Finite Group Databasebeta

← C5×C3⋊(C3⋊#10596817) #39908186

Subgroups — C5×C3⋊(C3⋊#10596817) #39908186

Order 26100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×D29C211yesmaximal, characteristic
2C5×C3⋊#10596817—34nomaximal
3C32×C52×C29C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊#10596817)C511yesmaximal, characteristic, direct product factor
5C5×C3⋊(C3⋊#1181)—51nomaximal
6C3×C52×D29D314yes—
7C5×#10596817—91noHall
8C32×C5×D29—22no—
9C32×C5×D29D511yescharacteristic
10C32×C5×D29C2×C511yescharacteristic
11C3×C52×C29Dic314yescomplemented
12C3⋊#10596817—34no—
13C5×C3⋊#1181—154no—
14C52×D29C3⋊D311yescharacteristic
15C32×C5×C29—22no—
16C32×C5×C29Dic511yescharacteristic, complemented
17C32×C5×C29C4×C511yescharacteristic, complemented
18C3⋊(C3⋊#1181)—51noHall
19C5×C3⋊Dic15—291nomaximal, Hall
20C3×C5×D29—28no—
21C3×C5×D29C5×D314yes—
22C3×C5×D29D1514yes—
23C52×C29C3⋊Dic311yescharacteristic, complemented, Hall
24#10596817—91no—
25C5×#1181—451no—
26C32×D29C5×D511yescharacteristic
27C2×C32×C52—291no—
28C3×C5×C29—28no—
29C3×C5×C29C5×Dic314yescomplemented
30C3×C5×C29Dic1514yescomplemented
31C3⋊#1181—154no—
32C5×Dic15—874no—
33C5×D29—22no—
34C5×D29C5×C3⋊D311yescharacteristic
35C5×D29C3⋊D1511yescharacteristic
36C32×C29C5×Dic511yescharacteristic, complemented, Hall
37C32×C52#118111yescharacteristic, complemented, Hall
38C3⋊Dic15—291no—
39C5×C3⋊Dic3—1451no—
40C3×D29C5×D1514yes—
41C2×C3×C52—294no—
42C5×C29—22no—
43C5×C29C5×C3⋊Dic311yescharacteristic, complemented
44C5×C29C3⋊Dic1511yescharacteristic, complemented
45#1181—451noHall
46C5×Dic5—2611noHall
47C2×C32×C5—291no—
48C2×C32×C5—291no—
49C2×C32×C5—582no—
50C3×C29C5×Dic1514yescomplemented
51C3×C52C3⋊#118114yescomplemented
52Dic15—874no—
53C5×Dic3—4354no—
54D29C5×C3⋊D1511yescharacteristic
55C2×C52—291no—
56C32×C5—22no—
57C32×C5C5×#118111yescharacteristic, complemented
58C32×C5#1059681711yescharacteristic, complemented
59C3⋊Dic3—1451noHall
60C2×C3×C5—294no—
61C2×C3×C5—294no—
62C2×C3×C5—588no—
63C29C5×C3⋊Dic1511yescharacteristic, complemented, Sylow
64C52C3⋊(C3⋊#1181)11yescharacteristic, complemented, Sylow
65C4×C5—13051no—
66Dic5—2611no—
67C2×C32—291no—
68C3×C5—28no—
69C3×C5C5×C3⋊#118114yescomplemented
70C3×C5C3⋊#1059681714yescomplemented
71Dic3—4354no—
72C2×C5—291no—
73C2×C5—291no—
74C2×C5—582no—
75C32C5×#1059681711yescharacteristic, complemented, Sylow
76C2×C3—294no—
77C5—22no—
78C5C5×C3⋊(C3⋊#1181)11yescharacteristic, complemented
79C5C3⋊(C3⋊#10596817)11yescharacteristic, direct product factor
80C4—13051noSylow
81C3C5×C3⋊#1059681714yescomplemented
82C2—291no—
subgroupG/H
center, hypercenterC5C3⋊(C3⋊#10596817)
commutator, hypocenterC32×C5×C29C4×C5
FrattiniC1G
Fitting, socleC32×C52×C29C4
prime radicalC32×C52×D29C2
cosocleC32×C5×D29C2×C5
LCSG ▷ C32×C5×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
3. C32×C52×C29C4semidirect
4. C3⋊(C3⋊#10596817)C5direct (N × H)
11. C3×C52×C29Dic3semidirect
16. C32×C5×C29Dic5semidirect
17. C32×C5×C29C4×C5semidirect
23. C52×C29C3⋊Dic3semidirect
29. C3×C5×C29C5×Dic3semidirect
30. C3×C5×C29Dic15semidirect
36. C32×C29C5×Dic5semidirect
37. C32×C52#1181semidirect
43. C5×C29C5×C3⋊Dic3semidirect
44. C5×C29C3⋊Dic15semidirect
50. C3×C29C5×Dic15semidirect
51. C3×C52C3⋊#1181semidirect
57. C32×C5C5×#1181semidirect
58. C32×C5#10596817semidirect
63. C29C5×C3⋊Dic15semidirect
64. C52C3⋊(C3⋊#1181)semidirect
69. C3×C5C5×C3⋊#1181semidirect
70. C3×C5C3⋊#10596817semidirect
75. C32C5×#10596817semidirect
78. C5C5×C3⋊(C3⋊#1181)semidirect
79. C5C3⋊(C3⋊#10596817)direct (N × H)
81. C3C5×C3⋊#10596817semidirect

Maximal subgroups

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

subgroupindex
C32×C52×D292
C5×C3⋊#105968173
C3⋊(C3⋊#10596817)5
C5×C3⋊(C3⋊#1181)5
C5×C3⋊Dic1529