Finite Group Databasebeta

← C2×C3×C11×C5⋊(D13⋊C3) #38788130

Subgroups — C2×C3×C11×C5⋊(D13⋊C3) #38788130

Order 25740.

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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×C11×C5⋊(D13⋊C3)C212yesmaximal, direct product factor
3C2×C3×C11×D65C311yesmaximal, characteristic, complemented
4C2×C11×C5⋊(D13⋊C3)C313yesmaximal, direct product factor
5C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×C3×C11×D13⋊C3—51nomaximal, Hall
7C11×C5⋊(D13⋊C3)C2×C316yesdirect product factor
8C3×C11×D65C2×C312yescomplemented
9C2×C5×C11×C13⋊C3C2×C313yescomplemented
10C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
11C2×C11×D65C3211yescharacteristic, complemented, Hall
12C2×C3×C11×C13⋊C3D511yescharacteristic, complemented
13C3×C11×D13⋊C3—52no—
14C2×C3×C5⋊(D13⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C11×C13⋊C3C22×C313yescomplemented
16C3×C5×C11×C13C22×C311yescharacteristic, complemented
17C2×C32×D5×C11—131nomaximal, Hall
18C2×C3×C11×D13—51no—
19C2×C11×D13⋊C3—53no—
20C2×C5×C11×C13C2×C3211yescharacteristic, complemented
21C11×D65C2×C3212yescomplemented
22C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
23C2×C3×C5×C13⋊C3C2×C1111yescharacteristic, complemented
24C3×C5⋊(D13⋊C3)C2×C1112yesdirect product factor
25C2×C32×C5×C11—131no—
26C32×D5×C11—132no—
27C2×C3×C11×C13C3×D511yescharacteristic, complemented
28C3×C11×D13—52no—
29C2×C11×C13⋊C3C3×D513yescomplemented
30C11×D13⋊C3—56no—
31C2×C3×D65C3×C1111yescharacteristic, complemented
32C2×C5⋊(D13⋊C3)C3×C1113yesdirect product factor
33C5×C11×C13C22×C3211yescharacteristic, complemented, Hall
34C2×C3×D5×C11—133no—
35C2×C3×D5×C11—131no—
36C3×C5×C13⋊C3C22×C1111yescharacteristic, complemented, Hall
37C2×C11×D13—51noHall
38C32×C5×C11—131noHall
39C2×C3×D13⋊C3—51noHall
40C3×C11×C13C2×C3×D511yescharacteristic, complemented
41C11×C13⋊C3C2×C3×D513yescomplemented
42C22×C32×C11—651noHall
43C2×C3×C5×C13C2×C3×C1111yescharacteristic, complemented
44C3×D65C2×C3×C1112yescomplemented
45C2×C5×C13⋊C3C2×C3×C1113yescomplemented
46C5⋊(D13⋊C3)C2×C3×C1116yesdirect product factor
47C2×C3×C5×C11—133no—
48C2×C3×C5×C11D13⋊C311yescharacteristic, complemented
49C3×D5×C11—136no—
50C3×D5×C11—132no—
51C2×C11×C13C32×D511yescharacteristic, complemented
52C11×D13—52no—
53C2×D65C32×C1111yescharacteristic, complemented, Hall
54C2×C3×C13⋊C3D5×C1111yescharacteristic, complemented
55C3×D13⋊C3—52no—
56C2×D5×C11—131noHall
57C2×C32×C11—131no—
58C2×C32×C11—652no—
59C3×C5×C13C22×C3×C1111yescharacteristic, complemented
60C5×C13⋊C3C22×C3×C1113yescomplemented
61C2×C32×D5—131noHall
62C3×C5×C11—133no—
63C3×C5×C11C2×D13⋊C311yescharacteristic, complemented
64C2×C3×D13—51no—
65C2×D13⋊C3—53no—
66C11×C13C2×C32×D511yescharacteristic, complemented, Hall
67C22×C3×C11—653no—
68C22×C3×C11—651no—
69C2×C5×C13C2×C32×C1111yescharacteristic, complemented
70D65C2×C32×C1112yescomplemented
71C3×C13⋊C3C2×D5×C1111yescharacteristic, complemented, Hall
72C2×C5×C11C3×D13⋊C311yescharacteristic, complemented
73D5×C11—132no—
74C32×C11—131noHall
75C2×C32×C5—131no—
76C32×D5—132no—
77C2×C3×C13C3×D5×C1111yescharacteristic, complemented
78C3×D13—52no—
79C2×C13⋊C3C3×D5×C1113yescomplemented
80D13⋊C3—56no—
81C2×C3×C11—133no—
82C2×C3×C11—656no—
83C2×C3×C11—652no—
84C2×C3×C11C5⋊(D13⋊C3)11yescharacteristic, direct product factor
85C5×C13C22×C32×C1111yescharacteristic, complemented, Hall
86C2×C3×D5—133no—
87C2×C3×D5—131no—
88C5×C11C2×C3×D13⋊C311yescharacteristic, complemented, Hall
89C2×D13—51noHall
