Subgroups — C₂²×C₃²×C₁₃×C₁₉ #22580234

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₁₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃×C₁₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	12	yes	direct product factor
5	C₂²×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₁₉	C₂²×C₃	1	4	yes	direct product factor
7	C₂²×C₃²×C₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₁₉	C₂×C₃²	1	3	yes	direct product factor
9	C₂²×C₃²×C₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²×C₁₉	C₂×C₁₃	1	3	yes	direct product factor
11	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃²×C₁₃	C₂×C₁₉	1	3	yes	direct product factor
13	C₂²×C₃×C₁₉	C₃×C₁₃	1	4	yes	direct product factor
14	C₃²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₃×C₁₃	C₃×C₁₉	1	4	yes	direct product factor
16	C₃²×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₉	C₂×C₃×C₁₃	1	12	yes	direct product factor
18	C₂×C₃×C₁₃	C₂×C₃×C₁₉	1	12	yes	direct product factor
19	C₂²×C₁₉	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₉	C₂²×C₃×C₁₃	1	4	yes	direct product factor
21	C₂²×C₁₃	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₃	C₂²×C₃×C₁₉	1	4	yes	direct product factor
23	C₂×C₁₉	C₂×C₃²×C₁₃	1	3	yes	direct product factor
24	C₂²×C₃²	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₃	C₂×C₃²×C₁₉	1	3	yes	direct product factor
26	C₁₉	C₂²×C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃²	C₂×C₁₃×C₁₉	1	3	yes	direct product factor
28	C₁₃	C₂²×C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃	C₃×C₁₃×C₁₉	1	4	yes	direct product factor
30	C₃²	C₂²×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₃×C₁₉	1	12	yes	direct product factor
32	C₂²	C₃²×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₁₃×C₁₉	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₁₃×C₁₉	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×C₃²×C₁₃×C₁₉	C₂	direct (N × H)
2. C₂²×C₃×C₁₃×C₁₉	C₃	direct (N × H)
3. C₃²×C₁₃×C₁₉	C₂²	direct (N × H)
4. C₂×C₃×C₁₃×C₁₉	C₂×C₃	direct (N × H)
5. C₂²×C₁₃×C₁₉	C₃²	direct (N × H)
6. C₃×C₁₃×C₁₉	C₂²×C₃	direct (N × H)
7. C₂²×C₃²×C₁₉	C₁₃	direct (N × H)
8. C₂×C₁₃×C₁₉	C₂×C₃²	direct (N × H)
9. C₂²×C₃²×C₁₃	C₁₉	direct (N × H)
10. C₂×C₃²×C₁₉	C₂×C₁₃	direct (N × H)
11. C₁₃×C₁₉	C₂²×C₃²	direct (N × H)
12. C₂×C₃²×C₁₃	C₂×C₁₉	direct (N × H)
13. C₂²×C₃×C₁₉	C₃×C₁₃	direct (N × H)
14. C₃²×C₁₉	C₂²×C₁₃	direct (N × H)
15. C₂²×C₃×C₁₃	C₃×C₁₉	direct (N × H)
16. C₃²×C₁₃	C₂²×C₁₉	direct (N × H)
17. C₂×C₃×C₁₉	C₂×C₃×C₁₃	direct (N × H)
18. C₂×C₃×C₁₃	C₂×C₃×C₁₉	direct (N × H)
19. C₂²×C₁₉	C₃²×C₁₃	direct (N × H)
20. C₃×C₁₉	C₂²×C₃×C₁₃	direct (N × H)
21. C₂²×C₁₃	C₃²×C₁₉	direct (N × H)
22. C₃×C₁₃	C₂²×C₃×C₁₉	direct (N × H)
23. C₂×C₁₉	C₂×C₃²×C₁₃	direct (N × H)
24. C₂²×C₃²	C₁₃×C₁₉	direct (N × H)
25. C₂×C₁₃	C₂×C₃²×C₁₉	direct (N × H)
26. C₁₉	C₂²×C₃²×C₁₃	direct (N × H)
27. C₂×C₃²	C₂×C₁₃×C₁₉	direct (N × H)
28. C₁₃	C₂²×C₃²×C₁₉	direct (N × H)
29. C₂²×C₃	C₃×C₁₃×C₁₉	direct (N × H)
30. C₃²	C₂²×C₁₃×C₁₉	direct (N × H)
31. C₂×C₃	C₂×C₃×C₁₃×C₁₉	direct (N × H)
32. C₂²	C₃²×C₁₃×C₁₉	direct (N × H)
33. C₃	C₂²×C₃×C₁₃×C₁₉	direct (N × H)
34. C₂	C₂×C₃²×C₁₃×C₁₉	direct (N × H)

Subgroups — C22×C32×C13×C19 #22580234

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃²×C₁₃×C₁₉ #22580234