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Forty five words put T first and E third, and fourteen of them repeat a letter. That is nearly a third of the page.
H takes the second box in seventeen words, thirty eight percent, and R takes fifteen. W adds six more. Together those three cover thirty eight of the forty five, and almost nothing appears outside them.
THEME, THERE, THESE, THEFT and THEIR are the ordinary words in the largest branch. THETA, THERM and THEIN fill it out and are less likely to be wanted.
They share three letters by definition, so a guess inside THE narrows only the last two boxes. E takes the fourth box in nine of the forty five, more than any other letter, which is where most of the repeats come from.
TREAT, TREND and TREAD carry the R branch, and TWEED, TWEET and TWEAK carry the W branch. Both are smaller than THE but their words are less alike, which makes a guess there worth more than the raw count suggests.
The EE shapes account for most of it. TEETH, TREES, TWEED and TWEET all put a second E straight after the third box.
They differ in two boxes and both are very common, so either works. THERE also tests R, which fifteen words use in the second box.
A rank in early English society, roughly a lord's retainer. It is one of the narrower entries in the H branch.