Subgroups — C₂×C₃×C₁₁×C₁₆×C₁₉ #72197708

Order 20064.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×C₁₆×C₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁×C₁₆×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₁×C₁₉	C₄	1	1	yes	characteristic
5	C₃×C₈×C₁₁×C₁₉	C₄	1	1	yes	characteristic
6	C₃×C₈×C₁₁×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₁₁×C₁₆×C₁₉	C₂×C₃	1	2	yes	direct product factor
9	C₂²×C₃×C₁₁×C₁₉	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₁×C₁₉	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₁×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₁₆×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₄×C₁₁×C₁₉	C₃×C₄	1	1	yes	characteristic
14	C₈×C₁₁×C₁₉	C₃×C₄	1	1	yes	characteristic
15	C₈×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₃×C₁₁×C₁₉	C₁₆	1	2	yes	direct product factor
17	C₂×C₃×C₁₁×C₁₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₃×C₁₁×C₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₈×C₁₉	C₂×C₁₁	1	1	yes	characteristic
20	C₃×C₁₆×C₁₉	C₂×C₁₁	1	2	yes	direct product factor
21	C₂²×C₁₁×C₁₉	C₃×C₈	1	1	yes	characteristic
22	C₄×C₁₁×C₁₉	C₃×C₈	1	1	yes	characteristic
23	C₄×C₁₁×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
24	C₃×C₁₁×C₁₉	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₆×C₁₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃×C₈×C₁₁	C₂×C₁₉	1	1	yes	characteristic
27	C₃×C₁₁×C₁₆	C₂×C₁₉	1	2	yes	direct product factor
28	C₂×C₃×C₄×C₁₉	C₄×C₁₁	1	1	yes	characteristic
29	C₃×C₈×C₁₉	C₄×C₁₁	1	1	yes	characteristic
30	C₃×C₈×C₁₉	C₂²×C₁₁	1	1	yes	characteristic
31	C₂×C₁₁×C₁₉	C₃×C₁₆	1	2	yes	direct product factor
32	C₂×C₁₁×C₁₉	C₂×C₃×C₈	1	1	yes	characteristic
33	C₂×C₁₁×C₁₆	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₈×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic
35	C₁₆×C₁₉	C₂×C₃×C₁₁	1	2	yes	direct product factor
36	C₂×C₃×C₄×C₁₁	C₄×C₁₉	1	1	yes	characteristic
37	C₃×C₈×C₁₁	C₄×C₁₉	1	1	yes	characteristic
38	C₃×C₈×C₁₁	C₂²×C₁₉	1	1	yes	characteristic
39	C₂²×C₃×C₁₉	C₈×C₁₁	1	1	yes	characteristic
40	C₃×C₄×C₁₉	C₈×C₁₁	1	1	yes	characteristic
41	C₃×C₄×C₁₉	C₂×C₄×C₁₁	1	1	yes	characteristic
42	C₁₁×C₁₉	C₂×C₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₈×C₁₁	C₂×C₃×C₁₉	1	1	yes	characteristic
44	C₁₁×C₁₆	C₂×C₃×C₁₉	1	2	yes	direct product factor
45	C₂×C₄×C₁₉	C₃×C₄×C₁₁	1	1	yes	characteristic
46	C₈×C₁₉	C₃×C₄×C₁₁	1	1	yes	characteristic
47	C₈×C₁₉	C₂²×C₃×C₁₁	1	1	yes	characteristic
48	C₂²×C₃×C₁₁	C₈×C₁₉	1	1	yes	characteristic
49	C₃×C₄×C₁₁	C₈×C₁₉	1	1	yes	characteristic
50	C₃×C₄×C₁₁	C₂×C₄×C₁₉	1	1	yes	characteristic
51	C₂×C₃×C₁₉	C₁₁×C₁₆	1	2	yes	direct product factor
52	C₂×C₃×C₁₉	C₂×C₈×C₁₁	1	1	yes	characteristic
53	C₂×C₃×C₁₆	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₄×C₁₁	C₃×C₄×C₁₉	1	1	yes	characteristic
55	C₈×C₁₁	C₃×C₄×C₁₉	1	1	yes	characteristic
56	C₈×C₁₁	C₂²×C₃×C₁₉	1	1	yes	characteristic
57	C₂²×C₁₉	C₃×C₈×C₁₁	1	1	yes	characteristic
58	C₄×C₁₉	C₃×C₈×C₁₁	1	1	yes	characteristic
59	C₄×C₁₉	C₂×C₃×C₄×C₁₁	1	1	yes	characteristic
60	C₂×C₃×C₁₁	C₁₆×C₁₉	1	2	yes	direct product factor
61	C₂×C₃×C₁₁	C₂×C₈×C₁₉	1	1	yes	characteristic
62	C₃×C₁₉	C₂×C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Hall
