Subgroups — C₃×C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄) #49178463

Order 37620.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅×Dic₂₀₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×C₁₁×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁×C₁₉⋊C₃	C₂×C₃	1	3	yes	—
7	C₂×C₃×C₅×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₅×Dic₂₀₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅×(C₁₉⋊C₃)⋊C₄	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₁₉⋊C₃	C₃×C₄	1	3	yes	complemented
12	C₃×C₅×C₁₁×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃×Dic₂₀₉	C₃×C₅	1	1	yes	characteristic, complemented
14	C₁₁⋊((C₁₉⋊C₃)⋊C₄)	C₃×C₅	1	3	yes	direct product factor
15	C₂×C₅×C₁₁×C₁₉	C₂×C₃²	1	1	yes	characteristic
16	C₃²×C₅×Dic₁₁	—	19	1	no	maximal, Hall
17	C₃×C₁₁×C₁₉⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₉⋊C₃	D₁₁	1	1	yes	characteristic
19	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
20	C₂×C₁₁×C₁₉⋊C₃	C₂×C₃×C₅	1	3	yes	—
21	C₃×C₅×Dic₁₉	—	11	1	no	—
22	C₅×(C₁₉⋊C₃)⋊C₄	—	11	3	no	—
23	C₅×C₁₁×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃²×C₅×C₁₁	—	19	1	no	—
25	C₃×C₅×C₁₉⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
26	Dic₂₀₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₃×(C₁₉⋊C₃)⋊C₄	—	11	1	no	Hall
28	C₃×C₅×Dic₁₁	—	19	3	no	—
29	C₃×C₅×Dic₁₁	—	19	1	no	—
30	C₃×C₁₁×C₁₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented
31	C₁₁×C₁₉⋊C₃	C₃×C₄×C₅	1	3	yes	complemented
32	C₂×C₃×C₅×C₁₉	C₃×D₁₁	1	1	yes	characteristic
33	C₂×C₅×C₁₉⋊C₃	C₃×D₁₁	1	3	yes	—
34	C₃²×C₅×C₁₁	—	19	1	no	Hall
35	C₂×C₁₁×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic
36	C₃²×Dic₁₁	—	19	1	no	Hall
37	C₅×Dic₁₉	—	11	1	no	Hall
38	C₂×C₃×C₁₉⋊C₃	C₅×D₁₁	1	1	yes	characteristic
39	C₂×C₃×C₅×C₁₁	—	19	3	no	—
40	C₂×C₃×C₅×C₁₁	D₁₉⋊C₃	1	1	yes	characteristic
41	C₃×C₅×C₁₉	C₃×Dic₁₁	1	1	yes	characteristic, complemented
42	C₅×C₁₉⋊C₃	C₃×Dic₁₁	1	3	yes	complemented
43	C₃×Dic₁₉	—	11	1	no	—
44	(C₁₉⋊C₃)⋊C₄	—	11	3	no	—
45	C₅×Dic₁₁	—	19	1	no	Hall
46	C₁₁×C₁₉	C₃²×C₄×C₅	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃²×C₁₁	—	19	1	no	—
48	C₂×C₅×C₁₉	C₃²×D₁₁	1	1	yes	characteristic
49	C₃²×C₄×C₅	—	209	1	no	Hall
50	C₃×C₁₉⋊C₃	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
51	C₃×C₅×C₁₁	—	19	3	no	—
52	C₃×C₅×C₁₁	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
53	C₃×Dic₁₁	—	19	3	no	—
54	C₃×Dic₁₁	—	19	1	no	—
55	C₂×C₃×C₁₉	C₃×C₅×D₁₁	1	1	yes	characteristic
56	C₂×C₁₉⋊C₃	C₃×C₅×D₁₁	1	3	yes	—
57	C₂×C₅×C₁₁	C₃×D₁₉⋊C₃	1	1	yes	characteristic
58	C₃²×C₁₁	—	19	1	no	Hall
59	C₅×C₁₉	C₃²×Dic₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₃²×C₅	—	19	1	no	—
61	Dic₁₉	—	11	1	no	Hall
62	C₂×C₃×C₁₁	—	19	3	no	—
63	C₂×C₃×C₁₁	C₅×D₁₉⋊C₃	1	1	yes	characteristic
64	C₃×C₄×C₅	—	209	3	no	—
65	C₃×C₄×C₅	—	209	1	no	—
66	C₃×C₁₉	C₃×C₅×Dic₁₁	1	1	yes	characteristic, complemented
67	C₁₉⋊C₃	C₃×C₅×Dic₁₁	1	3	yes	complemented
68	C₅×C₁₁	C₃×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
