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Extensions 1→N→G→Q→1 with N=C10 and Q=C3⋊D4

Direct product G=N×Q with N=C10 and Q=C3⋊D4
dρLabelID
C10×C3⋊D4120C10xC3:D4240,174

Semidirect products G=N:Q with N=C10 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C10⋊1(C3⋊D4) = C2×C3⋊D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C10120C10:1(C3:D4)240,146
C10⋊2(C3⋊D4) = C2×C15⋊D4φ: C3⋊D4/D6 → C2 ⊆ Aut C10120C10:2(C3:D4)240,145
C10⋊3(C3⋊D4) = C2×C15⋊7D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C10120C10:3(C3:D4)240,184

Non-split extensions G=N.Q with N=C10 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C10.1(C3⋊D4) = C3⋊D40φ: C3⋊D4/Dic3 → C2 ⊆ Aut C101204+C10.1(C3:D4)240,14
C10.2(C3⋊D4) = C6.D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C101204-C10.2(C3:D4)240,18
C10.3(C3⋊D4) = C15⋊SD16φ: C3⋊D4/Dic3 → C2 ⊆ Aut C101204+C10.3(C3:D4)240,19
C10.4(C3⋊D4) = C3⋊Dic20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C102404-C10.4(C3:D4)240,23
C10.5(C3⋊D4) = D30⋊4C4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C10120C10.5(C3:D4)240,28
C10.6(C3⋊D4) = C6.Dic10φ: C3⋊D4/Dic3 → C2 ⊆ Aut C10240C10.6(C3:D4)240,31
C10.7(C3⋊D4) = C15⋊D8φ: C3⋊D4/D6 → C2 ⊆ Aut C101204C10.7(C3:D4)240,13
C10.8(C3⋊D4) = C30.D4φ: C3⋊D4/D6 → C2 ⊆ Aut C101204C10.8(C3:D4)240,16
C10.9(C3⋊D4) = C20.D6φ: C3⋊D4/D6 → C2 ⊆ Aut C101204C10.9(C3:D4)240,17
C10.10(C3⋊D4) = C15⋊Q16φ: C3⋊D4/D6 → C2 ⊆ Aut C102404C10.10(C3:D4)240,22
C10.11(C3⋊D4) = D10⋊Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C10120C10.11(C3:D4)240,26
C10.12(C3⋊D4) = D6⋊Dic5φ: C3⋊D4/D6 → C2 ⊆ Aut C10120C10.12(C3:D4)240,27
C10.13(C3⋊D4) = Dic15⋊5C4φ: C3⋊D4/D6 → C2 ⊆ Aut C10240C10.13(C3:D4)240,30
C10.14(C3⋊D4) = C30.4Q8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C10240C10.14(C3:D4)240,73
C10.15(C3⋊D4) = D30⋊3C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C10120C10.15(C3:D4)240,75
C10.16(C3⋊D4) = D4⋊D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C101204+C10.16(C3:D4)240,76
C10.17(C3⋊D4) = D4.D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C101204-C10.17(C3:D4)240,77
C10.18(C3⋊D4) = Q8⋊2D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C101204+C10.18(C3:D4)240,78
C10.19(C3⋊D4) = C15⋊7Q16φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C102404-C10.19(C3:D4)240,79
C10.20(C3⋊D4) = C30.38D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C10120C10.20(C3:D4)240,80
C10.21(C3⋊D4) = C5×Dic3⋊C4central extension (φ=1)240C10.21(C3:D4)240,57
C10.22(C3⋊D4) = C5×D6⋊C4central extension (φ=1)120C10.22(C3:D4)240,59
C10.23(C3⋊D4) = C5×D4⋊S3central extension (φ=1)1204C10.23(C3:D4)240,60
C10.24(C3⋊D4) = C5×D4.S3central extension (φ=1)1204C10.24(C3:D4)240,61
C10.25(C3⋊D4) = C5×Q8⋊2S3central extension (φ=1)1204C10.25(C3:D4)240,62
C10.26(C3⋊D4) = C5×C3⋊Q16central extension (φ=1)2404C10.26(C3:D4)240,63
C10.27(C3⋊D4) = C5×C6.D4central extension (φ=1)120C10.27(C3:D4)240,64

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