Finite Group Databasebeta

← C₂⁵×C₂₆₃ #22554375

Subgroups — C₂⁵×C₂₆₃ #22554375

Order 8416.

748 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₂₆₃	C₂	1	31	yes	maximal, direct product factor
2	C₂³×C₂₆₃	C₂²	1	155	yes	direct product factor
3	C₂²×C₂₆₃	C₂³	1	155	yes	direct product factor
4	C₂×C₂₆₃	C₂⁴	1	31	yes	direct product factor
5	C₂₆₃	C₂⁵	1	1	yes	characteristic, direct product factor, Sylow
6	C₂⁵	C₂₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂⁴	C₂×C₂₆₃	1	31	yes	direct product factor
8	C₂³	C₂²×C₂₆₃	1	155	yes	direct product factor
9	C₂²	C₂³×C₂₆₃	1	155	yes	direct product factor
10	C₂	C₂⁴×C₂₆₃	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂⁴×C₂₆₃	C₂	direct (N × H)
2. C₂³×C₂₆₃	C₂²	direct (N × H)
3. C₂²×C₂₆₃	C₂³	direct (N × H)
4. C₂×C₂₆₃	C₂⁴	direct (N × H)
5. C₂₆₃	C₂⁵	direct (N × H)
6. C₂⁵	C₂₆₃	direct (N × H)
7. C₂⁴	C₂×C₂₆₃	direct (N × H)
8. C₂³	C₂²×C₂₆₃	direct (N × H)
9. C₂²	C₂³×C₂₆₃	direct (N × H)
10. C₂	C₂⁴×C₂₆₃	direct (N × H)