Subgroups — C₂×C₃²×C₁₁×C₅₃ #23783201

Order 10494.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₁×C₅₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₁×C₅₃	C₂×C₃	1	4	yes	direct product factor
4	C₂×C₁₁×C₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²×C₅₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₅₃	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₅₃	C₃×C₁₁	1	4	yes	direct product factor
9	C₂×C₃²×C₁₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅₃	C₂×C₃×C₁₁	1	4	yes	direct product factor
11	C₂×C₅₃	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₁₁	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₁	C₃×C₅₃	1	4	yes	direct product factor
14	C₅₃	C₂×C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₁	C₂×C₃×C₅₃	1	4	yes	direct product factor
16	C₂×C₁₁	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²	C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	C₂×C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₂×C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₁×C₅₃	1	4	yes	direct product factor
21	C₃	C₂×C₃×C₁₁×C₅₃	1	4	yes	direct product factor
22	C₂	C₃²×C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow

	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. C₃²×C₁₁×C₅₃	C₂	direct (N × H)
2. C₂×C₃×C₁₁×C₅₃	C₃	direct (N × H)
3. C₃×C₁₁×C₅₃	C₂×C₃	direct (N × H)
4. C₂×C₁₁×C₅₃	C₃²	direct (N × H)
5. C₂×C₃²×C₅₃	C₁₁	direct (N × H)
6. C₁₁×C₅₃	C₂×C₃²	direct (N × H)
7. C₃²×C₅₃	C₂×C₁₁	direct (N × H)
8. C₂×C₃×C₅₃	C₃×C₁₁	direct (N × H)
9. C₂×C₃²×C₁₁	C₅₃	direct (N × H)
10. C₃×C₅₃	C₂×C₃×C₁₁	direct (N × H)
11. C₂×C₅₃	C₃²×C₁₁	direct (N × H)
12. C₃²×C₁₁	C₂×C₅₃	direct (N × H)
13. C₂×C₃×C₁₁	C₃×C₅₃	direct (N × H)
14. C₅₃	C₂×C₃²×C₁₁	direct (N × H)
15. C₃×C₁₁	C₂×C₃×C₅₃	direct (N × H)
16. C₂×C₁₁	C₃²×C₅₃	direct (N × H)
17. C₂×C₃²	C₁₁×C₅₃	direct (N × H)
18. C₁₁	C₂×C₃²×C₅₃	direct (N × H)
19. C₃²	C₂×C₁₁×C₅₃	direct (N × H)
20. C₂×C₃	C₃×C₁₁×C₅₃	direct (N × H)
21. C₃	C₂×C₃×C₁₁×C₅₃	direct (N × H)
22. C₂	C₃²×C₁₁×C₅₃	direct (N × H)

Subgroups — C2×C32×C11×C53 #23783201

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₁₁×C₅₃ #23783201