By capturing some scientists and brainwashing them Nek founded Live Corp. Live Corp is an organization publicly dedicated to the betterment of humanity as a whole. Secretly it is an organization made to make the rest of humanity the slaves of Nek.  Nek has not yet figured out what to do about the others possessing ranger technology but he has startd to make his company work harder to develop new technology to equal the influx of new rangers. 
Member List: 
Nek Atlas- CEO/CVO

Edited.

Edited. 

*sips tea*

Ah youth, where foolish idealism springs forth.

This is probably the most capitalistic evil corporation i've ever seen. I've got no problem with since it seems like he wouldn't be able to succeed anyway.

Group Name: Yggdrasil
Objective: Improve living conditions in Zawame City and around the world (but that's only what they tell people..)
Alignment: Lawful Good (at least on the outside...)
History: The landscape of Japan was completely altered by the second World War and the dropping of the atomic bomb. Villages were destroyed, hundreds upon hundreds of lives lost. An era had ended and it was around this time that a new era was bound to begin.

Jack Wotan, a soldier of the Allied Forces, and his rather small battalion were checking out a rather decent village called Zawame. Every single one of its inhabitants seemed to have vanished over night and they were tasked with finding out why. It was during this search, that Wotan discovered strange plants growing in an alleyway. He was about to bite into one of the fruits, but stopped when he saw what appeared to be a giant zipper.

Cocking his rifle and not calling for any backup what so ever, he entered the zipper and found himself in a strange forest. At first he thought he might be hallucinating, but after being attacked by a monster and losing his right eye, he concluded this was undoubtedly real.

Wotan reported into his superiors a few hours later with a strip of cloth wrapped around the right side of his face. He explained how some of the villagers had been in hiding and had attacked him when he found himself separated from his group. He told no one of what really happened and of the big plans he now had.

He returned home sometime afterward and took over his father's struggling company after he had passed away while Jack was on tour. He rechristened it Yggdrasil and in just a few years it was already a corporate powerhouse. He moved the company's headquarters to Japan and funded the complete reconstruction of Zawame.

In only a year, Zawame City was up and running while Yggdrasil's researching into the mysterious realm Wotan had dubbed Helheim had begun. They quickly discovered that consuming the fruit that grows there well turn any poor soul that does eat one into a mindless creature Wotan calls Invess. A bright young Yggdrasil technician named Paul Herbert discovered the fruit had other applications and invented what he called Lockseeds.

Using these Lockseeds, you can summon an Invess into the real world and even control it. Wotan saw this an excellent business opportunity and mass marketed Lockseeds to the youth of Zawame and thus the Invess Game was born.

After making Herbert the Head of Research and Development, the young man created yet another marvelous masterpiece of Yggdrasil technology - the Sengoku Driver. Using the Driver, you can insert a Lockseed and become a Kamen Rider.

Luckily for business and Alexander Wong, Zawame's resident shady Lock Seed Dealer, Lockseeds don't last forever. Like real fruit, they rot away and are no longer usable. They've fond that when a Rider defeats an Invess though, they absorb their essence into their own Lockseed which holds off the rotting process a little longer.

Even before the Invess Game, Zawame's youth fought over territory by forming teams and battling it out through dance. Yggdrasil continues to promote such a practice with Jack Wotan publicly stating it's good for the youth of today to be all fired up.
Member List:

Jack Wotan - Chief Executive Officer 
Rene Russo - Wotan's Personal Secretary
Mr. Kureshima - Chief Financial Officer 
Neil Wotan - Son of the CEO; Potential Successor
Alexander Wong - Lock Seed Dealer (formerly) 

"Elite Five" 
Takatora Kureshima - Son of the CFO; Chief Operations Officer and Chief of Security
Lloyd Asplund - Head of Public Relations
Anders Andersen - Codenamed "Zed"; Head of Tyr and Special Ops
Paul Herbert - Head of Research and Development
Marcelo Sagara - Chief Intelligence Officer, "Pirate" DJ

Group Name: Tyr
Objective: Eliminate enemies of Yggdrasil
Alignment: Lawful Evil
History: Tyr is a top secret branch of Yggdrasil used to eliminate threats. Not much is known about the group unless you are a member, so I'll just give you that info; it is a private security company used for Black Ops missions. Standard fare for such missions includes eliminating whistleblowers, stealing equipment and individuals from other groups such as Smart Brain, and purging riders from the streets and 'reclaiming company property'.

Every member of Tyr is armed with a Sengoku Driver and a Lockseed. The members are also highly trained as soldiers and assassins, and are strictly loyal to Tyr. Tyr's men remain unnamed in Yggdrasil records, being paid under the titles "bodyguard" and "private contractor".
Member List:
Zed: The title of Tyr's chief and Lockseed supplier.