Subgroups — C₂×C₃²×C₇²×D₁₉ #45692765

Order 33516.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×D₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇²×D₁₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇²×D₁₉	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	4	yes	complemented
7	C₂×C₃²×C₇×D₁₉	C₇	1	8	yes	maximal, direct product factor
8	C₂×C₇²×D₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₉	C₂²×C₃	1	4	yes	complemented
10	C₃²×C₇×D₁₉	C₂×C₇	1	16	yes	direct product factor
11	C₂×C₃²×C₇×C₁₉	C₂×C₇	1	8	yes	complemented
12	C₂×C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
13	C₇²×D₁₉	C₂×C₃²	1	2	yes	direct product factor
14	C₂²×C₃²×C₇²	—	19	1	no	maximal, Hall
15	C₂×C₃×C₇×D₁₉	C₃×C₇	1	32	yes	direct product factor
16	C₃²×C₇×C₁₉	C₂²×C₇	1	8	yes	complemented
17	C₇²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₇²	—	19	2	no	—
19	C₂×C₃²×C₇²	D₁₉	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₇×C₁₉	C₂×C₃×C₇	1	32	yes	complemented
21	C₃×C₇×D₁₉	C₂×C₃×C₇	1	64	yes	direct product factor
22	C₂×C₃²×D₁₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₃×C₇²	—	19	4	no	—
24	C₂×C₇×D₁₉	C₃²×C₇	1	8	yes	direct product factor
25	C₃²×C₇²	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₇×C₁₉	C₂²×C₃×C₇	1	32	yes	complemented
27	C₂×C₃²×C₁₉	C₂×C₇²	1	1	yes	characteristic, complemented
28	C₃²×D₁₉	C₂×C₇²	1	2	yes	direct product factor
29	C₂×C₃×C₇²	—	19	8	no	—
30	C₂×C₃×C₇²	C₃×D₁₉	1	4	yes	direct product factor
31	C₂×C₇×C₁₉	C₂×C₃²×C₇	1	8	yes	complemented
32	C₇×D₁₉	C₂×C₃²×C₇	1	16	yes	direct product factor
33	C₂²×C₃²×C₇	—	19	8	no	—
34	C₂×C₃×D₁₉	C₃×C₇²	1	4	yes	direct product factor
35	C₂²×C₇²	—	19	1	no	Hall
36	C₃²×C₁₉	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	C₂×C₃×D₁₉	1	4	yes	direct product factor
38	C₇×C₁₉	C₂²×C₃²×C₇	1	8	yes	complemented
39	C₂×C₃²×C₇	—	19	16	no	—
40	C₂×C₃²×C₇	C₇×D₁₉	1	8	yes	direct product factor
41	C₂×C₃×C₁₉	C₂×C₃×C₇²	1	4	yes	complemented
42	C₃×D₁₉	C₂×C₃×C₇²	1	8	yes	direct product factor
43	C₂×C₇²	—	19	2	no	—
44	C₂×C₇²	C₃²×D₁₉	1	1	yes	characteristic, direct product factor
45	C₂²×C₃×C₇	—	19	32	no	—
46	C₂×D₁₉	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Hall
47	C₃²×C₇	C₂×C₇×D₁₉	1	8	yes	direct product factor
48	C₃×C₁₉	C₂²×C₃×C₇²	1	4	yes	complemented
49	C₇²	C₂×C₃²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃×C₇	—	19	64	no	—
51	C₂×C₃×C₇	C₃×C₇×D₁₉	1	32	yes	direct product factor
52	C₂×C₁₉	C₂×C₃²×C₇²	1	1	yes	characteristic, complemented
53	D₁₉	C₂×C₃²×C₇²	1	2	yes	direct product factor
54	C₂²×C₃²	—	19	1	no	Hall
55	C₂²×C₇	—	19	8	no	—
56	C₃×C₇	C₂×C₃×C₇×D₁₉	1	32	yes	direct product factor
57	C₁₉	C₂²×C₃²×C₇²	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃²	—	19	2	no	—
