Subgroups — C₂²×C₃×C₁₃×C₆₁ #23748916

Order 9516.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₆₁	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₆₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₆₁	C₂×C₃	1	3	yes	direct product factor
5	C₁₃×C₆₁	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₃×C₆₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₆₁	C₂×C₁₃	1	3	yes	direct product factor
8	C₂²×C₆₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₆₁	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₃×C₁₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₆₁	C₂×C₃×C₁₃	1	3	yes	direct product factor
12	C₂×C₃×C₁₃	C₂×C₆₁	1	3	yes	direct product factor
13	C₆₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₁₃	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃	C₂²×C₆₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	C₂×C₃×C₆₁	1	3	yes	direct product factor
17	C₁₃	C₂²×C₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₃×C₆₁	1	3	yes	direct product factor
20	C₂²	C₃×C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₁₃×C₆₁	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×C₃×C₁₃×C₆₁	C₂	direct (N × H)
2. C₂²×C₁₃×C₆₁	C₃	direct (N × H)
3. C₃×C₁₃×C₆₁	C₂²	direct (N × H)
4. C₂×C₁₃×C₆₁	C₂×C₃	direct (N × H)
5. C₁₃×C₆₁	C₂²×C₃	direct (N × H)
6. C₂²×C₃×C₆₁	C₁₃	direct (N × H)
7. C₂×C₃×C₆₁	C₂×C₁₃	direct (N × H)
8. C₂²×C₆₁	C₃×C₁₃	direct (N × H)
9. C₃×C₆₁	C₂²×C₁₃	direct (N × H)
10. C₂²×C₃×C₁₃	C₆₁	direct (N × H)
11. C₂×C₆₁	C₂×C₃×C₁₃	direct (N × H)
12. C₂×C₃×C₁₃	C₂×C₆₁	direct (N × H)
13. C₆₁	C₂²×C₃×C₁₃	direct (N × H)
14. C₂²×C₁₃	C₃×C₆₁	direct (N × H)
15. C₃×C₁₃	C₂²×C₆₁	direct (N × H)
16. C₂×C₁₃	C₂×C₃×C₆₁	direct (N × H)
17. C₁₃	C₂²×C₃×C₆₁	direct (N × H)
18. C₂²×C₃	C₁₃×C₆₁	direct (N × H)
19. C₂×C₃	C₂×C₁₃×C₆₁	direct (N × H)
20. C₂²	C₃×C₁₃×C₆₁	direct (N × H)
21. C₃	C₂²×C₁₃×C₆₁	direct (N × H)
22. C₂	C₂×C₃×C₁₃×C₆₁	direct (N × H)

Subgroups — C22×C3×C13×C61 #23748916

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃×C₁₃×C₆₁ #23748916