Distribution of groups in curves of genus 5

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 2
$C_4$ [4,1] 5
$C_2^2$ [4,2] 12
$S_3$ [6,1] 18
$C_6$ [6,2] 6
$C_8$ [8,1] 6
$C_2\times C_4$ [8,2] 27
$D_4$ [8,3] 22
$Q_8$ [8,4] 6
$C_2^3$ [8,5] 77
$D_5$ [10,1] 50
$C_{10}$ [10,2] 2
$C_{11}$ [11,1] 20
$C_3:C_4$ [12,1] 2
$C_{12}$ [12,2] 4
$A_4$ [12,3] 5
$D_6$ [12,4] 15
$C_2\times C_6$ [12,5] 12
$C_{15}$ [15,1] 4
$C_2^2:C_4$ [16,3] 28
$C_2\times C_8$ [16,5] 8
$OD_{16}$ [16,6] 2
$D_8$ [16,7] 8
$SD_{16}$ [16,8] 8
$C_2^2\times C_4$ [16,10] 48
$C_2\times D_4$ [16,11] 22
$D_4:C_2$ [16,13] 6
$C_2^4$ [16,14] 168
$C_5:C_4$ [20,1] 4
$C_{20}$ [20,2] 4
$D_{10}$ [20,4] 4
$C_{22}$ [22,2] 10
$C_2\times C_3:C_4$ [24,7] 4
$C_3:D_4$ [24,8] 4
$C_2\times C_{12}$ [24,9] 8
$S_4$ [24,12] 6
$C_2\times A_4$ [24,13] 6
$C_2^2\times S_3$ [24,14] 12
$C_3\times D_5$ [30,2] 4
$C_2.C_4^2$ [32,2] 16
$C_2^2:C_8$ [32,5] 8
$C_2^2.D_4$ [32,6] 2
$C_2^3.C_4$ [32,7] 4
$C_2^2\wr C_2$ [32,27] 24
$C_2^2:D_4$ [32,28] 8
$C_8:C_2^2$ [32,43] 4
$C_4\times D_5$ [40,5] 8
$D_6:C_4$ [48,14] 8
$A_4:C_4$ [48,30] 3
$C_2\times S_4$ [48,48] 3
$C_2^2\times A_4$ [48,49] 6
$A_5$ [60,5] 2
$C_2^2.SD_{16}$ [64,8] 8
$C_2\wr C_4$ [64,32] 4
$C_2^4:C_5$ [80,49] 6
$C_2^2.\SL(2,3)$ [96,3] 4
$\GL(2,Z/4)$ [96,195] 2
$C_2\times A_5$ [120,35] 2
$C_2^4:D_5$ [160,234] 6
$C_2^2.\GL(2,3)$ [192,181] 4