# Extensions 1→N→G→Q→1 with N=C20 and Q=D10

Direct product G=N×Q with N=C20 and Q=D10
dρLabelID
D5×C2×C2080D5xC2xC20400,182

Semidirect products G=N:Q with N=C20 and Q=D10
extensionφ:Q→Aut NdρLabelID
C201D10 = D5×D20φ: D10/C5C22 ⊆ Aut C20404+C20:1D10400,170
C202D10 = C20⋊D10φ: D10/C5C22 ⊆ Aut C20404C20:2D10400,171
C203D10 = D4×C5⋊D5φ: D10/C5C22 ⊆ Aut C20100C20:3D10400,195
C204D10 = C4×D52φ: D10/D5C2 ⊆ Aut C20404C20:4D10400,169
C205D10 = C5×D4×D5φ: D10/D5C2 ⊆ Aut C20404C20:5D10400,185
C206D10 = C2×C20⋊D5φ: D10/C10C2 ⊆ Aut C20200C20:6D10400,193
C207D10 = C2×C4×C5⋊D5φ: D10/C10C2 ⊆ Aut C20200C20:7D10400,192
C208D10 = C10×D20φ: D10/C10C2 ⊆ Aut C2080C20:8D10400,183

Non-split extensions G=N.Q with N=C20 and Q=D10
extensionφ:Q→Aut NdρLabelID
C20.1D10 = D4.D25φ: D10/C5C22 ⊆ Aut C202004-C20.1D10400,15
C20.2D10 = D4⋊D25φ: D10/C5C22 ⊆ Aut C202004+C20.2D10400,16
C20.3D10 = C25⋊Q16φ: D10/C5C22 ⊆ Aut C204004-C20.3D10400,17
C20.4D10 = Q8⋊D25φ: D10/C5C22 ⊆ Aut C202004+C20.4D10400,18
C20.5D10 = D4×D25φ: D10/C5C22 ⊆ Aut C201004+C20.5D10400,39
C20.6D10 = D42D25φ: D10/C5C22 ⊆ Aut C202004-C20.6D10400,40
C20.7D10 = Q8×D25φ: D10/C5C22 ⊆ Aut C202004-C20.7D10400,41
C20.8D10 = Q82D25φ: D10/C5C22 ⊆ Aut C202004+C20.8D10400,42
C20.9D10 = C522D8φ: D10/C5C22 ⊆ Aut C20804C20.9D10400,64
C20.10D10 = C5⋊D40φ: D10/C5C22 ⊆ Aut C20404+C20.10D10400,65
C20.11D10 = D20.D5φ: D10/C5C22 ⊆ Aut C20804C20.11D10400,66
C20.12D10 = C523SD16φ: D10/C5C22 ⊆ Aut C20804-C20.12D10400,67
C20.13D10 = C524SD16φ: D10/C5C22 ⊆ Aut C20404+C20.13D10400,68
C20.14D10 = C522Q16φ: D10/C5C22 ⊆ Aut C20804C20.14D10400,69
C20.15D10 = C523Q16φ: D10/C5C22 ⊆ Aut C20804-C20.15D10400,70
C20.16D10 = C527D8φ: D10/C5C22 ⊆ Aut C20200C20.16D10400,103
C20.17D10 = C528SD16φ: D10/C5C22 ⊆ Aut C20200C20.17D10400,104
C20.18D10 = C5210SD16φ: D10/C5C22 ⊆ Aut C20200C20.18D10400,105
C20.19D10 = C527Q16φ: D10/C5C22 ⊆ Aut C20400C20.19D10400,106
C20.20D10 = D5×Dic10φ: D10/C5C22 ⊆ Aut C20804-C20.20D10400,163
C20.21D10 = D205D5φ: D10/C5C22 ⊆ Aut C20804-C20.21D10400,164
C20.22D10 = D20⋊D5φ: D10/C5C22 ⊆ Aut C20404C20.22D10400,165
C20.23D10 = Dic10⋊D5φ: D10/C5C22 ⊆ Aut C20404C20.23D10400,166
C20.24D10 = C20.D10φ: D10/C5C22 ⊆ Aut C20200C20.24D10400,196
C20.25D10 = Q8×C5⋊D5φ: D10/C5C22 ⊆ Aut C20200C20.25D10400,197
C20.26D10 = C20.26D10φ: D10/C5C22 ⊆ Aut C20200C20.26D10400,198
C20.27D10 = Dic105D5φ: D10/D5C2 ⊆ Aut C20404+C20.27D10400,168
C20.28D10 = D5×C52C8φ: D10/D5C2 ⊆ Aut C20804C20.28D10400,60
