Finite Group Databasebeta

← D5×C11×C22⋊C4 #13183094

Subgroups — D5×C11×C22⋊C4 #13183094

Order 1760.

264 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 98 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×D5×C11C211yesmaximal, characteristic
2C2×C4×D5×C11C212yesmaximal, complemented
3C5×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4C11×C22⋊Dic5C211yesmaximal, characteristic, complemented
5C11×#685C212yesmaximal, complemented
6C23×C5×C11C2211yescharacteristic
7C22×D5×C11—24no—
8C22×D5×C11C414yescomplemented
9C22×D5×C11C2211yescharacteristic
10C22×D5×C11C2211yescharacteristic
11C2×C4×C5×C11C2212yescomplemented
12C2×C11×Dic5C2212yescomplemented
13C4×D5×C11—24no—
14C2×C11×C22⋊C4—51nomaximal, Hall
15C22×C5×C11—22no—
16C22×C5×C11C2×C412yescomplemented
17C22×C5×C11C2311yescharacteristic
18C2×D5×C11—22no—
19C2×D5×C11—28no—
20C2×D5×C11C2×C412yes—
21C2×D5×C11C2×C412yescomplemented
22C2×D5×C11D414yes—
23C4×C5×C11—22no—
24C11×Dic5—22no—
25C24×C11—51no—
26C22×C4×C11—52no—
27C11×C22⋊C4—51no—
28C11×C22⋊C4—52no—
29C11×C22⋊C4D511yescharacteristic, direct product factor
30D5×C22⋊C4C1111yesmaximal, characteristic, direct product factor, Hall
31C2×C5×C11—22no—
32C2×C5×C11C22×C411yescharacteristic
33C2×C5×C11C2×D412yes—
34D5×C11—22no—
35D5×C11C22⋊C414yesdirect product factor
36C23×C11—51no—
37C23×C11—54no—
38C23×C11—51no—
39C23×C11—104no—
40C23×C11C2×D511yescharacteristic
41C2×C4×C11—52no—
42C2×C4×C11—104no—
43C2×C4×C11C2×D512yescomplemented
44C23×D5C2×C1111yescharacteristic
45C2×C4×D5C2×C1112yescomplemented
46C5×C22⋊C4C2×C1111yescharacteristic, complemented
47C22⋊Dic5C2×C1111yescharacteristic, complemented
48#685C2×C1112yescomplemented
49C5×C11C2×C22⋊C411yescharacteristic, complemented, Hall
50C22×C11—22no—
51C22×C11—52no—
52C22×C11—54no—
53C22×C11—52no—
54C22×C11—108no—
55C22×C11—102no—
56C22×C11C4×D512yescomplemented
57C22×C11C22×D511yescharacteristic
58C4×C11—22no—
59C4×C11—102no—
60C23×C5C22×C1111yescharacteristic
61C22×D5—24no—
62C22×D5C4×C1114yescomplemented
63C22×D5C22×C1111yescharacteristic
64C22×D5C22×C1111yescharacteristic
65C2×C4×C5C22×C1112yescomplemented
66C2×Dic5C22×C1112yescomplemented
67C4×D5—24no—
68C2×C22⋊C4—51noSylow
69C2×C11—22no—
70C2×C11—54no—
71C2×C11—102no—
72C2×C11C2×C4×D511yescharacteristic
73C2×C11D4×D512yes—
74C22×C5—22no—
75C22×C5C2×C4×C1112yescomplemented
76C22×C5C23×C1111yescharacteristic
77C2×D5—22no—
78C2×D5—28no—
79C2×D5C2×C4×C1112yes—
80C2×D5C2×C4×C1112yescomplemented
81C2×D5D4×C1114yes—
82C4×C5—22no—
83Dic5—22no—
84C24—51no—
85C22×C4—52no—
86C22⋊C4—51no—
87C22⋊C4—52no—
88C22⋊C4D5×C1111yescharacteristic, direct product factor
89C11D5×C22⋊C411yescharacteristic, direct product factor, Sylow
90C2×C5—22no—
91C2×C5C22×C4×C1111yescharacteristic
92C2×C5C2×D4×C1112yes—
93D5—22no—
94D5C11×C22⋊C414yesdirect product factor
95C23—51no—
96C23—54no—
97C23—51no—
98C23—104no—
99C23C2×D5×C1111yescharacteristic
100C2×C4—52no—
101C2×C4—104no—
102C2×C4C2×D5×C1112yescomplemented
103C5C2×C11×C22⋊C411yescharacteristic, complemented, Sylow
104C22—22no—
105C22—52no—
106C22—54no—
107C22—52no—
108C22—108no—
109C22—102no—
110C22C4×D5×C1112yescomplemented
111C22C22×D5×C1111yescharacteristic
112C4—22no—
113C4—102no—
114C2—22no—
115C2—54no—
116C2—102no—
117C2C2×C4×D5×C1111yescharacteristic
118C2D4×D5×C1112yes—
subgroupG/H
centerC22×C11C22×D5
commutatorC2×C5C22×C4×C11
FrattiniC22C22×D5×C11
FittingC5×C11×C22⋊C4C2
socleC22×C5×C11C23
prime radicalC23×D5×C11C2
cosocleC22×C5C23×C11
hypercenterC11×C22⋊C4D5
hypocenterC5C2×C11×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C11×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D5×C11C2semidirect
3. C5×C11×C22⋊C4C2semidirect
4. C11×C22⋊Dic5C2semidirect
5. C11×#685C2semidirect
8. C22×D5×C11C4semidirect
11. C2×C4×C5×C11C22semidirect
12. C2×C11×Dic5C22semidirect
16. C22×C5×C11C2×C4semidirect
21. C2×D5×C11C2×C4semidirect
29. C11×C22⋊C4D5direct (N × H)
30. D5×C22⋊C4C11direct (N × H)
35. D5×C11C22⋊C4direct (N × H)
43. C2×C4×C11C2×D5semidirect
45. C2×C4×D5C2×C11semidirect
46. C5×C22⋊C4C2×C11semidirect
47. C22⋊Dic5C2×C11semidirect
48. #685C2×C11semidirect
49. C5×C11C2×C22⋊C4semidirect
56. C22×C11C4×D5semidirect
62. C22×D5C4×C11semidirect
65. C2×C4×C5C22×C11semidirect
66. C2×Dic5C22×C11semidirect
75. C22×C5C2×C4×C11semidirect
80. C2×D5C2×C4×C11semidirect
88. C22⋊C4D5×C11direct (N × H)
89. C11D5×C22⋊C4direct (N × H)
94. D5C11×C22⋊C4direct (N × H)
102. C2×C4C2×D5×C11semidirect
103. C5C2×C11×C22⋊C4semidirect
110. C22C4×D5×C11semidirect

Maximal subgroups

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

subgroupindex
C23×D5×C112
C2×C4×D5×C112
C5×C11×C22⋊C42
C11×C22⋊Dic52
C11×#6852
C2×C11×C22⋊C45
D5×C22⋊C411