Finite Group Databasebeta

← C3⋊(C3⋊(C31⋊#1042)) #42124956

Subgroups — C3⋊(C3⋊(C31⋊#1042)) #42124956

Order 27900.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×D5×C31C211yesmaximal, characteristic
2C3⋊(C31⋊#1042)—34nomaximal
3C32×C52×C31C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))—51nomaximal
5C3⋊Dic465—51nomaximal
6C3×C5×D5×C31D314yes—
7C31⋊#1042—91noHall
8C32×D5×C31D511yescharacteristic
9C2×C32×C5×C31—51no—
10C3×C52×C31Dic314yescomplemented
11C3⋊(C31⋊AGL(1,𝔽5))—154no—
12Dic465—154no—
13C5×D5×C31C3⋊D311yescharacteristic
14C32×C5×C31—41no—
15C32×C5×C31Dic511yescharacteristic, complemented
16C32×C5×C31AGL(1,𝔽5)11yescharacteristic, complemented
17C3⋊Dic93—251noHall
18C2×C3×C5×C31—54no—
19C3×D5×C31D1514yes—
20C3⋊(C3⋊#1042)—311nomaximal, Hall
21C52×C31C3⋊Dic311yescharacteristic, complemented, Hall
22C31⋊AGL(1,𝔽5)—451no—
23Dic155—451no—
24C2×C32×C31—51no—
25C3×C5×C31—44no—
26C3×C5×C31Dic1514yescomplemented
27C3×C5×C31ΓL(1,𝔽16)14yescomplemented
28C32×C5×D5D3111yescharacteristic
29Dic93—754no—
30C2×C5×C31—51no—
31D5×C31C3⋊D1511yescharacteristic
32C3⋊#1042—934no—
33C32×C31#104211yescharacteristic, complemented, Hall
34C32×C52Dic3111yescharacteristic, complemented, Hall
35C2×C3×C31—54no—
36C3⋊ΓL(1,𝔽16)—1551no—
37C3⋊Dic15—1551no—
38C5×C31—41no—
39C5×C31C3⋊Dic1511yescharacteristic, complemented
40C5×C31C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented
41C3×C5×D5D9314yes—
42Dic31—2251noHall
43#1042—2791noHall
44C3×C31C3⋊#104214yescomplemented
45C2×C32×C5—51no—
46C32×D5D15511yescharacteristic
47C3×C52Dic9314yescomplemented
48C2×C31—51no—
49ΓL(1,𝔽16)—4654no—
50Dic15—4654no—
51C5×D5C3⋊D9311yescharacteristic
52C32×C5—41no—
53C32×C5Dic15511yescharacteristic, complemented
54C32×C5C31⋊AGL(1,𝔽5)11yescharacteristic, complemented
55C3⋊Dic3—7751noHall
56C31C3⋊(C3⋊#1042)11yescharacteristic, complemented, Sylow
57C2×C3×C5—54no—
58C3×D5D46514yes—
59C52C3⋊Dic9311yescharacteristic, complemented, Sylow
60AGL(1,𝔽5)—13951no—
61Dic5—13951no—
62C2×C32—51no—
63C3×C5—44no—
64C3×C5Dic46514yescomplemented
65C3×C5C3⋊(C31⋊AGL(1,𝔽5))14yescomplemented
66Dic3—23254no—
67C2×C5—51no—
68D5C3⋊D46511yescharacteristic
69C32C31⋊#104211yescharacteristic, complemented, Sylow
70C2×C3—54no—
71C5—41no—
72C5C3⋊Dic46511yescharacteristic, complemented
73C5C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))11yescharacteristic, complemented
74C4—69751noSylow
75C3C3⋊(C31⋊#1042)14yescomplemented
76C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C52×C31C4
prime radical, cosocleC32×C5×D5×C31C2
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C52×C31C4semidirect
10. C3×C52×C31Dic3semidirect
15. C32×C5×C31Dic5semidirect
16. C32×C5×C31AGL(1,𝔽5)semidirect
21. C52×C31C3⋊Dic3semidirect
26. C3×C5×C31Dic15semidirect
27. C3×C5×C31ΓL(1,𝔽16)semidirect
33. C32×C31#1042semidirect
34. C32×C52Dic31semidirect
39. C5×C31C3⋊Dic15semidirect
40. C5×C31C3⋊ΓL(1,𝔽16)semidirect
44. C3×C31C3⋊#1042semidirect
47. C3×C52Dic93semidirect
53. C32×C5Dic155semidirect
54. C32×C5C31⋊AGL(1,𝔽5)semidirect
56. C31C3⋊(C3⋊#1042)semidirect
59. C52C3⋊Dic93semidirect
64. C3×C5Dic465semidirect
65. C3×C5C3⋊(C31⋊AGL(1,𝔽5))semidirect
69. C32C31⋊#1042semidirect
72. C5C3⋊Dic465semidirect
73. C5C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))semidirect
75. C3C3⋊(C31⋊#1042)semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C312
C3⋊(C31⋊#1042)3
C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))5
C3⋊Dic4655
C3⋊(C3⋊#1042)31