Finite Group Databasebeta

← C9⋊#16810005 #44477758

Subgroups — C9⋊#16810005 #44477758

Order 30420.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×C13×D65C211yesmaximal, characteristic
2C3⋊#16810005—31nomaximal
3C5×C9×C132C411yescharacteristic, complemented, Hall
4C9⋊#10621730—51nomaximal, Hall
5C3×C13×D65D311yescharacteristic
6#16810005—91noHall
7C9×C13×D13—51no—
8C3×C5×C132Dic311yescharacteristic
9C9⋊#63120—131nomaximal
10C9⋊#63122—131nomaximal
11C3⋊#10621730—151no—
12C13×D65D911yescharacteristic
13C9×C132AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C9×D65D1311yescharacteristic
15C9×D5×C13—131no—
16C3×C13×D13—51no—
17C5×C132Dic911yescharacteristic, complemented, Hall
18C3⋊#63120—391no—
19C3⋊#63122—391no—
20#10621730—451noHall
21C5×C9×C13—43no—
22C5×C9×C13Dic1311yescharacteristic, complemented
23C5×C9×C13#26111yescharacteristic, complemented
24C3×C132ΓL(1,𝔽16)11yescharacteristic
25C9⋊#261—651no—
26Dic117—651no—
27C3×D65D3911yescharacteristic
28C3×D5×C13—131no—
29C13×D13—51no—
30#63122—1171no—
31#63120—1171no—
32C2×C9×C13—651no—
33C9×D13—51no—
34C3×C5×C13—43no—
35C3×C5×C13Dic3911yescharacteristic
36C3×C5×C13C3⋊#26111yescharacteristic
37C9⋊AGL(1,𝔽5)—1691noHall
38C132C9⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
39C3⋊#261—1951no—
40Dic39—1951no—
41D65D11711yescharacteristic
42D5×C13—131no—
43C9×C13—43no—
44C9×C13#6312011yescharacteristic, complemented
45C9×C13#6312211yescharacteristic, complemented
46C9×D5—131no—
47C2×C3×C13—651no—
48C3×D13—51no—
49C5×C13—43no—
50C5×C13Dic11711yescharacteristic, complemented
51C5×C13C9⋊#26111yescharacteristic, complemented
52ΓL(1,𝔽16)—5071no—
53#261—5851no—
54Dic13—5851no—
55C5×C9#1062173011yescharacteristic, complemented, Hall
56C3×C13—43no—
57C3×C13C3⋊#6312211yescharacteristic
58C3×C13C3⋊#6312011yescharacteristic
59Dic9—8451noHall
60C3×D5—131no—
61C2×C13—651no—
62D13—51no—
63AGL(1,𝔽5)—15211noHall
64C2×C9—651no—
65C3×C5C3⋊#1062173011yescharacteristic
66C13—43no—
67C13C9⋊#6312211yescharacteristic, complemented
68C13C9⋊#6312011yescharacteristic, complemented
69Dic3—25351no—
70D5—131no—
71C9#1681000511yescharacteristic, complemented, Sylow
72C2×C3—651no—
73C5C9⋊#1062173011yescharacteristic, complemented, Sylow
74C4—76051noSylow
75C3C3⋊#1681000511yescharacteristic
76C2—651no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC5×C9×C132C4
FrattiniC3C3⋊#16810005
socleC3×C5×C132Dic3
prime radicalC3×C13×D65D3
cosocleC9×C13×D65C2
LCSG ▷ C5×C9×C132
UCSC1

Complements

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

NH ≅ G/Ntype
3. C5×C9×C132C4semidirect
13. C9×C132AGL(1,𝔽5)semidirect
17. C5×C132Dic9semidirect
22. C5×C9×C13Dic13semidirect
23. C5×C9×C13#261semidirect
38. C132C9⋊AGL(1,𝔽5)semidirect
44. C9×C13#63120semidirect
45. C9×C13#63122semidirect
50. C5×C13Dic117semidirect
51. C5×C13C9⋊#261semidirect
55. C5×C9#10621730semidirect
67. C13C9⋊#63122semidirect
68. C13C9⋊#63120semidirect
71. C9#16810005semidirect
73. C5C9⋊#10621730semidirect

Maximal subgroups

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

subgroupindex
C9×C13×D652
C3⋊#168100053
C9⋊#106217305
C9⋊#6312013
C9⋊#6312213