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The following is a list of unnamed Q.

With a few exceptions, all members of this species refer to themselves as "Q".

Quick Answers

What species are Trelane's parents in Star Trek? toggle section
In Star Trek, Trelane's parents are non-corporeal entities, appearing as translucent green blobs during Kirk's encounter with Trelane in 2267.
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How did Trelane's parents appear to Kirk? toggle section
Trelane's parents appeared to Kirk as glowing green lights hovering by a treetop. Kirk discovered Trelane was a spoiled child, with his parents calling him 'disobedient and cruel.' They apologized for his actions and assured Kirk they would maintain the planet's life-support systems until he left.
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What role did Trelane's parents play in his encounter with Kirk? toggle section
Trelane's parents intervened during his encounter with Kirk, appearing as glowing lights to scold him for being disobedient and cruel. They apologized to Kirk, acknowledging their fault in indulging Trelane and promising to punish him. They assured Kirk that they would not have allowed Trelane to intercept the Enterprise if they had known humans' vulnerability and promised to maintain life-support systems until Kirk left.
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What was the setting when Trelane's parents appeared? toggle section
Trelane's parents appeared as glowing green lights against a treetop while Trelane stood in a spotlight, arguing with them. Kirk overheard the argument, learning Trelane was a spoiled child. His parents labeled him disobedient and cruel, especially towards his 'pets,' and warned him to stop or face punishment. They apologized to Kirk, promising to maintain the planet's life-support systems until his departure.
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How did Trelane's parents communicate with him? toggle section
Trelane's parents communicated with him as glowing green lights, scolding him for his disobedience and cruelty. They repeatedly urged him to come along, but he resisted, complaining about his lack of fun. They warned him to cease his behavior or face restrictions on creating planets. Ultimately, they took him away, apologizing to Captain Kirk for their indulgence.
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Amanda Rogers' parents

Amanda Rodgers' parents

Amanda Rodgers' parents

Amanda Rogers' parents had taken Human form and then conceived a child. When Amanda was still a baby, They were executed, by the Q Continuum, for being unable to resist using the power of the Q while living on Earth in Topeka, Kansas. After their death, Amanda was adopted by a couple who served in Starfleet as marine biologists. (TNG: "True Q")

Amanda Rogers' mother and father were played by Kim Max Pemberton (who was uncredited) and an unknown actor, respectively.

Country folk

These Q, seen in the forms of three male and two female Humans, a dog, and a scarecrow, appeared in Q and Quinn's manifestation of the Q Continuum, as presented to fall within the comprehension of Captain Kathryn Janeway and Tuvok.

Encountered were an old man in a rocking chair, smoking a corncob pipe, while reading a book titled The Old, a young woman reading a magazine called The New, a young couple playing croquet with balls that resembled planets, and another older man playing a pinball game called Q Continuum Galaxy.

In addition, the dog, a bloodhound, simply laid on the ground, while the scarecrow, clad in a Starfleet uniform with a type 2 phaser on its waist, watched over an empty field. (VOY: "Death Wish")

These Q were described in the script as "country folk".
The Human actors filmed their scenes on Tuesday 17 October 1995 at Club Ed's in Lancaster, and are listed with the descriptors from the call sheet for that day seen below.

Freedom Faction soldiers

During the Q Civil War, multiple individuals were seen as soldiers of the Freedom Faction, who were led by Q, and fought against the soldiers of the status quo. In a version of the war made perceivable to Humans, members of the Freedom Faction appeared as Union Army soldiers. (VOY: "The Q and the Grey")

These soldiers were played by unknown performers.

Horse

The horse being led through Colonel Q's encampment

The horse being led through Colonel Q's encampment

This horse was seen at Colonel Q's Civil War encampment being led by a soldier of the status quo. (VOY: "The Q and the Grey")

This horse was played by an unknown animal actor.

