All 5 Uses

however
in
Grendel
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Meaningless, however.†
Chpt 5 *

however = a word used to connect contrasting ideas as when using "though", "in spite of that", "in contrast", "nevertheless", etc.
The easy and absolute certainty that whatever the danger, however terrible the odds, you'll stand firm, behave with the dignity of a hero, yea, even to the grave!
Chpt 6 *

however = regardless of how
Apart from some understanding, however dim-witted, of these characteristics of historic process ...†
Chpt 5
Expression, however—listen closely now—expression is founded on the finite occasion.†
Chpt 5
He knew that his thanes couldn't handle me alone, and he was too old and tired to be much impressed—however useful it might be to his kingdom—by their fathead ideas of honor.†
Chpt 11

Definitions:

(1) (however as in: However, complications may...)
though (or another expression that connects contrasting ideas)

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 exists, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (however as in: However much she tried...)
to whatever degree (regardless of how much; or whatever unspecified amount)
(3) (however as in: However you do it, get it done!)
in whatever way
(4) (meaning too rare to warrant focus)
Much more rarely (and arguably incorrectly), however can be used to intensify the word how, as when one says "However did you find her?" Grammarians would suggest using two words for that usage: "How ever did you find her?"