Finite Group Databasebeta

← C3×C3⋊#16810010 #44478259

Subgroups — C3×C3⋊#16810010 #44478259

Order 30420.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C13⋊D13C211yesmaximal, characteristic
2C3⋊#16810010C311yesmaximal, characteristic, direct product factor
3C3×#16810010—31nomaximal
4C32×C5×C132C411yescharacteristic, complemented, Hall
5C3×C3⋊#10621728—51nomaximal, Hall
6C3×C5×C13⋊D13—21no—
7C3×C5×C13⋊D13D311yescharacteristic
8C3×C5×C13⋊D13C2×C311yescharacteristic
9#16810010—31noHall
10C32×C13⋊D13D511yescharacteristic
11C3×C5×C132—21no—
12C3×C5×C132Dic311yescharacteristic, complemented
13C3×C5×C132C3×C411yescharacteristic, complemented
14C3×C3⋊#63118—1314nomaximal
15C3⋊#10621728—51no—
16C3×#10621728—151no—
17C5×C13⋊D13C3×D311yescharacteristic
18C32×C132Dic511yescharacteristic, complemented, Hall
19C32×C5×D13—1314no—
20C3×C13⋊D13—21no—
21C3×C13⋊D13C3×D511yescharacteristic
22C3×C13⋊D13D1511yescharacteristic
23C5×C132C3×Dic311yescharacteristic, complemented, Hall
24C3⋊#63118—1314no—
25C3×#63118—3914no—
26#10621728—151noHall
27C32×C5×C13#261114yescomplemented
28C3×C132—21no—
29C3×C132C3×Dic511yescharacteristic, complemented
30C3×C132Dic1511yescharacteristic, complemented
31C3×C3⋊#261—6514no—
32C3×C5×D13—1314no—
33C3×C5×D13—1314no—
34C3×C5×D13—2614no—
35C13⋊D13C3×D1511yescharacteristic
36#63118—3914no—
37C32×D13—1314no—
38C3×C5×C13—214no—
39C3×C5×C13C3×#261114yescomplemented
40C3×C5×C13C3⋊#261114yescomplemented
41C3×Dic15—1691noHall
42C132C3×Dic1511yescharacteristic, complemented, Sylow
43C3⋊#261—6514no—
44C3×#261—19514no—
45C5×D13—1314no—
46C32×C13#63118114yescomplemented
47C2×C32×C5—1691no—
48C3×D13—1314no—
49C3×D13—1314no—
50C3×D13—2614no—
51C5×C13C3×C3⋊#261114yescomplemented
52Dic15—1691no—
53C3×Dic5—5071no—
54#261—19514no—
55C32×C5#1062172811yescharacteristic, complemented, Hall
56C3×C13—214no—
57C3×C13C3×#63118114yescomplemented
58C3×C13C3⋊#63118114yescomplemented
59C3×Dic3—8451noHall
60C2×C3×C5—3381no—
61C2×C3×C5—1691no—
62C2×C3×C5—1691no—
63D13—1314no—
64Dic5—5071noHall
65C2×C32—1691no—
66C3×C5—21no—
67C3×C5C3×#1062172811yescharacteristic, complemented
68C3×C5C3⋊#1062172811yescharacteristic, complemented
69C13C3×C3⋊#63118114yescomplemented
70C3×C4—25351no—
71Dic3—8451no—
72C2×C5—1691no—
73C32#1681001011yescharacteristic, complemented, Sylow
74C2×C3—3381no—
75C2×C3—1691no—
76C2×C3—1691no—
77C5C3×C3⋊#1062172811yescharacteristic, complemented, Sylow
78C4—25351noSylow
79C3—21no—
80C3C3×#1681001011yescharacteristic, complemented
81C3C3⋊#1681001011yescharacteristic, direct product factor
82C2—1691no—
subgroupG/H
center, hypercenterC3C3⋊#16810010
commutator, hypocenterC3×C5×C132C3×C4
FrattiniC1G
Fitting, socleC32×C5×C132C4
prime radicalC32×C5×C13⋊D13C2
cosocleC3×C5×C13⋊D13C2×C3
LCSG ▷ C3×C5×C132
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊#16810010C3direct (N × H)
4. C32×C5×C132C4semidirect
12. C3×C5×C132Dic3semidirect
13. C3×C5×C132C3×C4semidirect
18. C32×C132Dic5semidirect
23. C5×C132C3×Dic3semidirect
27. C32×C5×C13#261semidirect
29. C3×C132C3×Dic5semidirect
30. C3×C132Dic15semidirect
39. C3×C5×C13C3×#261semidirect
40. C3×C5×C13C3⋊#261semidirect
42. C132C3×Dic15semidirect
46. C32×C13#63118semidirect
51. C5×C13C3×C3⋊#261semidirect
55. C32×C5#10621728semidirect
57. C3×C13C3×#63118semidirect
58. C3×C13C3⋊#63118semidirect
67. C3×C5C3×#10621728semidirect
68. C3×C5C3⋊#10621728semidirect
69. C13C3×C3⋊#63118semidirect
73. C32#16810010semidirect
77. C5C3×C3⋊#10621728semidirect
80. C3C3×#16810010semidirect
81. C3C3⋊#16810010direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C13⋊D132
C3⋊#168100103
C3×#168100103
C3×C3⋊#106217285
C3×C3⋊#6311813