Finite Group Databasebeta

← A42×C11⋊C5 #72247053

Subgroups — A42×C11⋊C5 #72247053

Order 7920.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×A4×C11⋊C5C312yesmaximal, complemented
2C22⋊A4×C11⋊C5C312yesmaximal, complemented
3C3×A4×C11⋊C5—42nomaximal
4C11×A42C511yesmaximal, characteristic, complemented, Hall
5C2×A4×C11⋊C5—32no—
6C24×C11⋊C5C3211yescharacteristic, complemented, Hall
7C5×A42—111nomaximal, Hall
8C22×C3×C11⋊C5—42no—
9A4×C11⋊C5—44no—
10A4×C11⋊C5—122no—
11A4×C11⋊C5A412yesdirect product factor
12C11×C22⋊A4C3×C512yescomplemented
13C22×C11×A4C3×C512yescomplemented
14C32×C11⋊C5—161noHall
15C23×C11⋊C5—32no—
16C23×C11⋊C5—91no—
17C3×C11×A4—42no—
18C2×C3×C11⋊C5—122no—
19C2×C11×A4—32no—
20C5×C22⋊A4—112no—
21C22×C5×A4—112no—
22C22×C11⋊C5—32no—
23C22×C11⋊C5—91no—
24C22×C11⋊C5—92no—
25C22×C11⋊C5C3×A412yescomplemented
26C3×C5×A4—442no—
27C24×C11C32×C511yescharacteristic, complemented, Hall
28C3×C11⋊C5—42no—
29C3×C11⋊C5—162no—
30A42C11⋊C511yescharacteristic, direct product factor, Hall
31C22×C3×C11—42no—
32C11×A4—44no—
33C11×A4—122no—
34C11×A4C5×A412yescomplemented
35C2×C5×A4—332no—
36C2×C11⋊C5—32no—
37C2×C11⋊C5—91no—
38C32×C11—161noHall
39C23×C11—32no—
40C23×C11—91no—
41C24×C5—111noHall
42C2×C3×C11—122no—
43C22×C3×C5—442no—
44C5×A4—112no—
45C5×A4—444no—
46C5×A4—1322no—
47C11⋊C5A4211yescharacteristic, direct product factor, Hall
48C22⋊A4C3×C11⋊C512yescomplemented
49C22×A4C3×C11⋊C512yescomplemented
50C32×C5—1761noHall
51C22×C11—32no—
52C22×C11—91no—
53C22×C11—92no—
54C22×C11C3×C5×A412yescomplemented
55C23×C5—332no—
56C23×C5—991no—
57C3×A4—42no—
58C3×C11—42no—
59C3×C11—162no—
60C2×C3×C5—1322no—
61C2×A4—32no—
62C2×C11—32no—
63C2×C11—91no—
64C22×C5—112no—
65C22×C5—332no—
66C22×C5—991no—
67C22×C5—992no—
68C24C32×C11⋊C511yescharacteristic, complemented, Sylow
69C3×C5—442no—
70C3×C5—1762no—
71C22×C3—42no—
72A4—44no—
73A4—122no—
74A4A4×C11⋊C512yesdirect product factor
75C11C5×A4211yescharacteristic, complemented, Sylow
76C2×C5—332no—
77C2×C5—991no—
78C32—161noSylow
79C23—32no—
80C23—91no—
81C2×C3—122no—
82C5—111noSylow
83C22—32no—
84C22—91no—
85C22—92no—
86C22C3×A4×C11⋊C512yescomplemented
87C3—42no—
88C3—162no—
89C2—32no—
90C2—91no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC24×C11C32×C5
LCSG ▷ C24×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C22×A4×C11⋊C5C3semidirect
2. C22⋊A4×C11⋊C5C3semidirect
4. C11×A42C5semidirect
6. C24×C11⋊C5C32semidirect
11. A4×C11⋊C5A4direct (N × H)
12. C11×C22⋊A4C3×C5semidirect
13. C22×C11×A4C3×C5semidirect
25. C22×C11⋊C5C3×A4semidirect
27. C24×C11C32×C5semidirect
30. A42C11⋊C5direct (N × H)
34. C11×A4C5×A4semidirect
47. C11⋊C5A42direct (N × H)
48. C22⋊A4C3×C11⋊C5semidirect
49. C22×A4C3×C11⋊C5semidirect
54. C22×C11C3×C5×A4semidirect
68. C24C32×C11⋊C5semidirect
74. A4A4×C11⋊C5direct (N × H)
75. C11C5×A42semidirect
86. C22C3×A4×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C22×A4×C11⋊C53
C22⋊A4×C11⋊C53
C3×A4×C11⋊C54
C11×A425
C5×A4211