Finite Group Databasebeta

← C5×C11⋊C5×Dic33 #49137264

Subgroups — C5×C11⋊C5×Dic33 #49137264

Order 36300.

200 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 90 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
2C5×Dic11×C11⋊C5—31nomaximal, Hall
3C3×C5×C11×C11⋊C5C411yescharacteristic, complemented, Hall
4C5×C11×Dic33C511yesmaximal, characteristic, complemented
5C11⋊C5×Dic33C515yesmaximal, direct product factor
6C2×C5×C11×C11⋊C5D311yescharacteristic
7C2×C3×C11×C11⋊C5C2×C515yes—
8C2×C3×C5×C112C2×C511yescharacteristic
9C52×Dic33—111nomaximal
10C5×Dic3×C11⋊C5—111nomaximal
11C5×C11×C11⋊C5Dic311yescharacteristic, complemented, Hall
12C5×C11×Dic11—31no—
13Dic11×C11⋊C5—35no—
14C3×C5×C112C4×C511yescharacteristic, complemented
15C3×C11×C11⋊C5C4×C515yescomplemented
16C2×C3×C52×C11—111no—
17C2×C3×C5×C11⋊C5D1111yescharacteristic
18C11×Dic33C5211yescharacteristic, complemented, Hall
19C2×C5×C112C5×D311yescharacteristic
20C2×C11×C11⋊C5C5×D315yes—
21C52×Dic11—331no—
22C4×C5×C11⋊C5—331no—
23C3×C52×C11—111no—
24C3×C5×C11⋊C5Dic1111yescharacteristic, complemented
25C2×C3×C112C2×C5211yescharacteristic
26C5×Dic33—115no—
27C5×Dic33C11⋊C511yescharacteristic, direct product factor
28C5×C11×Dic3—111no—
29Dic3×C11⋊C5—115no—
30C5×C112C5×Dic311yescharacteristic, complemented
31C11×C11⋊C5C5×Dic315yescomplemented
32C2×C52×C11—111no—
33C2×C5×C11⋊C5D3311yescharacteristic
34C11×Dic11—31noHall
35C3×C112C4×C5211yescharacteristic, complemented, Hall
36C2×C3×C5×C11—101no—
37C2×C3×C5×C11—115no—
38C2×C3×C5×C11C2×C11⋊C511yescharacteristic
39C2×C3×C5×C11C5×D1111yescharacteristic
40C2×C3×C11⋊C5C5×D1115yes—
41C52×Dic3—1211noHall
42C52×C11—111no—
43C5×C11⋊C5Dic3311yescharacteristic, direct product factor
44C2×C112C52×D311yescharacteristic
45C4×C5×C11—331no—
46C5×Dic11—31no—
47C5×Dic11—335no—
48C4×C11⋊C5—335no—
49C3×C5×C11—101no—
50C3×C5×C11—115no—
51C3×C5×C11C4×C11⋊C511yescharacteristic, complemented
52C3×C5×C11C5×Dic1111yescharacteristic, complemented
53C3×C11⋊C5C5×Dic1115yescomplemented
54C2×C3×C52—111no—
55Dic33C5×C11⋊C511yescharacteristic, direct product factor
56C11×Dic3—111no—
57C112C52×Dic311yescharacteristic, complemented, Sylow
58C2×C5×C11—101no—
59C2×C5×C11—115no—
60C2×C5×C11D3×C11⋊C511yescharacteristic
61C2×C5×C11C5×D3311yescharacteristic
62C2×C11⋊C5C5×D3315yes—
63C4×C52—3631noHall
64C3×C52—111noHall
65C2×C3×C11—101no—
66C2×C3×C11C2×C5×C11⋊C511yescharacteristic
67C2×C3×C11C52×D1111yescharacteristic
68C5×Dic3—111no—
69C5×Dic3—1215no—
70C5×C11—101no—
71C5×C11—115no—
72C5×C11Dic3×C11⋊C511yescharacteristic, complemented
73C5×C11C5×Dic3311yescharacteristic, complemented
74C11⋊C5C5×Dic3315yesdirect product factor
75C2×C52—111no—
76C4×C11—331no—
77Dic11—31no—
78C3×C11—101no—
79C3×C11C4×C5×C11⋊C511yescharacteristic, complemented
80C3×C11C52×Dic1111yescharacteristic, complemented
81C2×C3×C5—115no—
82C2×C3×C5D11×C11⋊C511yescharacteristic
83C52—111noSylow
84C2×C11—101no—
85C2×C11C5×D3×C11⋊C511yescharacteristic
86C2×C11C52×D3311yescharacteristic
87C4×C5—331no—
88C4×C5—3635no—
89C3×C5—115no—
90C3×C5Dic11×C11⋊C511yescharacteristic, complemented
91Dic3—111noHall
92C11—101no—
93C11C5×Dic3×C11⋊C511yescharacteristic, complemented
94C11C52×Dic3311yescharacteristic, complemented
95C2×C5—115no—
96C2×C5C11⋊C5×D3311yescharacteristic
97C2×C3C5×D11×C11⋊C511yescharacteristic
98C5—115no—
99C5C11⋊C5×Dic3311yescharacteristic, direct product factor
100C4—331noSylow
101C3C5×Dic11×C11⋊C511yescharacteristic, complemented, Sylow
102C2C5×C11⋊C5×D3311yescharacteristic
subgroupG/H
center, hypercenterC2×C5C11⋊C5×D33
commutator, hypocenterC3×C112C4×C52
FrattiniC2C5×C11⋊C5×D33
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C3×C112C2×C52
LCSG ▷ C3×C112
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
3. C3×C5×C11×C11⋊C5C4semidirect
4. C5×C11×Dic33C5semidirect
5. C11⋊C5×Dic33C5direct (N × H)
11. C5×C11×C11⋊C5Dic3semidirect
14. C3×C5×C112C4×C5semidirect
15. C3×C11×C11⋊C5C4×C5semidirect
18. C11×Dic33C52semidirect
24. C3×C5×C11⋊C5Dic11semidirect
27. C5×Dic33C11⋊C5direct (N × H)
30. C5×C112C5×Dic3semidirect
31. C11×C11⋊C5C5×Dic3semidirect
35. C3×C112C4×C52semidirect
43. C5×C11⋊C5Dic33direct (N × H)
51. C3×C5×C11C4×C11⋊C5semidirect
52. C3×C5×C11C5×Dic11semidirect
53. C3×C11⋊C5C5×Dic11semidirect
55. Dic33C5×C11⋊C5direct (N × H)
57. C112C52×Dic3semidirect
72. C5×C11Dic3×C11⋊C5semidirect
73. C5×C11C5×Dic33semidirect
74. C11⋊C5C5×Dic33direct (N × H)
79. C3×C11C4×C5×C11⋊C5semidirect
80. C3×C11C52×Dic11semidirect
90. C3×C5Dic11×C11⋊C5semidirect
93. C11C5×Dic3×C11⋊C5semidirect
94. C11C52×Dic33semidirect
99. C5C11⋊C5×Dic33direct (N × H)
101. C3C5×Dic11×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
C5×Dic11×C11⋊C53
C5×C11×Dic335
C11⋊C5×Dic335
C52×Dic3311
C5×Dic3×C11⋊C511