Alice Cutter is alleged to have won the competition organised by National Action after taking on the nickname Buchenwald Princess in reference to the Nazi death camp.
Cutter, 22, billed herself "Buchenwald Princess" - after the German concentration camp where thousands of Jews were slaughtered during the Second World War.
The 22-year-old is standing trial at Birmingham Crown Court alongside her partner Mark Jones, who is accused of posing for a photograph while giving a Nazi salute in Buchenwald's execution room.
She had entered the competition in a bid to recruit more members to the extremist group and "raise the profile" of National Action, jurors were told.
A court heard that it was "no coincidence" that her fiancé Mark Jones, 24, had been pictured doing a Nazi salute in an execution room at the camp just a month earlier.
The engaged couple have gone on trial accused of being members of the banned far-right organisation, which was proscribed in December 2016.
Jones, 24, and Cutter, both of Mulhalls Mill, Sowerby Bridge, near Halifax, deny being members of National Action between December 2016 and September 2017.
The Crown also alleges that Garry Jack, 23, from Heathland Avenue, Shard End, Birmingham, and 18-year-old Connor Scothern, of Bagnall Avenue, Nottingham, are guilty of belonging to the banned organisation between the same dates.
Opening the case against the four defendants, prosecutor Barnaby Jameson QC said: "Terror comes in many different forms.
"None, perhaps, more chilling than the particular brand of terror the four accused were seeking to spread.
"The terror of the gun, the terror of the knife, the terror of the noose,the terror of the explosive, the terror of the gas chamber.
"The terror of an ideology so warped, so extreme and so twisted, its continued existence will be shocking to many of you, if not all.
"It is the terror of pathological racial prejudice. It is the terror of society lacerated by division. It is the terror of ethnic cleaning.
"It is the terror of life without mercy. It is the terror of violent dictatorship. It is the terror neo-Nazi white supremacy.
"It is, above all, the terror of hate.
"This case is about a fellowship of hate. A hate so fanatical and a fellowship so defiant that the accused would sooner break the law than break their bonds of hate.
"This case is about a tiny, self-selecting group of young people in this country, for whom Hitler’s work will always be unfinished.
"A group for whom the Final Solution to the Jewish question, to use Hitler’s words, remains to be answered by complete eradication.
"We are talking about a group seeking to mimic Hitler’s ‘Sturmabteilung’ or storm detachment – the original paramilitary wing of the Nazi party.
"The Crown should make it clear at this early stage that this case, involving as it does Nazi fanatics, will by its nature lead you, the jury, into a world as dark as a black sun.
"The words ‘black sun’ are chosen for a reason. Why will become clear in due course.
"It is a world that will transport the court back to the horrors of Nazi Germany: the concentration camps, the gas chambers, the mass executions, the crematoria and the Satanic chimneys."
Mr Jameson said Jones flew to Germany in 2016 to visit Buchenwald.
After showing the jury a picture featuring two men standing in the camp's execution room holding a National Action flag, Mr Jameson told the jury: "Buchenwald was a Nazi concentration camp that stood out, even by the standards of Nazi concentration camps, for its depravity.
"Like Auschwitz, Buchenwald is a permanent museum to honour the victims and remind the world of the horrors perpetrated in the name of Nazism."
He said Cutter entered the National Action-organised beauty contest in June 2016 - days after the murder of MP Jo Cox.
The prosecutor told the jury of seven men and five women: "On 24 June 2016 National Action staged, if you can believe this, a beauty contest titled Miss Hitler 2016.
"This was, no doubt, a publicity stunt to raise the group's profile and attract more members.
"One of those who entered and, I think, in fact, won the competition, was Alice Cutter.
"She entered the competition as Buchenwald Princess and she set out her mission statement in a detailed interview.
"The beauty contest was anything but funny. The name Buchenwald Princess was, perhaps, you may think, no coincidence given that Jones had visited the execution room at Buchenwald the previous month."
Mr Jameson told the jury the defendants were seeking to spread terror from "an ideology so warped, so extreme and so twisted, its continued existence will be shocking to many of you, if not all".
The jury was shown a picture alleged to show Cutter wearing a National Action mask, which was posted online.
In an "interview" accompanying the photo, the competition entrant said: "It is important to me that there's a balance of feminine to masculine in the movement - without feminine involvement, what would a movement be? A sad sausage fest with no appeal?
"Women are the most important figures when it comes to teaching and raising the next generation to be strong and proud.
"We need to step up, be the lionesses we ought to be and rip apart the hyenas laughing at us as we get raped, beaten, brainwashed and de-feminised en masse.
"Hyenas have no part in our pride and never will."
The four defendants are charged with membership of the group between December 17, 2016 and September 5, 2017 after it was banned by then-Home Secretary Amber Rudd.
Cutter, of Halifax, West Yorks., and Scothern, of Nottingham, remain on bail, while Jones, of Halifax, and Jack, of Shard End, Birmingham, are in custody.
They deny the charges and the trial continues.