Extensions 1→N→G→Q→1 with N=C₃₀ and Q=C₂²

Direct product G=N×Q with N=C₃₀ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₃₀		120		C2^2xC30	120,47

Semidirect products G=N:Q with N=C₃₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀⋊C₂² = C₂×S₃×D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	30	4+	C30:C2^2	120,42
C₃₀⋊₂C₂² = C₂²×D₁₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60		C30:2C2^2	120,46
C₃₀⋊₃C₂² = D₅×C₂×C₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60		C30:3C2^2	120,44
C₃₀⋊₄C₂² = S₃×C₂×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60		C30:4C2^2	120,45

Non-split extensions G=N.Q with N=C₃₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁C₂² = D₅×Dic₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	60	4-	C30.1C2^2	120,8
C₃₀.₂C₂² = S₃×Dic₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	60	4-	C30.2C2^2	120,9
C₃₀.₃C₂² = D₃₀.C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	60	4+	C30.3C2^2	120,10
C₃₀.₄C₂² = C₁₅⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	60	4-	C30.4C2^2	120,11
C₃₀.₅C₂² = C₃⋊D₂₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	60	4+	C30.5C2^2	120,12
C₃₀.₆C₂² = C₅⋊D₁₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	60	4+	C30.6C2^2	120,13
C₃₀.₇C₂² = C₁₅⋊Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₃₀	120	4-	C30.7C2^2	120,14
C₃₀.₈C₂² = Dic₃₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	120	2-	C30.8C2^2	120,26
C₃₀.₉C₂² = C₄×D₁₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.9C2^2	120,27
C₃₀.₁₀C₂² = D₆₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2+	C30.10C2^2	120,28
C₃₀.₁₁C₂² = C₂×Dic₁₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	120		C30.11C2^2	120,29
C₃₀.₁₂C₂² = C₁₅⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.12C2^2	120,30
C₃₀.₁₃C₂² = C₃×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	120	2	C30.13C2^2	120,16
C₃₀.₁₄C₂² = D₅×C₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.14C2^2	120,17
C₃₀.₁₅C₂² = C₃×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.15C2^2	120,18
C₃₀.₁₆C₂² = C₆×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	120		C30.16C2^2	120,19
C₃₀.₁₇C₂² = C₃×C₅⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.17C2^2	120,20
C₃₀.₁₈C₂² = C₅×Dic₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	120	2	C30.18C2^2	120,21
C₃₀.₁₉C₂² = S₃×C₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.19C2^2	120,22
C₃₀.₂₀C₂² = C₅×D₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.20C2^2	120,23
C₃₀.₂₁C₂² = C₁₀×Dic₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	120		C30.21C2^2	120,24
C₃₀.₂₂C₂² = C₅×C₃⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₃₀	60	2	C30.22C2^2	120,25
C₃₀.₂₃C₂² = D₄×C₁₅	central extension (φ=1)	60	2	C30.23C2^2	120,32
C₃₀.₂₄C₂² = Q₈×C₁₅	central extension (φ=1)	120	2	C30.24C2^2	120,33

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Extensions 1→N→G→Q→1 with N=C30 and Q=C22

Extensions 1→N→G→Q→1 with N=C₃₀ and Q=C₂²