Finite Group Databasebeta

← C11×#4144 #13183431

Subgroups — C11×#4144 #13183431

Order 1760.

332 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 170 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×C5×D4×C11C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊D5C214yesmaximal, complemented
3C11×#711C214yesmaximal, complemented
4D4×D5×C11C214yesmaximal, complemented
5C11×#709C212yesmaximal, complemented
6C23×C5×C11C2212yescomplemented
7C22×D5×C11C2214yescomplemented
8C5×D4×C11C2214yescomplemented
9C2×C4×C5×C11C2211yescharacteristic, complemented
10C11×C22⋊D5C2214yescomplemented
11C11×C22⋊D5C2218yescomplemented
12C2×C11×Dic5C2214yescomplemented
13C11×D20C2212yescomplemented
14C4×D5×C11C2214yescomplemented
15C11×Dic10C2212yescomplemented
16C11×H(5,𝔽2)—51nomaximal, Hall
17C22×C5×C11—42no—
18C22×C5×C11C2314yes—
19C22×C5×C11C2311yescharacteristic
20C2×D5×C11—44no—
21C2×D5×C11C2314yes—
22C4×C5×C11C2312yes—
23C11×Dic5C2314yes—
24C11×#41—54no—
25C11×#41—52no—
26C2×D4×C11—54no—
27C2×D4×C11—54no—
28C2×D4×C11D511yescharacteristic, complemented
29#4144C1111yesmaximal, characteristic, direct product factor, Hall
30C2×C5×C11—24no—
31C2×C5×C11—21no—
32C2×C5×C11C2411yescharacteristic
33D5×C11—24no—
34C23×C11—54no—
35C23×C11C2×D512yescomplemented
36Q8×C11—52no—
37D4×C11—58no—
38D4×C11—54no—
39D4×C11—52no—
40D4×C11C2×D514yescomplemented
41C2×C4×C11—54no—
42C2×C4×C11—54no—
43C2×C4×C11C2×D511yescharacteristic, complemented
44C2×C5×D4C2×C1111yescharacteristic, complemented
45C2×C22⋊D5C2×C1114yescomplemented
46#711C2×C1114yescomplemented
47D4×D5C2×C1114yescomplemented
48#709C2×C1112yescomplemented
49C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
50C22×C11—42no—
51C22×C11—54no—
52C22×C11—204no—
53C22×C11C22×D514yes—
54C22×C11C22×D511yescharacteristic
55C4×C11—54no—
56C4×C11C22×D512yes—
57C23×C5C22×C1112yescomplemented
58C22×D5C22×C1114yescomplemented
59C5×D4C22×C1114yescomplemented
60C2×C4×C5C22×C1111yescharacteristic, complemented
61C22⋊D5C22×C1114yescomplemented
62C22⋊D5C22×C1118yescomplemented
63C2×Dic5C22×C1114yescomplemented
64D20C22×C1112yescomplemented
65C4×D5C22×C1114yescomplemented
66Dic10C22×C1112yescomplemented
67H(5,𝔽2)—51noSylow
68C2×C11—21no—
69C2×C11—24no—
70C2×C11—104no—
71C2×C11C23×D511yescharacteristic
72C22×C5—42no—
73C22×C5C23×C1114yes—
74C22×C5C23×C1111yescharacteristic
75C2×D5—44no—
76C2×D5C23×C1114yes—
77C4×C5C23×C1112yes—
78Dic5C23×C1114yes—
79#41—54no—
80#41—52no—
81C2×D4—54no—
82C2×D4—54no—
83C2×D4D5×C1111yescharacteristic, complemented
84C11#414411yescharacteristic, direct product factor, Sylow
85C2×C5—24no—
86C2×C5—21no—
87C2×C5C24×C1111yescharacteristic
88D5—24no—
89C23—54no—
90C23C2×D5×C1112yescomplemented
91Q8—52no—
92D4—58no—
93D4—54no—
94D4—52no—
95D4C2×D5×C1114yescomplemented
96C2×C4—54no—
97C2×C4—54no—
98C2×C4C2×D5×C1111yescharacteristic, complemented
99C5C11×H(5,𝔽2)11yescharacteristic, complemented, Sylow
100C22—42no—
101C22—54no—
102C22—204no—
103C22C22×D5×C1114yes—
104C22C22×D5×C1111yescharacteristic
105C4—54no—
106C4C22×D5×C1112yes—
107C2—21no—
108C2—24no—
109C2—104no—
110C2C23×D5×C1111yescharacteristic
subgroupG/H
centerC2×C11C23×D5
commutator, cosocleC2×C5C24×C11
FrattiniC2C23×D5×C11
FittingC2×C5×D4×C11C2
socleC2×C5×C11C24
hypercenterC2×D4×C11D5
hypocenterC5C11×H(5,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C2×D4×C11

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×C11C2semidirect
2. C2×C11×C22⋊D5C2semidirect
3. C11×#711C2semidirect
4. D4×D5×C11C2semidirect
5. C11×#709C2semidirect
6. C23×C5×C11C22semidirect
7. C22×D5×C11C22semidirect
8. C5×D4×C11C22semidirect
9. C2×C4×C5×C11C22semidirect
10. C11×C22⋊D5C22semidirect
11. C11×C22⋊D5C22semidirect
12. C2×C11×Dic5C22semidirect
13. C11×D20C22semidirect
14. C4×D5×C11C22semidirect
15. C11×Dic10C22semidirect
28. C2×D4×C11D5semidirect
29. #4144C11direct (N × H)
35. C23×C11C2×D5semidirect
40. D4×C11C2×D5semidirect
43. C2×C4×C11C2×D5semidirect
44. C2×C5×D4C2×C11semidirect
45. C2×C22⋊D5C2×C11semidirect
46. #711C2×C11semidirect
47. D4×D5C2×C11semidirect
48. #709C2×C11semidirect
49. C5×C11H(5,𝔽2)semidirect
57. C23×C5C22×C11semidirect
58. C22×D5C22×C11semidirect
59. C5×D4C22×C11semidirect
60. C2×C4×C5C22×C11semidirect
61. C22⋊D5C22×C11semidirect
62. C22⋊D5C22×C11semidirect
63. C2×Dic5C22×C11semidirect
64. D20C22×C11semidirect
65. C4×D5C22×C11semidirect
66. Dic10C22×C11semidirect
83. C2×D4D5×C11semidirect
84. C11#4144direct (N × H)
90. C23C2×D5×C11semidirect
95. D4C2×D5×C11semidirect
98. C2×C4C2×D5×C11semidirect
99. C5C11×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×C112
C2×C11×C22⋊D52
C11×#7112
D4×D5×C112
C11×#7092
C11×H(5,𝔽2)5
#414411