Finite Group Databasebeta

← C2×C5×D4×D11 #13183414

Subgroups — C2×C5×D4×D11 #13183414

Order 1760.

472 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 194 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
1C23×C5×D11C212yesmaximal, complemented
2C2×C5×D4×C11C211yesmaximal, characteristic, complemented
3C2×C5×C22⋊D11C212yesmaximal, complemented
4C5×D4×D11C218yesmaximal, direct product factor
5C2×C5×D44C211yesmaximal, characteristic, complemented
6C2×C4×C5×D11C211yesmaximal, characteristic, complemented
7C23×C5×C11C2212yescomplemented
8C22×C5×D11—28no—
9C22×C5×D11C2211yescharacteristic
10C22×C5×D11C2218yescomplemented
11C22×C5×D11C2212yescomplemented
12C5×D4×C11C2214yescomplemented
13C2×C4×C5×C11C2211yescharacteristic, complemented
14C5×C22⋊D11C2218yescomplemented
15C2×C5×Dic11C2211yescharacteristic, complemented
16C5×D44C2214yescomplemented
17C4×C5×D11C2214yescomplemented
18C2×D4×D11C511yesmaximal, characteristic, direct product factor, Hall
19C22×C5×C11—24no—
20C22×C5×C11C2311yescharacteristic
21C22×C5×C11C2314yescomplemented
22C2×C5×D11—24no—
23C2×C5×D11—216no—
24C2×C5×D11D414yesdirect product factor
25C2×C5×D11C2312yes—
26C2×C5×D11C2314yescomplemented
27C4×C5×C11C2312yescomplemented
28C5×Dic11C2312yescomplemented
29C23×D11C2×C512yescomplemented
30C2×D4×C11C2×C511yescharacteristic, complemented
31C2×C22⋊D11C2×C512yescomplemented
32D4×D11C2×C518yesdirect product factor
33C2×D44C2×C511yescharacteristic, complemented
34C2×C4×D11C2×C511yescharacteristic, complemented
35C22×C5×D4—111nomaximal, Hall
36C2×C5×C11—24no—
37C2×C5×C11C2×D412yescomplemented
38C2×C5×C11C2411yescharacteristic
39C5×D11—24no—
40C5×D11C2×D414yesdirect product factor
41C23×C11C22×C512yescomplemented
42C22×D11—28no—
43C22×D11C22×C511yescharacteristic
44C22×D11C22×C518yescomplemented
45C22×D11C22×C512yescomplemented
46D4×C11C22×C514yescomplemented
47C2×C4×C11C22×C511yescharacteristic, complemented
48C22⋊D11C22×C518yescomplemented
49C2×Dic11C22×C511yescharacteristic, complemented
50D44C22×C514yescomplemented
51C4×D11C22×C514yescomplemented
52C24×C5—112no—
53C2×C5×D4—112no—
54C2×C5×D4—118no—
55C2×C5×D4—111no—
56C2×C5×D4D1111yescharacteristic, direct product factor
57C22×C4×C5—111no—
58C5×C11C22×D411yescharacteristic, complemented, Hall
59C22×C11—24no—
60C22×C11C23×C511yescharacteristic
61C22×C11C23×C514yescomplemented
62C2×D11—24no—
63C2×D11—216no—
64C2×D11C5×D414yesdirect product factor
65C2×D11C23×C512yes—
66C2×D11C23×C514yescomplemented
67C4×C11C23×C512yescomplemented
68Dic11C23×C512yescomplemented
69C23×C5—111no—
70C23×C5—112no—
71C23×C5—118no—
72C23×C5—228no—
73C23×C5C2×D1112yescomplemented
74C5×D4—118no—
75C5×D4—114no—
76C5×D4C2×D1114yesdirect product factor
77C2×C4×C5—111no—
78C2×C4×C5—114no—
79C2×C4×C5C2×D1111yescharacteristic, complemented
80C22×D4—111noSylow
81C2×C11—24no—
82C2×C11C2×C5×D412yescomplemented
83C2×C11C24×C511yescharacteristic
84D11—24no—
85D11C2×C5×D414yesdirect product factor
86C22×C5—24no—
87C22×C5—114no—
88C22×C5—112no—
89C22×C5—114no—
90C22×C5—2216no—
91C22×C5—224no—
92C22×C5C22×D1111yescharacteristic
93C22×C5C22×D1114yescomplemented
