Παρά το γεγονός ότι διαφώνησαν, βοήθησαν.

It introduces a concession: something like despite the fact that or even though.

So the structure is:

• Παρά το γεγονός ότι = despite the fact that / even though
• διαφώνησαν = they disagreed
• βοήθησαν = they helped

This is a fairly common and natural way to connect two ideas when the second happens in spite of the first.

It is a bit more formal or heavier than shorter alternatives such as:

• αν και
• παρόλο που

Here παρά means despite, and in this use it is followed by the accusative.

That is why you get:

• το γεγονός = the fact in the accusative/neuter form

Because γεγονός is a neuter noun, its nominative and accusative singular look the same:

• nominative: το γεγονός
• accusative: το γεγονός

So even though the form does not change visibly, grammatically it is functioning as the object of παρά.

Here ότι introduces a content clause, like English that in the fact that...

So:

• το γεγονός ότι διαφώνησαν = the fact that they disagreed

This is very standard Greek.

You may also see πως in some contexts after verbs of saying, thinking, etc., but after το γεγονός the normal and expected choice is ότι.

Both are in the aorist active indicative, 3rd person plural.

• διαφώνησαν = they disagreed
• βοήθησαν = they helped

The aorist presents each action as a completed whole. It is the normal tense if you mean something like:

• they disagreed, and then
• they helped

or simply

• despite disagreeing, they did help

If the sentence used the imperfect, it would suggest ongoing or repeated action instead.

The aorist is used because the sentence treats both actions as whole events:

• the disagreement happened
• the help happened

The imperfect would sound more like background or ongoing action, for example:

• διαφωνούσαν = they were disagreeing / they used to disagree
• βοηθούσαν = they were helping / they used to help

So the actual sentence suggests a specific situation or completed event, not an ongoing scene.

Greek often leaves subject pronouns out because the verb ending already shows the person and number.

Here:

• διαφώνησαν = they disagreed
• βοήθησαν = they helped

The ending -αν tells you the subject is they.

Greek usually adds a pronoun like αυτοί only for emphasis, contrast, or clarity.

For example:

• Αυτοί βοήθησαν = They were the ones who helped

But in your sentence, no explicit pronoun is needed.

By itself, διαφώνησαν simply means they disagreed. The exact target of the disagreement is not stated.

Depending on context, it could mean:

• they disagreed with each other
• they disagreed with another person or group
• they disagreed about an issue

If Greek wants to make that clearer, it can add more information, for example:

• διαφώνησαν μεταξύ τους = they disagreed with each other
• διαφώνησαν με τον διευθυντή = they disagreed with the director
• διαφώνησαν για το σχέδιο = they disagreed about the plan

So in your sentence, the object or target of disagreement is simply left unstated.

Yes. Very common alternatives are:

• αν και διαφώνησαν, βοήθησαν
• παρόλο που διαφώνησαν, βοήθησαν

These are all natural, but they differ slightly in tone:

• παρά το γεγονός ότι = a bit more formal, more explicit
• αν και = simple and common
• παρόλο που = very common in everyday Greek

So the original sentence is correct and natural, but somewhat more formal or written in style.

The comma separates the initial subordinate clause from the main clause.

Structure:

• Παρά το γεγονός ότι διαφώνησαν = subordinate concessive clause
• βοήθησαν = main clause

This is similar to English punctuation in a sentence like:

• Although they disagreed, they helped.

Greek commonly uses a comma here.

Yes. Greek word order is fairly flexible.

You could also say:

• Βοήθησαν, παρά το γεγονός ότι διαφώνησαν.

This means the same thing, but the focus changes slightly:

• original order: first highlights the contrast
• reversed order: first highlights the action they helped

The original version is probably the most neutral if you want to foreground the concessive idea.

No. Παρά has several uses in Greek, and its meaning depends on context.

For example, it can mean things like:

• beside / next to
• against
• despite

In your sentence, because it is followed by το γεγονός ότι, it clearly has the concessive meaning despite.

So it is best to learn παρά το γεγονός ότι as a fixed expression meaning despite the fact that.

Modern Greek does not normally use an English-style -ing clause in the same way.

Instead, Greek usually prefers a full clause such as:

• Παρόλο που διαφώνησαν, βοήθησαν.
• Αν και διαφώνησαν, βοήθησαν.
• Παρά το γεγονός ότι διαφώνησαν, βοήθησαν.

So while English can compress the idea into despite disagreeing, Greek more naturally uses a finite verb clause.