Subgroups — C₂×C₃×C₅⋊D₅×C₁₉⋊C₃ #30685830

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×C₅⋊D₅×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₅×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₅²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₅×C₁₉⋊C₃	—	5	6	no	maximal
7	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₅⋊D₅×C₁₉⋊C₃	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₁₉×C₅⋊D₅	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₉⋊C₃	D₅	1	6	yes	complemented
13	C₃×D₅×C₁₉⋊C₃	—	5	12	no	—
14	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₅²×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
16	C₂×C₃×D₅×C₁₉	—	5	6	no	—
17	C₂×D₅×C₁₉⋊C₃	—	5	18	no	—
18	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₁₉×C₅⋊D₅	C₂×C₃²	1	2	yes	complemented
20	C₂×C₃²×C₅⋊D₅	—	19	1	no	maximal, Hall
21	C₃×C₅×C₁₉⋊C₃	C₂×D₅	1	6	yes	complemented
22	C₂²×C₃×C₁₉⋊C₃	—	25	1	no	Hall
23	C₂×C₃×C₅×C₁₉	C₃×D₅	1	6	yes	complemented
24	C₃×D₅×C₁₉	—	5	12	no	—
25	C₂×C₅×C₁₉⋊C₃	C₃×D₅	1	18	yes	complemented
26	D₅×C₁₉⋊C₃	—	5	36	no	—
27	C₅²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃²×C₅²	—	19	1	no	—
29	C₃²×C₅⋊D₅	—	19	2	no	—
30	C₂×D₅×C₁₉	—	5	6	no	—
31	C₂×C₃×C₁₉⋊C₃	—	25	2	no	—
32	C₂×C₃×C₁₉⋊C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₅⋊D₅	—	19	3	no	—
34	C₂×C₃×C₅⋊D₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₁₉	C₂×C₃×D₅	1	6	yes	complemented
36	C₅×C₁₉⋊C₃	C₂×C₃×D₅	1	18	yes	complemented
37	C₂²×C₃×C₁₉	—	25	1	no	—
38	C₂²×C₁₉⋊C₃	—	25	3	no	—
39	C₃²×C₅²	—	19	1	no	Hall
40	C₂×C₅×C₁₉	C₃²×D₅	1	6	yes	complemented
41	D₅×C₁₉	—	5	12	no	—
42	C₂×C₃²×D₅	—	95	6	no	—
43	C₃×C₁₉⋊C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃×C₅²	—	19	3	no	—
45	C₂×C₃×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
46	C₃×C₅⋊D₅	—	19	6	no	—
47	C₃×C₅⋊D₅	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
48	C₂×C₃×C₁₉	—	25	2	no	—
49	C₂×C₃×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
50	C₂×C₁₉⋊C₃	—	25	6	no	—
51	C₂×C₁₉⋊C₃	C₃×C₅⋊D₅	1	3	yes	direct product factor
52	C₂×C₅⋊D₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
53	C₅×C₁₉	C₂×C₃²×D₅	1	6	yes	complemented
54	C₂×C₃²×C₅	—	19	6	no	—
55	C₃²×D₅	—	95	12	no	—
56	C₂²×C₁₉	—	25	1	no	Hall
57	C₃×C₅²	—	19	3	no	—
58	C₃×C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×D₅	—	5	6	no	—
60	C₂×C₃×D₅	—	95	18	no	—
61	C₃×C₁₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
62	C₁₉⋊C₃	C₂×C₃×C₅⋊D₅	1	3	yes	direct product factor
63	C₂×C₅²	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
64	C₅⋊D₅	C₂×C₃×C₁₉⋊C₃	1	2	yes	direct product factor
65	C₃²×C₅	—	19	6	no	—
66	C₂×C₁₉	—	25	2	no	—
67	C₂×C₁₉	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented
68	C₂²×C₃²	—	475	1	no	Hall
69	C₂×C₃×C₅	—	19	18	no	—
70	C₂×C₃×C₅	D₅×C₁₉⋊C₃	1	6	yes	complemented
71	C₃×D₅	—	5	12	no	—
72	C₃×D₅	—	95	36	no	—
73	C₅²	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
74	C₂×D₅	—	5	6	no	—
75	C₁₉	C₂×C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃²	—	19	1	no	—
77	C₂×C₃²	—	475	2	no	—
78	C₃×C₅	—	19	18	no	—
79	C₃×C₅	C₂×D₅×C₁₉⋊C₃	1	6	yes	complemented
80	C₂²×C₃	—	25	1	no	—
81	C₂²×C₃	—	475	3	no	—
82	C₂×C₅	C₃×D₅×C₁₉⋊C₃	1	6	yes	complemented
83	D₅	—	5	12	no	—
84	C₃²	—	19	1	no	Sylow
85	C₂×C₃	—	19	3	no	—
86	C₂×C₃	—	25	2	no	—
87	C₂×C₃	—	475	6	no	—
88	C₂×C₃	C₅⋊D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
89	C₅	C₂×C₃×D₅×C₁₉⋊C₃	1	6	yes	complemented
90	C₂²	—	25	1	no	Sylow
91	C₃	—	19	3	no	—
92	C₃	C₂×C₅⋊D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
93	C₂	—	25	2	no	—
94	C₂	C₃×C₅⋊D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅²×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₃

