Finite Group Databasebeta

← C₂⁷×C₁₃₁ #30663779

Subgroups — C₂⁷×C₁₃₁ #30663779

Order 16768.

58424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₃₁	C₂	1	127	yes	maximal, direct product factor
2	C₂⁵×C₁₃₁	C₂²	1	2667	yes	direct product factor
3	C₂⁴×C₁₃₁	C₂³	1	11811	yes	direct product factor
4	C₂³×C₁₃₁	C₂⁴	1	11811	yes	direct product factor
5	C₂²×C₁₃₁	C₂⁵	1	2667	yes	direct product factor
6	C₂×C₁₃₁	C₂⁶	1	127	yes	direct product factor
7	C₁₃₁	C₂⁷	1	1	yes	characteristic, direct product factor, Sylow
8	C₂⁷	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂⁶	C₂×C₁₃₁	1	127	yes	direct product factor
10	C₂⁵	C₂²×C₁₃₁	1	2667	yes	direct product factor
11	C₂⁴	C₂³×C₁₃₁	1	11811	yes	direct product factor
12	C₂³	C₂⁴×C₁₃₁	1	11811	yes	direct product factor
13	C₂²	C₂⁵×C₁₃₁	1	2667	yes	direct product factor
14	C₂	C₂⁶×C₁₃₁	1	127	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. C₂⁶×C₁₃₁	C₂	direct (N × H)
2. C₂⁵×C₁₃₁	C₂²	direct (N × H)
3. C₂⁴×C₁₃₁	C₂³	direct (N × H)
4. C₂³×C₁₃₁	C₂⁴	direct (N × H)
5. C₂²×C₁₃₁	C₂⁵	direct (N × H)
6. C₂×C₁₃₁	C₂⁶	direct (N × H)
7. C₁₃₁	C₂⁷	direct (N × H)
8. C₂⁷	C₁₃₁	direct (N × H)
9. C₂⁶	C₂×C₁₃₁	direct (N × H)
10. C₂⁵	C₂²×C₁₃₁	direct (N × H)
11. C₂⁴	C₂³×C₁₃₁	direct (N × H)
12. C₂³	C₂⁴×C₁₃₁	direct (N × H)
13. C₂²	C₂⁵×C₁₃₁	direct (N × H)
14. C₂	C₂⁶×C₁₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁶×C₁₃₁	2
C₂⁷	131