Finite Group Databasebeta

← C11×C11⋊C5×Dic15 #49137267

Subgroups — C11×C11⋊C5×Dic15 #49137267

Order 36300.

152 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 54 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×C11⋊C5C211yesmaximal, characteristic
2C11×Dic5×C11⋊C5—31nomaximal, Hall
3C3×C5×C11×C11⋊C5C411yescharacteristic, complemented, Hall
4C112×Dic15C511yesmaximal, characteristic, complemented
5C11×Dic3×C11⋊C5—51nomaximal
6C2×C5×C11×C11⋊C5D311yescharacteristic
7C2×C3×C11×C11⋊C5—22no—
8C2×C3×C11×C11⋊C5D511yescharacteristic
9C2×C3×C5×C112C2×C511yescharacteristic
10C5×C11×Dic15—111nomaximal
11C11⋊C5×Dic15C1111yesmaximal, characteristic, direct product factor
12C5×C11×C11⋊C5Dic311yescharacteristic, complemented, Hall
13C112×Dic5—31no—
14C4×C11×C11⋊C5—151no—
15C3×C5×C112C4×C511yescharacteristic, complemented
16C3×C11×C11⋊C5—22no—
17C3×C11×C11⋊C5Dic511yescharacteristic, complemented
18C2×C3×C52×C11—111no—
19C2×C3×C5×C11⋊C5C2×C1111yescharacteristic
20C112×Dic3—51noHall
21C2×C5×C112C5×D311yescharacteristic
22C2×C11×C11⋊C5—22no—
23C2×C11×C11⋊C5D1511yescharacteristic
24C5×C11×Dic5—331no—
25Dic5×C11⋊C5—31no—
26C3×C52×C11—111no—
27C3×C5×C11⋊C5C4×C1111yescharacteristic, complemented
28C2×C3×C112C5×D511yescharacteristic
29C11×Dic15—52no—
30C11×Dic15C11⋊C511yescharacteristic, direct product factor
31C11×Dic15C5×C1111yescharacteristic, complemented
32C5×C11×Dic3—551no—
33Dic3×C11⋊C5—51no—
34C5×C112C5×Dic311yescharacteristic, complemented
35C11×C11⋊C5—22no—
36C11×C11⋊C5Dic1511yescharacteristic, direct product factor
37C2×C52×C11—111no—
38C2×C5×C11⋊C5D3×C1111yescharacteristic
39C4×C112—151noHall
40C3×C112C5×Dic511yescharacteristic, complemented, Hall
41C2×C3×C5×C11—52no—
42C2×C3×C5×C11—111no—
43C2×C3×C5×C11—222no—
44C2×C3×C5×C11C2×C11⋊C511yescharacteristic
45C2×C3×C5×C11C2×C5×C1111yescharacteristic
46C2×C3×C11⋊C5—22no—
47C2×C3×C11⋊C5D5×C1111yescharacteristic
48C5×Dic15—111noHall
49C52×C11—111no—
50C5×C11⋊C5C11×Dic311yescharacteristic, complemented
51C2×C112C5×D1511yescharacteristic
52C4×C5×C11—1651no—
53C11×Dic5—31no—
54C11×Dic5—31no—
55C11×Dic5—152no—
56C4×C11⋊C5—151no—
57C3×C5×C11—52no—
58C3×C5×C11—111no—
59C3×C5×C11—222no—
60C3×C5×C11C4×C11⋊C511yescharacteristic, complemented
61C3×C5×C11C4×C5×C1111yescharacteristic, complemented
62C3×C11⋊C5—22no—
63C3×C11⋊C5C11×Dic511yescharacteristic, complemented
64C2×C3×C52—111no—
65C11×Dic3—51no—
66C11×Dic3—51no—
67C11×Dic3—252no—
68C112C5×Dic1511yescharacteristic, complemented, Sylow
69C2×C5×C11—52no—
70C2×C5×C11—111no—
71C2×C5×C11—222no—
72C2×C5×C11D3×C11⋊C511yescharacteristic
73C2×C5×C11C5×D3×C1111yescharacteristic
74C2×C11⋊C5—22no—
75C2×C11⋊C5C11×D1511yescharacteristic
