Finite Group Databasebeta

← C2×C3×#13133721⋊C3 #44501774

Subgroups — C2×C3×#13133721⋊C3 #44501774

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#13133721⋊C3C211yesmaximal, characteristic, direct product factor, Hall
2C2×#13133721⋊C3C313yesmaximal, direct product factor
3C2×C3×#13133721C311yesmaximal, characteristic, complemented
4C2×C3×C11×C31⋊C3C511yesmaximal, characteristic, complemented, Hall
5#13133721⋊C3C2×C313yesdirect product factor
6C3×#13133721C2×C311yescharacteristic, complemented
7C2×#13133721C3211yescharacteristic, complemented, Hall
8C3×C11×C31⋊C3C2×C511yescharacteristic, complemented, Hall
9C2×C3×(C31⋊C3)⋊C5—111nomaximal, Hall
10C2×C11×C31⋊C3C3×C513yescomplemented
11C2×C3×C11×C31C3×C511yescharacteristic, complemented
12#13133721C2×C3211yescharacteristic, complemented, Hall
13C3×(C31⋊C3)⋊C5—111noHall
14C3×C11×C31C2×C3×C511yescharacteristic, complemented
15C11×C31⋊C3C2×C3×C513yescomplemented
16C2×C32×C11⋊C5—311nomaximal, Hall
17C2×C3×ΓL(1,𝔽32)—111no—
18C2×(C31⋊C3)⋊C5—113no—
19C2×C11×C31C32×C511yescharacteristic, complemented, Hall
20C2×C3×C31⋊C3C11⋊C511yescharacteristic, complemented, Hall
21C32×C11⋊C5—311noHall
22C3×ΓL(1,𝔽32)—111no—
23(C31⋊C3)⋊C5—113no—
24C11×C31C2×C32×C511yescharacteristic, complemented, Hall
25C2×C3×C11⋊C5—313no—
26C2×C3×C11⋊C5—311no—
27C2×ΓL(1,𝔽32)—111noHall
28C3×C31⋊C3C2×C11⋊C511yescharacteristic, complemented, Hall
29C2×C32×C11—311noHall
30C2×C3×C31C3×C11⋊C511yescharacteristic, complemented
31C2×C31⋊C3C3×C11⋊C513yescomplemented
32C3×C11⋊C5—313no—
33C3×C11⋊C5—311no—
34ΓL(1,𝔽32)—111noHall
35C2×C11⋊C5—311noHall
36C32×C11—311noHall
37C3×C31C2×C3×C11⋊C511yescharacteristic, complemented
38C31⋊C3C2×C3×C11⋊C513yescomplemented
39C2×C32×C5—3411noHall
40C2×C3×C11—313no—
41C2×C3×C11(C31⋊C3)⋊C511yescharacteristic, complemented
42C2×C31C32×C11⋊C511yescharacteristic, complemented, Hall
43C11⋊C5—311noHall
44C32×C5—3411noHall
45C3×C11—313no—
46C3×C11C2×(C31⋊C3)⋊C511yescharacteristic, complemented
47C31C2×C32×C11⋊C511yescharacteristic, complemented, Sylow
48C2×C3×C5—3413no—
49C2×C3×C5—3411no—
50C2×C11C3×(C31⋊C3)⋊C511yescharacteristic, complemented, Hall
51C2×C32—311noHall
52C3×C5—3413no—
53C3×C5—3411no—
54C11C2×C3×(C31⋊C3)⋊C511yescharacteristic, complemented, Sylow
55C2×C5—3411noHall
56C32—311noSylow
57C2×C3—313no—
58C2×C3#13133721⋊C311yescharacteristic, direct product factor
59C5—3411noSylow
60C3—313no—
61C3C2×#13133721⋊C311yescharacteristic, direct product factor
62C2C3×#13133721⋊C311yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3#13133721⋊C3
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C31C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#13133721⋊C3C2direct (N × H)
2. C2×#13133721⋊C3C3direct (N × H)
3. C2×C3×#13133721C3semidirect
4. C2×C3×C11×C31⋊C3C5semidirect
5. #13133721⋊C3C2×C3direct (N × H)
6. C3×#13133721C2×C3semidirect
7. C2×#13133721C32semidirect
8. C3×C11×C31⋊C3C2×C5semidirect
10. C2×C11×C31⋊C3C3×C5semidirect
11. C2×C3×C11×C31C3×C5semidirect
12. #13133721C2×C32semidirect
14. C3×C11×C31C2×C3×C5semidirect
15. C11×C31⋊C3C2×C3×C5semidirect
19. C2×C11×C31C32×C5semidirect
20. C2×C3×C31⋊C3C11⋊C5semidirect
24. C11×C31C2×C32×C5semidirect
28. C3×C31⋊C3C2×C11⋊C5semidirect
30. C2×C3×C31C3×C11⋊C5semidirect
31. C2×C31⋊C3C3×C11⋊C5semidirect
37. C3×C31C2×C3×C11⋊C5semidirect
38. C31⋊C3C2×C3×C11⋊C5semidirect
41. C2×C3×C11(C31⋊C3)⋊C5semidirect
42. C2×C31C32×C11⋊C5semidirect
46. C3×C11C2×(C31⋊C3)⋊C5semidirect
47. C31C2×C32×C11⋊C5semidirect
50. C2×C11C3×(C31⋊C3)⋊C5semidirect
54. C11C2×C3×(C31⋊C3)⋊C5semidirect
58. C2×C3#13133721⋊C3direct (N × H)
61. C3C2×#13133721⋊C3direct (N × H)
62. C2C3×#13133721⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#13133721⋊C32
C2×#13133721⋊C33
C2×C3×#131337213
C2×C3×C11×C31⋊C35
C2×C3×(C31⋊C3)⋊C511
C2×C32×C11⋊C531