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Extensions 1→N→G→Q→1 with N=C52 and Q=C2×C4

Direct product G=N×Q with N=C52 and Q=C2×C4
dρLabelID
C2×C4×C52416C2xC4xC52416,175

Semidirect products G=N:Q with N=C52 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C52⋊(C2×C4) = D4×C13⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C52528+C52:(C2xC4)416,206
C52⋊2(C2×C4) = C2×C52⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C52104C52:2(C2xC4)416,203
C52⋊3(C2×C4) = C2×C4×C13⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C52104C52:3(C2xC4)416,202
C52⋊4(C2×C4) = C4⋊C4×D13φ: C2×C4/C2 → C22 ⊆ Aut C52208C52:4(C2xC4)416,112
C52⋊5(C2×C4) = D52⋊8C4φ: C2×C4/C2 → C22 ⊆ Aut C52208C52:5(C2xC4)416,114
C52⋊6(C2×C4) = D4×Dic13φ: C2×C4/C2 → C22 ⊆ Aut C52208C52:6(C2xC4)416,155
C52⋊7(C2×C4) = C4×D52φ: C2×C4/C4 → C2 ⊆ Aut C52208C52:7(C2xC4)416,94
C52⋊8(C2×C4) = C42×D13φ: C2×C4/C4 → C2 ⊆ Aut C52208C52:8(C2xC4)416,92
C52⋊9(C2×C4) = D4×C52φ: C2×C4/C4 → C2 ⊆ Aut C52208C52:9(C2xC4)416,179
C52⋊10(C2×C4) = C2×C52⋊3C4φ: C2×C4/C22 → C2 ⊆ Aut C52416C52:10(C2xC4)416,146
C52⋊11(C2×C4) = C2×C4×Dic13φ: C2×C4/C22 → C2 ⊆ Aut C52416C52:11(C2xC4)416,143
C52⋊12(C2×C4) = C4⋊C4×C26φ: C2×C4/C22 → C2 ⊆ Aut C52416C52:12(C2xC4)416,177

