Finite Group Databasebeta

← C3⋊(C3⋊(C31⋊#1043)) #42124970

Subgroups — C3⋊(C3⋊(C31⋊#1043)) #42124970

Order 27900.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C31×C5⋊D5C211yesmaximal, characteristic
2C3⋊(C31⋊#1043)—34nomaximal
3C32×C52×C31C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))—56nomaximal
5C3×C31×C5⋊D5D314yes—
6C31⋊#1043—91noHall
7C32×D5×C31—56no—
8C3×C52×C31Dic314yescomplemented
9C3⋊(C31⋊AGL(1,𝔽5))—1524no—
10C31×C5⋊D5C3⋊D311yescharacteristic
11C32×C5×C31AGL(1,𝔽5)16yescomplemented
12C3⋊Dic93—251noHall
13C3×D5×C31—524no—
14C3⋊(C3⋊#1043)—311nomaximal, Hall
15C52×C31C3⋊Dic311yescharacteristic, complemented, Hall
16C31⋊AGL(1,𝔽5)—456no—
17C2×C32×C31—251no—
18C3×C5×C31ΓL(1,𝔽16)124yescomplemented
19C32×C5⋊D5D3111yescharacteristic
20Dic93—754no—
21D5×C31—56no—
22C3⋊#1043—934no—
23C32×C31#104311yescharacteristic, complemented, Hall
24C32×C52Dic3111yescharacteristic, complemented, Hall
25C2×C3×C31—254no—
26C3⋊ΓL(1,𝔽16)—1556no—
27C5×C31C3⋊ΓL(1,𝔽16)16yescomplemented
28C3×C5⋊D5D9314yes—
29Dic31—2251noHall
30#1043—2791noHall
31C3×C31C3⋊#104314yescomplemented
32C32×D5—56no—
33C3×C52Dic9314yescomplemented
34C2×C31—251no—
35ΓL(1,𝔽16)—46524no—
36C5⋊D5C3⋊D9311yescharacteristic
37C32×C5C31⋊AGL(1,𝔽5)16yescomplemented
38C3⋊Dic3—7751noHall
39C31C3⋊(C3⋊#1043)11yescharacteristic, complemented, Sylow
40C3×D5—524no—
41C52C3⋊Dic9311yescharacteristic, complemented, Sylow
42AGL(1,𝔽5)—13956no—
43C2×C32—251no—
44C3×C5C3⋊(C31⋊AGL(1,𝔽5))124yescomplemented
45Dic3—23254no—
46D5—56no—
47C32C31⋊#104311yescharacteristic, complemented, Sylow
48C2×C3—254no—
49C5C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))16yescomplemented
50C4—69751noSylow
51C3C3⋊(C31⋊#1043)14yescomplemented
52C2—251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C52×C31C4
prime radical, cosocleC32×C31×C5⋊D5C2
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C52×C31C4semidirect
8. C3×C52×C31Dic3semidirect
11. C32×C5×C31AGL(1,𝔽5)semidirect
15. C52×C31C3⋊Dic3semidirect
18. C3×C5×C31ΓL(1,𝔽16)semidirect
23. C32×C31#1043semidirect
24. C32×C52Dic31semidirect
27. C5×C31C3⋊ΓL(1,𝔽16)semidirect
31. C3×C31C3⋊#1043semidirect
33. C3×C52Dic93semidirect
37. C32×C5C31⋊AGL(1,𝔽5)semidirect
39. C31C3⋊(C3⋊#1043)semidirect
41. C52C3⋊Dic93semidirect
44. C3×C5C3⋊(C31⋊AGL(1,𝔽5))semidirect
47. C32C31⋊#1043semidirect
49. C5C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))semidirect
51. C3C3⋊(C31⋊#1043)semidirect

Maximal subgroups

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

subgroupindex
C32×C31×C5⋊D52
C3⋊(C31⋊#1043)3
C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))5
C3⋊(C3⋊#1043)31