The Injustice Society may have ultimately proved a failure when battling their opposite number, the Justice Society, however two of their members succeeded beyond their wildest dreams in ruling the world. Of a kind.
Vandal Savage had the longest run of a rogue's reign, when he schemed to have Superman follow him back through the ages the detonate various time bombs that reset history. As a result, Earth-One was transformed into a perpetual kingdom was the Earth-Two Savage as its sole sovereign for centuries. Or at least for several days, though it seemed longer given how the time stream was altered.
Vandal was known for pilfering the equipment of his fellow Socialites back when he worked with them in the late 1940's, and thus it would've been his ally Per Degaton's temporal technology that was instrumental in the immortal villain's victory. Although Superman figured this out and reverts history to how it was intended to be.
And speaking of Degaton, when he was a lowly lab assistant for Time Trust scientist Professor Malachi Zee, he gained access to temporal technology. In 1947, Per stole Zee's time cabinet and journeyed back in time with armies and 20th century weaponry in order to alter the course of the key Battle of Arbela in 331 BC which changed the course of history. As such, Earth-Two did not technologically advance past a medieval state, while Degaton secured his modern armaments in a chromium lined cave. Even into the late 1950's, this resulted in this tyrant having unmatched power which even the Justice Society could not overcome.
That is, until Green Lantern journeyed back in time with his teammates and tipped the Battle of Arbela back in favor of the true victors according to history. This led to time being reset, with Per's reign of tyranny ending. Although, the memory of his fleeting victory would remain and prompt him to pursue this path once more.
On his second attempt, Degaton stole atomic weapons from Earth-Prime,enlisting the aid of Earth-Three's Crime Syndicate in order to control Earth-Two. Apparently, this was the decisive step needed so that into the 1980's, Degaton's new history proved him master of his native world. In this reality, superheroes still existed however the Crime Syndicate members Ultraman, Superwoman, Owlman, Johnny Quick and Power Ring remained as his enforcers allowing them to subjugate this world.
The combined efforts of the Justice Society, Justice League and All-Star Squadron were needed to thwart Degaton's determination for dominance. In the process, they changed back the altered timeline on Earth-Prime that had resulted from the Syndicate's theft of weaponry, when that world was reduced to a devastated landscape. With not atom bombs nor his Syndicate at his disposal, Degaton once more retreated to his native 1947 leaving all save him forgetting about this encounter. His desire would remain.
On Earth-One, Professor Ronson accidentally unleashed via his chronal transponder an energy wave that altered that planet's future causing its superheroes to be eliminated with only their alter egos remaining. Thankfully, the World's Finest Team from the future of Earths One and Two restored reality to its natural course.
Interestingly, the first chronological reset of history on Earth-One was actually the creation of a deviant planet and universe spawned by Earth-Two's Thunderbolt at the behest of the criminal Johnny Thunder who wanted the Justice League eliminated. Replacing them with his Lawless League, themselves counterparts to the Crime Syndicate that were displaced in the alternate timeline on Earth-Two, this quintet of crooks had fleeting careers before they were dispatched by the visiting Justice Society. Although this world exists somewhere within the Multiverse, as does the altered timelines we've considered, they've been folded back into non-existence from whence they came as far as we're concerned.
Nevertheless, an interesting aside is one final artificially created timeline/universe in the form of Earth-Zero, which was made manifest when Mister Mxyztplk and the entity known as Aethyr destroyed the short-lived planet Aethyr in Earth-One's reality yet projected it and its Bizarro inhabitants into a pocket universe much like Earth-A or these timelines. With their own evil replicas of Justice League and Justice Society members, these worlds would only be liberated from such oppression (although the Bizarro's enjoyed it, given their warped nature living in reverse) when the champions of main-stream realities intervened.
So while history cannot be changed in the universes of the Multiverse, it can be branched off into timelines or universes distinct and different from each individual universe. Although due to the nature of time and the fluidity of their states of being, such existence is transient to say the least!