Judges

These two judges flanked the central judge Q when presiding over the trial of Q's son in 2378 aboard the Voyager. (VOY: "Q2")

The "Q-Judges" to the right and left were played by background actors Mark Pash and David Campagna. (Star Trek Encyclopedia, 4th ed., vol. 2, p. 190)
According to the episode's script, they were noted as being "attired in the same "robes" that Q wore in the TNG episodes "Encounter at Farpoint" and "All Good Things..."."

Shadow

A Q shadow

A Q shadow

This shadow asked Q for a report on his progress with Amanda Rogers. Q informed him that, "As anticipated, there have been some problems... but the Humans are cooperating. I need more time. There is a possibility we won't have to terminate her." (TNG: "True Q")

This Q, who was identified in the script as a "Q Shadow", was voiced by an unknown actor.
According to the script notes, his appearance was described as "Suddenly a DARK SHADOW appears on the wall ahead of him. Q stops, annoyed. We HEAR the voice of the shadow... it is futzed and sepulchral."

Status quo soldiers

During the Q Civil War, multiple individuals were seen as soldiers of the status quo, who were led by Colonel Q, and fought against the soldiers of the Freedom Faction. In a version of the war made perceivable to Humans, members of the status quo appeared as Confederate Army soldiers. (VOY: "The Q and the Grey")

These soldiers were played by unknown performers.

Trelane's mother

Trelane's parents

Trelane's parents

Towards the end of James T. Kirk's encounter with Trelane in 2267, Trelane's mother and father revealed themselves, appearing in front of a treetop as little more than indistinct, oddly pulsating, hovering translucent green blobs. They chastised Trelane as he stood in a pool of light pleading with them, and eventually removed him from the surface of Gothos. They spoke in rich, faintly echoing voices.

Most of their conversation was directed at Trelane, but Kirk was right there to hear every word of it. Kirk learned that Trelane was a spoiled child, who had created the planet of Gothos and everything on it for his own enjoyment, and everyone he sent down to Gothos were playmates to him. Trelane's father told him he was "disobedient and cruel." and Trelane's mother told him that if he could not take proper care of his pets, he could not have them at all. His father also told him: "They're beings, Trelane. They have spirit, they're superior." His mother then told Trelane that he'll grow up, and he'll understand. Trelane's arguments descended into childish whining, which drew a sharp rebuke from his father: "Stop that nonsense at once, or you will not be permitted to make any more planets!"

After Trelane left, his parents apologized to Kirk, but his questions - "Who are you?" and "Who is Trelane?" - were unanswered. Instead, Trelane's parents told Kirk he must forgive their child, and the fault was theirs for indulging him too much, and he will be punished. They also said they would not have allowed Trelane to intercept them, had they known how vulnerable Humans really were, and they promised to maintain the planet's life support systems until Kirk returned to his ship. (TOS: "The Squire of Gothos")

Trelane's mother was voiced by Barbara Babcock, who received no on-screen credit despite having dialogue. James Doohan has often been credited as the voice of Trelane's father, by sources including the Star Trek Concordance (1st ed., p. 20), The Star Trek Compendium (1st ed., p. 88), Star Trek Encyclopedia, 3rd ed., p. 460, and Cinefantastique (27, Vol 2 #12, p. 50). Doohan dispelled this rumor in a 1988 interview in Starlog magazine (page number?edit), which in turn, had been previously dispelled on a 1-900 number (citation needededit) set up in 1986 where listeners could call in and hear Doohan reminiscence about his Star Trek career.
The novel Q-Squared was based upon the premise that Trelane and Q are linked or related, going so far as to suggest that Trelane is Q's illegitimate son, although Q informs Captain Jean-Luc Picard that Trelane's parents are very highly regarded in the Q Continuum, making the idea of a relationship between Trelane's mother and Q scandalous, at best. This was all but canonized in SNW: "Wedding Bell Blues", wherein it is heavily implied that Trelane's father is, in fact, Q.
In the script for "The Squire of Gothos", Trelane's parents were described as "two large pulsating globes of green light, one slightly larger than the other, both hanging in mid-air, radiating color."