Aren't they summed up by Deuteronomy 26:8: And the LORD brought us forth out of Egypt with a mighty hand [two plagues], and with an outstretched arm [two more], and with great terribleness [two more], and with signs [two more], and with wonders [two more].
You could also think of the plagues as three sets of three plagues with a final plague: distinguishing between God's servants and Egypt's servants, between His people and Egypt's people, between Himself and other gods, and the final plague. They sort of flow along the lines of the first plague in the set has Moses and Aaron standing in the morning waiting for the Pharaoh, then the second plague has them going to Pharaoh, then the third is a no warning plague God does on his own. Also, each of the plagues attacks one of the Egyptian gods, like the water turning to blood attacked the Nile god Hopi.
So for the first set, the magicians (or servants) of Egypt were able to recreate some of the signs and wonders up to a point, but then had to admit that what Moses and Aaron (God's servants) were doing was the finger of God when they couldn't reproduce lice (see Exodus 7:12), obviously demonstrating God's superiour power.
And how about the second set, where Goshen, then land where the Hebrews live, is spared from the plagues (see Exodus 8:22)?
third set...
The final plague defies any natural explanation (like it could be said that a mud slide made the nile silty or red, which killed off the fish, which drove the frogs onto dry land, which died, which attracted the lice and flies, which poisend the cattle somehow, which caused the boils, then could have had a freaky storm that drove the locust across the land and also darkened the sky). And more...
See Numbers 9:6-11, 2 Chron 30:2-3, and 1 Kings 12:32-33 for an exception to to passover being on the 14th day of the first month