Finite Group Databasebeta

← C32×C5×D11×D19 #49178657

Subgroups — C32×C5×D11×D19 #49178657

Order 37620.

240 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×D19C211yesmaximal, characteristic, complemented
2C32×C5×C19×D11C211yesmaximal, characteristic, complemented
3C32×C5×D209C211yesmaximal, characteristic, complemented
4C3×C5×D11×D19C314yesmaximal, direct product factor
5C32×C5×C11×C19C2211yescharacteristic, complemented, Hall
6C32×D11×D19C511yesmaximal, characteristic, direct product factor, Hall
7C3×C5×D209C2×C314yescomplemented
8C3×C5×C19×D11C2×C314yescomplemented
9C3×C5×C11×D19C2×C314yescomplemented
10C5×D11×D19C3211yescharacteristic, direct product factor, Hall
11C32×D209C2×C511yescharacteristic, complemented
12C32×C19×D11C2×C511yescharacteristic, complemented
13C32×C11×D19C2×C511yescharacteristic, complemented
14C2×C32×C5×D19—111nomaximal, Hall
15C3×C5×C11×C19C22×C314yescomplemented
16C3×D11×D19C3×C514yesdirect product factor
17C5×D209C2×C3211yescharacteristic, complemented
18C5×C19×D11C2×C3211yescharacteristic, complemented
19C5×C11×D19C2×C3211yescharacteristic, complemented
20C2×C32×C5×D11—191nomaximal, Hall
21C32×C11×C19C22×C511yescharacteristic, complemented, Hall
22C2×C32×C5×C19—111no—
23C32×C5×D19—111no—
24C32×C5×D19D1111yescharacteristic, direct product factor
25C3×D209C2×C3×C514yescomplemented
26C3×C19×D11C2×C3×C514yescomplemented
27C3×C11×D19C2×C3×C514yescomplemented
28C2×C3×C5×D19—114no—
29C5×C11×C19C22×C3211yescharacteristic, complemented, Hall
30C2×C32×C5×C11—191no—
31C32×C5×D11—191no—
32C32×C5×D11D1911yescharacteristic, direct product factor
33C32×C5×C19C2×D1111yescharacteristic, complemented, Hall
34D11×D19C32×C511yescharacteristic, direct product factor, Hall
35C2×C32×D19—111noHall
36C2×C3×C5×D11—194no—
37C3×C11×C19C22×C3×C514yescomplemented
38C2×C3×C5×C19—114no—
39C3×C5×D19—114no—
40C3×C5×D19C3×D1114yesdirect product factor
41C32×C5×C11C2×D1911yescharacteristic, complemented, Hall
42D209C2×C32×C511yescharacteristic, complemented
43C11×D19C2×C32×C511yescharacteristic, complemented
44C19×D11C2×C32×C511yescharacteristic, complemented
45C2×C32×D11—191noHall
46C2×C5×D19—111noHall
47C2×C32×C19—111no—
48C32×D19—111no—
49C32×D19C5×D1111yescharacteristic, direct product factor
50C2×C3×C5×C11—194no—
51C3×C5×D11—194no—
52C3×C5×D11C3×D1914yesdirect product factor
53C3×C5×C19C2×C3×D1114yescomplemented
54C2×C3×D19—114no—
55C2×C5×D11—191noHall
56C11×C19C22×C32×C511yescharacteristic, complemented, Hall
57C2×C32×C11—191no—
58C32×D11—191no—
59C32×D11C5×D1911yescharacteristic, direct product factor
60C2×C5×C19—111no—
61C5×D19—111no—
62C5×D19C32×D1111yescharacteristic, direct product factor
63C22×C32×C5—2091noHall
64C32×C19C2×C5×D1111yescharacteristic, complemented, Hall
65C3×C5×C11C2×C3×D1914yescomplemented
66C2×C3×D11—194no—
67C2×C3×C19—114no—
68C3×D19—114no—
69C3×D19C3×C5×D1114yesdirect product factor
70C2×C5×C11—191no—
71C5×D11—191no—
72C5×D11C32×D1911yescharacteristic, direct product factor
73C32×C11C2×C5×D1911yescharacteristic, complemented, Hall
74C5×C19C2×C32×D1111yescharacteristic, complemented, Hall
75C2×C32×C5—111no—
76C2×C32×C5—191no—
77C2×C32×C5—2091no—
78C2×D19—111noHall
79C2×C3×C11—194no—
80C3×D11—194no—
81C3×D11C3×C5×D1914yesdirect product factor
82C22×C3×C5—2094no—
