Extensions 1→N→G→Q→1 with N=C30 and Q=C2×C4

Direct product G=N×Q with N=C30 and Q=C2×C4
dρLabelID
C22×C60240C2^2xC60240,185

Semidirect products G=N:Q with N=C30 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C30⋊(C2×C4) = C2×S3×F5φ: C2×C4/C1C2×C4 ⊆ Aut C30308+C30:(C2xC4)240,195
C302(C2×C4) = C22×C3⋊F5φ: C2×C4/C2C4 ⊆ Aut C3060C30:2(C2xC4)240,201
C303(C2×C4) = C2×C6×F5φ: C2×C4/C2C4 ⊆ Aut C3060C30:3(C2xC4)240,200
C304(C2×C4) = C2×D5×Dic3φ: C2×C4/C2C22 ⊆ Aut C30120C30:4(C2xC4)240,139
C305(C2×C4) = C2×S3×Dic5φ: C2×C4/C2C22 ⊆ Aut C30120C30:5(C2xC4)240,142
C306(C2×C4) = C2×D30.C2φ: C2×C4/C2C22 ⊆ Aut C30120C30:6(C2xC4)240,144
C307(C2×C4) = C2×C4×D15φ: C2×C4/C4C2 ⊆ Aut C30120C30:7(C2xC4)240,176
C308(C2×C4) = D5×C2×C12φ: C2×C4/C4C2 ⊆ Aut C30120C30:8(C2xC4)240,156
C309(C2×C4) = S3×C2×C20φ: C2×C4/C4C2 ⊆ Aut C30120C30:9(C2xC4)240,166
C3010(C2×C4) = C22×Dic15φ: C2×C4/C22C2 ⊆ Aut C30240C30:10(C2xC4)240,183
C3011(C2×C4) = C2×C6×Dic5φ: C2×C4/C22C2 ⊆ Aut C30240C30:11(C2xC4)240,163
C3012(C2×C4) = Dic3×C2×C10φ: C2×C4/C22C2 ⊆ Aut C30240C30:12(C2xC4)240,173

