Finite Group Databasebeta

← C5×D11×C3⋊D33 #36345349

Subgroups — C5×D11×C3⋊D33 #36345349

Order 21780.

360 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C5×C11×D11C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊D33C211yesmaximal, characteristic, complemented
3C5×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4C5×D11×D33—34nomaximal
5C32×C5×C112C2211yescharacteristic, complemented, Hall
6D11×C3⋊D33C511yesmaximal, characteristic, direct product factor, Hall
7C5×C3⋊(C11⋊D11)—34no—
8C5×C11×D33—34no—
9C3×C5×C11×D11D314yescomplemented
10C5×D112—91noHall
11C3⋊(C3⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C11×C3⋊D33C2×C511yescharacteristic, complemented
13C32×C11×D11C2×C511yescharacteristic, complemented
14C2×C5×C3⋊D33—111nomaximal
15C5×C3⋊D3×D11—111nomaximal
16C3×C5×C112C2×D314yescomplemented
17D11×D33—34no—
18C5×C11⋊D11—91no—
19C5×C11×D11—91no—
20C5×C11×D11C3⋊D311yescharacteristic, complemented
21C32×C112C22×C511yescharacteristic, complemented, Hall
22C2×C32×C5×C11—111no—
23C5×C3⋊D33—111no—
24C5×C3⋊D33—111no—
25C5×C3⋊D33—225no—
26C5×C3⋊D33D1111yescharacteristic, direct product factor
27C5×C11×C3⋊D3—111no—
28C32×C5×D11D1111yescharacteristic, complemented
29C3⋊(C11⋊D11)—34no—
30C11×D33—34no—
31C3×C11×D11C5×D314yescomplemented
32C2×C5×D33—334no—
33C5×D3×D11—334no—
34C5×C112C2×C3⋊D311yescharacteristic, complemented, Hall
35C32×C5×C11—25no—
36C32×C5×C11C2×D1111yescharacteristic, complemented
37C32×C5×C11C2×D1111yescharacteristic, complemented
38D112—91noHall
39C2×C3⋊D33—111no—
40C3⋊D3×D11—111no—
41C3×C112C2×C5×D314yescomplemented
42C2×C3×C5×C11—114no—
43C5×D33—34no—
44C5×D33—334no—
45C5×D33—334no—
46C5×D33—6620no—
47C5×D3×C11—334no—
48C3×C5×D11D3314yescomplemented
49C11⋊D11—91no—
50C11×D11—91no—
51C11×D11C5×C3⋊D311yescharacteristic, complemented
52C2×C5×D11—991no—
53C2×C5×D11—991no—
54C2×C32×C11—111no—
55C3⋊D33—111no—
56C3⋊D33—111no—
57C3⋊D33—225no—
58C3⋊D33C5×D1111yescharacteristic, direct product factor
59C11×C3⋊D3—111no—
60C32×D11C5×D1111yescharacteristic, complemented
61C2×C5×C3⋊D3—1211noHall
62C3×C5×C11—220no—
63C3×C5×C11D3×D1114yescomplemented
64C3×C5×C11C2×D3314yescomplemented
65C2×D33—334no—
66D3×D11—334no—
67C112C2×C5×C3⋊D311yescharacteristic, complemented, Sylow
68C2×C5×C11—111no—
69C2×C5×C11—991no—
70C5×D11—91no—
71C5×D11—991no—
72C5×D11—991no—
73C5×D11—1985no—
74C5×D11C3⋊D3311yescharacteristic, direct product factor
75C32×C11—25no—
76C32×C11C2×C5×D1111yescharacteristic, complemented
77C32×C11C2×C5×D1111yescharacteristic, complemented
78C2×C32×C5—111no—
79C5×C3⋊D3—111no—
80C5×C3⋊D3—1211no—
81C2×C3×C11—114no—
82D33—34no—
83D33—334no—
84D33—334no—
85D33—6620no—
86C3×D11C5×D3314yescomplemented
