Finite Group Databasebeta

← C2×C5×(C11⋊C5)⋊D11 #27130941

Subgroups — C2×C5×(C11⋊C5)⋊D11 #27130941

Order 12100.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×C11⋊C5C211yesmaximal, characteristic, complemented
2C5×(C11⋊C5)⋊D11C212yesmaximal, direct product factor
3C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
4C2×C5×C11⋊D11C511yesmaximal, characteristic, complemented
5C2×(C11⋊C5)⋊D11C515yesmaximal, direct product factor
6C2×C5×C112C2×C511yescharacteristic, complemented
7C5×C11⋊D11C2×C512yescomplemented
8C2×C11×C11⋊C5C2×C515yescomplemented
9(C11⋊C5)⋊D11C2×C5110yesdirect product factor
10C2×C52×D11—111nomaximal
11C2×C5×AGL(1,𝔽11)—111nomaximal
12C5×C112C22×C511yescharacteristic, complemented
13C11×C11⋊C5C22×C515yescomplemented
14C2×C52×C11—111no—
15C52×D11—112no—
16C2×C5×C11⋊C5D1111yescharacteristic, complemented
17C5×AGL(1,𝔽11)—112no—
18C2×C11⋊D11C5211yescharacteristic, complemented, Hall
19C52×C11—111no—
20C5×C11⋊C5C2×D1111yescharacteristic, complemented
21C2×C112C2×C5211yescharacteristic, complemented
22C11⋊D11C2×C5212yescomplemented
23C2×C5×D11—115no—
24C2×C5×D11—111no—
25C2×C5×D11—111no—
26C2×C5×D11—552no—
27C2×AGL(1,𝔽11)—115no—
28C112C22×C5211yescharacteristic, complemented, Sylow
29C2×C5×C11—52no—
30C2×C5×C11—115no—
31C2×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
32C2×C5×C11C5×D1111yescharacteristic, complemented
33C5×D11—1110no—
34C5×D11—112no—
35C5×D11—112no—
36C5×D11—554no—
37C2×C11⋊C5C5×D1115yescomplemented
38AGL(1,𝔽11)—1110no—
39C22×C52—1211noHall
40C5×C11—52no—
41C5×C11—115no—
42C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
43C5×C11C2×C5×D1111yescharacteristic, complemented
44C11⋊C5C2×C5×D1115yescomplemented
45C2×C52—111no—
46C2×C52—1212no—
47C2×D11—111no—
48C2×D11—111no—
49C2×D11—552no—
50C52—111noSylow
51C2×C11—52no—
52C2×C11C5×AGL(1,𝔽11)11yescharacteristic, complemented
53C2×C11C52×D1111yescharacteristic, complemented
54D11—112no—
55D11—112no—
56D11—554no—
57C22×C5—1215no—
58C22×C5—1211no—
59C11—52no—
60C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
61C11C2×C52×D1111yescharacteristic, complemented
62C2×C5—115no—
63C2×C5—12110no—
64C2×C5—1212no—
65C2×C5(C11⋊C5)⋊D1111yescharacteristic, direct product factor
66C5—115no—
67C5C2×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
68C22—1211noSylow
69C2—1212no—
70C2C5×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5(C11⋊C5)⋊D11
commutator, cosocle, hypocenterC112C22×C52
FrattiniC1G
Fitting, socleC2×C5×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×C11×C11⋊C5C2semidirect
2. C5×(C11⋊C5)⋊D11C2direct (N × H)
3. C5×C11×C11⋊C5C22semidirect
4. C2×C5×C11⋊D11C5semidirect
5. C2×(C11⋊C5)⋊D11C5direct (N × H)
6. C2×C5×C112C2×C5semidirect
7. C5×C11⋊D11C2×C5semidirect
8. C2×C11×C11⋊C5C2×C5semidirect
9. (C11⋊C5)⋊D11C2×C5direct (N × H)
12. C5×C112C22×C5semidirect
13. C11×C11⋊C5C22×C5semidirect
16. C2×C5×C11⋊C5D11semidirect
18. C2×C11⋊D11C52semidirect
20. C5×C11⋊C5C2×D11semidirect
21. C2×C112C2×C52semidirect
22. C11⋊D11C2×C52semidirect
28. C112C22×C52semidirect
31. C2×C5×C11AGL(1,𝔽11)semidirect
32. C2×C5×C11C5×D11semidirect
37. C2×C11⋊C5C5×D11semidirect
42. C5×C11C2×AGL(1,𝔽11)semidirect
43. C5×C11C2×C5×D11semidirect
44. C11⋊C5C2×C5×D11semidirect
52. C2×C11C5×AGL(1,𝔽11)semidirect
53. C2×C11C52×D11semidirect
60. C11C2×C5×AGL(1,𝔽11)semidirect
61. C11C2×C52×D11semidirect
65. C2×C5(C11⋊C5)⋊D11direct (N × H)
67. C5C2×(C11⋊C5)⋊D11direct (N × H)
70. C2C5×(C11⋊C5)⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×C11⋊C52
C5×(C11⋊C5)⋊D112
C2×C5×C11⋊D115
C2×(C11⋊C5)⋊D115
C2×C52×D1111
C2×C5×AGL(1,𝔽11)11