Finite Group Databasebeta

← C₂⁶×C₂₇₇ #31799720

Subgroups — C₂⁶×C₂₇₇ #31799720

Order 17728.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₂₇₇	C₂	1	63	yes	maximal, direct product factor
2	C₂⁴×C₂₇₇	C₂²	1	651	yes	direct product factor
3	C₂³×C₂₇₇	C₂³	1	1395	yes	direct product factor
4	C₂²×C₂₇₇	C₂⁴	1	651	yes	direct product factor
5	C₂×C₂₇₇	C₂⁵	1	63	yes	direct product factor
6	C₂₇₇	C₂⁶	1	1	yes	characteristic, direct product factor, Sylow
7	C₂⁶	C₂₇₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂⁵	C₂×C₂₇₇	1	63	yes	direct product factor
9	C₂⁴	C₂²×C₂₇₇	1	651	yes	direct product factor
10	C₂³	C₂³×C₂₇₇	1	1395	yes	direct product factor
11	C₂²	C₂⁴×C₂₇₇	1	651	yes	direct product factor
12	C₂	C₂⁵×C₂₇₇	1	63	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. C₂⁵×C₂₇₇	C₂	direct (N × H)
2. C₂⁴×C₂₇₇	C₂²	direct (N × H)
3. C₂³×C₂₇₇	C₂³	direct (N × H)
4. C₂²×C₂₇₇	C₂⁴	direct (N × H)
5. C₂×C₂₇₇	C₂⁵	direct (N × H)
6. C₂₇₇	C₂⁶	direct (N × H)
7. C₂⁶	C₂₇₇	direct (N × H)
8. C₂⁵	C₂×C₂₇₇	direct (N × H)
9. C₂⁴	C₂²×C₂₇₇	direct (N × H)
10. C₂³	C₂³×C₂₇₇	direct (N × H)
11. C₂²	C₂⁴×C₂₇₇	direct (N × H)
12. C₂	C₂⁵×C₂₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₂₇₇	2
C₂⁶	277