Subgroups — C₂×C₃×C₇×C₁₉×D₁₃ #35209199

Order 20748.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₉×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₉×D₁₃	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₁₉×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₃×C₇×C₁₉	—	13	1	no	maximal, Hall
10	C₂×C₃×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃×C₁₉×D₁₃	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₃×C₇×D₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₉×D₁₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₁₉	—	13	2	no	—
15	C₂×C₃×C₇×C₁₉	D₁₃	1	1	yes	characteristic, direct product factor
16	C₃×C₁₃×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
18	C₃×C₇×D₁₃	C₂×C₁₉	1	2	yes	direct product factor
19	C₂²×C₇×C₁₉	—	13	1	no	Hall
20	C₂×C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
21	C₁₉×D₁₃	C₂×C₃×C₇	1	2	yes	direct product factor
22	C₃×C₇×C₁₉	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×D₁₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₉	—	13	2	no	—
26	C₂×C₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic, direct product factor
27	C₁₃×C₁₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₃×C₁₉	—	13	1	no	Hall
29	C₂×C₇×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
30	C₇×D₁₃	C₂×C₃×C₁₉	1	2	yes	direct product factor
31	C₂×C₃×D₁₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
32	C₇×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₁₉	—	13	2	no	—
34	C₂×C₃×C₁₉	C₇×D₁₃	1	1	yes	characteristic, direct product factor
35	C₇×C₁₃	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃×C₇	—	13	1	no	Hall
37	C₂×C₃×C₁₃	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
38	C₃×D₁₃	C₂×C₇×C₁₉	1	2	yes	direct product factor
39	C₂²×C₁₉	—	13	1	no	Hall
40	C₃×C₁₉	C₂×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Hall
41	C₂×D₁₃	C₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃×C₇	—	13	2	no	—
43	C₂×C₃×C₇	C₁₉×D₁₃	1	1	yes	characteristic, direct product factor
44	C₃×C₁₃	C₂²×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
45	C₂×C₁₉	—	13	2	no	—
46	C₂×C₁₉	C₃×C₇×D₁₃	1	1	yes	characteristic, direct product factor
47	C₂²×C₇	—	13	1	no	Hall
48	C₂×C₁₃	C₂×C₃×C₇×C₁₉	1	1	yes	characteristic, complemented
49	D₁₃	C₂×C₃×C₇×C₁₉	1	2	yes	direct product factor
50	C₃×C₇	C₂×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Hall
51	C₁₉	C₂×C₃×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₇	—	13	2	no	—
53	C₂×C₇	C₃×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor
54	C₁₃	C₂²×C₃×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	13	1	no	Hall
56	C₇	C₂×C₃×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	—	13	2	no	—
58	C₂×C₃	C₇×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor
59	C₂²	—	13	1	no	Sylow
60	C₃	C₂×C₇×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	13	2	no	—
62	C₂	C₃×C₇×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₇×C₁₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₇×C₁₉×D₁₃	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃×C₁₉	C₂	semidirect
3. C₂×C₇×C₁₉×D₁₃	C₃	direct (N × H)
4. C₃×C₇×C₁₃×C₁₉	C₂²	semidirect
5. C₇×C₁₉×D₁₃	C₂×C₃	direct (N × H)
6. C₂×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₂×C₃×C₁₉×D₁₃	C₇	direct (N × H)
8. C₇×C₁₃×C₁₉	C₂²×C₃	semidirect
10. C₂×C₃×C₁₃×C₁₉	C₂×C₇	semidirect
11. C₃×C₁₉×D₁₃	C₂×C₇	direct (N × H)
12. C₂×C₃×C₇×D₁₃	C₁₉	direct (N × H)
13. C₂×C₁₉×D₁₃	C₃×C₇	direct (N × H)
15. C₂×C₃×C₇×C₁₉	D₁₃	direct (N × H)
16. C₃×C₁₃×C₁₉	C₂²×C₇	semidirect
17. C₂×C₃×C₇×C₁₃	C₂×C₁₉	semidirect
18. C₃×C₇×D₁₃	C₂×C₁₉	direct (N × H)
20. C₂×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
21. C₁₉×D₁₃	C₂×C₃×C₇	direct (N × H)
22. C₃×C₇×C₁₉	C₂×D₁₃	direct (N × H)
23. C₂×C₇×D₁₃	C₃×C₁₉	direct (N × H)
24. C₃×C₇×C₁₃	C₂²×C₁₉	semidirect
26. C₂×C₇×C₁₉	C₃×D₁₃	direct (N × H)
27. C₁₃×C₁₉	C₂²×C₃×C₇	semidirect
29. C₂×C₇×C₁₃	C₂×C₃×C₁₉	semidirect
30. C₇×D₁₃	C₂×C₃×C₁₉	direct (N × H)
31. C₂×C₃×D₁₃	C₇×C₁₉	direct (N × H)
32. C₇×C₁₉	C₂×C₃×D₁₃	direct (N × H)
34. C₂×C₃×C₁₉	C₇×D₁₃	direct (N × H)
35. C₇×C₁₃	C₂²×C₃×C₁₉	semidirect
37. C₂×C₃×C₁₃	C₂×C₇×C₁₉	semidirect
38. C₃×D₁₃	C₂×C₇×C₁₉	direct (N × H)
40. C₃×C₁₉	C₂×C₇×D₁₃	direct (N × H)
41. C₂×D₁₃	C₃×C₇×C₁₉	direct (N × H)
43. C₂×C₃×C₇	C₁₉×D₁₃	direct (N × H)
44. C₃×C₁₃	C₂²×C₇×C₁₉	semidirect
46. C₂×C₁₉	C₃×C₇×D₁₃	direct (N × H)
48. C₂×C₁₃	C₂×C₃×C₇×C₁₉	semidirect
49. D₁₃	C₂×C₃×C₇×C₁₉	direct (N × H)
50. C₃×C₇	C₂×C₁₉×D₁₃	direct (N × H)
51. C₁₉	C₂×C₃×C₇×D₁₃	direct (N × H)
53. C₂×C₇	C₃×C₁₉×D₁₃	direct (N × H)
54. C₁₃	C₂²×C₃×C₇×C₁₉	semidirect
56. C₇	C₂×C₃×C₁₉×D₁₃	direct (N × H)
58. C₂×C₃	C₇×C₁₉×D₁₃	direct (N × H)
60. C₃	C₂×C₇×C₁₉×D₁₃	direct (N × H)
62. C₂	C₃×C₇×C₁₉×D₁₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×C₁₉×D₁₃	2
C₂×C₃×C₇×C₁₃×C₁₉	2
C₂×C₇×C₁₉×D₁₃	3
C₂×C₃×C₁₉×D₁₃	7
C₂²×C₃×C₇×C₁₉	13
C₂×C₃×C₇×D₁₃	19

Subgroups — C2×C3×C7×C19×D13 #35209199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₉×D₁₃ #35209199