Gradius is a game a lot of people who are familiar with the Shmup genre are familiar with. It is just not a simple little shmup that can be found on many platforms but there's a link to a very well known game that a lot of people are not aware of. The Gradius series actually originated with the game of Scramble (1981).
At least perhaps not right away but the company shows us in the FMV intro sequence of the Gradius Galaxies/Gradius Advance series (2001) on the Gameboy Advance.
Gradius, Nemesis, Parodius, Salamander, Lifeforce are all games set in the same universe and are all created by Konami. Enjoy!