Finite Group Databasebeta

← C11×C9⋊#63120 #38787891

Subgroups — C11×C9⋊#63120 #38787891

Order 25740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×D5×C11×C13C211yesmaximal, characteristic
2C11×C3⋊#63120—31nomaximal
3C5×C9×C11×C13C411yescharacteristic, complemented, Hall
4C11×Dic117—51nomaximal, Hall
5C3×D5×C11×C13D311yescharacteristic
6C11×#63120—91noHall
7C2×C9×C11×C13—51no—
8C9⋊#63120C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C11×C13Dic311yescharacteristic
10C11×C9⋊AGL(1,𝔽5)—131nomaximal, Hall
11C11×Dic39—151no—
12D5×C11×C13D911yescharacteristic
13C9×C11×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C9×D5×C13C2×C1111yescharacteristic
15C9×D5×C11D1311yescharacteristic
16C2×C3×C11×C13—51no—
17C3⋊#63120—31no—
18C5×C11×C13Dic911yescharacteristic, complemented, Hall
19C11×ΓL(1,𝔽16)—391no—
20C5×C9×C13C4×C1111yescharacteristic, complemented, Hall
21C11×Dic13—451noHall
22C5×C9×C11Dic1311yescharacteristic, complemented, Hall
23Dic117—51noHall
24C3×C11×C13ΓL(1,𝔽16)11yescharacteristic
25C11×Dic9—651noHall
26C3×D5×C13D3×C1111yescharacteristic
27C3×D5×C11D3911yescharacteristic
28C2×C11×C13—51no—
29#63120—91noHall
30C2×C9×C13—51no—
31C11×AGL(1,𝔽5)—1171noHall
32C2×C9×C11—51no—
33C3×C5×C13C11×Dic311yescharacteristic
34C9⋊AGL(1,𝔽5)—131noHall
35C3×C5×C11Dic3911yescharacteristic
36Dic39—151no—
37C11×C13C9⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C11×Dic3—1951no—
39D5×C13C11×D911yescharacteristic
40C9×C13C11×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
41D5×C11D11711yescharacteristic
42C9×C11#6312011yescharacteristic, complemented, Hall
43C9×D5C11×D1311yescharacteristic
44C2×C3×C13—51no—
45C2×C3×C11—51no—
46C5×C13C11×Dic911yescharacteristic, complemented, Hall
47ΓL(1,𝔽16)—391no—
48C5×C11Dic11711yescharacteristic, complemented, Hall
49Dic13—451noHall
50C5×C9C11×Dic1311yescharacteristic, complemented, Hall
51C4×C11—5851noHall
52C3×C13C11×ΓL(1,𝔽16)11yescharacteristic
53Dic9—651noHall
54C3×C11C3⋊#6312011yescharacteristic
55C3×D5C11×D3911yescharacteristic
56C2×C13—51no—
57C2×C11—51no—
58AGL(1,𝔽5)—1171noHall
59C2×C9—51no—
60C3×C5C11×Dic3911yescharacteristic
61C13C11×C9⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
62Dic3—1951no—
63C11C9⋊#6312011yescharacteristic, direct product factor, Sylow
64D5C11×D11711yescharacteristic
65C9C11×#6312011yescharacteristic, complemented, Sylow
66C2×C3—51no—
67C5C11×Dic11711yescharacteristic, complemented, Sylow
68C4—5851noSylow
69C3C11×C3⋊#6312011yescharacteristic
70C2—51no—
subgroupG/H
center, hypercenterC11C9⋊#63120
commutator, hypocenterC5×C9×C13C4×C11
FrattiniC3C11×C3⋊#63120
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13Dic3
prime radicalC3×D5×C11×C13D3
cosocleC9×D5×C13C2×C11
LCSG ▷ C5×C9×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
3. C5×C9×C11×C13C4semidirect
8. C9⋊#63120C11direct (N × H)
13. C9×C11×C13AGL(1,𝔽5)semidirect
18. C5×C11×C13Dic9semidirect
20. C5×C9×C13C4×C11semidirect
22. C5×C9×C11Dic13semidirect
37. C11×C13C9⋊AGL(1,𝔽5)semidirect
40. C9×C13C11×AGL(1,𝔽5)semidirect
42. C9×C11#63120semidirect
46. C5×C13C11×Dic9semidirect
48. C5×C11Dic117semidirect
50. C5×C9C11×Dic13semidirect
61. C13C11×C9⋊AGL(1,𝔽5)semidirect
63. C11C9⋊#63120direct (N × H)
65. C9C11×#63120semidirect
67. C5C11×Dic117semidirect

Maximal subgroups

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

subgroupindex
C9×D5×C11×C132
C11×C3⋊#631203
C11×Dic1175
C9⋊#6312011
C11×C9⋊AGL(1,𝔽5)13