Subgroups — C₂²×C₃³×C₇×C₁₉ #72192523

Order 14364.

560 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₇×C₁₉	C₂	1	3	yes	maximal, direct product factor
2	C₃³×C₇×C₁₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₃³×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃²×C₇×C₁₉	C₃	1	13	yes	maximal, direct product factor
5	C₂×C₃²×C₇×C₁₉	C₂×C₃	1	39	yes	direct product factor
6	C₂²×C₃×C₇×C₁₉	C₃²	1	13	yes	direct product factor
7	C₃²×C₇×C₁₉	C₂²×C₃	1	13	yes	direct product factor
8	C₂×C₃³×C₁₉	C₂×C₇	1	3	yes	direct product factor
9	C₂×C₃×C₇×C₁₉	C₂×C₃²	1	39	yes	direct product factor
10	C₂²×C₃³×C₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃²×C₁₉	C₃×C₇	1	13	yes	direct product factor
12	C₂²×C₇×C₁₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
13	C₃³×C₁₉	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₉	C₂²×C₃²	1	13	yes	direct product factor
15	C₂×C₃³×C₇	C₂×C₁₉	1	3	yes	direct product factor
16	C₂×C₃²×C₁₉	C₂×C₃×C₇	1	39	yes	direct product factor
17	C₂×C₇×C₁₉	C₂×C₃³	1	3	yes	direct product factor
18	C₂²×C₃²×C₇	C₃×C₁₉	1	13	yes	direct product factor
19	C₂²×C₃×C₁₉	C₃²×C₇	1	13	yes	direct product factor
20	C₃³×C₇	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃²×C₁₉	C₂²×C₃×C₇	1	13	yes	direct product factor
22	C₇×C₁₉	C₂²×C₃³	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃²×C₇	C₂×C₃×C₁₉	1	39	yes	direct product factor
24	C₂×C₃×C₁₉	C₂×C₃²×C₇	1	39	yes	direct product factor
25	C₂²×C₃³	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃×C₇	C₃²×C₁₉	1	13	yes	direct product factor
27	C₂²×C₁₉	C₃³×C₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃²×C₇	C₂²×C₃×C₁₉	1	13	yes	direct product factor
29	C₃×C₁₉	C₂²×C₃²×C₇	1	13	yes	direct product factor
30	C₂×C₃³	C₂×C₇×C₁₉	1	3	yes	direct product factor
31	C₂×C₃×C₇	C₂×C₃²×C₁₉	1	39	yes	direct product factor
32	C₂×C₁₉	C₂×C₃³×C₇	1	3	yes	direct product factor
33	C₂²×C₃²	C₃×C₇×C₁₉	1	13	yes	direct product factor
34	C₂²×C₇	C₃³×C₁₉	1	1	yes	characteristic, direct product factor, Hall
35	C₃³	C₂²×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₇	C₂²×C₃²×C₁₉	1	13	yes	direct product factor
37	C₁₉	C₂²×C₃³×C₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₃²	C₂×C₃×C₇×C₁₉	1	39	yes	direct product factor
39	C₂×C₇	C₂×C₃³×C₁₉	1	3	yes	direct product factor
40	C₂²×C₃	C₃²×C₇×C₁₉	1	13	yes	direct product factor
41	C₃²	C₂²×C₃×C₇×C₁₉	1	13	yes	direct product factor
42	C₇	C₂²×C₃³×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₂×C₃²×C₇×C₁₉	1	39	yes	direct product factor
44	C₂²	C₃³×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂²×C₃²×C₇×C₁₉	1	13	yes	direct product factor
46	C₂	C₂×C₃³×C₇×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×C₃³×C₇×C₁₉	C₂	direct (N × H)
2. C₃³×C₇×C₁₉	C₂²	direct (N × H)
3. C₂²×C₃³×C₁₉	C₇	direct (N × H)
4. C₂²×C₃²×C₇×C₁₉	C₃	direct (N × H)
5. C₂×C₃²×C₇×C₁₉	C₂×C₃	direct (N × H)
6. C₂²×C₃×C₇×C₁₉	C₃²	direct (N × H)
7. C₃²×C₇×C₁₉	C₂²×C₃	direct (N × H)
8. C₂×C₃³×C₁₉	C₂×C₇	direct (N × H)
9. C₂×C₃×C₇×C₁₉	C₂×C₃²	direct (N × H)
10. C₂²×C₃³×C₇	C₁₉	direct (N × H)
11. C₂²×C₃²×C₁₉	C₃×C₇	direct (N × H)
12. C₂²×C₇×C₁₉	C₃³	direct (N × H)
13. C₃³×C₁₉	C₂²×C₇	direct (N × H)
14. C₃×C₇×C₁₉	C₂²×C₃²	direct (N × H)
15. C₂×C₃³×C₇	C₂×C₁₉	direct (N × H)
16. C₂×C₃²×C₁₉	C₂×C₃×C₇	direct (N × H)
17. C₂×C₇×C₁₉	C₂×C₃³	direct (N × H)
18. C₂²×C₃²×C₇	C₃×C₁₉	direct (N × H)
19. C₂²×C₃×C₁₉	C₃²×C₇	direct (N × H)
20. C₃³×C₇	C₂²×C₁₉	direct (N × H)
21. C₃²×C₁₉	C₂²×C₃×C₇	direct (N × H)
22. C₇×C₁₉	C₂²×C₃³	direct (N × H)
23. C₂×C₃²×C₇	C₂×C₃×C₁₉	direct (N × H)
24. C₂×C₃×C₁₉	C₂×C₃²×C₇	direct (N × H)
25. C₂²×C₃³	C₇×C₁₉	direct (N × H)
26. C₂²×C₃×C₇	C₃²×C₁₉	direct (N × H)
27. C₂²×C₁₉	C₃³×C₇	direct (N × H)
28. C₃²×C₇	C₂²×C₃×C₁₉	direct (N × H)
29. C₃×C₁₉	C₂²×C₃²×C₇	direct (N × H)
30. C₂×C₃³	C₂×C₇×C₁₉	direct (N × H)
31. C₂×C₃×C₇	C₂×C₃²×C₁₉	direct (N × H)
32. C₂×C₁₉	C₂×C₃³×C₇	direct (N × H)
33. C₂²×C₃²	C₃×C₇×C₁₉	direct (N × H)
34. C₂²×C₇	C₃³×C₁₉	direct (N × H)
35. C₃³	C₂²×C₇×C₁₉	direct (N × H)
36. C₃×C₇	C₂²×C₃²×C₁₉	direct (N × H)
37. C₁₉	C₂²×C₃³×C₇	direct (N × H)
38. C₂×C₃²	C₂×C₃×C₇×C₁₉	direct (N × H)
39. C₂×C₇	C₂×C₃³×C₁₉	direct (N × H)
40. C₂²×C₃	C₃²×C₇×C₁₉	direct (N × H)
41. C₃²	C₂²×C₃×C₇×C₁₉	direct (N × H)
42. C₇	C₂²×C₃³×C₁₉	direct (N × H)
43. C₂×C₃	C₂×C₃²×C₇×C₁₉	direct (N × H)
44. C₂²	C₃³×C₇×C₁₉	direct (N × H)
45. C₃	C₂²×C₃²×C₇×C₁₉	direct (N × H)
46. C₂	C₂×C₃³×C₇×C₁₉	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×C₃³×C₇×C₁₉	2
C₂²×C₃³×C₁₉	7
C₂²×C₃²×C₇×C₁₉	3
C₂²×C₃³×C₇	19

Subgroups — C22×C33×C7×C19 #72192523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃³×C₇×C₁₉ #72192523