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The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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Parity	Cyclic	Solvable	Primitive	Equivalent siblings

Degree	$T$-number	Order	Group	Nilpotency class

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Results (8 matches)

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Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
6T15	$A_6$	$360$	$1$		$-1$	$7$		6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
10T26	$\PSL(2,9)$	$360$	$1$		$-1$	$7$		6T15 x 2, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
15T20	$A_6$	$360$	$1$		$-1$	$7$		6T15 x 2, 10T26, 15T20, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
20T89	$A_6$	$360$	$1$		$-1$	$7$	$\PSL(2,9)$	6T15 x 2, 10T26, 15T20 x 2, 30T88 x 2, 36T555, 40T304, 45T49
30T88	$A_6$	$360$	$1$		$-1$	$7$	$A_6$, $A_6$	6T15 x 2, 10T26, 15T20 x 2, 20T89, 30T88, 36T555, 40T304, 45T49
36T555	$A_6$	$360$	$1$		$-1$	$7$	$A_6$ x 2	6T15 x 2, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 40T304, 45T49
40T304	$A_6$	$360$	$1$		$-1$	$7$	$\PSL(2,9)$, $A_6$	6T15 x 2, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 45T49
45T49	$A_6$	$360$	$1$		$-1$	$7$	$A_6$ x 2	6T15 x 2, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304

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Results are complete for degrees $\leq 23$.