76C5×Dic5—331noHall
77C3×C52—111noHall
78C2×C3×C11—52no—
79C2×C3×C11D5×C11⋊C511yescharacteristic
80C2×C3×C11C5×D5×C1111yescharacteristic
81Dic15C11×C11⋊C511yescharacteristic, direct product factor
82C5×Dic3—551no—
83C5×C11—52no—
84C5×C11—111no—
85C5×C11—222no—
86C5×C11Dic3×C11⋊C511yescharacteristic, complemented
87C5×C11C5×C11×Dic311yescharacteristic, complemented
88C11⋊C5—22no—
89C11⋊C5C11×Dic1511yescharacteristic, direct product factor
90C2×C52—111no—
91C4×C11—151no—
92C4×C11—151no—
93C4×C11—752no—
94C3×C11—52no—
95C3×C11Dic5×C11⋊C511yescharacteristic, complemented
96C3×C11C5×C11×Dic511yescharacteristic, complemented
97C2×C3×C5—111no—
98C2×C3×C5—222no—
99C2×C3×C5C2×C11×C11⋊C511yescharacteristic
100C52—111noSylow
101C2×C11—52no—
102C2×C11D15×C11⋊C511yescharacteristic
103C2×C11C5×C11×D1511yescharacteristic
104C4×C5—1651no—
105Dic5—31no—
106C3×C5—111no—
107C3×C5—222no—
108C3×C5C4×C11×C11⋊C511yescharacteristic, complemented
109Dic3—51noHall
110C11—52no—
111C11C11⋊C5×Dic1511yescharacteristic, direct product factor
112C11C5×C11×Dic1511yescharacteristic, complemented
113C2×C5—111no—
114C2×C5—222no—
115C2×C5D3×C11×C11⋊C511yescharacteristic
116C2×C3D5×C11×C11⋊C511yescharacteristic
117C5—111no—
118C5—222no—
119C5C11×Dic3×C11⋊C511yescharacteristic, complemented
120C4—151noSylow
121C3C11×Dic5×C11⋊C511yescharacteristic, complemented, Sylow
122C2C11×D15×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC2×C11D15×C11⋊C5
commutator, hypocenterC3×C5×C11C4×C5×C11
FrattiniC2C11×D15×C11⋊C5
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C3×C5×C11C2×C5×C11
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
3. C3×C5×C11×C11⋊C5C4semidirect
4. C112×Dic15C5semidirect
11. C11⋊C5×Dic15C11direct (N × H)
12. C5×C11×C11⋊C5Dic3semidirect
15. C3×C5×C112C4×C5semidirect
17. C3×C11×C11⋊C5Dic5semidirect
27. C3×C5×C11⋊C5C4×C11semidirect
30. C11×Dic15C11⋊C5direct (N × H)
31. C11×Dic15C5×C11semidirect
34. C5×C112C5×Dic3semidirect
36. C11×C11⋊C5Dic15direct (N × H)
40. C3×C112C5×Dic5semidirect
50. C5×C11⋊C5C11×Dic3semidirect
60. C3×C5×C11C4×C11⋊C5semidirect
61. C3×C5×C11C4×C5×C11semidirect
63. C3×C11⋊C5C11×Dic5semidirect
68. C112C5×Dic15semidirect
81. Dic15C11×C11⋊C5direct (N × H)
86. C5×C11Dic3×C11⋊C5semidirect
87. C5×C11C5×C11×Dic3semidirect
89. C11⋊C5C11×Dic15direct (N × H)
95. C3×C11Dic5×C11⋊C5semidirect
96. C3×C11C5×C11×Dic5semidirect
108. C3×C5C4×C11×C11⋊C5semidirect
111. C11C11⋊C5×Dic15direct (N × H)
112. C11C5×C11×Dic15semidirect
119. C5C11×Dic3×C11⋊C5semidirect
121. C3C11×Dic5×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C11⋊C52
C11×Dic5×C11⋊C53
C112×Dic155
C11×Dic3×C11⋊C55
C5×C11×Dic1511
C11⋊C5×Dic1511