Alice Cutter denies being a member of National Action after it was outlawed as a terrorist organisation by the Government in December 2016.
The 22-year-old is standing trial alongside her partner, Mark Jones, who is accused of being a "leader and strategist" for the proscribed group.
Jones, 24, and Cutter, both of Mulhalls Mill, Sowerby Bridge, near Halifax, West Yorkshire, 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.
On the second day of the trial at Birmingham Crown Court, prosecutor Barnaby Jameson QC made clear that Cutter did not win the Miss Hitler competition in 2016.
Mr Jameson, who began opening the Crown's case on Wednesday, told the jury of seven men and five women that Cutter "was a central spoke in the National Action wheel", having been photographed giving the Nazi salute on the steps of Leeds Town Hall in May 2016.
The prosecutor told the jury panel: "As you will see, Alice Cutter shared Jones' obsession with knives, guns and the ideology of violent ethnic cleansing.
"Cutter's violent racist mindset leeches right through the National Action chat groups.
"This was not simply Alice Cutter playing to the gallery.
"As you will hear, in a private one-to-one chat group with (a convicted National Action member) she said that what she considered a good thing was a game of football in which the ball was a Jew's decapitated head so that the Jew, in her words, or similar words, got a good kicking every time."
Cutter, who began a relationship with Jones during 2017, is alleged to have been a member of the same online chat group as both Jack and Scothern.
Addressing Scothern's alleged role in what he described as a fellowship of twisted racial hatred, Mr Jameson said the teenager had previously practised Islam.
Mr Jameson said: "One of National Action's strategies was to target the young and Scothern was plainly a young recruit.
"You will hear that Scothern came to Nazism via a circuitous route. He was drawn apparently to communism at one stage, and for a short time when he was 12 or 13 practised Islam.
"But make no mistake, however, that when Scothern found Nazism he never looked back."
Mr Jameson added: "He ended up linked to all the key players, we say, in National Action.
"By the end of September 2016 you will hear that Scothern was doing National Action recruitment in his own right."
The court heard that Scothern was photographed giving the Nazi salute with other National Action members in Dudley, West Midlands, in October 2016, and at the cemetery in Nottingham the following month.
Scothern was well aware of the implications of National Action being banned, Mr Jameson claimed, telling jurors: "You will hear that, during the banned phase of National Action, Scothern was effectively an activist's activist."
The trial continues.