Finite Group Databasebeta

← D11×C3⋊(C5⋊D55) #49137788

Subgroups — D11×C3⋊(C5⋊D55) #49137788

Order 36300.

480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×C52×C11×D11C211yesmaximal, characteristic, complemented
2C11×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊(C5⋊(C11⋊D11)))C211yesmaximal, characteristic, complemented
4D11×C5⋊D55—31nomaximal, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6D11×D165—56nomaximal
7C5⋊(C5⋊(C11⋊D11))—31no—
8C11×C5⋊D55—31no—
9C52×C11×D11D311yescharacteristic, complemented
10C3⋊(C5⋊(C11⋊D11))—56no—
11C11×D165—56no—
12C3×C5×C11×D11D516yescomplemented
13C2×C3⋊(C5⋊D55)—111nomaximal
14D11×C3⋊(C5⋊D5)—111nomaximal
15C52×C112C2×D311yescharacteristic, complemented, Hall
16D11×D55—156no—
17C3×C5×C112C2×D516yescomplemented
18C2×C3×C52×C11—111no—
19C3⋊(C5⋊D55)—111no—
20C3⋊(C5⋊D55)—111no—
21C3⋊(C5⋊D55)—225no—
22C3⋊(C5⋊D55)D1111yescharacteristic, direct product factor
23C11×C3⋊(C5⋊D5)—111no—
24C3×C52×D11D1111yescharacteristic, complemented
25D11×D33—251noHall
26C5⋊(C11⋊D11)—156no—
27C11×D55—156no—
28C5×C11×D11D1516yescomplemented
29C2×C5⋊D55—331no—
30D11×C5⋊D5—331no—
31C3×C52×C11—25no—
32C3×C52×C11C2×D1111yescharacteristic, complemented
33C3×C52×C11C2×D1111yescharacteristic, complemented
34C3⋊(C11⋊D11)—251no—
35C11×D33—251no—
36C3×C11×D11C5⋊D511yescharacteristic, complemented
37C2×D165—556no—
38D11×D15—556no—
39C5×C112C2×D1516yescomplemented
40C2×C52×C11—111no—
41C5⋊D55—31no—
42C5⋊D55—331no—
43C5⋊D55—331no—
44C5⋊D55—665no—
45C11×C5⋊D5—331no—
46C52×D11D3311yescharacteristic, complemented
47D112—751noHall
48C3×C112C2×C5⋊D511yescharacteristic, complemented, Hall
49C2×C3×C5×C11—116no—
50D165—56no—
51D165—556no—
52D165—556no—
53D165—11030no—
54C11×D15—556no—
55C3×C5×D11D5516yescomplemented
56C2×C3⋊(C5⋊D5)—1211noHall
57C52×C11—25no—
58C52×C11D3×D1111yescharacteristic, complemented
59C52×C11C2×D3311yescharacteristic, complemented
60C11⋊D11—751no—
61C11×D11—751no—
62C11×D11C3⋊(C5⋊D5)11yescharacteristic, complemented
63C2×D55—1656no—
64D5×D11—1656no—
65C3×C5×C11—230no—
66C3×C5×C11D5×D1116yescomplemented
67C3×C5×C11C2×D5516yescomplemented
68C2×C3×C52—111no—
69C3⋊(C5⋊D5)—111no—
70C3⋊(C5⋊D5)—1211no—
71C2×D33—2751no—
72D3×D11—2751no—
73C112C2×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
74C2×C5×C11—116no—
75D55—156no—
76D55—33030no—
77D55—1656no—
78D55—1656no—
79C5×D11D16516yescomplemented
80D5×C11—1656no—
81C2×C5⋊D5—3631noHall
82C3×C52D11211yescharacteristic, complemented, Hall
83C2×C3×C11—111no—
84D33—2751no—
85D33—2751no—
86D33—251no—
87D33—5505no—
88C3×D11C5⋊D5511yescharacteristic, complemented
89D3×C11—2751no—
90C2×D15—6056no—
91C5×C11—230no—
92C5×C11D11×D1516yescomplemented
93C5×C11C2×D16516yescomplemented
94C2×C52—111no—
95C5⋊D5—331no—
96C5⋊D5—3631no—
97C2×D11—8251no—
98C2×D11—8251no—
99C3×C11—25no—
100C3×C11D11×C5⋊D511yescharacteristic, complemented
101C3×C11C2×C5⋊D5511yescharacteristic, complemented
102C2×C3×C5—116no—
103D15—556no—
104D15—6056no—
105C52D11×D3311yescharacteristic, complemented, Sylow
106C2×C11—111no—
107C2×C11—8251no—
108D11—8251no—
109D11—8251no—
110D11—751no—
111D11—16505no—
112D11C3⋊(C5⋊D55)11yescharacteristic, direct product factor
113C2×D5—18156no—
114C3×C5D11×D5516yescomplemented
115C2×D3—30251noHall
116C11—25no—
117C11D11×C3⋊(C5⋊D5)11yescharacteristic, complemented
118C11C2×C3⋊(C5⋊D55)11yescharacteristic, complemented
119C2×C5—116no—
120D5—18156no—
121D5—1656no—
122C2×C3—111no—
123D3—2751no—
124D3—30251no—
125C5D11×D16516yescomplemented
126C22—90751noSylow
127C3D11×C5⋊D5511yescharacteristic, complemented, Sylow
128C2—111no—
129C2—8251no—
130C2—90751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C112C22
LCSG ▷ C3×C52×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D11C2semidirect
2. C11×C3⋊(C5⋊D55)C2semidirect
3. C3⋊(C5⋊(C5⋊(C11⋊D11)))C2semidirect
5. C3×C52×C112C22semidirect
9. C52×C11×D11D3semidirect
12. C3×C5×C11×D11D5semidirect
15. C52×C112C2×D3semidirect
17. C3×C5×C112C2×D5semidirect
22. C3⋊(C5⋊D55)D11direct (N × H)
24. C3×C52×D11D11semidirect
28. C5×C11×D11D15semidirect
32. C3×C52×C11C2×D11semidirect
33. C3×C52×C11C2×D11semidirect
36. C3×C11×D11C5⋊D5semidirect
39. C5×C112C2×D15semidirect
46. C52×D11D33semidirect
48. C3×C112C2×C5⋊D5semidirect
55. C3×C5×D11D55semidirect
58. C52×C11D3×D11semidirect
59. C52×C11C2×D33semidirect
62. C11×D11C3⋊(C5⋊D5)semidirect
66. C3×C5×C11D5×D11semidirect
67. C3×C5×C11C2×D55semidirect
73. C112C2×C3⋊(C5⋊D5)semidirect
79. C5×D11D165semidirect
82. C3×C52D112semidirect
88. C3×D11C5⋊D55semidirect
92. C5×C11D11×D15semidirect
93. C5×C11C2×D165semidirect
100. C3×C11D11×C5⋊D5semidirect
101. C3×C11C2×C5⋊D55semidirect
105. C52D11×D33semidirect
112. D11C3⋊(C5⋊D55)direct (N × H)
114. C3×C5D11×D55semidirect
117. C11D11×C3⋊(C5⋊D5)semidirect
118. C11C2×C3⋊(C5⋊D55)semidirect
125. C5D11×D165semidirect
127. C3D11×C5⋊D55semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C11×D112
C11×C3⋊(C5⋊D55)2
C3⋊(C5⋊(C5⋊(C11⋊D11)))2
D11×C5⋊D553
D11×D1655
C2×C3⋊(C5⋊D55)11
D11×C3⋊(C5⋊D5)11