Finite Group Databasebeta

← C5×C3⋊(C3⋊#63122) #26043779

Subgroups — C5×C3⋊(C3⋊#63122) #26043779

Order 11700.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×D65C211yesmaximal, characteristic
2C5×C3⋊#63122—34nomaximal
3C32×C52×C13C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊#63122)C511yesmaximal, characteristic, direct product factor
5C5×C3⋊(C3⋊#261)—51nomaximal
6C3×C5×D65D314yes—
7C5×#63122—91noHall
8C32×D65C2×C511yescharacteristic
9C32×C5×D13—51no—
10C3×C52×C13Dic314yescomplemented
11C5×C3⋊ΓL(1,𝔽16)—131nomaximal, Hall
12C3⋊#63122—34no—
13C5×C3⋊#261—154no—
14C5×D65C3⋊D311yescharacteristic
15C32×C5×C13—41no—
16C32×C5×C13C4×C511yescharacteristic, complemented
17C32×C5×C13AGL(1,𝔽5)11yescharacteristic, complemented
18C3⋊(C3⋊#261)—51noHall
19C32×C5×D5—131no—
20C3×D65C5×D314yes—
21C3×C5×D13—54no—
22C52×C13C3⋊Dic311yescharacteristic, complemented, Hall
23C5×ΓL(1,𝔽16)—394no—
24#63122—91no—
25C5×#261—451no—
26C32×D13—51no—
27C32×C52#26111yescharacteristic, complemented, Hall
28C3×C5×C13—44no—
29C3×C5×C13C5×Dic314yescomplemented
30C3×C5×C13ΓL(1,𝔽16)14yescomplemented
31C3⋊ΓL(1,𝔽16)—131no—
32C5×C3⋊Dic3—651no—
33C3⋊#261—154no—
34C3×C5×D5—134no—
35D65C5×C3⋊D311yescharacteristic
36C5×D13—51no—
37C32×C13C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C5×AGL(1,𝔽5)—1171noHall
39C2×C32×C5—651no—
40C32×D5—131no—
41C3×D13—54no—
42C3×C52C3⋊#26114yescomplemented
43C5×C13—41no—
44C5×C13C5×C3⋊Dic311yescharacteristic, complemented
45C5×C13C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented
46ΓL(1,𝔽16)—394no—
47C5×Dic3—1954no—
48#261—451noHall
49C5×D5—131no—
50C32×C5—41no—
51C32×C5C5×#26111yescharacteristic, complemented
52C32×C5#6312211yescharacteristic, complemented
53C3×C13C5×ΓL(1,𝔽16)14yescomplemented
54C3⋊Dic3—651noHall
55C2×C3×C5—654no—
56C3×D5—134no—
57D13—51no—
58C52C3⋊(C3⋊#261)11yescharacteristic, complemented, Sylow
59AGL(1,𝔽5)—1171no—
60C4×C5—5851no—
61C2×C32—651no—
62C3×C5—44no—
63C3×C5C5×C3⋊#26114yescomplemented
64C3×C5C3⋊#6312214yescomplemented
65C13C5×C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
66Dic3—1954no—
67C2×C5—651no—
68D5—131no—
69C32C5×#6312211yescharacteristic, complemented, Sylow
70C2×C3—654no—
71C5—41no—
72C5C5×C3⋊(C3⋊#261)11yescharacteristic, complemented
73C5C3⋊(C3⋊#63122)11yescharacteristic, direct product factor
74C4—5851noSylow
75C3C5×C3⋊#6312214yescomplemented
76C2—651no—
subgroupG/H
center, hypercenterC5C3⋊(C3⋊#63122)
commutator, hypocenterC32×C5×C13C4×C5
FrattiniC1G
Fitting, socleC32×C52×C13C4
prime radicalC32×C5×D65C2
cosocleC32×D65C2×C5
LCSG ▷ C32×C5×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
3. C32×C52×C13C4semidirect
4. C3⋊(C3⋊#63122)C5direct (N × H)
10. C3×C52×C13Dic3semidirect
16. C32×C5×C13C4×C5semidirect
17. C32×C5×C13AGL(1,𝔽5)semidirect
22. C52×C13C3⋊Dic3semidirect
27. C32×C52#261semidirect
29. C3×C5×C13C5×Dic3semidirect
30. C3×C5×C13ΓL(1,𝔽16)semidirect
37. C32×C13C5×AGL(1,𝔽5)semidirect
42. C3×C52C3⋊#261semidirect
44. C5×C13C5×C3⋊Dic3semidirect
45. C5×C13C3⋊ΓL(1,𝔽16)semidirect
51. C32×C5C5×#261semidirect
52. C32×C5#63122semidirect
53. C3×C13C5×ΓL(1,𝔽16)semidirect
58. C52C3⋊(C3⋊#261)semidirect
63. C3×C5C5×C3⋊#261semidirect
64. C3×C5C3⋊#63122semidirect
65. C13C5×C3⋊ΓL(1,𝔽16)semidirect
69. C32C5×#63122semidirect
72. C5C5×C3⋊(C3⋊#261)semidirect
73. C5C3⋊(C3⋊#63122)direct (N × H)
75. C3C5×C3⋊#63122semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D652
C5×C3⋊#631223
C3⋊(C3⋊#63122)5
C5×C3⋊(C3⋊#261)5
C5×C3⋊ΓL(1,𝔽16)13