Extensions 1→N→G→Q→1 with N=C10 and Q=C22×S3

Direct product G=N×Q with N=C10 and Q=C22×S3
dρLabelID
S3×C22×C10120S3xC2^2xC10240,206

Semidirect products G=N:Q with N=C10 and Q=C22×S3
extensionφ:Q→Aut NdρLabelID
C101(C22×S3) = C22×S3×D5φ: C22×S3/D6C2 ⊆ Aut C1060C10:1(C2^2xS3)240,202
C102(C22×S3) = C23×D15φ: C22×S3/C2×C6C2 ⊆ Aut C10120C10:2(C2^2xS3)240,207

Non-split extensions G=N.Q with N=C10 and Q=C22×S3
extensionφ:Q→Aut NdρLabelID
C10.1(C22×S3) = D5×Dic6φ: C22×S3/D6C2 ⊆ Aut C101204-C10.1(C2^2xS3)240,125
C10.2(C22×S3) = D205S3φ: C22×S3/D6C2 ⊆ Aut C101204-C10.2(C2^2xS3)240,126
C10.3(C22×S3) = D20⋊S3φ: C22×S3/D6C2 ⊆ Aut C101204C10.3(C2^2xS3)240,127
C10.4(C22×S3) = S3×Dic10φ: C22×S3/D6C2 ⊆ Aut C101204-C10.4(C2^2xS3)240,128
C10.5(C22×S3) = D12⋊D5φ: C22×S3/D6C2 ⊆ Aut C101204C10.5(C2^2xS3)240,129
C10.6(C22×S3) = D60⋊C2φ: C22×S3/D6C2 ⊆ Aut C101204+C10.6(C2^2xS3)240,130
C10.7(C22×S3) = D15⋊Q8φ: C22×S3/D6C2 ⊆ Aut C101204C10.7(C2^2xS3)240,131
C10.8(C22×S3) = D6.D10φ: C22×S3/D6C2 ⊆ Aut C101204C10.8(C2^2xS3)240,132
C10.9(C22×S3) = D125D5φ: C22×S3/D6C2 ⊆ Aut C101204-C10.9(C2^2xS3)240,133
C10.10(C22×S3) = C12.28D10φ: C22×S3/D6C2 ⊆ Aut C101204+C10.10(C2^2xS3)240,134
C10.11(C22×S3) = C4×S3×D5φ: C22×S3/D6C2 ⊆ Aut C10604C10.11(C2^2xS3)240,135
C10.12(C22×S3) = D5×D12φ: C22×S3/D6C2 ⊆ Aut C10604+C10.12(C2^2xS3)240,136
C10.13(C22×S3) = S3×D20φ: C22×S3/D6C2 ⊆ Aut C10604+C10.13(C2^2xS3)240,137
C10.14(C22×S3) = C20⋊D6φ: C22×S3/D6C2 ⊆ Aut C10604C10.14(C2^2xS3)240,138
C10.15(C22×S3) = C2×D5×Dic3φ: C22×S3/D6C2 ⊆ Aut C10120C10.15(C2^2xS3)240,139
C10.16(C22×S3) = Dic5.D6φ: C22×S3/D6C2 ⊆ Aut C101204C10.16(C2^2xS3)240,140
C10.17(C22×S3) = C30.C23φ: C22×S3/D6C2 ⊆ Aut C101204-C10.17(C2^2xS3)240,141
C10.18(C22×S3) = C2×S3×Dic5φ: C22×S3/D6C2 ⊆ Aut C10120C10.18(C2^2xS3)240,142
C10.19(C22×S3) = Dic3.D10φ: C22×S3/D6C2 ⊆ Aut C101204C10.19(C2^2xS3)240,143
C10.20(C22×S3) = C2×D30.C2φ: C22×S3/D6C2 ⊆ Aut C10120C10.20(C2^2xS3)240,144
C10.21(C22×S3) = C2×C15⋊D4φ: C22×S3/D6C2 ⊆ Aut C10120C10.21(C2^2xS3)240,145
