Subgroups — C₂×C₃×C₅²×D₁₉⋊C₃ #30685826

Order 17100.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅²×D₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×D₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₅²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₁₉⋊C₃	C₅	1	6	yes	maximal, direct product factor
7	C₃×C₅²×D₁₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₅²×D₁₉⋊C₃	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	6	yes	complemented
13	C₃×C₅×D₁₉⋊C₃	C₂×C₅	1	12	yes	direct product factor
14	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₅²×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
16	C₂×C₃×C₅×D₁₉	C₃×C₅	1	6	yes	complemented
17	C₂×C₅×D₁₉⋊C₃	C₃×C₅	1	18	yes	direct product factor
18	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₅²×D₁₉	C₂×C₃²	1	2	yes	complemented
20	C₂²×C₃²×C₅²	—	19	1	no	maximal, Hall
21	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	6	yes	complemented
22	C₂×C₃×D₁₉⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
24	C₃×C₅×D₁₉	C₂×C₃×C₅	1	12	yes	complemented
25	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	1	18	yes	complemented
26	C₅×D₁₉⋊C₃	C₂×C₃×C₅	1	36	yes	direct product factor
27	C₅²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃²×C₅²	—	19	2	no	—
29	C₂×C₃²×C₅²	—	19	1	no	—
30	C₂×C₅×D₁₉	C₃²×C₅	1	6	yes	complemented
31	C₂×C₃×C₁₉⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented
32	C₃×D₁₉⋊C₃	C₂×C₅²	1	2	yes	direct product factor
33	C₂²×C₃×C₅²	—	19	3	no	—
34	C₂²×C₃×C₅²	—	19	1	no	—
35	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	6	yes	complemented
36	C₅×C₁₉⋊C₃	C₂²×C₃×C₅	1	18	yes	complemented
37	C₂×C₃×D₁₉	C₃×C₅²	1	1	yes	characteristic, complemented
38	C₂×D₁₉⋊C₃	C₃×C₅²	1	3	yes	direct product factor
39	C₃²×C₅²	—	19	1	no	Hall
40	C₂×C₅×C₁₉	C₂×C₃²×C₅	1	6	yes	complemented
41	C₅×D₁₉	C₂×C₃²×C₅	1	12	yes	complemented
42	C₂²×C₃²×C₅	—	19	6	no	—
43	C₃×C₁₉⋊C₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅²	—	19	6	no	—
45	C₂×C₃×C₅²	—	19	2	no	—
46	C₂×C₃×C₅²	—	19	3	no	—
47	C₂×C₃×C₅²	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
49	C₃×D₁₉	C₂×C₃×C₅²	1	2	yes	complemented
50	C₂×C₁₉⋊C₃	C₂×C₃×C₅²	1	3	yes	complemented
51	D₁₉⋊C₃	C₂×C₃×C₅²	1	6	yes	direct product factor
52	C₂²×C₅²	—	19	1	no	Hall
53	C₅×C₁₉	C₂²×C₃²×C₅	1	6	yes	complemented
54	C₂×C₃²×C₅	—	19	12	no	—
55	C₂×C₃²×C₅	—	19	6	no	—
56	C₂×D₁₉	C₃²×C₅²	1	1	yes	characteristic, complemented, Hall
57	C₃×C₅²	—	19	3	no	—
58	C₃×C₅²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
59	C₂²×C₃×C₅	—	19	18	no	—
60	C₂²×C₃×C₅	—	19	6	no	—
61	C₃×C₁₉	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented
62	C₁₉⋊C₃	C₂²×C₃×C₅²	1	3	yes	complemented
63	C₂×C₅²	—	19	2	no	—
64	C₂×C₅²	C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
65	C₃²×C₅	—	19	6	no	—
66	C₂×C₁₉	C₂×C₃²×C₅²	1	1	yes	characteristic, complemented
67	D₁₉	C₂×C₃²×C₅²	1	2	yes	complemented
68	C₂²×C₃²	—	19	1	no	Hall
69	C₂×C₃×C₅	—	19	36	no	—
70	C₂×C₃×C₅	—	19	12	no	—
71	C₂×C₃×C₅	—	19	18	no	—
72	C₂×C₃×C₅	C₅×D₁₉⋊C₃	1	6	yes	direct product factor
73	C₅²	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₅	—	19	6	no	—
