Who are the 13 families? Here are the first search results:

Time, 1940, citing SEC: "The 13 most potent family groups’ holdings were worth $2,700,000,000, comprised over 8% of the stock of the 200 corporations: Fords, $624,975,000; Du Fonts, $573,690,000; Rockefellers, $396,583,000; Mellons, $390,943,000; McCormicks (International Harvester), $111,102,000; Hartfords (A. & P.), $105,702,000; Harknesses (Standard Oil), $104,891,000; Dukes (tobacco, power), $89,459,000; Pews (Sun Oil), $75,628,000; Pitcairns (Pittsburgh Plate Glass), $65,576,000; Clarks (Singer), $57,215,000; Reynolds (tobacco), $54,766,000; Kresses (S. H. Kress), $50,044,000." It emphasizes that this cutoff of 13 lists the primary groupings that maintained power over the top 200 corporations. However, it's not a resource actually used even though the names are significant:

1. Ford family
2. du Pont family
3. Rockefeller family
4. Mellon family
5. McCormick family
6. George Huntington Hartford
7. Stephen V. Harkness
8. James Buchanan Duke
9. Joseph Newton Pew
10. John Pitcairn Jr.
11. Edward Cabot Clark
12. R. J. Reynolds
13. Samuel Henry Kress

CIA, 1995, quoting Fritz Springmeier, Bloodlines of Illuminati (ne Viktor Schoof; convicted of bank robbery and jailed 2003-2011, claiming he was framed). "Several people from different places have confirmed that there are 13 Illuminati bloodlines. Further, several ex-Illuminati people have confirmed my list of 13 families. It is possible that my list is off on a name or two, but if it might be off, it can not be off much, if any. I believe the facts speak for themselves." (Chapter titles begin "The Astor Family", etc., but four chapters are added after the 13th family and chapter has been named; this is a compilation of many articles from different periods.)

1. Astor family (John Jacob Astor)
2. "Bundy Bloodline" (Ted Bundy, McGeorge Bundy)
3. "Collins Bloodline" and Todd "branch" (Joan Collins, Mary Todd)
4. du Pont family (Pierre Samuel du Pont de Nemours)
5. "Freeman Bloodline" (Walter Jackson Freeman II, Roger A. Freeman (economist))
6. Kennedy family (P. J. Kennedy)
7. House of Li (Zhuanxu)
8. "Onassis Bloodline" (Aristotle Onassis, Jacqueline Kennedy Onassis)
9. Rockefeller family (John D. Rockefeller)
10. Rothschild family (Mayer Amschel Rothschild)
11. "Russell Bloodline" (Charles Taze Russell, Richard Russell Jr.)
12. Vanderbilt family and "Van Duyn Bloodline" (Mona Van Duyn)
13. Merovingian dynasty (Clovis I)
14. Disney family (Walt Disney)
15. "Reynolds bloodline" (R. J. Reynolds, Richard S. Reynolds Jr.)
16. Clan Donald (Richard and Maurice McDonald)
17. Krupp family (Friedrich Krupp)

This music album gives the same names as Springmeier 1-13: Rothschild Rockefeller Kennedy Astor Bundy Collins du Pont Onassis Li Van Duyn Freeman Merovingian Russell. So does this blog and this tweet. Here a researcher changes Merovingian to Reynolds. And https://grokipedia.com/page/Fritz_Springmeier gives the original list of 13.

Before leaving Springmeier, I made one more try by checking out "List of banking families", which is of course arbitrary WP which I will make further arbitrary by listing only ones that I like: Barclay, Baring, Fugger, Goldman-Sachs, Hinduja, Lazard, Li, Medici, Mellon, Morgan, Rockefeller, Rothschild, Warburg. Wow, 13 without trying, I must be inspired.

So it appears all real claims of 13 families come from Springmeier 1995 and refer to the same people, not listed as a particular club, but instead offered as "if there is a club here's evidence this named group is a member". In particular the names I put in quotes above are not recognized as directly connected families but just very common surnames. So I'm disappointed because this isn't what I was directly looking for. An ordinary list of Davos participants any year would cast a wider net. The Time list happens to use the framing "13 families" but is merely the American rich list. If I were to say here are 17 likely families, even though they appear in different periods and have different connections and overlaps, well, I can use the list, but it's effectively useless to hold a claim that there is an organized list of 13 that all have the same status at the same time or that get substituted one for another at times from a larger group.

So once again, the cabal is disconnected, the rumors of organization on either our side or theirs are exaggerated. What I always say is that there are many many families, they shift and rearrange, merge and separate, and they don't make any real public list available; the rich list is a known farce that gives no indication of the true level-pullers. Therefore this is a very poor way of going about an international question.

One reason for my interest is Q's statement about focusing on three, Saud, Rothschild, and Soros. The context indicates that the Q operation wants us to focus on the first one (with Trump's connections) overpowering the other two. This leaves one to guess where all the rest of the wealth in the world is controlled, and I'm just not finding any useful list. And genealogists know that tracing a "single" family through its branches is very sketchy, let alone to trace actual movements of money and power as if these automatically follow names when they don't. I'm left with the conclusion that there's no real core network of any number, but rather my conclusion from Carroll Quigley that each circle thinks it is the real inner circle, and the hydra is not slain by counting its heads.

Add: Not really related, but if anyone wants to know the original Illuminati (Perfectibilists), there were thousands. A Masonic site yields a little detail on: founder, Adam Weishaupt (Spartacus); first four novices, Franz Anton von Massenhausen (Ajax), Franz Xaver von Bauhof(f) (Agathon), Max Edler von Merz (Tiberius), Andreas Sutor (Erasmus Roterodamus/Rotterdamus); Franz Xaver von Zwackh, Adolph Knigge, Charles of Hesse-Kassel, Charles Savalette de Langes, Alexandre Roettiers de Montaleau, Ernest II of Saxe-Gotha-Altenburg, Johann Joachim Christoph Bode, and (the) Johann von Goethe. Also on WP are many others such as Johann Friedrich Baring (I just named his family independently), Junius Frey (Frankist converso), Franz Georg Karl von Metternich (German diplomat), Donato Tommasi (Italian politician).