Finite Group Databasebeta

← C5×C3⋊((C11⋊C5)⋊Dic11) #49137260

Subgroups — C5×C3⋊((C11⋊C5)⋊Dic11) #49137260

Order 36300.

216 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 88 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×(C11⋊C5)⋊Dic11—31nomaximal, Hall
3C3×C5×C11×C11⋊C5C411yescharacteristic, complemented, Hall
4C5×C3⋊(C11⋊Dic11)C511yesmaximal, characteristic, complemented
5C3⋊((C11⋊C5)⋊Dic11)C515yesmaximal, direct product factor
6C2×C5×C11×C11⋊C5D311yescharacteristic
7C2×C3×C11×C11⋊C5C2×C515yes—
8C2×C3×C5×C112C2×C511yescharacteristic
9C52×Dic33—111nomaximal
10C5×C3⋊(Dic11⋊C5)—111nomaximal
11C5×C11×C11⋊C5Dic311yescharacteristic, complemented, Hall
12C5×C11⋊Dic11—31no—
13(C11⋊C5)⋊Dic11—35no—
14C3×C5×C112C4×C511yescharacteristic, complemented
15C3×C11×C11⋊C5C4×C515yescomplemented
16C2×C3×C52×C11—111no—
17C2×C3×C5×C11⋊C5D1111yescharacteristic
18C3⋊(C11⋊Dic11)C5211yescharacteristic, complemented, Hall
19C2×C5×C112C5×D311yescharacteristic
20C2×C11×C11⋊C5C5×D315yes—
21C52×Dic11—331no—
22C5×Dic11⋊C5—331no—
23C3×C52×C11—111no—
24C3×C5×C11⋊C5Dic1111yescharacteristic, complemented
25C2×C3×C112C2×C5211yescharacteristic
26C5×Dic33—111no—
27C5×Dic33—115no—
28C5×Dic33—552no—
29C5×Dic33—551no—
30C3⋊(Dic11⋊C5)—115no—
31C5×C112C5×Dic311yescharacteristic, complemented
32C11×C11⋊C5C5×Dic315yescomplemented
33C2×C52×C11—111no—
34C2×C5×C11⋊C5D3311yescharacteristic
35C11⋊Dic11—31noHall
36C3×C112C4×C5211yescharacteristic, complemented, Hall
37C2×C3×C5×C11—52no—
38C2×C3×C5×C11—115no—
39C2×C3×C5×C11AGL(1,𝔽11)11yescharacteristic
40C2×C3×C5×C11C5×D1111yescharacteristic
41C2×C3×C11⋊C5C5×D1115yes—
42C52×Dic3—1211noHall
43C52×C11—111no—
44C5×C11⋊C5Dic3311yescharacteristic, complemented
45C2×C112C52×D311yescharacteristic
46C5×Dic11—331no—
47C5×Dic11—335no—
48C5×Dic11—1652no—
49C5×Dic11—1651no—
50Dic11⋊C5—335no—
51C3×C5×C11—52no—
52C3×C5×C11—115no—
53C3×C5×C11Dic11⋊C511yescharacteristic, complemented
54C3×C5×C11C5×Dic1111yescharacteristic, complemented
55C3×C11⋊C5C5×Dic1115yescomplemented
56C2×C3×C52—111no—
57Dic33—111no—
58Dic33—552no—
59Dic33—551no—
60C112C52×Dic311yescharacteristic, complemented, Sylow
61C2×C5×C11—52no—
62C2×C5×C11—115no—
63C2×C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic
64C2×C5×C11C5×D3311yescharacteristic
65C2×C11⋊C5C5×D3315yes—
66C4×C52—3631noHall
67C3×C52—111noHall
68C2×C3×C11—52no—
69C2×C3×C11C5×AGL(1,𝔽11)11yescharacteristic
70C2×C3×C11C52×D1111yescharacteristic
71C5×Dic3—6051no—
72C5×Dic3—1215no—
73C5×C11—52no—
74C5×C11—115no—
75C5×C11C3⋊(Dic11⋊C5)11yescharacteristic, complemented
76C5×C11C5×Dic3311yescharacteristic, complemented
77C11⋊C5C5×Dic3315yescomplemented
78C2×C52—111no—
79Dic11—331no—
80Dic11—1652no—
81Dic11—1651no—
82C3×C11—52no—
83C3×C11C5×Dic11⋊C511yescharacteristic, complemented
84C3×C11C52×Dic1111yescharacteristic, complemented
85C2×C3×C5—115no—
86C2×C3×C5(C11⋊C5)⋊D1111yescharacteristic
87C52—111noSylow
88C2×C11—52no—
89C2×C11C5×C3⋊AGL(1,𝔽11)11yescharacteristic
90C2×C11C52×D3311yescharacteristic
91C4×C5—18151no—
92C4×C5—3635no—
93C3×C5—115no—
94C3×C5(C11⋊C5)⋊Dic1111yescharacteristic, complemented
95Dic3—6051noHall
96C11—52no—
97C11C5×C3⋊(Dic11⋊C5)11yescharacteristic, complemented
98C11C52×Dic3311yescharacteristic, complemented
99C2×C5—115no—
100C2×C5C3⋊((C11⋊C5)⋊D11)11yescharacteristic
101C2×C3C5×(C11⋊C5)⋊D1111yescharacteristic
102C5—115no—
103C5C3⋊((C11⋊C5)⋊Dic11)11yescharacteristic, direct product factor
104C4—18151noSylow
105C3C5×(C11⋊C5)⋊Dic1111yescharacteristic, complemented, Sylow
106C2C5×C3⋊((C11⋊C5)⋊D11)11yescharacteristic
subgroupG/H
center, hypercenterC2×C5C3⋊((C11⋊C5)⋊D11)
commutator, hypocenterC3×C112C4×C52
FrattiniC2C5×C3⋊((C11⋊C5)⋊D11)
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×C3⋊(C11⋊Dic11)C5semidirect
5. C3⋊((C11⋊C5)⋊Dic11)C5direct (N × H)
11. C5×C11×C11⋊C5Dic3semidirect
14. C3×C5×C112C4×C5semidirect
15. C3×C11×C11⋊C5C4×C5semidirect
18. C3⋊(C11⋊Dic11)C52semidirect
24. C3×C5×C11⋊C5Dic11semidirect
31. C5×C112C5×Dic3semidirect
32. C11×C11⋊C5C5×Dic3semidirect
36. C3×C112C4×C52semidirect
44. C5×C11⋊C5Dic33semidirect
53. C3×C5×C11Dic11⋊C5semidirect
54. C3×C5×C11C5×Dic11semidirect
55. C3×C11⋊C5C5×Dic11semidirect
60. C112C52×Dic3semidirect
75. C5×C11C3⋊(Dic11⋊C5)semidirect
76. C5×C11C5×Dic33semidirect
77. C11⋊C5C5×Dic33semidirect
83. C3×C11C5×Dic11⋊C5semidirect
84. C3×C11C52×Dic11semidirect
94. C3×C5(C11⋊C5)⋊Dic11semidirect
97. C11C5×C3⋊(Dic11⋊C5)semidirect
98. C11C52×Dic33semidirect
103. C5C3⋊((C11⋊C5)⋊Dic11)direct (N × H)
105. C3C5×(C11⋊C5)⋊Dic11semidirect

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×(C11⋊C5)⋊Dic113
C5×C3⋊(C11⋊Dic11)5
C3⋊((C11⋊C5)⋊Dic11)5
C52×Dic3311
C5×C3⋊(Dic11⋊C5)11