69	C₃²×C₅	—	19	1	no	Hall
70	Dic₁₁	—	19	1	no	Hall
71	C₂×C₁₉	C₃²×C₅×D₁₁	1	1	yes	characteristic
72	C₃²×C₄	—	209	1	no	Hall
73	C₃×C₁₁	—	19	3	no	—
74	C₃×C₁₁	C₅×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
75	C₂×C₃×C₅	—	19	3	no	—
76	C₂×C₃×C₅	C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
77	C₂×C₁₁	C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic
78	C₄×C₅	—	209	1	no	Hall
79	C₁₉	C₃²×C₅×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃²	—	19	1	no	—
81	C₃×C₅	—	19	3	no	—
82	C₃×C₅	C₁₁⋊((C₁₉⋊C₃)⋊C₄)	1	1	yes	characteristic, direct product factor
83	C₃×C₄	—	209	3	no	—
84	C₃×C₄	—	209	1	no	—
85	C₁₁	C₃×C₅×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
86	C₂×C₅	C₃×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
87	C₃²	—	19	1	no	Sylow
88	C₂×C₃	—	19	3	no	—
89	C₂×C₃	C₅×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
90	C₅	C₃×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	1	1	yes	characteristic, direct product factor, Sylow
91	C₄	—	209	1	no	Sylow
92	C₃	—	19	3	no	—
93	C₃	C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	1	1	yes	characteristic, direct product factor
94	C₂	C₃×C₅×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	C₁₁⋊(D₁₉⋊C₃)
commutator, hypocenter	C₁₁×C₁₉	C₃²×C₄×C₅
Frattini	C₂	C₃×C₅×C₁₁⋊(D₁₉⋊C₃)
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅×C₁₁×C₁₉⋊C₃	C₂
cosocle	C₂×C₁₁×C₁₉	C₂×C₃²×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	C₃	direct (N × H)
3. C₃×C₅×Dic₂₀₉	C₃	semidirect
4. C₃×C₅×C₁₁×C₁₉⋊C₃	C₄	semidirect
5. C₃×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	C₅	direct (N × H)
8. C₅×Dic₂₀₉	C₃²	semidirect
11. C₅×C₁₁×C₁₉⋊C₃	C₃×C₄	semidirect
12. C₃×C₅×C₁₁×C₁₉	C₃×C₄	semidirect
13. C₃×Dic₂₀₉	C₃×C₅	semidirect
14. C₁₁⋊((C₁₉⋊C₃)⋊C₄)	C₃×C₅	direct (N × H)
17. C₃×C₁₁×C₁₉⋊C₃	C₄×C₅	semidirect
23. C₅×C₁₁×C₁₉	C₃²×C₄	semidirect
25. C₃×C₅×C₁₉⋊C₃	Dic₁₁	semidirect
26. Dic₂₀₉	C₃²×C₅	semidirect
30. C₃×C₁₁×C₁₉	C₃×C₄×C₅	semidirect
31. C₁₁×C₁₉⋊C₃	C₃×C₄×C₅	semidirect
41. C₃×C₅×C₁₉	C₃×Dic₁₁	semidirect
42. C₅×C₁₉⋊C₃	C₃×Dic₁₁	semidirect
46. C₁₁×C₁₉	C₃²×C₄×C₅	semidirect
50. C₃×C₁₉⋊C₃	C₅×Dic₁₁	semidirect
52. C₃×C₅×C₁₁	(C₁₉⋊C₃)⋊C₄	semidirect
59. C₅×C₁₉	C₃²×Dic₁₁	semidirect
66. C₃×C₁₉	C₃×C₅×Dic₁₁	semidirect
67. C₁₉⋊C₃	C₃×C₅×Dic₁₁	semidirect
68. C₅×C₁₁	C₃×(C₁₉⋊C₃)⋊C₄	semidirect
74. C₃×C₁₁	C₅×(C₁₉⋊C₃)⋊C₄	semidirect
79. C₁₉	C₃²×C₅×Dic₁₁	semidirect
82. C₃×C₅	C₁₁⋊((C₁₉⋊C₃)⋊C₄)	direct (N × H)
85. C₁₁	C₃×C₅×(C₁₉⋊C₃)⋊C₄	semidirect
90. C₅	C₃×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	direct (N × H)
93. C₃	C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	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×C₅×C₁₁×C₁₉⋊C₃	2
C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	3
C₃×C₅×Dic₂₀₉	3
C₃×C₁₁⋊((C₁₉⋊C₃)⋊C₄)	5
C₃×C₅×(C₁₉⋊C₃)⋊C₄	11
C₃²×C₅×Dic₁₁	19

Subgroups — C3×C5×C11⋊((C19⋊C3)⋊C4) #49178463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁⋊((C₁₉⋊C₃)⋊C₄) #49178463