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Extensions 1→N→G→Q→1 with N=C30 and Q=C2×C6

Direct product G=N×Q with N=C30 and Q=C2×C6
dρLabelID
C2×C6×C30360C2xC6xC30360,162

Semidirect products G=N:Q with N=C30 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C30⋊(C2×C6) = S3×C6×D5φ: C2×C6/C3 → C22 ⊆ Aut C30604C30:(C2xC6)360,151
C30⋊2(C2×C6) = C2×C6×D15φ: C2×C6/C6 → C2 ⊆ Aut C30120C30:2(C2xC6)360,159
C30⋊3(C2×C6) = D5×C62φ: C2×C6/C6 → C2 ⊆ Aut C30180C30:3(C2xC6)360,157
C30⋊4(C2×C6) = S3×C2×C30φ: C2×C6/C6 → C2 ⊆ Aut C30120C30:4(C2xC6)360,158

Non-split extensions G=N.Q with N=C30 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C30.1(C2×C6) = C3×D5×Dic3φ: C2×C6/C3 → C22 ⊆ Aut C30604C30.1(C2xC6)360,58
C30.2(C2×C6) = C3×S3×Dic5φ: C2×C6/C3 → C22 ⊆ Aut C301204C30.2(C2xC6)360,59
C30.3(C2×C6) = C3×D30.C2φ: C2×C6/C3 → C22 ⊆ Aut C301204C30.3(C2xC6)360,60
C30.4(C2×C6) = C3×C15⋊D4φ: C2×C6/C3 → C22 ⊆ Aut C30604C30.4(C2xC6)360,61
C30.5(C2×C6) = C3×C3⋊D20φ: C2×C6/C3 → C22 ⊆ Aut C30604C30.5(C2xC6)360,62
C30.6(C2×C6) = C3×C5⋊D12φ: C2×C6/C3 → C22 ⊆ Aut C301204C30.6(C2xC6)360,63
C30.7(C2×C6) = C3×C15⋊Q8φ: C2×C6/C3 → C22 ⊆ Aut C301204C30.7(C2xC6)360,64
C30.8(C2×C6) = C3×Dic30φ: C2×C6/C6 → C2 ⊆ Aut C301202C30.8(C2xC6)360,100
C30.9(C2×C6) = C12×D15φ: C2×C6/C6 → C2 ⊆ Aut C301202C30.9(C2xC6)360,101
C30.10(C2×C6) = C3×D60φ: C2×C6/C6 → C2 ⊆ Aut C301202C30.10(C2xC6)360,102
C30.11(C2×C6) = C6×Dic15φ: C2×C6/C6 → C2 ⊆ Aut C30120C30.11(C2xC6)360,103
C30.12(C2×C6) = C3×C15⋊7D4φ: C2×C6/C6 → C2 ⊆ Aut C30602C30.12(C2xC6)360,104
C30.13(C2×C6) = C9×Dic10φ: C2×C6/C6 → C2 ⊆ Aut C303602C30.13(C2xC6)360,15
C30.14(C2×C6) = D5×C36φ: C2×C6/C6 → C2 ⊆ Aut C301802C30.14(C2xC6)360,16
C30.15(C2×C6) = C9×D20φ: C2×C6/C6 → C2 ⊆ Aut C301802C30.15(C2xC6)360,17
C30.16(C2×C6) = C18×Dic5φ: C2×C6/C6 → C2 ⊆ Aut C30360C30.16(C2xC6)360,18
C30.17(C2×C6) = C9×C5⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C301802C30.17(C2xC6)360,19
C30.18(C2×C6) = D5×C2×C18φ: C2×C6/C6 → C2 ⊆ Aut C30180C30.18(C2xC6)360,47
C30.19(C2×C6) = C32×Dic10φ: C2×C6/C6 → C2 ⊆ Aut C30360C30.19(C2xC6)360,90
C30.20(C2×C6) = D5×C3×C12φ: C2×C6/C6 → C2 ⊆ Aut C30180C30.20(C2xC6)360,91
C30.21(C2×C6) = C32×D20φ: C2×C6/C6 → C2 ⊆ Aut C30180C30.21(C2xC6)360,92
C30.22(C2×C6) = C3×C6×Dic5φ: C2×C6/C6 → C2 ⊆ Aut C30360C30.22(C2xC6)360,93
C30.23(C2×C6) = C32×C5⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C30180C30.23(C2xC6)360,94
C30.24(C2×C6) = C15×Dic6φ: C2×C6/C6 → C2 ⊆ Aut C301202C30.24(C2xC6)360,95
C30.25(C2×C6) = S3×C60φ: C2×C6/C6 → C2 ⊆ Aut C301202C30.25(C2xC6)360,96
C30.26(C2×C6) = C15×D12φ: C2×C6/C6 → C2 ⊆ Aut C301202C30.26(C2xC6)360,97
C30.27(C2×C6) = Dic3×C30φ: C2×C6/C6 → C2 ⊆ Aut C30120C30.27(C2xC6)360,98
C30.28(C2×C6) = C15×C3⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C30602C30.28(C2xC6)360,99
C30.29(C2×C6) = D4×C45central extension (φ=1)1802C30.29(C2xC6)360,31
C30.30(C2×C6) = Q8×C45central extension (φ=1)3602C30.30(C2xC6)360,32
C30.31(C2×C6) = D4×C3×C15central extension (φ=1)180C30.31(C2xC6)360,116
C30.32(C2×C6) = Q8×C3×C15central extension (φ=1)360C30.32(C2xC6)360,117

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