Non-split extensions G=N.Q with N=C30 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C30.1(C2×C4) = Dic3×F5φ: C2×C4/C1C2×C4 ⊆ Aut C30608-C30.1(C2xC4)240,95
C30.2(C2×C4) = D6⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C30608+C30.2(C2xC4)240,96
C30.3(C2×C4) = Dic3⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C30608-C30.3(C2xC4)240,97
C30.4(C2×C4) = S3×C5⋊C8φ: C2×C4/C1C2×C4 ⊆ Aut C301208-C30.4(C2xC4)240,98
C30.5(C2×C4) = D15⋊C8φ: C2×C4/C1C2×C4 ⊆ Aut C301208+C30.5(C2xC4)240,99
C30.6(C2×C4) = D6.F5φ: C2×C4/C1C2×C4 ⊆ Aut C301208-C30.6(C2xC4)240,100
C30.7(C2×C4) = Dic3.F5φ: C2×C4/C1C2×C4 ⊆ Aut C301208+C30.7(C2xC4)240,101
C30.8(C2×C4) = C60.C4φ: C2×C4/C2C4 ⊆ Aut C301204C30.8(C2xC4)240,118
C30.9(C2×C4) = C12.F5φ: C2×C4/C2C4 ⊆ Aut C301204C30.9(C2xC4)240,119
C30.10(C2×C4) = C4×C3⋊F5φ: C2×C4/C2C4 ⊆ Aut C30604C30.10(C2xC4)240,120
C30.11(C2×C4) = C60⋊C4φ: C2×C4/C2C4 ⊆ Aut C30604C30.11(C2xC4)240,121
C30.12(C2×C4) = C2×C15⋊C8φ: C2×C4/C2C4 ⊆ Aut C30240C30.12(C2xC4)240,122
C30.13(C2×C4) = C158M4(2)φ: C2×C4/C2C4 ⊆ Aut C301204C30.13(C2xC4)240,123
C30.14(C2×C4) = D10.D6φ: C2×C4/C2C4 ⊆ Aut C30604C30.14(C2xC4)240,124
C30.15(C2×C4) = C3×D5⋊C8φ: C2×C4/C2C4 ⊆ Aut C301204C30.15(C2xC4)240,111
C30.16(C2×C4) = C3×C4.F5φ: C2×C4/C2C4 ⊆ Aut C301204C30.16(C2xC4)240,112
C30.17(C2×C4) = C12×F5φ: C2×C4/C2C4 ⊆ Aut C30604C30.17(C2xC4)240,113
C30.18(C2×C4) = C3×C4⋊F5φ: C2×C4/C2C4 ⊆ Aut C30604C30.18(C2xC4)240,114
C30.19(C2×C4) = C6×C5⋊C8φ: C2×C4/C2C4 ⊆ Aut C30240C30.19(C2xC4)240,115
C30.20(C2×C4) = C3×C22.F5φ: C2×C4/C2C4 ⊆ Aut C301204C30.20(C2xC4)240,116
C30.21(C2×C4) = C3×C22⋊F5φ: C2×C4/C2C4 ⊆ Aut C30604C30.21(C2xC4)240,117
C30.22(C2×C4) = D5×C3⋊C8φ: C2×C4/C2C22 ⊆ Aut C301204C30.22(C2xC4)240,7
C30.23(C2×C4) = S3×C52C8φ: C2×C4/C2C22 ⊆ Aut C301204C30.23(C2xC4)240,8
C30.24(C2×C4) = D152C8φ: C2×C4/C2C22 ⊆ Aut C301204C30.24(C2xC4)240,9
C30.25(C2×C4) = C20.32D6φ: C2×C4/C2C22 ⊆ Aut C301204C30.25(C2xC4)240,10
C30.26(C2×C4) = D6.Dic5φ: C2×C4/C2C22 ⊆ Aut C301204C30.26(C2xC4)240,11
C30.27(C2×C4) = D30.5C4φ: C2×C4/C2C22 ⊆ Aut C301204C30.27(C2xC4)240,12
C30.28(C2×C4) = Dic3×Dic5φ: C2×C4/C2C22 ⊆ Aut C30240C30.28(C2xC4)240,25
C30.29(C2×C4) = D10⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C30120C30.29(C2xC4)240,26
C30.30(C2×C4) = D6⋊Dic5φ: C2×C4/C2C22 ⊆ Aut C30120C30.30(C2xC4)240,27
C30.31(C2×C4) = D304C4φ: C2×C4/C2C22 ⊆ Aut C30120C30.31(C2xC4)240,28
C30.32(C2×C4) = C30.Q8φ: C2×C4/C2C22 ⊆ Aut C30240C30.32(C2xC4)240,29
C30.33(C2×C4) = Dic155C4φ: C2×C4/C2C22 ⊆ Aut C30240C30.33(C2xC4)240,30
C30.34(C2×C4) = C6.Dic10φ: C2×C4/C2C22 ⊆ Aut C30240C30.34(C2xC4)240,31
C30.35(C2×C4) = C8×D15φ: C2×C4/C4C2 ⊆ Aut C301202C30.35(C2xC4)240,65
C30.36(C2×C4) = C40⋊S3φ: C2×C4/C4C2 ⊆ Aut C301202C30.36(C2xC4)240,66
C30.37(C2×C4) = C4×Dic15φ: C2×C4/C4C2 ⊆ Aut C30240C30.37(C2xC4)240,72
C30.38(C2×C4) = C30.4Q8φ: C2×C4/C4C2 ⊆ Aut C30240C30.38(C2xC4)240,73
C30.39(C2×C4) = D303C4φ: C2×C4/C4C2 ⊆ Aut C30120C30.39(C2xC4)240,75
C30.40(C2×C4) = D5×C24φ: C2×C4/C4C2 ⊆ Aut C301202C30.40(C2xC4)240,33
C30.41(C2×C4) = C3×C8⋊D5φ: C2×C4/C4C2 ⊆ Aut C301202C30.41(C2xC4)240,34
C30.42(C2×C4) = C12×Dic5φ: C2×C4/C4C2 ⊆ Aut C30240C30.42(C2xC4)240,40
C30.43(C2×C4) = C3×C10.D4φ: C2×C4/C4C2 ⊆ Aut C30240C30.43(C2xC4)240,41
C30.44(C2×C4) = C3×D10⋊C4φ: C2×C4/C4C2 ⊆ Aut C30120C30.44(C2xC4)240,43
C30.45(C2×C4) = S3×C40φ: C2×C4/C4C2 ⊆ Aut C301202C30.45(C2xC4)240,49
C30.46(C2×C4) = C5×C8⋊S3φ: C2×C4/C4C2 ⊆ Aut C301202C30.46(C2xC4)240,50
C30.47(C2×C4) = Dic3×C20φ: C2×C4/C4C2 ⊆ Aut C30240C30.47(C2xC4)240,56
C30.48(C2×C4) = C5×Dic3⋊C4φ: C2×C4/C4C2 ⊆ Aut C30240C30.48(C2xC4)240,57
C30.49(C2×C4) = C5×D6⋊C4φ: C2×C4/C4C2 ⊆ Aut C30120C30.49(C2xC4)240,59
C30.50(C2×C4) = C2×C153C8φ: C2×C4/C22C2 ⊆ Aut C30240C30.50(C2xC4)240,70
C30.51(C2×C4) = C60.7C4φ: C2×C4/C22C2 ⊆ Aut C301202C30.51(C2xC4)240,71
C30.52(C2×C4) = C605C4φ: C2×C4/C22C2 ⊆ Aut C30240C30.52(C2xC4)240,74
C30.53(C2×C4) = C30.38D4φ: C2×C4/C22C2 ⊆ Aut C30120C30.53(C2xC4)240,80
C30.54(C2×C4) = C6×C52C8φ: C2×C4/C22C2 ⊆ Aut C30240C30.54(C2xC4)240,38
C30.55(C2×C4) = C3×C4.Dic5φ: C2×C4/C22C2 ⊆ Aut C301202C30.55(C2xC4)240,39
C30.56(C2×C4) = C3×C4⋊Dic5φ: C2×C4/C22C2 ⊆ Aut C30240C30.56(C2xC4)240,42
C30.57(C2×C4) = C3×C23.D5φ: C2×C4/C22C2 ⊆ Aut C30120C30.57(C2xC4)240,48
C30.58(C2×C4) = C10×C3⋊C8φ: C2×C4/C22C2 ⊆ Aut C30240C30.58(C2xC4)240,54
C30.59(C2×C4) = C5×C4.Dic3φ: C2×C4/C22C2 ⊆ Aut C301202C30.59(C2xC4)240,55
C30.60(C2×C4) = C5×C4⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C30240C30.60(C2xC4)240,58
C30.61(C2×C4) = C5×C6.D4φ: C2×C4/C22C2 ⊆ Aut C30120C30.61(C2xC4)240,64
C30.62(C2×C4) = C15×C22⋊C4central extension (φ=1)120C30.62(C2xC4)240,82
C30.63(C2×C4) = C15×C4⋊C4central extension (φ=1)240C30.63(C2xC4)240,83
C30.64(C2×C4) = C15×M4(2)central extension (φ=1)1202C30.64(C2xC4)240,85

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