Subgroups — C₂²×C₅×C₁₁×C₅₃ #26042913

Order 11660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₅₃	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₁₁×C₅₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₁×C₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₁×C₅₃	C₂×C₅	1	3	yes	direct product factor
5	C₂²×C₅×C₅₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₅₃	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₅₃	C₂×C₁₁	1	3	yes	direct product factor
8	C₅×C₅₃	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂²×C₅×C₁₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₅₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₁	C₂×C₅₃	1	3	yes	direct product factor
12	C₂×C₅₃	C₂×C₅×C₁₁	1	3	yes	direct product factor
13	C₅×C₁₁	C₂²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₅₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₂²×C₁₁	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₁	C₂×C₅×C₅₃	1	3	yes	direct product factor
17	C₂²×C₅	C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	C₂²×C₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₁×C₅₃	1	3	yes	direct product factor
20	C₅	C₂²×C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₅×C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₁₁×C₅₃	1	3	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. C₂×C₅×C₁₁×C₅₃	C₂	direct (N × H)
2. C₅×C₁₁×C₅₃	C₂²	direct (N × H)
3. C₂²×C₁₁×C₅₃	C₅	direct (N × H)
4. C₂×C₁₁×C₅₃	C₂×C₅	direct (N × H)
5. C₂²×C₅×C₅₃	C₁₁	direct (N × H)
6. C₁₁×C₅₃	C₂²×C₅	direct (N × H)
7. C₂×C₅×C₅₃	C₂×C₁₁	direct (N × H)
8. C₅×C₅₃	C₂²×C₁₁	direct (N × H)
9. C₂²×C₅×C₁₁	C₅₃	direct (N × H)
10. C₂²×C₅₃	C₅×C₁₁	direct (N × H)
11. C₂×C₅×C₁₁	C₂×C₅₃	direct (N × H)
12. C₂×C₅₃	C₂×C₅×C₁₁	direct (N × H)
13. C₅×C₁₁	C₂²×C₅₃	direct (N × H)
14. C₅₃	C₂²×C₅×C₁₁	direct (N × H)
15. C₂²×C₁₁	C₅×C₅₃	direct (N × H)
16. C₂×C₁₁	C₂×C₅×C₅₃	direct (N × H)
17. C₂²×C₅	C₁₁×C₅₃	direct (N × H)
18. C₁₁	C₂²×C₅×C₅₃	direct (N × H)
19. C₂×C₅	C₂×C₁₁×C₅₃	direct (N × H)
20. C₅	C₂²×C₁₁×C₅₃	direct (N × H)
21. C₂²	C₅×C₁₁×C₅₃	direct (N × H)
22. C₂	C₂×C₅×C₁₁×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
C₂×C₅×C₁₁×C₅₃	2
C₂²×C₁₁×C₅₃	5
C₂²×C₅×C₅₃	11
C₂²×C₅×C₁₁	53

Subgroups — C22×C5×C11×C53 #26042913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₁₁×C₅₃ #26042913