87D3×C11—334no—
88C2×C5×D3—3634no—
89C5×C11—25no—
90C5×C11C3⋊D3×D1111yescharacteristic, complemented
91C5×C11C2×C3⋊D3311yescharacteristic, complemented
92C32×C5D11211yescharacteristic, complemented, Hall
93C2×D11—991no—
94C2×D11—991no—
95C2×C3⋊D3—1211noHall
96C3×C11—220no—
97C3×C11C5×D3×D1114yescomplemented
98C3×C11C2×C5×D3314yescomplemented
99C2×C3×C5—114no—
100C5×D3—334no—
101C5×D3—3634no—
102C2×C11—111no—
103C2×C11—991no—
104D11—91no—
105D11—991no—
106D11—991no—
107D11—1985no—
108D11C5×C3⋊D3311yescharacteristic, direct product factor
109C22×C5—10891noHall
110C2×C32—111no—
111C3⋊D3—111no—
112C3⋊D3—1211no—
113C3×C5D11×D3314yescomplemented
114C2×D3—3634no—
115C11—25no—
116C11C5×C3⋊D3×D1111yescharacteristic, complemented
117C11C2×C5×C3⋊D3311yescharacteristic, complemented
118C2×C5—111no—
119C2×C5—10891no—
120C2×C5—991no—
121C32C5×D11211yescharacteristic, complemented, Sylow
122C2×C3—114no—
123D3—334no—
124D3—3634no—
125C5D11×C3⋊D3311yescharacteristic, direct product factor, Sylow
126C22—10891noSylow
127C3C5×D11×D3314yescomplemented
128C2—111no—
129C2—10891no—
130C2—991no—
subgroupG/H
center, hypercenterC5D11×C3⋊D33
commutator, cosocle, hypocenterC32×C112C22×C5
FrattiniC1G
Fitting, socleC32×C5×C112C22
LCSG ▷ C32×C112
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D11C2semidirect
2. C5×C11×C3⋊D33C2semidirect
3. C5×C3⋊(C3⋊(C11⋊D11))C2semidirect
5. C32×C5×C112C22semidirect
6. D11×C3⋊D33C5direct (N × H)
9. C3×C5×C11×D11D3semidirect
11. C3⋊(C3⋊(C11⋊D11))C2×C5semidirect
12. C11×C3⋊D33C2×C5semidirect
13. C32×C11×D11C2×C5semidirect
16. C3×C5×C112C2×D3semidirect
20. C5×C11×D11C3⋊D3semidirect
21. C32×C112C22×C5semidirect
26. C5×C3⋊D33D11direct (N × H)
28. C32×C5×D11D11semidirect
31. C3×C11×D11C5×D3semidirect
34. C5×C112C2×C3⋊D3semidirect
36. C32×C5×C11C2×D11semidirect
37. C32×C5×C11C2×D11semidirect
41. C3×C112C2×C5×D3semidirect
48. C3×C5×D11D33semidirect
51. C11×D11C5×C3⋊D3semidirect
58. C3⋊D33C5×D11direct (N × H)
60. C32×D11C5×D11semidirect
63. C3×C5×C11D3×D11semidirect
64. C3×C5×C11C2×D33semidirect
67. C112C2×C5×C3⋊D3semidirect
74. C5×D11C3⋊D33direct (N × H)
76. C32×C11C2×C5×D11semidirect
77. C32×C11C2×C5×D11semidirect
86. C3×D11C5×D33semidirect
90. C5×C11C3⋊D3×D11semidirect
91. C5×C11C2×C3⋊D33semidirect
92. C32×C5D112semidirect
97. C3×C11C5×D3×D11semidirect
98. C3×C11C2×C5×D33semidirect
108. D11C5×C3⋊D33direct (N × H)
113. C3×C5D11×D33semidirect
116. C11C5×C3⋊D3×D11semidirect
117. C11C2×C5×C3⋊D33semidirect
121. C32C5×D112semidirect
125. C5D11×C3⋊D33direct (N × H)
127. C3C5×D11×D33semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C11×D112
C5×C11×C3⋊D332
C5×C3⋊(C3⋊(C11⋊D11))2
C5×D11×D333
D11×C3⋊D335
C2×C5×C3⋊D3311
C5×C3⋊D3×D1111