Finite Group Databasebeta

← C4×A4×C11⋊C5 #72276491

Subgroups — C4×A4×C11⋊C5 #72276491

Order 2640.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×A4×C11⋊C5C211yesmaximal, characteristic
2C22×C4×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3A4×C11⋊C5C411yescharacteristic, direct product factor
4C3×C4×C11⋊C5—41nomaximal
5C4×C11×A4C511yesmaximal, characteristic, complemented, Hall
6C23×C11⋊C5C2×C311yescharacteristic
7C2×C4×C11⋊C5—31no—
8C2×C4×C11⋊C5—31no—
9C2×C3×C11⋊C5—41no—
10C2×C11×A4C2×C511yescharacteristic
11C4×C5×A4—111nomaximal, Hall
12C22×C11⋊C5—31no—
13C22×C11⋊C5—31no—
14C22×C11⋊C5C3×C411yescharacteristic, complemented
15C4×C11⋊C5—31no—
16C4×C11⋊C5A411yescharacteristic, direct product factor
17C22×C4×C11C3×C511yescharacteristic, complemented, Hall
18C3×C11⋊C5—41noHall
19C11×A4C4×C511yescharacteristic, complemented
20C3×C4×C11—41no—
21C2×C5×A4—111no—
22C2×C11⋊C5—31no—
23C2×C11⋊C5—31no—
24C2×C11⋊C5C2×A411yescharacteristic
25C23×C11C2×C3×C511yescharacteristic
26C2×C4×C11—31no—
27C2×C4×C11—31no—
28C22×C4×C5—111noHall
29C2×C3×C11—41no—
30C5×A4—111no—
31C3×C4×C5—441no—
32C11⋊C5C4×A411yescharacteristic, direct product factor, Hall
33C4×A4C11⋊C511yescharacteristic, direct product factor, Hall
34C22×C11—31no—
35C22×C11—31no—
36C22×C11C3×C4×C511yescharacteristic, complemented
37C4×C11—31no—
38C4×C11C5×A411yescharacteristic, complemented
39C23×C5—111no—
40C2×C4×C5—331no—
41C2×C4×C5—331no—
42C3×C11—41noHall
43C2×C3×C5—441no—
44C2×A4C2×C11⋊C511yescharacteristic
45C2×C11—31no—
46C2×C11—31no—
47C2×C11C2×C5×A411yescharacteristic
48C22×C5—111no—
49C22×C5—331no—
50C22×C5—331no—
51C4×C5—111no—
52C4×C5—331no—
53C22×C4C3×C11⋊C511yescharacteristic, complemented, Sylow
54C3×C5—441noHall
55A4C4×C11⋊C511yescharacteristic, direct product factor
56C3×C4—41no—
57C11C4×C5×A411yescharacteristic, complemented, Sylow
58C2×C5—111no—
59C2×C5—331no—
60C2×C5—331no—
61C23C2×C3×C11⋊C511yescharacteristic
62C2×C4—31no—
63C2×C4—31no—
64C2×C3—41no—
65C5—111noSylow
66C22—31no—
67C22—31no—
68C22C3×C4×C11⋊C511yescharacteristic, complemented
69C4—31no—
70C4A4×C11⋊C511yescharacteristic, direct product factor
71C3—41noSylow
72C2—31no—
73C2—31no—
74C2C2×A4×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC4A4×C11⋊C5
commutator, hypocenterC22×C11C3×C4×C5
FrattiniC2C2×A4×C11⋊C5
FittingC22×C4×C11C3×C5
socle, cosocleC23×C11C2×C3×C5
prime radicalC2×A4×C11⋊C5C2
LCSG ▷ C22×C11
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C11⋊C5C3semidirect
3. A4×C11⋊C5C4direct (N × H)
5. C4×C11×A4C5semidirect
14. C22×C11⋊C5C3×C4semidirect
16. C4×C11⋊C5A4direct (N × H)
17. C22×C4×C11C3×C5semidirect
19. C11×A4C4×C5semidirect
32. C11⋊C5C4×A4direct (N × H)
33. C4×A4C11⋊C5direct (N × H)
36. C22×C11C3×C4×C5semidirect
38. C4×C11C5×A4semidirect
53. C22×C4C3×C11⋊C5semidirect
55. A4C4×C11⋊C5direct (N × H)
57. C11C4×C5×A4semidirect
68. C22C3×C4×C11⋊C5semidirect
70. C4A4×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×C11⋊C52
C22×C4×C11⋊C53
C3×C4×C11⋊C54
C4×C11×A45
C4×C5×A411