83C3×C19C2×C3×C5×D1114yescomplemented
84C5×C11C2×C32×D1911yescharacteristic, complemented, Hall
85C32×C5D11×D1911yescharacteristic, direct product factor, Hall
86C2×D11—191noHall
87C2×C19—111no—
88D19—111no—
89D19C32×C5×D1111yescharacteristic, direct product factor
90C22×C32—2091noHall
91C3×C11C2×C3×C5×D1914yescomplemented
92C2×C3×C5—114no—
93C2×C3×C5—194no—
94C2×C3×C5—2094no—
95C2×C11—191no—
96D11—191no—
97D11C32×C5×D1911yescharacteristic, direct product factor
98C22×C5—2091noHall
99C19C2×C32×C5×D1111yescharacteristic, complemented, Sylow
100C2×C32—111no—
101C2×C32—191no—
102C2×C32—2091no—
103C3×C5C3×D11×D1914yesdirect product factor
104C22×C3—2094no—
105C11C2×C32×C5×D1911yescharacteristic, complemented, Sylow
106C2×C5—111no—
107C2×C5—191no—
108C2×C5—2091no—
109C32C5×D11×D1911yescharacteristic, direct product factor, Sylow
110C2×C3—114no—
111C2×C3—194no—
112C2×C3—2094no—
113C5C32×D11×D1911yescharacteristic, direct product factor, Sylow
114C22—2091noSylow
115C3C3×C5×D11×D1914yesdirect product factor
116C2—111no—
117C2—191no—
118C2—2091no—
subgroupG/H
center, hypercenterC32×C5D11×D19
commutator, cosocle, hypocenterC11×C19C22×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C11×C19
UCSC1 ◁ C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D19C2semidirect
2. C32×C5×C19×D11C2semidirect
3. C32×C5×D209C2semidirect
4. C3×C5×D11×D19C3direct (N × H)
5. C32×C5×C11×C19C22semidirect
6. C32×D11×D19C5direct (N × H)
7. C3×C5×D209C2×C3semidirect
8. C3×C5×C19×D11C2×C3semidirect
9. C3×C5×C11×D19C2×C3semidirect
10. C5×D11×D19C32direct (N × H)
11. C32×D209C2×C5semidirect
12. C32×C19×D11C2×C5semidirect
13. C32×C11×D19C2×C5semidirect
15. C3×C5×C11×C19C22×C3semidirect
16. C3×D11×D19C3×C5direct (N × H)
17. C5×D209C2×C32semidirect
18. C5×C19×D11C2×C32semidirect
19. C5×C11×D19C2×C32semidirect
21. C32×C11×C19C22×C5semidirect
24. C32×C5×D19D11direct (N × H)
25. C3×D209C2×C3×C5semidirect
26. C3×C19×D11C2×C3×C5semidirect
27. C3×C11×D19C2×C3×C5semidirect
29. C5×C11×C19C22×C32semidirect
32. C32×C5×D11D19direct (N × H)
33. C32×C5×C19C2×D11semidirect
34. D11×D19C32×C5direct (N × H)
37. C3×C11×C19C22×C3×C5semidirect
40. C3×C5×D19C3×D11direct (N × H)
41. C32×C5×C11C2×D19semidirect
42. D209C2×C32×C5semidirect
43. C11×D19C2×C32×C5semidirect
44. C19×D11C2×C32×C5semidirect
49. C32×D19C5×D11direct (N × H)
52. C3×C5×D11C3×D19direct (N × H)
53. C3×C5×C19C2×C3×D11semidirect
56. C11×C19C22×C32×C5semidirect
59. C32×D11C5×D19direct (N × H)
62. C5×D19C32×D11direct (N × H)
64. C32×C19C2×C5×D11semidirect
65. C3×C5×C11C2×C3×D19semidirect
69. C3×D19C3×C5×D11direct (N × H)
72. C5×D11C32×D19direct (N × H)
73. C32×C11C2×C5×D19semidirect
74. C5×C19C2×C32×D11semidirect
81. C3×D11C3×C5×D19direct (N × H)
83. C3×C19C2×C3×C5×D11semidirect
84. C5×C11C2×C32×D19semidirect
85. C32×C5D11×D19direct (N × H)
89. D19C32×C5×D11direct (N × H)
91. C3×C11C2×C3×C5×D19semidirect
97. D11C32×C5×D19direct (N × H)
99. C19C2×C32×C5×D11semidirect
103. C3×C5C3×D11×D19direct (N × H)
105. C11C2×C32×C5×D19semidirect
109. C32C5×D11×D19direct (N × H)
113. C5C32×D11×D19direct (N × H)
115. C3C3×C5×D11×D19direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C11×D192
C32×C5×C19×D112
C32×C5×D2092
C3×C5×D11×D193
C32×D11×D195
C2×C32×C5×D1911
C2×C32×C5×D1119