C20.29D10 = C20.29D10φ: D10/D5C2 ⊆ Aut C20404C20.29D10400,61
C20.30D10 = C20.30D10φ: D10/D5C2 ⊆ Aut C20804C20.30D10400,62
C20.31D10 = C20.31D10φ: D10/D5C2 ⊆ Aut C20404C20.31D10400,63
C20.32D10 = D10.9D10φ: D10/D5C2 ⊆ Aut C20404C20.32D10400,167
C20.33D10 = C5×D4⋊D5φ: D10/D5C2 ⊆ Aut C20404C20.33D10400,87
C20.34D10 = C5×D4.D5φ: D10/D5C2 ⊆ Aut C20404C20.34D10400,88
C20.35D10 = C5×Q8⋊D5φ: D10/D5C2 ⊆ Aut C20804C20.35D10400,89
C20.36D10 = C5×C5⋊Q16φ: D10/D5C2 ⊆ Aut C20804C20.36D10400,90
C20.37D10 = C5×D42D5φ: D10/D5C2 ⊆ Aut C20404C20.37D10400,186
C20.38D10 = C5×Q8×D5φ: D10/D5C2 ⊆ Aut C20804C20.38D10400,187
C20.39D10 = C5×Q82D5φ: D10/D5C2 ⊆ Aut C20804C20.39D10400,188
C20.40D10 = Dic100φ: D10/C10C2 ⊆ Aut C204002-C20.40D10400,4
C20.41D10 = C200⋊C2φ: D10/C10C2 ⊆ Aut C202002C20.41D10400,7
C20.42D10 = D200φ: D10/C10C2 ⊆ Aut C202002+C20.42D10400,8
C20.43D10 = C2×Dic50φ: D10/C10C2 ⊆ Aut C20400C20.43D10400,35
C20.44D10 = C2×D100φ: D10/C10C2 ⊆ Aut C20200C20.44D10400,37
C20.45D10 = D1005C2φ: D10/C10C2 ⊆ Aut C202002C20.45D10400,38
C20.46D10 = C402D5φ: D10/C10C2 ⊆ Aut C20200C20.46D10400,94
C20.47D10 = C525D8φ: D10/C10C2 ⊆ Aut C20200C20.47D10400,95
C20.48D10 = C40.D5φ: D10/C10C2 ⊆ Aut C20400C20.48D10400,96
C20.49D10 = C2×C524Q8φ: D10/C10C2 ⊆ Aut C20400C20.49D10400,191
C20.50D10 = C20.50D10φ: D10/C10C2 ⊆ Aut C20200C20.50D10400,194
C20.51D10 = C8×D25φ: D10/C10C2 ⊆ Aut C202002C20.51D10400,5
C20.52D10 = C8⋊D25φ: D10/C10C2 ⊆ Aut C202002C20.52D10400,6
C20.53D10 = C2×C252C8φ: D10/C10C2 ⊆ Aut C20400C20.53D10400,9
C20.54D10 = C4.Dic25φ: D10/C10C2 ⊆ Aut C202002C20.54D10400,10
C20.55D10 = C2×C4×D25φ: D10/C10C2 ⊆ Aut C20200C20.55D10400,36
C20.56D10 = C8×C5⋊D5φ: D10/C10C2 ⊆ Aut C20200C20.56D10400,92
C20.57D10 = C40⋊D5φ: D10/C10C2 ⊆ Aut C20200C20.57D10400,93
C20.58D10 = C2×C527C8φ: D10/C10C2 ⊆ Aut C20400C20.58D10400,97
C20.59D10 = C20.59D10φ: D10/C10C2 ⊆ Aut C20200C20.59D10400,98
C20.60D10 = C5×C40⋊C2φ: D10/C10C2 ⊆ Aut C20802C20.60D10400,78
C20.61D10 = C5×D40φ: D10/C10C2 ⊆ Aut C20802C20.61D10400,79
C20.62D10 = C5×Dic20φ: D10/C10C2 ⊆ Aut C20802C20.62D10400,80
C20.63D10 = C10×Dic10φ: D10/C10C2 ⊆ Aut C2080C20.63D10400,181
C20.64D10 = D5×C40central extension (φ=1)802C20.64D10400,76
C20.65D10 = C5×C8⋊D5central extension (φ=1)802C20.65D10400,77
C20.66D10 = C10×C52C8central extension (φ=1)80C20.66D10400,81
C20.67D10 = C5×C4.Dic5central extension (φ=1)402C20.67D10400,82
C20.68D10 = C5×C4○D20central extension (φ=1)402C20.68D10400,184

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