In order to prevent one man from gaining as much power as Horus had, the branches of the Imperial armed forces were separated, the Inquisition was founded, and the loyal Space Marine Legions were divided into Chapters of roughly one thousand Marines in accordance with the Codex Astartes.
The Second Founding was not universally accepted; the Space Wolves and Imperial Fists in particular objected to dividing their Legions, and the Imperium was nearly torn apart by another civil war. For better or for worse, Leman Russ was given an exemption to the Codex's requirements and Rogal Dorn finally relented, although the Black Templars have since grown their numbers to many more times the usual size - which is perfectly legal, since the Codex and the law allow "crusading chapters" to ignore the limitations due to the expectation of constant fatalities needing replacement.
Despite what you might think, exploiting this by having the chapters realize that they are all technically crusading (and even if they weren't, the Great Crusade never officially ended, therefore...) would likely be a very skubby idea; on one hand, it could very quickly turn every little Astartes secession party (like the Badab War) into another Horus Heresy and make already borderline rogue chapters even worse. On the other hand, it's possible that they could always split up into more Chapters as "we're crusading but we want to show our sincere desire to avoid another Horus Heresy so we'll split our excess instead of keeping it", which would be a nice way around the limitations while the High Lords can only grit their teeth at their loss of control.
(1st Edition even says the Chapters are self-sufficient and build their own wargear and vehicles and stuff, too, so everything a Chapter needs could possibly be built by the parent Chapter. It's unclear how much this holds in the current setting, but it'd be implausible for the Chapters to not have at least some in-house manufacturing capability.)
List of Second Founding Chapters
- Angels of Absolution
- Angels of Redemption
- Angels of Vengeance
- Lions Sable (destroyed trying to apprehend several Fallen in what was later revealed to be a massive trap set by Cypher shortly before The Beheading and all records of their existence were erased to hide the involvement of the Fallen in their collapse.)
- Star Phantoms (maybe, though this chapter definitely did exist in M31)
- Angels of Vigilance (again maybe, though this one is more likely)
According to The Unforgiven by Gav Thorpe, the Angels didn't get started with their Inner Circle and Fallen Hunting until some decades after the Second Founding so it may be possible that some of the Dark Angels Second Founding chapters are exempted from this practice and hierarchy. Since all twelve chapters were present at Cypher's revelation and that the majority of officers would have been veterans of the Horus Heresy and the Scouring, it's more likely that Unforgiven would been of one mind and joined willingly and any dissenting voices silenced or sworn to absolute secrecy.
While much of the truth is lost to apocrypha and LIES, it does at least provide a potential explanation for the Star Phantoms' temporal fuckery, as they might have been the Chapter where the Astartes who decided that the Fallen hunting affair would be dumb were allowed to join in exchange for vows of silence.
- Black Templars
- Crimson Fists
- Soul Drinkers (sort of, it's a long story)
- Fists Exemplar: Mostly destroyed by The Beast. Majority of the survivors went on to re-establish the destroyed Imperial Fists under the Last Wall Protocol, barring one unit that lost contact in the fighting and defected to the Iron Warriors. The records of the Fists Exemplar were subsequently put to the torch by their own Chapter Master to cover up the shame of being the first Chapter to (technically) fall to Chaos since the days of the Horus Heresy
- Iron Knights (found before Fourth Founding)
The Apocrypha of Skaros indicates that the Ultramarines sired 23 chapters, but doesn't name them all. The listed second founding chapters are given below:
- Aurora Chapter
- Black Consuls
- Desert Lions
- Doom Eagles
- Eagle Warriors
- Genesis Chapter
- Iron Snakes
- Patriarchs of Ulixis
- Praetors of Orpheus
- Silver Eagles
- Silver Skulls (post-retcon; they were previously a Third Founding Chapter)
- White Consuls
- Yellow Jackets
The rest of the second founding Ultramarines have been added piecemeal as time goes by.
Also note that the Ultramarines "adopted" some of the loyalist forces from otherwise traitorous legions and permitted them to call themselves Ultramarine Second Founding chapters. More details can be found here.
The Scythes of the Emperor were the Ultramarines 199th Company on Sotha, who became the Ultramarines eleventh company as part of the second founding; Guilliman unofficially gave himself an extra company to guard the Pharos device, but after he was placed in stasis following his injuries at the hands of Fulgrim they were eventually rolled into their own chapter during the Third Founding.
None, as there weren't enough Salamanders left after the Horus Heresy to fill one Chapter, let alone two.
The Grey Knights were not created from any of the Space Marine Legions, as their gene-seed was specially created by the God-Emperor of Mankind himself and their founding members were hand-picked by Malcador the Sigillite; at least two of the eight founding Grand Masters were loyalists who had formerly been a part of a Traitor Legion (Revuel Arvida/Janus, Thousand Sons; Iapto/Severian "the Wolf", Luna Wolves; Crius/Garvel Loken would have been the ninth had he not refused the position). They were founded to supply the newly-formed Inquisition with a strike force against future Chaos threats.
Some chapters have histories which stretch back to the Second Founding but have deliberately obfuscated their parent legion for one reason or another.
- Red Hunters - likely down to their status as the Inquisition's lapdogs, which results in regular mind-scrubbing and their history being 1984'd after every few campaigns. They're implied to be Second Founding, however.
- Purple Stars