94C4×C5—112no—
95C4×C5C22×D1112yescomplemented
96C24—112no—
97C2×D4—112no—
98C2×D4—118no—
99C2×D4—111no—
100C2×D4C5×D1111yescharacteristic, direct product factor
101C22×C4—111no—
102C11C22×C5×D411yescharacteristic, complemented, Sylow
103C2×C5—24no—
104C2×C5—114no—
105C2×C5—224no—
106C2×C5D4×D1112yesdirect product factor
107C2×C5C23×D1111yescharacteristic
108C23—111no—
109C23—112no—
110C23—118no—
111C23—228no—
112C23C2×C5×D1112yescomplemented
113D4—118no—
114D4—114no—
115D4C2×C5×D1114yesdirect product factor
116C2×C4—111no—
117C2×C4—114no—
118C2×C4C2×C5×D1111yescharacteristic, complemented
119C5C2×D4×D1111yescharacteristic, direct product factor, Sylow
120C22—24no—
121C22—114no—
122C22—112no—
123C22—114no—
124C22—2216no—
125C22—224no—
126C22C22×C5×D1111yescharacteristic
127C22C22×C5×D1114yescomplemented
128C4—112no—
129C4C22×C5×D1112yescomplemented
130C2—24no—
131C2—114no—
132C2—224no—
133C2C5×D4×D1112yesdirect product factor
134C2C23×C5×D1111yescharacteristic
subgroupG/H
centerC22×C5C22×D11
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×C5×D11
FittingC2×C5×D4×C11C2
socleC22×C5×C11C23
hypercenterC2×C5×D4D11
hypocenterC11C22×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
1. C23×C5×D11C2semidirect
2. C2×C5×D4×C11C2semidirect
3. C2×C5×C22⋊D11C2semidirect
4. C5×D4×D11C2direct (N × H)
5. C2×C5×D44C2semidirect
6. C2×C4×C5×D11C2semidirect
7. C23×C5×C11C22semidirect
10. C22×C5×D11C22semidirect
11. C22×C5×D11C22semidirect
12. C5×D4×C11C22semidirect
13. C2×C4×C5×C11C22semidirect
14. C5×C22⋊D11C22semidirect
15. C2×C5×Dic11C22semidirect
16. C5×D44C22semidirect
17. C4×C5×D11C22semidirect
18. C2×D4×D11C5direct (N × H)
21. C22×C5×C11C23semidirect
24. C2×C5×D11D4direct (N × H)
26. C2×C5×D11C23semidirect
27. C4×C5×C11C23semidirect
28. C5×Dic11C23semidirect
29. C23×D11C2×C5semidirect
30. C2×D4×C11C2×C5semidirect
31. C2×C22⋊D11C2×C5semidirect
32. D4×D11C2×C5direct (N × H)
33. C2×D44C2×C5semidirect
34. C2×C4×D11C2×C5semidirect
37. C2×C5×C11C2×D4semidirect
40. C5×D11C2×D4direct (N × H)
41. C23×C11C22×C5semidirect
44. C22×D11C22×C5semidirect
45. C22×D11C22×C5semidirect
46. D4×C11C22×C5semidirect
47. C2×C4×C11C22×C5semidirect
48. C22⋊D11C22×C5semidirect
49. C2×Dic11C22×C5semidirect
50. D44C22×C5semidirect
51. C4×D11C22×C5semidirect
56. C2×C5×D4D11direct (N × H)
58. C5×C11C22×D4semidirect
61. C22×C11C23×C5semidirect
64. C2×D11C5×D4direct (N × H)
66. C2×D11C23×C5semidirect
67. C4×C11C23×C5semidirect
68. Dic11C23×C5semidirect
73. C23×C5C2×D11semidirect
76. C5×D4C2×D11direct (N × H)
79. C2×C4×C5C2×D11semidirect
82. C2×C11C2×C5×D4semidirect
85. D11C2×C5×D4direct (N × H)
93. C22×C5C22×D11semidirect
95. C4×C5C22×D11semidirect
100. C2×D4C5×D11direct (N × H)
102. C11C22×C5×D4semidirect
106. C2×C5D4×D11direct (N × H)
112. C23C2×C5×D11semidirect
115. D4C2×C5×D11direct (N × H)
118. C2×C4C2×C5×D11semidirect
119. C5C2×D4×D11direct (N × H)
127. C22C22×C5×D11semidirect
129. C4C22×C5×D11semidirect
133. C2C5×D4×D11direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×D112
C2×C5×D4×C112
C2×C5×C22⋊D112
C5×D4×D112
C2×C5×D442
C2×C4×C5×D112
C2×D4×D115
C22×C5×D411