Finite Group Databasebeta

← C9×C11⋊#63120 #38787871

Subgroups — C9×C11⋊#63120 #38787871

Order 25740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×D5×C11×C13C211yesmaximal, characteristic
2C3×C11⋊#63120C311yesmaximal, characteristic
3C5×C9×C11×C13C411yescharacteristic, complemented, Hall
4C9×Dic143—51nomaximal, Hall
5C3×D5×C11×C13C2×C311yescharacteristic
6C11⋊#63120C911yescharacteristic, direct product factor, Hall
7C2×C9×C11×C13—51no—
8C9×#63120—111nomaximal, Hall
9C3×C5×C11×C13C3×C411yescharacteristic
10C9×C11⋊AGL(1,𝔽5)—131nomaximal, Hall
11C3×Dic143—51no—
12D5×C11×C13C2×C911yescharacteristic
13C9×C11×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C9×D5×C13D1111yescharacteristic
15C9×D5×C11D1311yescharacteristic
16C2×C3×C11×C13—51no—
17C3×#63120—111no—
18C5×C11×C13C4×C911yescharacteristic, complemented, Hall
19C3×C11⋊AGL(1,𝔽5)—131no—
20C5×C9×C13Dic1111yescharacteristic, complemented, Hall
21Dic143—51noHall
22C5×C9×C11Dic1311yescharacteristic, complemented, Hall
23C9×Dic13—551noHall
24C3×C11×C13C3×AGL(1,𝔽5)11yescharacteristic
25C9×Dic11—651noHall
26C3×D5×C13C3×D1111yescharacteristic
27C3×D5×C11C3×D1311yescharacteristic
28C2×C11×C13—51no—
29#63120—111noHall
30C2×C9×C13—51no—
31C11⋊AGL(1,𝔽5)—131noHall
32C2×C9×C11—51no—
33C3×C5×C13C3×Dic1111yescharacteristic
34C9×AGL(1,𝔽5)—1431noHall
35C3×C5×C11C3×Dic1311yescharacteristic
36C3×Dic13—551no—
37C11×C13C9×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C3×Dic11—651no—
39D5×C13C9×D1111yescharacteristic
40C9×C13C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
41D5×C11C9×D1311yescharacteristic
42C9×C11#6312011yescharacteristic, complemented, Hall
43C9×D5D14311yescharacteristic
44C2×C3×C13—51no—
45C2×C3×C11—51no—
46C5×C13C9×Dic1111yescharacteristic, complemented, Hall
47C3×AGL(1,𝔽5)—1431no—
48C5×C11C9×Dic1311yescharacteristic, complemented, Hall
49Dic13—551noHall
50C5×C9Dic14311yescharacteristic, complemented, Hall
51Dic11—651noHall
52C3×C13C3×C11⋊AGL(1,𝔽5)11yescharacteristic
53C4×C9—7151noHall
54C3×C11C3×#6312011yescharacteristic
55C3×D5C3×D14311yescharacteristic
56C2×C13—51no—
57C2×C11—51no—
58AGL(1,𝔽5)—1431noHall
59C2×C9—51no—
60C3×C5C3×Dic14311yescharacteristic
61C13C9×C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
62C3×C4—7151no—
63C11C9×#6312011yescharacteristic, complemented, Sylow
64D5C9×D14311yescharacteristic
65C9C11⋊#6312011yescharacteristic, direct product factor, Sylow
66C2×C3—51no—
67C5C9×Dic14311yescharacteristic, complemented, Sylow
68C4—7151noSylow
69C3C3×C11⋊#6312011yescharacteristic
70C2—51no—
subgroupG/H
center, hypercenterC9C11⋊#63120
commutator, hypocenterC5×C11×C13C4×C9
FrattiniC3C3×C11⋊#63120
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13C3×C4
prime radical, cosocleC3×D5×C11×C13C2×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
3. C5×C9×C11×C13C4semidirect
6. C11⋊#63120C9direct (N × H)
13. C9×C11×C13AGL(1,𝔽5)semidirect
18. C5×C11×C13C4×C9semidirect
20. C5×C9×C13Dic11semidirect
22. C5×C9×C11Dic13semidirect
37. C11×C13C9×AGL(1,𝔽5)semidirect
40. C9×C13C11⋊AGL(1,𝔽5)semidirect
42. C9×C11#63120semidirect
46. C5×C13C9×Dic11semidirect
48. C5×C11C9×Dic13semidirect
50. C5×C9Dic143semidirect
61. C13C9×C11⋊AGL(1,𝔽5)semidirect
63. C11C9×#63120semidirect
65. C9C11⋊#63120direct (N × H)
67. C5C9×Dic143semidirect

Maximal subgroups

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

subgroupindex
C9×D5×C11×C132
C3×C11⋊#631203
C9×Dic1435
C9×#6312011
C9×C11⋊AGL(1,𝔽5)13