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The ordering of large cardinals by consistency strength is well known.
I was wondering what one can say regarding an ordering by direct implication.
In particular, I am looking for is a parsimonious axiom of the form "There exists an XYZ cardinal" which 'picks up' as many other large cardinals as possible by directly implying that they exist.

So the best I can think of is:
Extendible cardinal $\implies$ Supercompact cardinal $\implies$ Measurable cardinal $\implies$ Loads of other large cardinals (There are also many other in between these categories that are directly implied, I believe)

But is it possible to go further ?

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    $\begingroup$ Honestly, I don't understand what you are asking. A table with all known large cardinals and for any two of them a decision on whether or not the existence of one kind of cardinal implies the existence of the other? $\endgroup$
    – Andrés E. Caicedo
    Commented Jan 31, 2020 at 2:45
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    $\begingroup$ I0 cardinals? $\endgroup$
    – Conifold
    Commented Jan 31, 2020 at 8:25
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    $\begingroup$ See also MathOverflow.net/questions/219132 $\endgroup$
    – user44143
    Commented Jan 31, 2020 at 9:15

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