Subgroups — C₅×C₁₁×A₄×C₁₉⋊C₃ #49178627

Order 37620.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₁×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×A₄×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₂²⋊(C₁₉⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₃×C₅×C₁₁×C₁₉⋊C₃	—	4	1	no	maximal, Hall
5	C₁₁×A₄×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁×C₁₉⋊C₃	—	3	1	no	—
7	C₂²×C₅×C₁₁×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₅×A₄×C₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₁₉⋊C₃	—	4	2	no	—
10	C₅×C₁₁×C₁₉⋊C₃	A₄	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₁₁×C₁₉	—	4	1	no	—
12	C₁₁×C₂²⋊(C₁₉⋊C₃)	C₃×C₅	1	2	yes	complemented
13	C₁₁×A₄×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented
14	C₂²×C₁₁×C₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
15	C₂×C₅×C₁₁×C₁₉	—	3	1	no	—
16	C₃×C₅×C₁₁×A₄	—	19	1	no	maximal, Hall
17	C₃×C₁₁×C₁₉⋊C₃	—	4	1	no	Hall
18	C₂×C₁₁×C₁₉⋊C₃	—	3	1	no	—
19	C₅×C₂²⋊(C₁₉⋊C₃)	C₃×C₁₁	1	2	yes	complemented
20	C₅×A₄×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented
21	C₂²×C₅×C₁₉⋊C₃	C₃×C₁₁	1	1	yes	characteristic, complemented
22	C₅×C₁₁×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₉⋊C₃	—	4	1	no	Hall
24	C₂²×C₁₁×C₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
25	A₄×C₁₉⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃×C₅×C₁₁	—	19	1	no	—
27	C₅×C₁₁×A₄	—	19	2	no	—
28	C₅×C₁₁×A₄	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
29	C₃×C₁₁×C₁₉	—	4	1	no	—
30	C₁₁×C₁₉⋊C₃	—	4	2	no	—
31	C₁₁×C₁₉⋊C₃	C₅×A₄	1	1	yes	characteristic, direct product factor
32	C₂×C₅×C₁₉⋊C₃	—	3	1	no	—
33	C₃²×C₅×C₁₁	—	76	1	no	Hall
34	C₂×C₁₁×C₁₉	—	3	1	no	—
35	C₃×C₁₁×A₄	—	19	1	no	Hall
36	C₂²×C₅×C₁₉	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₁₁	—	57	1	no	—
38	C₃×C₅×C₁₉	—	4	1	no	—
39	C₅×C₁₉⋊C₃	—	4	2	no	—
40	C₅×C₁₉⋊C₃	C₁₁×A₄	1	1	yes	characteristic, direct product factor
41	C₂²⋊(C₁₉⋊C₃)	C₃×C₅×C₁₁	1	2	yes	complemented
42	A₄×C₁₉	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
43	C₂²×C₁₉⋊C₃	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
44	C₂²×C₅×C₁₁	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
45	C₁₁×C₁₉	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Hall
46	C₂×C₅×C₁₉	—	3	1	no	—
47	C₃×C₅×A₄	—	19	1	no	Hall
48	C₃×C₁₉⋊C₃	—	4	1	no	Hall
49	C₃×C₅×C₁₁	—	4	1	no	—
50	C₃×C₅×C₁₁	—	19	1	no	—
51	C₃×C₅×C₁₁	—	76	2	no	—
52	C₂²×C₃×C₁₁	—	19	1	no	—
53	C₁₁×A₄	—	19	2	no	—
54	C₁₁×A₄	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
55	C₂×C₁₉⋊C₃	—	3	1	no	—
56	C₂×C₅×C₁₁	—	3	1	no	—
57	C₃²×C₁₁	—	76	1	no	Hall
58	C₅×C₁₉	C₃×C₁₁×A₄	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₁₉	C₃²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₃×C₁₁	—	57	1	no	—
61	C₂²×C₃×C₅	—	19	1	no	—
62	C₅×A₄	—	19	2	no	—
63	C₅×A₄	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
64	C₃×C₁₉	—	4	1	no	—
