*2.1. Swift/BAT*

The Third *Swift*/BAT Catalogue [76] contains 1388 bursts detected between 17 December 2004 and 28 August 2020 and provides the durations, spectral fit parameters, fluxes, and fluences calculated in the simple Power-Law (PL) and Cut-off Power-Law (CPL) models. The hardness ratio HR<sup>32</sup> for each GRB was calculated as the ratio of the fluence in energy range 3 (50–100 keV) to energy range 2 (25–50 keV), given by

$$\text{HR}\_{32} = \frac{\int\_{50\,\text{keV}}^{100\,\text{keV}} Ef(E)dE}{\int\_{25\,\text{keV}}^{50\,\text{keV}} Ef(E)dE} \text{\textdegree} \tag{1}$$

where *f*(*E*) is the photon flux at energy *E*. For the PL model, this is given by

$$f(E) = K\_{50}^{\text{PL}} \left(\frac{E}{50 \text{ keV}}\right)^{\alpha^{\text{PL}}},\tag{2}$$

where *α* PL is the PL index, and *K PL* <sup>50</sup> is the normalisation factor at 50 keV, with units of photons cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> keV−<sup>1</sup> . The CPL model is described as

$$f(E) = K\_{50}^{\text{CPL}} \left(\frac{E}{50 \text{ keV}}\right)^{a^{\text{CPL}}} \exp\left(\frac{-E(2 + a^{\text{CPL}})}{E\_{\text{peak}}}\right),\tag{3}$$

where *α* CPL is the CPL index, *K CPL* <sup>50</sup> is the normalisation factor at 50 keV, with units of photons cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> keV−<sup>1</sup> , and *E*peak is the peak energy in keV of the *νF<sup>ν</sup>* or *E* 2 *f*(*E*) spectrum. This is the flux density integrated over the energy range, also known as the spectral flux density.

The sample of 1388 bursts was filtered to remove 52 GRBs for which no duration or best-fit model was documented. A further 20 GRBs with duration or hardness errors in excess of 50% of their magnitude were removed, resulting in a final sample of 1316 GRBs for clustering.