63	C₂×C₃×C₈	C₂×C₁₁×C₁₉	1	1	yes	characteristic
64	C₃×C₁₆	C₂×C₁₁×C₁₉	1	2	yes	direct product factor
65	C₂²×C₁₁	C₃×C₈×C₁₉	1	1	yes	characteristic
66	C₄×C₁₁	C₃×C₈×C₁₉	1	1	yes	characteristic
67	C₄×C₁₁	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
68	C₂×C₁₉	C₃×C₁₁×C₁₆	1	2	yes	direct product factor
69	C₂×C₁₉	C₂×C₃×C₈×C₁₁	1	1	yes	characteristic
70	C₃×C₁₁	C₂×C₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Hall
71	C₂×C₁₆	C₃×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×C₃×C₄	C₄×C₁₁×C₁₉	1	1	yes	characteristic
73	C₃×C₈	C₄×C₁₁×C₁₉	1	1	yes	characteristic
74	C₃×C₈	C₂²×C₁₁×C₁₉	1	1	yes	characteristic
75	C₂×C₁₁	C₃×C₁₆×C₁₉	1	2	yes	direct product factor
76	C₂×C₁₁	C₂×C₃×C₈×C₁₉	1	1	yes	characteristic
77	C₁₉	C₂×C₃×C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₈	C₂×C₃×C₁₁×C₁₉	1	1	yes	characteristic
79	C₁₆	C₂×C₃×C₁₁×C₁₉	1	2	yes	direct product factor
80	C₂²×C₃	C₈×C₁₁×C₁₉	1	1	yes	characteristic
81	C₃×C₄	C₈×C₁₁×C₁₉	1	1	yes	characteristic
82	C₃×C₄	C₂×C₄×C₁₁×C₁₉	1	1	yes	characteristic
83	C₁₁	C₂×C₃×C₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂×C₄	C₃×C₄×C₁₁×C₁₉	1	1	yes	characteristic
85	C₈	C₃×C₄×C₁₁×C₁₉	1	1	yes	characteristic
86	C₈	C₂²×C₃×C₁₁×C₁₉	1	1	yes	characteristic
87	C₂×C₃	C₁₁×C₁₆×C₁₉	1	2	yes	direct product factor
88	C₂×C₃	C₂×C₈×C₁₁×C₁₉	1	1	yes	characteristic
89	C₂²	C₃×C₈×C₁₁×C₁₉	1	1	yes	characteristic
90	C₄	C₃×C₈×C₁₁×C₁₉	1	1	yes	characteristic
91	C₄	C₂×C₃×C₄×C₁₁×C₁₉	1	1	yes	characteristic
92	C₃	C₂×C₁₁×C₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	C₃×C₁₁×C₁₆×C₁₉	1	2	yes	direct product factor
94	C₂	C₂×C₃×C₈×C₁₁×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₃×C₁₁×C₁₉
socle, prime radical	C₂²×C₃×C₁₁×C₁₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₁×C₁₆×C₁₉	C₂	direct (N × H)
3. C₂×C₁₁×C₁₆×C₁₉	C₃	direct (N × H)
8. C₁₁×C₁₆×C₁₉	C₂×C₃	direct (N × H)
12. C₂×C₃×C₁₆×C₁₉	C₁₁	direct (N × H)
16. C₂×C₃×C₁₁×C₁₉	C₁₆	direct (N × H)
18. C₂×C₃×C₁₁×C₁₆	C₁₉	direct (N × H)
20. C₃×C₁₆×C₁₉	C₂×C₁₁	direct (N × H)
24. C₃×C₁₁×C₁₉	C₂×C₁₆	direct (N × H)
25. C₂×C₁₆×C₁₉	C₃×C₁₁	direct (N × H)
27. C₃×C₁₁×C₁₆	C₂×C₁₉	direct (N × H)
31. C₂×C₁₁×C₁₉	C₃×C₁₆	direct (N × H)
33. C₂×C₁₁×C₁₆	C₃×C₁₉	direct (N × H)
35. C₁₆×C₁₉	C₂×C₃×C₁₁	direct (N × H)
42. C₁₁×C₁₉	C₂×C₃×C₁₆	direct (N × H)
44. C₁₁×C₁₆	C₂×C₃×C₁₉	direct (N × H)
51. C₂×C₃×C₁₉	C₁₁×C₁₆	direct (N × H)
53. C₂×C₃×C₁₆	C₁₁×C₁₉	direct (N × H)
60. C₂×C₃×C₁₁	C₁₆×C₁₉	direct (N × H)
62. C₃×C₁₉	C₂×C₁₁×C₁₆	direct (N × H)
64. C₃×C₁₆	C₂×C₁₁×C₁₉	direct (N × H)
68. C₂×C₁₉	C₃×C₁₁×C₁₆	direct (N × H)
70. C₃×C₁₁	C₂×C₁₆×C₁₉	direct (N × H)
71. C₂×C₁₆	C₃×C₁₁×C₁₉	direct (N × H)
75. C₂×C₁₁	C₃×C₁₆×C₁₉	direct (N × H)
77. C₁₉	C₂×C₃×C₁₁×C₁₆	direct (N × H)
79. C₁₆	C₂×C₃×C₁₁×C₁₉	direct (N × H)
83. C₁₁	C₂×C₃×C₁₆×C₁₉	direct (N × H)
87. C₂×C₃	C₁₁×C₁₆×C₁₉	direct (N × H)
92. C₃	C₂×C₁₁×C₁₆×C₁₉	direct (N × H)
93. C₂	C₃×C₁₁×C₁₆×C₁₉	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×C₈×C₁₁×C₁₉	2
C₃×C₁₁×C₁₆×C₁₉	2
C₂×C₁₁×C₁₆×C₁₉	3
C₂×C₃×C₁₆×C₁₉	11
C₂×C₃×C₁₁×C₁₆	19

Subgroups — C2×C3×C11×C16×C19 #72197708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁×C₁₆×C₁₉ #72197708