Finite Group Databasebeta

← C13×C9⋊#63121 #44477753

Subgroups — C13×C9⋊#63121 #44477753

Order 30420.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×C13×D65C211yesmaximal, characteristic
2C13×C3⋊#63121—31nomaximal
3C5×C9×C132C411yescharacteristic, complemented, Hall
4C13×C9⋊#261—51nomaximal, Hall
5C3×C13×D65D311yescharacteristic
6C13×#63121—91noHall
7C9×C13×D13—51no—
8C3×C5×C132Dic311yescharacteristic
9C9⋊#63121C1311yesmaximal, characteristic, direct product factor
10C13×C9⋊AGL(1,𝔽5)—131nomaximal
11C13×C3⋊#261—151no—
12C13×D65D911yescharacteristic
13C9×C132AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C9×D65C2×C1311yescharacteristic
15C9×D5×C13—131no—
16C3×C13×D13—51no—
17C5×C132Dic911yescharacteristic, complemented, Hall
18C3⋊#63121—31no—
19C13×ΓL(1,𝔽16)—391no—
20C13×#261—451noHall
21C5×C9×C13—43no—
22C5×C9×C13C4×C1311yescharacteristic, complemented
23C5×C9×C13#26111yescharacteristic, complemented
24C3×C132ΓL(1,𝔽16)11yescharacteristic
25C9⋊#261—51no—
26C13×Dic9—651no—
27C3×D65D3×C1311yescharacteristic
28C3×D5×C13—131no—
29C13×D13—51no—
30#63121—91no—
31C13×AGL(1,𝔽5)—1171no—
32C2×C9×C13—651no—
33C9×D13—51no—
34C3×C5×C13—43no—
35C3×C5×C13Dic3×C1311yescharacteristic
36C3×C5×C13C3⋊#26111yescharacteristic
37C9⋊AGL(1,𝔽5)—131noHall
38C132C9⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
39C3⋊#261—151no—
40Dic3×C13—1951no—
41D65C13×D911yescharacteristic
42D5×C13—131no—
43C9×C13—43no—
44C9×C13C13×AGL(1,𝔽5)11yescharacteristic, complemented
45C9×C13#6312111yescharacteristic, complemented
46C9×D5—131no—
47C2×C3×C13—651no—
48C3×D13—51no—
49C5×C13—43no—
50C5×C13C13×Dic911yescharacteristic, complemented
51C5×C13C9⋊#26111yescharacteristic, complemented
52ΓL(1,𝔽16)—391no—
53#261—451no—
54C4×C13—5851no—
55C5×C9C13×#26111yescharacteristic, complemented, Hall
56C3×C13—43no—
57C3×C13C13×ΓL(1,𝔽16)11yescharacteristic
58C3×C13C3⋊#6312111yescharacteristic
59Dic9—651noHall
60C3×D5—131no—
61C2×C13—651no—
62D13—51no—
63AGL(1,𝔽5)—1171noHall
64C2×C9—651no—
65C3×C5C13×C3⋊#26111yescharacteristic
66C13—43no—
67C13C13×C9⋊AGL(1,𝔽5)11yescharacteristic, complemented
68C13C9⋊#6312111yescharacteristic, direct product factor
69Dic3—1951no—
70D5—131no—
71C9C13×#6312111yescharacteristic, complemented, Sylow
72C2×C3—651no—
73C5C13×C9⋊#26111yescharacteristic, complemented, Sylow
74C4—5851noSylow
75C3C13×C3⋊#6312111yescharacteristic
76C2—651no—
subgroupG/H
center, hypercenterC13C9⋊#63121
commutator, hypocenterC5×C9×C13C4×C13
FrattiniC3C13×C3⋊#63121
FittingC5×C9×C132C4
socleC3×C5×C132Dic3
prime radicalC3×C13×D65D3
cosocleC9×D65C2×C13
LCSG ▷ C5×C9×C13
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
3. C5×C9×C132C4semidirect
9. C9⋊#63121C13direct (N × H)
13. C9×C132AGL(1,𝔽5)semidirect
17. C5×C132Dic9semidirect
22. C5×C9×C13C4×C13semidirect
23. C5×C9×C13#261semidirect
38. C132C9⋊AGL(1,𝔽5)semidirect
44. C9×C13C13×AGL(1,𝔽5)semidirect
45. C9×C13#63121semidirect
50. C5×C13C13×Dic9semidirect
51. C5×C13C9⋊#261semidirect
55. C5×C9C13×#261semidirect
67. C13C13×C9⋊AGL(1,𝔽5)semidirect
68. C13C9⋊#63121direct (N × H)
71. C9C13×#63121semidirect
73. C5C13×C9⋊#261semidirect

Maximal subgroups

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

subgroupindex
C9×C13×D652
C13×C3⋊#631213
C13×C9⋊#2615
C9⋊#6312113
C13×C9⋊AGL(1,𝔽5)13