65	C₁₉⋊C₃	—	4	2	no	—
66	C₁₉⋊C₃	C₅×C₁₁×A₄	1	1	yes	characteristic, direct product factor
67	C₅×C₁₁	A₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
68	C₃²×C₅	—	76	1	no	Hall
69	C₂²×C₁₁	C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
70	C₂×C₁₉	—	3	1	no	—
71	C₃×A₄	—	19	1	no	Hall
72	C₃×C₁₁	—	4	1	no	—
73	C₃×C₁₁	—	19	1	no	—
74	C₃×C₁₁	—	76	2	no	—
75	C₂×C₃×C₅	—	57	1	no	—
76	C₂×C₁₁	—	3	1	no	—
77	C₂²×C₅	C₃×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
78	C₁₉	C₃×C₅×C₁₁×A₄	1	1	yes	characteristic, complemented, Sylow
79	C₃×C₅	—	4	1	no	—
80	C₃×C₅	—	19	1	no	—
81	C₃×C₅	—	76	2	no	—
82	C₂²×C₃	—	19	1	no	—
83	A₄	—	19	2	no	—
84	A₄	C₅×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
85	C₁₁	C₅×A₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₅	—	3	1	no	—
87	C₃²	—	76	1	no	Sylow
88	C₂×C₃	—	57	1	no	—
89	C₅	C₁₁×A₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²	C₃×C₅×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
91	C₃	—	4	1	no	—
92	C₃	—	19	1	no	—
93	C₃	—	76	2	no	—
94	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	A₄×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₂²×C₁₉	C₃²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁×C₁₉	C₃²
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₁×C₁₉⋊C₃	C₃	semidirect
2. C₅×C₁₁×A₄×C₁₉	C₃	semidirect
3. C₅×C₁₁×C₂²⋊(C₁₉⋊C₃)	C₃	semidirect
5. C₁₁×A₄×C₁₉⋊C₃	C₅	direct (N × H)
7. C₂²×C₅×C₁₁×C₁₉	C₃²	semidirect
8. C₅×A₄×C₁₉⋊C₃	C₁₁	direct (N × H)
10. C₅×C₁₁×C₁₉⋊C₃	A₄	direct (N × H)
12. C₁₁×C₂²⋊(C₁₉⋊C₃)	C₃×C₅	semidirect
13. C₁₁×A₄×C₁₉	C₃×C₅	semidirect
14. C₂²×C₁₁×C₁₉⋊C₃	C₃×C₅	semidirect
19. C₅×C₂²⋊(C₁₉⋊C₃)	C₃×C₁₁	semidirect
20. C₅×A₄×C₁₉	C₃×C₁₁	semidirect
21. C₂²×C₅×C₁₉⋊C₃	C₃×C₁₁	semidirect
22. C₅×C₁₁×C₁₉	C₃×A₄	semidirect
24. C₂²×C₁₁×C₁₉	C₃²×C₅	semidirect
25. A₄×C₁₉⋊C₃	C₅×C₁₁	direct (N × H)
28. C₅×C₁₁×A₄	C₁₉⋊C₃	direct (N × H)
31. C₁₁×C₁₉⋊C₃	C₅×A₄	direct (N × H)
36. C₂²×C₅×C₁₉	C₃²×C₁₁	semidirect
40. C₅×C₁₉⋊C₃	C₁₁×A₄	direct (N × H)
41. C₂²⋊(C₁₉⋊C₃)	C₃×C₅×C₁₁	semidirect
42. A₄×C₁₉	C₃×C₅×C₁₁	semidirect
43. C₂²×C₁₉⋊C₃	C₃×C₅×C₁₁	semidirect
44. C₂²×C₅×C₁₁	C₃×C₁₉⋊C₃	semidirect
45. C₁₁×C₁₉	C₃×C₅×A₄	semidirect
54. C₁₁×A₄	C₅×C₁₉⋊C₃	direct (N × H)
58. C₅×C₁₉	C₃×C₁₁×A₄	semidirect
59. C₂²×C₁₉	C₃²×C₅×C₁₁	semidirect
63. C₅×A₄	C₁₁×C₁₉⋊C₃	direct (N × H)
66. C₁₉⋊C₃	C₅×C₁₁×A₄	direct (N × H)
67. C₅×C₁₁	A₄×C₁₉⋊C₃	direct (N × H)
69. C₂²×C₁₁	C₃×C₅×C₁₉⋊C₃	semidirect
77. C₂²×C₅	C₃×C₁₁×C₁₉⋊C₃	semidirect
78. C₁₉	C₃×C₅×C₁₁×A₄	semidirect
84. A₄	C₅×C₁₁×C₁₉⋊C₃	direct (N × H)
85. C₁₁	C₅×A₄×C₁₉⋊C₃	direct (N × H)
89. C₅	C₁₁×A₄×C₁₉⋊C₃	direct (N × H)
90. C₂²	C₃×C₅×C₁₁×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₁×C₁₉⋊C₃	3
C₅×C₁₁×A₄×C₁₉	3
C₅×C₁₁×C₂²⋊(C₁₉⋊C₃)	3
C₃×C₅×C₁₁×C₁₉⋊C₃	4
C₁₁×A₄×C₁₉⋊C₃	5
C₅×A₄×C₁₉⋊C₃	11
C₃×C₅×C₁₁×A₄	19

Subgroups — C5×C11×A4×C19⋊C3 #49178627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×A₄×C₁₉⋊C₃ #49178627