Finite Group Databasebeta

← C2×C3×C5×D11×C13⋊C3 #38788129

Subgroups — C2×C3×C5×D11×C13⋊C3 #38788129

Order 25740.

240 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×C3×C5×C11×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C5×D11×C13⋊C3C212yesmaximal, direct product factor
3C2×C3×C5×C13×D11C311yesmaximal, characteristic, complemented
4C2×C5×D11×C13⋊C3C313yesmaximal, direct product factor
5C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×C3×D11×C13⋊C3C511yesmaximal, characteristic, direct product factor, Hall
7C5×D11×C13⋊C3C2×C316yesdirect product factor
8C3×C5×C13×D11C2×C312yescomplemented
9C2×C5×C11×C13⋊C3C2×C313yescomplemented
10C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
11C2×C5×C13×D11C3211yescharacteristic, complemented, Hall
12C2×C3×C11×C13⋊C3C2×C511yescharacteristic, complemented
13C3×D11×C13⋊C3C2×C512yesdirect product factor
14C22×C3×C5×C13⋊C3—111nomaximal, Hall
15C5×C11×C13⋊C3C22×C313yescomplemented
16C3×C5×C11×C13C22×C311yescharacteristic, complemented
17C2×C32×C5×D11—131nomaximal, Hall
18C2×C3×C13×D11C3×C511yescharacteristic, complemented
19C2×D11×C13⋊C3C3×C513yesdirect product factor
20C2×C5×C11×C13C2×C3211yescharacteristic, complemented
21C5×C13×D11C2×C3212yescomplemented
22C3×C11×C13⋊C3C22×C511yescharacteristic, complemented, Hall
23C2×C3×C5×C13⋊C3—112no—
24C2×C3×C5×C13⋊C3D1111yescharacteristic, direct product factor
25C2×C32×C5×C11—131no—
26C32×C5×D11—132no—
27C2×C3×C11×C13C2×C3×C511yescharacteristic, complemented
28C3×C13×D11C2×C3×C512yescomplemented
29C2×C11×C13⋊C3C2×C3×C513yescomplemented
30D11×C13⋊C3C2×C3×C516yesdirect product factor
31C22×C3×C5×C13—111no—
32C22×C5×C13⋊C3—113no—
33C5×C11×C13C22×C3211yescharacteristic, complemented, Hall
34C2×C3×C5×D11—133no—
35C2×C3×C5×D11C13⋊C311yescharacteristic, direct product factor
36C3×C5×C13⋊C3C2×D1111yescharacteristic, direct product factor, Hall
37C2×C13×D11C32×C511yescharacteristic, complemented, Hall
38C32×C5×C11—131noHall
39C22×C3×C13⋊C3—111noHall
40C3×C11×C13C22×C3×C511yescharacteristic, complemented
41C11×C13⋊C3C22×C3×C513yescomplemented
42C2×C32×D11—131noHall
43C2×C3×C5×C13—112no—
44C2×C3×C5×C13C3×D1111yescharacteristic, complemented
45C2×C5×C13⋊C3—116no—
46C2×C5×C13⋊C3C3×D1113yesdirect product factor
47C2×C3×C5×C11—133no—
48C2×C3×C5×C11C2×C13⋊C311yescharacteristic, complemented
49C3×C5×D11—136no—
50C3×C5×D11C2×C13⋊C312yesdirect product factor
51C2×C11×C13C2×C32×C511yescharacteristic, complemented
52C13×D11C2×C32×C512yescomplemented
53C22×C5×C13—111noHall
54C2×C3×C13⋊C3—112no—
55C2×C3×C13⋊C3C5×D1111yescharacteristic, direct product factor
56C2×C5×D11C3×C13⋊C311yescharacteristic, direct product factor, Hall