Non-split extensions G=N.Q with N=C52 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C52.1(C2×C4) = D52⋊1C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C521048+C52.1(C2xC4)416,82
C52.2(C2×C4) = Dic26⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C521048-C52.2(C2xC4)416,83
C52.3(C2×C4) = D13.Q16φ: C2×C4/C1 → C2×C4 ⊆ Aut C521048-C52.3(C2xC4)416,84
C52.4(C2×C4) = D52⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C521048+C52.4(C2xC4)416,85
C52.5(C2×C4) = Dic26.C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C522088-C52.5(C2xC4)416,205
C52.6(C2×C4) = D52.C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C522088+C52.6(C2xC4)416,207
C52.7(C2×C4) = Q8×C13⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C521048-C52.7(C2xC4)416,208
C52.8(C2×C4) = D26.8D4φ: C2×C4/C2 → C4 ⊆ Aut C521044C52.8(C2xC4)416,68
C52.9(C2×C4) = D13.D8φ: C2×C4/C2 → C4 ⊆ Aut C521044C52.9(C2xC4)416,69
C52.10(C2×C4) = C104.C4φ: C2×C4/C2 → C4 ⊆ Aut C522084C52.10(C2xC4)416,70
C52.11(C2×C4) = C104.1C4φ: C2×C4/C2 → C4 ⊆ Aut C522084C52.11(C2xC4)416,71
C52.12(C2×C4) = C2×C52.C4φ: C2×C4/C2 → C4 ⊆ Aut C52208C52.12(C2xC4)416,200
C52.13(C2×C4) = D13⋊C16φ: C2×C4/C2 → C4 ⊆ Aut C522084C52.13(C2xC4)416,64
C52.14(C2×C4) = D26.C8φ: C2×C4/C2 → C4 ⊆ Aut C522084C52.14(C2xC4)416,65
C52.15(C2×C4) = C8×C13⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C521044C52.15(C2xC4)416,66
C52.16(C2×C4) = C104⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C521044C52.16(C2xC4)416,67
C52.17(C2×C4) = C2×C13⋊C16φ: C2×C4/C2 → C4 ⊆ Aut C52416C52.17(C2xC4)416,72
C52.18(C2×C4) = C52.C8φ: C2×C4/C2 → C4 ⊆ Aut C522084C52.18(C2xC4)416,73
C52.19(C2×C4) = C2×D13⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C52208C52.19(C2xC4)416,199
C52.20(C2×C4) = D13⋊M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C521044C52.20(C2xC4)416,201
C52.21(C2×C4) = D26.C23φ: C2×C4/C2 → C4 ⊆ Aut C521044C52.21(C2xC4)416,204
C52.22(C2×C4) = C26.D8φ: C2×C4/C2 → C22 ⊆ Aut C52416C52.22(C2xC4)416,14
C52.23(C2×C4) = C52.Q8φ: C2×C4/C2 → C22 ⊆ Aut C52416C52.23(C2xC4)416,15
C52.24(C2×C4) = D52⋊6C4φ: C2×C4/C2 → C22 ⊆ Aut C52208C52.24(C2xC4)416,16
C52.25(C2×C4) = C26.Q16φ: C2×C4/C2 → C22 ⊆ Aut C52416C52.25(C2xC4)416,17
C52.26(C2×C4) = C52.53D4φ: C2×C4/C2 → C22 ⊆ Aut C522084C52.26(C2xC4)416,29
C52.27(C2×C4) = D52⋊7C4φ: C2×C4/C2 → C22 ⊆ Aut C521044C52.27(C2xC4)416,32
C52.28(C2×C4) = D4⋊Dic13φ: C2×C4/C2 → C22 ⊆ Aut C52208C52.28(C2xC4)416,39
C52.29(C2×C4) = Q8⋊Dic13φ: C2×C4/C2 → C22 ⊆ Aut C52416C52.29(C2xC4)416,42
C52.30(C2×C4) = C52.56D4φ: C2×C4/C2 → C22 ⊆ Aut C521044C52.30(C2xC4)416,44
C52.31(C2×C4) = Dic13⋊3Q8φ: C2×C4/C2 → C22 ⊆ Aut C52416C52.31(C2xC4)416,108
C52.32(C2×C4) = C4⋊C4⋊7D13φ: C2×C4/C2 → C22 ⊆ Aut C52208C52.32(C2xC4)416,113
C52.33(C2×C4) = M4(2)×D13φ: C2×C4/C2 → C22 ⊆ Aut C521044C52.33(C2xC4)416,127
C52.34(C2×C4) = D52.2C4φ: C2×C4/C2 → C22 ⊆ Aut C522084C52.34(C2xC4)416,128
C52.35(C2×C4) = Q8×Dic13φ: C2×C4/C2 → C22 ⊆ Aut C52416C52.35(C2xC4)416,166
C52.36(C2×C4) = D4.Dic13φ: C2×C4/C2 → C22 ⊆ Aut C522084C52.36(C2xC4)416,169
C52.37(C2×C4) = D52⋊4C4φ: C2×C4/C4 → C2 ⊆ Aut C521042C52.37(C2xC4)416,12
C52.38(C2×C4) = C52.44D4φ: C2×C4/C4 → C2 ⊆ Aut C52416C52.38(C2xC4)416,23
C52.39(C2×C4) = D52⋊5C4φ: C2×C4/C4 → C2 ⊆ Aut C52208C52.39(C2xC4)416,28
C52.40(C2×C4) = C4×Dic26φ: C2×C4/C4 → C2 ⊆ Aut C52416C52.40(C2xC4)416,89
C52.41(C2×C4) = D52.3C4φ: C2×C4/C4 → C2 ⊆ Aut C522082C52.41(C2xC4)416,122
C52.42(C2×C4) = C16×D13φ: C2×C4/C4 → C2 ⊆ Aut C522082C52.42(C2xC4)416,4
C52.43(C2×C4) = C208⋊C2φ: C2×C4/C4 → C2 ⊆ Aut C522082C52.43(C2xC4)416,5
C52.44(C2×C4) = C4×C13⋊2C8φ: C2×C4/C4 → C2 ⊆ Aut C52416C52.44(C2xC4)416,9
C52.45(C2×C4) = C26.7C42φ: C2×C4/C4 → C2 ⊆ Aut C52416C52.45(C2xC4)416,10
C52.46(C2×C4) = C42⋊D13φ: C2×C4/C4 → C2 ⊆ Aut C52208C52.46(C2xC4)416,93
C52.47(C2×C4) = C2×C8×D13φ: C2×C4/C4 → C2 ⊆ Aut C52208C52.47(C2xC4)416,120
C52.48(C2×C4) = C2×C8⋊D13φ: C2×C4/C4 → C2 ⊆ Aut C52208C52.48(C2xC4)416,121
C52.49(C2×C4) = C13×D4⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C52208C52.49(C2xC4)416,52
C52.50(C2×C4) = C13×Q8⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C52416C52.50(C2xC4)416,53
C52.51(C2×C4) = C13×C4≀C2φ: C2×C4/C4 → C2 ⊆ Aut C521042C52.51(C2xC4)416,54
C52.52(C2×C4) = Q8×C52φ: C2×C4/C4 → C2 ⊆ Aut C52416C52.52(C2xC4)416,180
C52.53(C2×C4) = C13×C8○D4φ: C2×C4/C4 → C2 ⊆ Aut C522082C52.53(C2xC4)416,192
C52.54(C2×C4) = C104⋊6C4φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.54(C2xC4)416,24
C52.55(C2×C4) = C104⋊5C4φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.55(C2xC4)416,25
C52.56(C2×C4) = C104.6C4φ: C2×C4/C22 → C2 ⊆ Aut C522082C52.56(C2xC4)416,26
C52.57(C2×C4) = C2×C52.4C4φ: C2×C4/C22 → C2 ⊆ Aut C52208C52.57(C2xC4)416,142
C52.58(C2×C4) = C23.21D26φ: C2×C4/C22 → C2 ⊆ Aut C52208C52.58(C2xC4)416,147
C52.59(C2×C4) = C2×C13⋊2C16φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.59(C2xC4)416,18
C52.60(C2×C4) = C52.4C8φ: C2×C4/C22 → C2 ⊆ Aut C522082C52.60(C2xC4)416,19
C52.61(C2×C4) = C8×Dic13φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.61(C2xC4)416,20
C52.62(C2×C4) = C104⋊8C4φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.62(C2xC4)416,22
C52.63(C2×C4) = C22×C13⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.63(C2xC4)416,141
C52.64(C2×C4) = C13×C4.Q8φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.64(C2xC4)416,56
C52.65(C2×C4) = C13×C2.D8φ: C2×C4/C22 → C2 ⊆ Aut C52416C52.65(C2xC4)416,57
C52.66(C2×C4) = C13×C8.C4φ: C2×C4/C22 → C2 ⊆ Aut C522082C52.66(C2xC4)416,58
C52.67(C2×C4) = C13×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Aut C52208C52.67(C2xC4)416,178
C52.68(C2×C4) = M4(2)×C26φ: C2×C4/C22 → C2 ⊆ Aut C52208C52.68(C2xC4)416,191
C52.69(C2×C4) = C13×C8⋊C4central extension (φ=1)416C52.69(C2xC4)416,47
C52.70(C2×C4) = C13×M5(2)central extension (φ=1)2082C52.70(C2xC4)416,60

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