59	C₂×C₃²	C₇²×D₁₉	1	1	yes	characteristic, direct product factor
60	C₂×C₇	—	19	16	no	—
61	C₂×C₇	C₃²×C₇×D₁₉	1	8	yes	direct product factor
62	C₂²×C₃	—	19	4	no	—
63	C₃²	C₂×C₇²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
64	C₇	C₂×C₃²×C₇×D₁₉	1	8	yes	direct product factor
65	C₂×C₃	—	19	8	no	—
66	C₂×C₃	C₃×C₇²×D₁₉	1	4	yes	direct product factor
67	C₂²	—	19	1	no	Sylow
68	C₃	C₂×C₃×C₇²×D₁₉	1	4	yes	direct product factor
69	C₂	—	19	2	no	—
70	C₂	C₃²×C₇²×D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₇²	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇²×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃²×C₇²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×D₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₇²×C₁₉	C₂	semidirect
3. C₂×C₃×C₇²×D₁₉	C₃	direct (N × H)
4. C₃²×C₇²×C₁₉	C₂²	semidirect
5. C₃×C₇²×D₁₉	C₂×C₃	direct (N × H)
6. C₂×C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. C₂×C₃²×C₇×D₁₉	C₇	direct (N × H)
8. C₂×C₇²×D₁₉	C₃²	direct (N × H)
9. C₃×C₇²×C₁₉	C₂²×C₃	semidirect
10. C₃²×C₇×D₁₉	C₂×C₇	direct (N × H)
11. C₂×C₃²×C₇×C₁₉	C₂×C₇	semidirect
12. C₂×C₇²×C₁₉	C₂×C₃²	semidirect
13. C₇²×D₁₉	C₂×C₃²	direct (N × H)
15. C₂×C₃×C₇×D₁₉	C₃×C₇	direct (N × H)
16. C₃²×C₇×C₁₉	C₂²×C₇	semidirect
17. C₇²×C₁₉	C₂²×C₃²	semidirect
19. C₂×C₃²×C₇²	D₁₉	direct (N × H)
20. C₂×C₃×C₇×C₁₉	C₂×C₃×C₇	semidirect
21. C₃×C₇×D₁₉	C₂×C₃×C₇	direct (N × H)
22. C₂×C₃²×D₁₉	C₇²	direct (N × H)
24. C₂×C₇×D₁₉	C₃²×C₇	direct (N × H)
25. C₃²×C₇²	C₂×D₁₉	direct (N × H)
26. C₃×C₇×C₁₉	C₂²×C₃×C₇	semidirect
27. C₂×C₃²×C₁₉	C₂×C₇²	semidirect
28. C₃²×D₁₉	C₂×C₇²	direct (N × H)
30. C₂×C₃×C₇²	C₃×D₁₉	direct (N × H)
31. C₂×C₇×C₁₉	C₂×C₃²×C₇	semidirect
32. C₇×D₁₉	C₂×C₃²×C₇	direct (N × H)
34. C₂×C₃×D₁₉	C₃×C₇²	direct (N × H)
36. C₃²×C₁₉	C₂²×C₇²	semidirect
37. C₃×C₇²	C₂×C₃×D₁₉	direct (N × H)
38. C₇×C₁₉	C₂²×C₃²×C₇	semidirect
40. C₂×C₃²×C₇	C₇×D₁₉	direct (N × H)
41. C₂×C₃×C₁₉	C₂×C₃×C₇²	semidirect
42. C₃×D₁₉	C₂×C₃×C₇²	direct (N × H)
44. C₂×C₇²	C₃²×D₁₉	direct (N × H)
46. C₂×D₁₉	C₃²×C₇²	direct (N × H)
47. C₃²×C₇	C₂×C₇×D₁₉	direct (N × H)
48. C₃×C₁₉	C₂²×C₃×C₇²	semidirect
49. C₇²	C₂×C₃²×D₁₉	direct (N × H)
51. C₂×C₃×C₇	C₃×C₇×D₁₉	direct (N × H)
52. C₂×C₁₉	C₂×C₃²×C₇²	semidirect
53. D₁₉	C₂×C₃²×C₇²	direct (N × H)
56. C₃×C₇	C₂×C₃×C₇×D₁₉	direct (N × H)
57. C₁₉	C₂²×C₃²×C₇²	semidirect
59. C₂×C₃²	C₇²×D₁₉	direct (N × H)
61. C₂×C₇	C₃²×C₇×D₁₉	direct (N × H)
63. C₃²	C₂×C₇²×D₁₉	direct (N × H)
64. C₇	C₂×C₃²×C₇×D₁₉	direct (N × H)
66. C₂×C₃	C₃×C₇²×D₁₉	direct (N × H)
68. C₃	C₂×C₃×C₇²×D₁₉	direct (N × H)
70. C₂	C₃²×C₇²×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇²×D₁₉	2
C₂×C₃²×C₇²×C₁₉	2
C₂×C₃×C₇²×D₁₉	3
C₂×C₃²×C₇×D₁₉	7
C₂²×C₃²×C₇²	19

Subgroups — C2×C32×C72×D19 #45692765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₇²×D₁₉ #45692765