57C2×C32×C11—131no—
58C32×D11—132no—
59C3×C5×C13C2×C3×D1111yescharacteristic, complemented
60C5×C13⋊C3C2×C3×D1113yesdirect product factor
61C22×C32×C5—1431noHall
62C3×C5×C11—133no—
63C3×C5×C11C22×C13⋊C311yescharacteristic, complemented
64C22×C3×C13—111no—
65C22×C13⋊C3—113no—
66C11×C13C22×C32×C511yescharacteristic, complemented, Hall
67C2×C3×D11—133no—
68C2×C3×D11C5×C13⋊C311yescharacteristic, direct product factor
69C2×C5×C13—112no—
70C2×C5×C13C32×D1111yescharacteristic, complemented
71C3×C13⋊C3C2×C5×D1111yescharacteristic, direct product factor, Hall
72C2×C5×C11C2×C3×C13⋊C311yescharacteristic, complemented
73C5×D11C2×C3×C13⋊C312yesdirect product factor
74C32×C11—131noHall
75C2×C32×C5—131no—
76C2×C32×C5—1432no—
77C2×C3×C13—112no—
78C2×C3×C13C3×C5×D1111yescharacteristic, complemented
79C2×C13⋊C3—116no—
80C2×C13⋊C3C3×C5×D1113yesdirect product factor
81C2×C3×C11—133no—
82C2×C3×C11C2×C5×C13⋊C311yescharacteristic, complemented
83C3×D11—136no—
84C3×D11C2×C5×C13⋊C312yesdirect product factor
85C5×C13C2×C32×D1111yescharacteristic, complemented, Hall
86C22×C3×C5—111no—
87C22×C3×C5—1433no—
88C5×C11C22×C3×C13⋊C311yescharacteristic, complemented, Hall
89C22×C13—111noHall
90C32×C5—131noHall
91C2×D11C3×C5×C13⋊C311yescharacteristic, direct product factor, Hall
92C3×C13C2×C3×C5×D1111yescharacteristic, complemented
93C13⋊C3C2×C3×C5×D1113yesdirect product factor
94C22×C32—1431noHall
95C3×C11—133no—
96C3×C11C22×C5×C13⋊C311yescharacteristic, complemented
97C2×C3×C5—112no—
98C2×C3×C5—133no—
99C2×C3×C5—1436no—
100C2×C3×C5D11×C13⋊C311yescharacteristic, direct product factor
101C2×C13—112no—
102C2×C13C32×C5×D1111yescharacteristic, complemented
103C2×C11C2×C3×C5×C13⋊C311yescharacteristic, complemented
104D11C2×C3×C5×C13⋊C312yesdirect product factor
105C22×C5—111noHall
106C2×C32—131no—
107C2×C32—1432no—
108C3×C5—133no—
109C3×C5C2×D11×C13⋊C311yescharacteristic, direct product factor
110C13C2×C32×C5×D1111yescharacteristic, complemented, Sylow
111C22×C3—111no—
112C22×C3—1433no—
113C11C22×C3×C5×C13⋊C311yescharacteristic, complemented, Sylow
114C2×C5—112no—
115C2×C5C3×D11×C13⋊C311yescharacteristic, direct product factor
116C32—131noSylow
117C2×C3—112no—
118C2×C3—133no—
119C2×C3—1436no—
120C2×C3C5×D11×C13⋊C311yescharacteristic, direct product factor
121C5C2×C3×D11×C13⋊C311yescharacteristic, direct product factor, Sylow
122C22—111noSylow
123C3—133no—
124C3C2×C5×D11×C13⋊C311yescharacteristic, direct product factor
125C2—112no—
126C2C3×C5×D11×C13⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D11×C13⋊C3
commutator, cosocle, hypocenterC11×C13C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C11×C13⋊C3C2semidirect