90C32×C5—131noHall
91C22×C11—651noHall
92C3×C13C2×C3×D5×C1111yescharacteristic, complemented
93C13⋊C3C2×C3×D5×C1113yescomplemented
94C22×C32—651noHall
95C3×C11—133no—
96C3×C11C2×C5⋊(D13⋊C3)11yescharacteristic, direct product factor
97C2×C3×C5—133no—
98C2×C3×C5C11×D13⋊C311yescharacteristic, complemented
99C3×D5—136no—
100C3×D5—132no—
101C2×C13C32×D5×C1111yescharacteristic, complemented
102D13—52no—
103C2×C11—652no—
104C2×C11C3×C5⋊(D13⋊C3)11yescharacteristic, direct product factor
105C2×D5—131noHall
106C2×C32—131no—
107C2×C32—652no—
108C3×C5—133no—
109C3×C5C2×C11×D13⋊C311yescharacteristic, complemented
110C13C2×C32×D5×C1111yescharacteristic, complemented, Sylow
111C22×C3—653no—
112C22×C3—651no—
113C11C2×C3×C5⋊(D13⋊C3)11yescharacteristic, direct product factor, Sylow
114C2×C5C3×C11×D13⋊C311yescharacteristic, complemented
115D5—132no—
116C32—131noSylow
117C2×C3—133no—
118C2×C3—656no—
119C2×C3—652no—
120C2×C3C11×C5⋊(D13⋊C3)11yescharacteristic, direct product factor
121C5C2×C3×C11×D13⋊C311yescharacteristic, complemented, Sylow
122C22—651noSylow
123C3—133no—
124C3C2×C11×C5⋊(D13⋊C3)11yescharacteristic, direct product factor
125C2—652no—
126C2C3×C11×C5⋊(D13⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C11×C13⋊C3C2semidirect
2. C3×C11×C5⋊(D13⋊C3)C2direct (N × H)
3. C2×C3×C11×D65C3semidirect
4. C2×C11×C5⋊(D13⋊C3)C3direct (N × H)
5. C3×C5×C11×C13⋊C3C22semidirect
7. C11×C5⋊(D13⋊C3)C2×C3direct (N × H)
8. C3×C11×D65C2×C3semidirect
9. C2×C5×C11×C13⋊C3C2×C3semidirect
10. C2×C3×C5×C11×C13C2×C3semidirect
11. C2×C11×D65C32semidirect
12. C2×C3×C11×C13⋊C3D5semidirect
14. C2×C3×C5⋊(D13⋊C3)C11direct (N × H)
15. C5×C11×C13⋊C3C22×C3semidirect
16. C3×C5×C11×C13C22×C3semidirect
20. C2×C5×C11×C13C2×C32semidirect
21. C11×D65C2×C32semidirect
22. C3×C11×C13⋊C3C2×D5semidirect
23. C2×C3×C5×C13⋊C3C2×C11semidirect
24. C3×C5⋊(D13⋊C3)C2×C11direct (N × H)
27. C2×C3×C11×C13C3×D5semidirect
29. C2×C11×C13⋊C3C3×D5semidirect
31. C2×C3×D65C3×C11semidirect
32. C2×C5⋊(D13⋊C3)C3×C11direct (N × H)
33. C5×C11×C13C22×C32semidirect
36. C3×C5×C13⋊C3C22×C11semidirect
40. C3×C11×C13C2×C3×D5semidirect
41. C11×C13⋊C3C2×C3×D5semidirect
43. C2×C3×C5×C13C2×C3×C11semidirect
44. C3×D65C2×C3×C11semidirect
45. C2×C5×C13⋊C3C2×C3×C11semidirect
46. C5⋊(D13⋊C3)C2×C3×C11direct (N × H)
48. C2×C3×C5×C11D13⋊C3semidirect
51. C2×C11×C13C32×D5semidirect
53. C2×D65C32×C11semidirect
54. C2×C3×C13⋊C3D5×C11semidirect
59. C3×C5×C13C22×C3×C11semidirect
60. C5×C13⋊C3C22×C3×C11semidirect
63. C3×C5×C11C2×D13⋊C3semidirect
66. C11×C13C2×C32×D5semidirect
69. C2×C5×C13C2×C32×C11semidirect
70. D65C2×C32×C11semidirect
71. C3×C13⋊C3C2×D5×C11semidirect
72. C2×C5×C11C3×D13⋊C3semidirect
77. C2×C3×C13C3×D5×C11semidirect
79. C2×C13⋊C3C3×D5×C11semidirect
84. C2×C3×C11C5⋊(D13⋊C3)direct (N × H)
85. C5×C13C22×C32×C11semidirect
88. C5×C11C2×C3×D13⋊C3semidirect
92. C3×C13C2×C3×D5×C11semidirect
93. C13⋊C3C2×C3×D5×C11semidirect
96. C3×C11C2×C5⋊(D13⋊C3)direct (N × H)
98. C2×C3×C5C11×D13⋊C3semidirect
101. C2×C13C32×D5×C11semidirect
104. C2×C11C3×C5⋊(D13⋊C3)direct (N × H)
109. C3×C5C2×C11×D13⋊C3semidirect
110. C13C2×C32×D5×C11semidirect
113. C11C2×C3×C5⋊(D13⋊C3)direct (N × H)
114. C2×C5C3×C11×D13⋊C3semidirect
120. C2×C3C11×C5⋊(D13⋊C3)direct (N × H)
121. C5C2×C3×C11×D13⋊C3semidirect
124. C3C2×C11×C5⋊(D13⋊C3)direct (N × H)
126. C2C3×C11×C5⋊(D13⋊C3)direct (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×C11×C5⋊(D13⋊C3)2
C2×C3×C11×D653
C2×C11×C5⋊(D13⋊C3)3
C2×C3×C11×D13⋊C35
C2×C3×C5⋊(D13⋊C3)11
C2×C32×D5×C1113