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×C₅⋊D₅×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₁₉×C₅⋊D₅	C₃	semidirect
4. C₂×C₅⋊D₅×C₁₉⋊C₃	C₃	direct (N × H)
5. C₃×C₅²×C₁₉⋊C₃	C₂²	semidirect
7. C₃×C₁₉×C₅⋊D₅	C₂×C₃	semidirect
8. C₂×C₅²×C₁₉⋊C₃	C₂×C₃	semidirect
9. C₅⋊D₅×C₁₉⋊C₃	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
11. C₂×C₁₉×C₅⋊D₅	C₃²	semidirect
12. C₂×C₃×C₅×C₁₉⋊C₃	D₅	semidirect
14. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
15. C₅²×C₁₉⋊C₃	C₂²×C₃	semidirect
18. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
19. C₁₉×C₅⋊D₅	C₂×C₃²	semidirect
21. C₃×C₅×C₁₉⋊C₃	C₂×D₅	semidirect
23. C₂×C₃×C₅×C₁₉	C₃×D₅	semidirect
25. C₂×C₅×C₁₉⋊C₃	C₃×D₅	semidirect
27. C₅²×C₁₉	C₂²×C₃²	semidirect
32. C₂×C₃×C₁₉⋊C₃	C₅⋊D₅	direct (N × H)
34. C₂×C₃×C₅⋊D₅	C₁₉⋊C₃	direct (N × H)
35. C₃×C₅×C₁₉	C₂×C₃×D₅	semidirect
36. C₅×C₁₉⋊C₃	C₂×C₃×D₅	semidirect
40. C₂×C₅×C₁₉	C₃²×D₅	semidirect
43. C₃×C₁₉⋊C₃	C₂×C₅⋊D₅	direct (N × H)
45. C₂×C₃×C₅²	C₂×C₁₉⋊C₃	semidirect
47. C₃×C₅⋊D₅	C₂×C₁₉⋊C₃	direct (N × H)
49. C₂×C₃×C₁₉	C₃×C₅⋊D₅	semidirect
51. C₂×C₁₉⋊C₃	C₃×C₅⋊D₅	direct (N × H)
52. C₂×C₅⋊D₅	C₃×C₁₉⋊C₃	direct (N × H)
53. C₅×C₁₉	C₂×C₃²×D₅	semidirect
58. C₃×C₅²	C₂²×C₁₉⋊C₃	semidirect
61. C₃×C₁₉	C₂×C₃×C₅⋊D₅	semidirect
62. C₁₉⋊C₃	C₂×C₃×C₅⋊D₅	direct (N × H)
63. C₂×C₅²	C₂×C₃×C₁₉⋊C₃	semidirect
64. C₅⋊D₅	C₂×C₃×C₁₉⋊C₃	direct (N × H)
67. C₂×C₁₉	C₃²×C₅⋊D₅	semidirect
70. C₂×C₃×C₅	D₅×C₁₉⋊C₃	semidirect
73. C₅²	C₂²×C₃×C₁₉⋊C₃	semidirect
75. C₁₉	C₂×C₃²×C₅⋊D₅	semidirect
79. C₃×C₅	C₂×D₅×C₁₉⋊C₃	semidirect
82. C₂×C₅	C₃×D₅×C₁₉⋊C₃	semidirect
88. C₂×C₃	C₅⋊D₅×C₁₉⋊C₃	direct (N × H)
89. C₅	C₂×C₃×D₅×C₁₉⋊C₃	semidirect
92. C₃	C₂×C₅⋊D₅×C₁₉⋊C₃	direct (N × H)
94. C₂	C₃×C₅⋊D₅×C₁₉⋊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×C₅⋊D₅×C₁₉⋊C₃	2
C₂×C₃×C₁₉×C₅⋊D₅	3
C₂×C₅⋊D₅×C₁₉⋊C₃	3
C₂×C₃×D₅×C₁₉⋊C₃	5
C₂×C₃²×C₅⋊D₅	19

Subgroups — C2×C3×C5⋊D5×C19⋊C3 #30685830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅⋊D₅×C₁₉⋊C₃ #30685830