2. C3×C5×D11×C13⋊C3C2direct (N × H)
3. C2×C3×C5×C13×D11C3semidirect
4. C2×C5×D11×C13⋊C3C3direct (N × H)
5. C3×C5×C11×C13⋊C3C22semidirect
6. C2×C3×D11×C13⋊C3C5direct (N × H)
7. C5×D11×C13⋊C3C2×C3direct (N × H)
8. C3×C5×C13×D11C2×C3semidirect
9. C2×C5×C11×C13⋊C3C2×C3semidirect
10. C2×C3×C5×C11×C13C2×C3semidirect
11. C2×C5×C13×D11C32semidirect
12. C2×C3×C11×C13⋊C3C2×C5semidirect
13. C3×D11×C13⋊C3C2×C5direct (N × H)
15. C5×C11×C13⋊C3C22×C3semidirect
16. C3×C5×C11×C13C22×C3semidirect
18. C2×C3×C13×D11C3×C5semidirect
19. C2×D11×C13⋊C3C3×C5direct (N × H)
20. C2×C5×C11×C13C2×C32semidirect
21. C5×C13×D11C2×C32semidirect
22. C3×C11×C13⋊C3C22×C5semidirect
24. C2×C3×C5×C13⋊C3D11direct (N × H)
27. C2×C3×C11×C13C2×C3×C5semidirect
28. C3×C13×D11C2×C3×C5semidirect
29. C2×C11×C13⋊C3C2×C3×C5semidirect
30. D11×C13⋊C3C2×C3×C5direct (N × H)
33. C5×C11×C13C22×C32semidirect
35. C2×C3×C5×D11C13⋊C3direct (N × H)
36. C3×C5×C13⋊C3C2×D11direct (N × H)
37. C2×C13×D11C32×C5semidirect
40. C3×C11×C13C22×C3×C5semidirect
41. C11×C13⋊C3C22×C3×C5semidirect
44. C2×C3×C5×C13C3×D11semidirect
46. C2×C5×C13⋊C3C3×D11direct (N × H)
48. C2×C3×C5×C11C2×C13⋊C3semidirect
50. C3×C5×D11C2×C13⋊C3direct (N × H)
51. C2×C11×C13C2×C32×C5semidirect
52. C13×D11C2×C32×C5semidirect
55. C2×C3×C13⋊C3C5×D11direct (N × H)
56. C2×C5×D11C3×C13⋊C3direct (N × H)
59. C3×C5×C13C2×C3×D11semidirect
60. C5×C13⋊C3C2×C3×D11direct (N × H)
63. C3×C5×C11C22×C13⋊C3semidirect
66. C11×C13C22×C32×C5semidirect
68. C2×C3×D11C5×C13⋊C3direct (N × H)
70. C2×C5×C13C32×D11semidirect
71. C3×C13⋊C3C2×C5×D11direct (N × H)
72. C2×C5×C11C2×C3×C13⋊C3semidirect
73. C5×D11C2×C3×C13⋊C3direct (N × H)
78. C2×C3×C13C3×C5×D11semidirect
80. C2×C13⋊C3C3×C5×D11direct (N × H)
82. C2×C3×C11C2×C5×C13⋊C3semidirect
84. C3×D11C2×C5×C13⋊C3direct (N × H)
85. C5×C13C2×C32×D11semidirect
88. C5×C11C22×C3×C13⋊C3semidirect
91. C2×D11C3×C5×C13⋊C3direct (N × H)
92. C3×C13C2×C3×C5×D11semidirect
93. C13⋊C3C2×C3×C5×D11direct (N × H)
96. C3×C11C22×C5×C13⋊C3semidirect
100. C2×C3×C5D11×C13⋊C3direct (N × H)
102. C2×C13C32×C5×D11semidirect
103. C2×C11C2×C3×C5×C13⋊C3semidirect
104. D11C2×C3×C5×C13⋊C3direct (N × H)
109. C3×C5C2×D11×C13⋊C3direct (N × H)
110. C13C2×C32×C5×D11semidirect
113. C11C22×C3×C5×C13⋊C3semidirect
115. C2×C5C3×D11×C13⋊C3direct (N × H)
120. C2×C3C5×D11×C13⋊C3direct (N × H)
121. C5C2×C3×D11×C13⋊C3direct (N × H)
124. C3C2×C5×D11×C13⋊C3direct (N × H)
126. C2C3×C5×D11×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C13⋊C32
C3×C5×D11×C13⋊C32
C2×C3×C5×C13×D113
C2×C5×D11×C13⋊C33
C2×C3×D11×C13⋊C35
C22×C3×C5×C13⋊C311
C2×C32×C5×D1113