Finite Group Databasebeta

← C₂⁸×C₅₃ #27270616

Subgroups — C₂⁸×C₅₃ #27270616

Order 13568.

834398 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₅₃	C₂	1	255	yes	maximal, direct product factor
2	C₂⁶×C₅₃	C₂²	1	10795	yes	direct product factor
3	C₂⁵×C₅₃	C₂³	1	97155	yes	direct product factor
4	C₂⁴×C₅₃	C₂⁴	1	200787	yes	direct product factor
5	C₂³×C₅₃	C₂⁵	1	97155	yes	direct product factor
6	C₂⁸	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₅₃	C₂⁶	1	10795	yes	direct product factor
8	C₂⁷	C₂×C₅₃	1	255	yes	direct product factor
9	C₂×C₅₃	C₂⁷	1	255	yes	direct product factor
10	C₂⁶	C₂²×C₅₃	1	10795	yes	direct product factor
11	C₅₃	C₂⁸	1	1	yes	characteristic, direct product factor, Sylow
12	C₂⁵	C₂³×C₅₃	1	97155	yes	direct product factor
13	C₂⁴	C₂⁴×C₅₃	1	200787	yes	direct product factor
14	C₂³	C₂⁵×C₅₃	1	97155	yes	direct product factor
15	C₂²	C₂⁶×C₅₃	1	10795	yes	direct product factor
16	C₂	C₂⁷×C₅₃	1	255	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. C₂⁷×C₅₃	C₂	direct (N × H)
2. C₂⁶×C₅₃	C₂²	direct (N × H)
3. C₂⁵×C₅₃	C₂³	direct (N × H)
4. C₂⁴×C₅₃	C₂⁴	direct (N × H)
5. C₂³×C₅₃	C₂⁵	direct (N × H)
6. C₂⁸	C₅₃	direct (N × H)
7. C₂²×C₅₃	C₂⁶	direct (N × H)
8. C₂⁷	C₂×C₅₃	direct (N × H)
9. C₂×C₅₃	C₂⁷	direct (N × H)
10. C₂⁶	C₂²×C₅₃	direct (N × H)
11. C₅₃	C₂⁸	direct (N × H)
12. C₂⁵	C₂³×C₅₃	direct (N × H)
13. C₂⁴	C₂⁴×C₅₃	direct (N × H)
14. C₂³	C₂⁵×C₅₃	direct (N × H)
15. C₂²	C₂⁶×C₅₃	direct (N × H)
16. C₂	C₂⁷×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁷×C₅₃	2
C₂⁸	53