Extensions 1→N→G→Q→1 with N=C₅²⋊₆C₄ and Q=C₂²

Direct product G=N×Q with N=C₅²⋊₆C₄ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₅²⋊₆C₄		400		C2^2xC5^2:6C4	400,199

Semidirect products G=N:Q with N=C₅²⋊₆C₄ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊₆C₄⋊C₂² = D₅×C₅⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4:C2^2	400,179
C₅²⋊₆C₄⋊₂C₂² = C₄×D₅²	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4:2C2^2	400,169
C₅²⋊₆C₄⋊₃C₂² = C₂₀⋊D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4:3C2^2	400,171
C₅²⋊₆C₄⋊₄C₂² = C₂×D₅×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4:4C2^2	400,172
C₅²⋊₆C₄⋊₅C₂² = C₂×C₅²⋊₂D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4:5C2^2	400,176
C₅²⋊₆C₄⋊₆C₂² = D₄×C₅⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	100		C5^2:6C4:6C2^2	400,195
C₅²⋊₆C₄⋊₇C₂² = C₂×C₅²⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4:7C2^2	400,200
C₅²⋊₆C₄⋊₈C₂² = C₂×C₄×C₅⋊D₅	φ: trivial image	200		C5^2:6C4:8C2^2	400,192

Non-split extensions G=N.Q with N=C₅²⋊₆C₄ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊₆C₄.₁C₂² = D₅×Dic₁₀	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	80	4-	C5^2:6C4.1C2^2	400,163
C₅²⋊₆C₄.₂C₂² = D₂₀⋊₅D₅	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	80	4-	C5^2:6C4.2C2^2	400,164
C₅²⋊₆C₄.₃C₂² = Dic₅.D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.3C2^2	400,173
C₅²⋊₆C₄.₄C₂² = D₁₀.₂F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4.4C2^2	400,127
C₅²⋊₆C₄.₅C₂² = C₅²⋊₄M₄(2)	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4.5C2^2	400,128
C₅²⋊₆C₄.₆C₂² = C₅²⋊D₈	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.6C2^2	400,131
C₅²⋊₆C₄.₇C₂² = C₅²⋊SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	40	4-	C5^2:6C4.7C2^2	400,132
C₅²⋊₆C₄.₈C₂² = C₅²⋊Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₅²⋊₆C₄	80	4-	C5^2:6C4.8C2^2	400,133
C₅²⋊₆C₄.₉C₂² = D₂₀⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.9C2^2	400,165
C₅²⋊₆C₄.₁₀C₂² = Dic₁₀⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.10C2^2	400,166
C₅²⋊₆C₄.₁₁C₂² = D₁₀.₉D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.11C2^2	400,167
C₅²⋊₆C₄.₁₂C₂² = D₁₀.₄D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4-	C5^2:6C4.12C2^2	400,174
C₅²⋊₆C₄.₁₃C₂² = C₂×C₅²⋊₂Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4.13C2^2	400,178
C₅²⋊₆C₄.₁₄C₂² = C₂×C₅²⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	400		C5^2:6C4.14C2^2	400,191
C₅²⋊₆C₄.₁₅C₂² = C₂₀.₅₀D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.15C2^2	400,194
C₅²⋊₆C₄.₁₆C₂² = C₂₀.D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.16C2^2	400,196
C₅²⋊₆C₄.₁₇C₂² = Q₈×C₅⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.17C2^2	400,197
C₅²⋊₆C₄.₁₈C₂² = C₂₀.F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.18C2^2	400,149
C₅²⋊₆C₄.₁₉C₂² = C₅²⋊₇M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.19C2^2	400,150
C₅²⋊₆C₄.₂₀C₂² = C₂×C₅²⋊₄C₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	400		C5^2:6C4.20C2^2	400,153
C₅²⋊₆C₄.₂₁C₂² = C₅²⋊₁₃M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.21C2^2	400,154
C₅²⋊₆C₄.₂₂C₂² = C₂₀.₁₁F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.22C2^2	400,156
C₅²⋊₆C₄.₂₃C₂² = C₅²⋊₈M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.23C2^2	400,157
C₅²⋊₆C₄.₂₄C₂² = C₂×C₅²⋊₅C₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4.24C2^2	400,160
C₅²⋊₆C₄.₂₅C₂² = C₅²⋊₁₄M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4-	C5^2:6C4.25C2^2	400,161
C₅²⋊₆C₄.₂₆C₂² = C₂₀.₂₆D₁₀	φ: trivial image	200		C5^2:6C4.26C2^2	400,198

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Extensions 1→N→G→Q→1 with N=C52⋊6C4 and Q=C22

Extensions 1→N→G→Q→1 with N=C₅²⋊₆C₄ and Q=C₂²