75	C₁₉	C₂²×C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃²	—	19	2	no	—
77	C₂×C₃²	—	19	1	no	—
78	C₃×C₅	—	19	18	no	—
79	C₃×C₅	C₂×C₅×D₁₉⋊C₃	1	6	yes	direct product factor
80	C₂²×C₃	—	19	3	no	—
81	C₂²×C₃	—	19	1	no	—
82	C₂×C₅	—	19	12	no	—
83	C₂×C₅	C₃×C₅×D₁₉⋊C₃	1	6	yes	direct product factor
84	C₃²	—	19	1	no	Sylow
85	C₂×C₃	—	19	6	no	—
86	C₂×C₃	—	19	2	no	—
87	C₂×C₃	—	19	3	no	—
88	C₂×C₃	C₅²×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
89	C₅	C₂×C₃×C₅×D₁₉⋊C₃	1	6	yes	direct product factor
90	C₂²	—	19	1	no	Sylow
91	C₃	—	19	3	no	—
92	C₃	C₂×C₅²×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
93	C₂	—	19	2	no	—
94	C₂	C₃×C₅²×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅²×C₁₉⋊C₃	C₂	semidirect
2. C₃×C₅²×D₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₅²×D₁₉	C₃	semidirect
4. C₂×C₅²×D₁₉⋊C₃	C₃	direct (N × H)
5. C₃×C₅²×C₁₉⋊C₃	C₂²	semidirect
6. C₂×C₃×C₅×D₁₉⋊C₃	C₅	direct (N × H)
7. C₃×C₅²×D₁₉	C₂×C₃	semidirect
8. C₂×C₅²×C₁₉⋊C₃	C₂×C₃	semidirect
9. C₅²×D₁₉⋊C₃	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
11. C₂×C₅²×D₁₉	C₃²	semidirect
12. C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	semidirect
13. C₃×C₅×D₁₉⋊C₃	C₂×C₅	direct (N × H)
14. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
15. C₅²×C₁₉⋊C₃	C₂²×C₃	semidirect
16. C₂×C₃×C₅×D₁₉	C₃×C₅	semidirect
17. C₂×C₅×D₁₉⋊C₃	C₃×C₅	direct (N × H)
18. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
19. C₅²×D₁₉	C₂×C₃²	semidirect
21. C₃×C₅×C₁₉⋊C₃	C₂²×C₅	semidirect
22. C₂×C₃×D₁₉⋊C₃	C₅²	direct (N × H)
23. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
24. C₃×C₅×D₁₉	C₂×C₃×C₅	semidirect
25. C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
26. C₅×D₁₉⋊C₃	C₂×C₃×C₅	direct (N × H)
27. C₅²×C₁₉	C₂²×C₃²	semidirect
30. C₂×C₅×D₁₉	C₃²×C₅	semidirect
31. C₂×C₃×C₁₉⋊C₃	C₂×C₅²	semidirect
32. C₃×D₁₉⋊C₃	C₂×C₅²	direct (N × H)
35. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
36. C₅×C₁₉⋊C₃	C₂²×C₃×C₅	semidirect
37. C₂×C₃×D₁₉	C₃×C₅²	semidirect
38. C₂×D₁₉⋊C₃	C₃×C₅²	direct (N × H)
40. C₂×C₅×C₁₉	C₂×C₃²×C₅	semidirect
41. C₅×D₁₉	C₂×C₃²×C₅	semidirect
43. C₃×C₁₉⋊C₃	C₂²×C₅²	semidirect
47. C₂×C₃×C₅²	D₁₉⋊C₃	direct (N × H)
48. C₂×C₃×C₁₉	C₂×C₃×C₅²	semidirect
49. C₃×D₁₉	C₂×C₃×C₅²	semidirect
50. C₂×C₁₉⋊C₃	C₂×C₃×C₅²	semidirect
51. D₁₉⋊C₃	C₂×C₃×C₅²	direct (N × H)
53. C₅×C₁₉	C₂²×C₃²×C₅	semidirect
56. C₂×D₁₉	C₃²×C₅²	semidirect
58. C₃×C₅²	C₂×D₁₉⋊C₃	direct (N × H)
61. C₃×C₁₉	C₂²×C₃×C₅²	semidirect
62. C₁₉⋊C₃	C₂²×C₃×C₅²	semidirect
64. C₂×C₅²	C₃×D₁₉⋊C₃	direct (N × H)
66. C₂×C₁₉	C₂×C₃²×C₅²	semidirect
67. D₁₉	C₂×C₃²×C₅²	semidirect
72. C₂×C₃×C₅	C₅×D₁₉⋊C₃	direct (N × H)
73. C₅²	C₂×C₃×D₁₉⋊C₃	direct (N × H)
75. C₁₉	C₂²×C₃²×C₅²	semidirect
79. C₃×C₅	C₂×C₅×D₁₉⋊C₃	direct (N × H)
83. C₂×C₅	C₃×C₅×D₁₉⋊C₃	direct (N × H)
88. C₂×C₃	C₅²×D₁₉⋊C₃	direct (N × H)
89. C₅	C₂×C₃×C₅×D₁₉⋊C₃	direct (N × H)
92. C₃	C₂×C₅²×D₁₉⋊C₃	direct (N × H)
94. C₂	C₃×C₅²×D₁₉⋊C₃	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×C₃×C₅²×C₁₉⋊C₃	2
C₃×C₅²×D₁₉⋊C₃	2
C₂×C₃×C₅²×D₁₉	3
C₂×C₅²×D₁₉⋊C₃	3
C₂×C₃×C₅×D₁₉⋊C₃	5
C₂²×C₃²×C₅²	19

Subgroups — C2×C3×C52×D19⋊C3 #30685826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅²×D₁₉⋊C₃ #30685826