Subgroups — C₃×C₅×C₁₁×C₂²⋊(C₁₉⋊C₃) #49178769

Order 37620.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₂²⋊(C₁₉⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₅×C₁₁×C₁₉	C₃	semidirect
4. C₃×C₁₁×C₂²⋊(C₁₉⋊C₃)	C₅	direct (N × H)
6. C₂²×C₅×C₁₁×C₁₉	C₃²	semidirect
7. C₃×C₅×C₂²⋊(C₁₉⋊C₃)	C₁₁	direct (N × H)
9. C₃×C₅×C₁₁×C₁₉	A₄	semidirect
10. C₁₁×C₂²⋊(C₁₉⋊C₃)	C₃×C₅	direct (N × H)
11. C₂²×C₃×C₁₁×C₁₉	C₃×C₅	semidirect
16. C₂²×C₃×C₅×C₁₉	C₃×C₁₁	semidirect
17. C₅×C₂²⋊(C₁₉⋊C₃)	C₃×C₁₁	direct (N × H)
18. C₅×C₁₁×C₁₉	C₃×A₄	semidirect
20. C₂²×C₁₁×C₁₉	C₃²×C₅	semidirect
21. C₃×C₂²⋊(C₁₉⋊C₃)	C₅×C₁₁	direct (N × H)
22. C₂²×C₃×C₅×C₁₁	C₁₉⋊C₃	semidirect
24. C₃×C₁₁×C₁₉	C₅×A₄	semidirect
30. C₂²×C₅×C₁₉	C₃²×C₁₁	semidirect
32. C₃×C₅×C₁₉	C₁₁×A₄	semidirect
34. C₂²×C₃×C₁₉	C₃×C₅×C₁₁	semidirect
35. C₂²⋊(C₁₉⋊C₃)	C₃×C₅×C₁₁	direct (N × H)
36. C₂²×C₅×C₁₁	C₃×C₁₉⋊C₃	semidirect
37. C₁₁×C₁₉	C₃×C₅×A₄	semidirect
42. C₃×C₅×C₁₁	C₂²⋊(C₁₉⋊C₃)	direct (N × H)
43. C₂²×C₃×C₁₁	C₅×C₁₉⋊C₃	semidirect
48. C₅×C₁₉	C₃×C₁₁×A₄	semidirect
49. C₂²×C₁₉	C₃²×C₅×C₁₁	semidirect
51. C₂²×C₃×C₅	C₁₁×C₁₉⋊C₃	semidirect
53. C₃×C₁₉	C₅×C₁₁×A₄	semidirect
55. C₅×C₁₁	C₃×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
57. C₂²×C₁₁	C₃×C₅×C₁₉⋊C₃	semidirect
61. C₃×C₁₁	C₅×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
64. C₂²×C₅	C₃×C₁₁×C₁₉⋊C₃	semidirect
65. C₁₉	C₃×C₅×C₁₁×A₄	semidirect
67. C₃×C₅	C₁₁×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
68. C₂²×C₃	C₅×C₁₁×C₁₉⋊C₃	semidirect
70. C₁₁	C₃×C₅×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
74. C₅	C₃×C₁₁×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
75. C₂²	C₃×C₅×C₁₁×C₁₉⋊C₃	semidirect
77. C₃	C₅×C₁₁×C₂²⋊(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
C₅×C₁₁×C₂²⋊(C₁₉⋊C₃)	3
C₂²×C₃×C₅×C₁₁×C₁₉	3
C₃×C₅×C₁₁×C₁₉⋊C₃	4
C₃×C₁₁×C₂²⋊(C₁₉⋊C₃)	5
C₃×C₅×C₂²⋊(C₁₉⋊C₃)	11
C₃×C₅×C₁₁×A₄	19

Subgroups — C3×C5×C11×C22⋊(C19⋊C3) #49178769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁×C₂²⋊(C₁₉⋊C₃) #49178769