C10.22(C22×S3) = C2×C3⋊D20φ: C22×S3/D6C2 ⊆ Aut C10120C10.22(C2^2xS3)240,146
C10.23(C22×S3) = C2×C5⋊D12φ: C22×S3/D6C2 ⊆ Aut C10120C10.23(C2^2xS3)240,147
C10.24(C22×S3) = C2×C15⋊Q8φ: C22×S3/D6C2 ⊆ Aut C10240C10.24(C2^2xS3)240,148
C10.25(C22×S3) = D5×C3⋊D4φ: C22×S3/D6C2 ⊆ Aut C10604C10.25(C2^2xS3)240,149
C10.26(C22×S3) = S3×C5⋊D4φ: C22×S3/D6C2 ⊆ Aut C10604C10.26(C2^2xS3)240,150
C10.27(C22×S3) = D10⋊D6φ: C22×S3/D6C2 ⊆ Aut C10604+C10.27(C2^2xS3)240,151
C10.28(C22×S3) = C2×Dic30φ: C22×S3/C2×C6C2 ⊆ Aut C10240C10.28(C2^2xS3)240,175
C10.29(C22×S3) = C2×C4×D15φ: C22×S3/C2×C6C2 ⊆ Aut C10120C10.29(C2^2xS3)240,176
C10.30(C22×S3) = C2×D60φ: C22×S3/C2×C6C2 ⊆ Aut C10120C10.30(C2^2xS3)240,177
C10.31(C22×S3) = D6011C2φ: C22×S3/C2×C6C2 ⊆ Aut C101202C10.31(C2^2xS3)240,178
C10.32(C22×S3) = D4×D15φ: C22×S3/C2×C6C2 ⊆ Aut C10604+C10.32(C2^2xS3)240,179
C10.33(C22×S3) = D42D15φ: C22×S3/C2×C6C2 ⊆ Aut C101204-C10.33(C2^2xS3)240,180
C10.34(C22×S3) = Q8×D15φ: C22×S3/C2×C6C2 ⊆ Aut C101204-C10.34(C2^2xS3)240,181
C10.35(C22×S3) = Q83D15φ: C22×S3/C2×C6C2 ⊆ Aut C101204+C10.35(C2^2xS3)240,182
C10.36(C22×S3) = C22×Dic15φ: C22×S3/C2×C6C2 ⊆ Aut C10240C10.36(C2^2xS3)240,183
C10.37(C22×S3) = C2×C157D4φ: C22×S3/C2×C6C2 ⊆ Aut C10120C10.37(C2^2xS3)240,184
C10.38(C22×S3) = C10×Dic6central extension (φ=1)240C10.38(C2^2xS3)240,165
C10.39(C22×S3) = S3×C2×C20central extension (φ=1)120C10.39(C2^2xS3)240,166
C10.40(C22×S3) = C10×D12central extension (φ=1)120C10.40(C2^2xS3)240,167
C10.41(C22×S3) = C5×C4○D12central extension (φ=1)1202C10.41(C2^2xS3)240,168
C10.42(C22×S3) = C5×S3×D4central extension (φ=1)604C10.42(C2^2xS3)240,169
C10.43(C22×S3) = C5×D42S3central extension (φ=1)1204C10.43(C2^2xS3)240,170
C10.44(C22×S3) = C5×S3×Q8central extension (φ=1)1204C10.44(C2^2xS3)240,171
C10.45(C22×S3) = C5×Q83S3central extension (φ=1)1204C10.45(C2^2xS3)240,172
C10.46(C22×S3) = Dic3×C2×C10central extension (φ=1)240C10.46(C2^2xS3)240,173
C10.47(C22×S3) = C10×C3⋊D4central extension (φ=1)120C10.47(C2^2xS3)240,174

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