The above write-up fills in a lot I hadn't known and enables me to make sense of what until now had been jumbled lists of dukes, kings, and electors.

Electors of Saxony

  1. Friedrich I, the Warlike 1423-1428
    He was Margrave Friedrich IV of Meissen; he was awarded the duchy of Saxe-Wittenberg in 1423, a title that conferred the electorate on him.
  2. Friedrich II, the Gentle 1428-1464
  3. Ernst 1464-1486
    Founder of the Ernestine branch. When Saxony was divided in 1485 he received Saxe-Wittenberg and Thuringia.
  4. Friedrich III, the Wise 1486-1525
  5. Johann the Constant 1525-1532
  6. Johann Friedrich the Magnanimous 1532-1547
    Magnanimity served him poorly; he was deprived of the electorate by emperor Charles V.
  7. Moritz 1547-1553
    First of the Albertine branch.
  8. August 1553-1586
  9. Christian I 1586-1591
  10. Christian II 1591-1611
  11. Johann Georg I 1611-1656
  12. Johann Georg II 1656-1680
  13. Johann Georg III 1680-1691
  14. Johann Georg IV 1691-1694
  15. Friedrich August I the Strong 1694-1733
  16. Friedrich August II 1733-1763
  17. Friedrich Christian 1763
  18. Friedrich August III 1763-1806(-1827)
    Elevated to King of Saxony in December 1806.

Kings of Saxony

  1. Friedrich August I (1763-)1806-1827
    Also Duke of Warsaw 1807-1813.
  2. Anton 1827-1836
  3. Friedrich August II 1836-1854
    Co-regent from 1830.
  4. Johann 1854-1873
  5. Albrecht 1873-1902
  6. Georg 1902-1904
  7. Friedrich August III 1902-1918
    Swept away up by the republic November 1918.

Dukes of Saxony

  1. Albrecht the Bold 1464-1500
    Awarded Meissen and Osterland on the division of Saxony in 1485. Evidently he and his immediate heirs bore the title of Duke of Saxony, until they became Electors. But I don't know what the situation was between 1464 and 1485.
  2. Georg the Bearded 1500-1539
  3. Heinrich the Pious 1539-1541
  4. Moritz 1541-1547(-1553)
    Became Elector of Saxony in 1547.
The Upper Saxon duchies that survived to the end were the following four. Their capitals were respectively Weimar, Meiningen, Coburg, and Altenburg.

Dukes of Saxe-Weimar-Eisenach

  1. Ernst August I 1741-1748
  2. Ernst August II 1748-1758
  3. Carl August 1758-1815(-1828)
    Elevated to Grand Duke in 1815.

Grand Dukes of Saxe-Weimar-Eisenach

  1. Carl August (1758-)1815-1828
  2. Carl Friedrich 1828-1853
  3. Carl Alexander 1853-1901
  4. Wilhelm Ernst 1901-1918

Dukes of Saxe-Meiningen(-Hildburghausen)

  1. Carl and Georg I 1763-1782
  2. Georg I alone 1782-1803
  3. Bernhard II 1803-1866
    Don't ask me what bits Bernhard I was duke of.
  4. Georg II 1866-1914
  5. Bernhard III 1914-1918

Dukes of Saxe-Coburg-Gotha

  1. Ernst I 1806-1844
  2. Ernst II 1844-1893
  3. Alfred 1893-1900
    Son of Victoria and Albert.
  4. Karl Eduard 1900-1918

Dukes of Saxe-Altenburg

  1. Friedrich 1826-1834
  2. Joseph 1834-1848
  3. Georg 1848-1853
  4. Ernst I 1853-1908
  5. Ernst II 1908-1918
The former kingdom of Saxony was a state of the republic of Germany from 1918 to 1945. Between 1945 and 1952 East Germany had two states Saxony and Saxony-Anhalt. This level of government was then abolished, but it was these post-War states that were restored after the Berlin Wall fell, and which were admitted as Länder to the Federal Republic in 1990. The capital of Saxony-Anhalt is Halle.

I have not covered places such as Thuringia, Oldenburg, and so on, which should be sought in their own place. (But they're not there yet.)