Finite Group Databasebeta

← C2×C3×#11925898 #20300055

Subgroups — C2×C3×#11925898 #20300055

Order 7260.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#10597244C211yesmaximal, characteristic, complemented
2C3×#11925898C212yesmaximal, direct product factor
3C2×#11925898C311yesmaximal, characteristic, direct product factor, Hall
4C3×#10597244C2211yescharacteristic, complemented, Hall
5C2×C3×C11×D11C511yesmaximal, characteristic, complemented, Hall
6C2×#10597244C2×C311yescharacteristic, complemented
7#11925898C2×C312yesdirect product factor
8C2×C3×C112C2×C511yescharacteristic, complemented
9C3×C11×D11C2×C512yescomplemented
10C22×C3×C11⋊C5—111nomaximal
11C2×C3×AGL(1,𝔽11)—111nomaximal
12#10597244C22×C311yescharacteristic, complemented, Hall
13C2×C11×D11C3×C511yescharacteristic, complemented, Hall
14C3×C112C22×C511yescharacteristic, complemented, Hall
15C2×C3×C11⋊C5—112no—
16C2×C3×C11⋊C5—111no—
17C2×C3×C11⋊C5—111no—
18C3×AGL(1,𝔽11)—112no—
19C2×C112C2×C3×C511yescharacteristic, complemented
20C11×D11C2×C3×C512yescomplemented
21C22×C11⋊C5—111no—
22C2×AGL(1,𝔽11)—111no—
23C3×C11⋊C5—111no—
24C3×C11⋊C5—111no—
25C22×C3×C11—111no—
26C2×C3×D11C11⋊C511yescharacteristic, complemented
27C112C22×C3×C511yescharacteristic, complemented, Sylow
28C2×C11⋊C5—112no—
29C2×C11⋊C5—111no—
30C2×C11⋊C5—111no—
31AGL(1,𝔽11)—112no—
32C2×C3×C11—101no—
33C2×C3×C11—112no—
34C2×C3×C11AGL(1,𝔽11)11yescharacteristic, complemented
35C2×C3×C11C2×C11⋊C511yescharacteristic, complemented
36C3×D11C2×C11⋊C512yescomplemented
37C22×C3×C5—1211noHall
38C11⋊C5—111no—
39C11⋊C5—111no—
40C22×C11—111no—
41C2×D11C3×C11⋊C511yescharacteristic, complemented
42C3×C11—101no—
43C3×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
44C3×C11C22×C11⋊C511yescharacteristic, complemented
45C2×C3×C5—1212no—
46C2×C3×C5—1211no—
47C2×C11—101no—
48C2×C11—112no—
49C2×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
50C2×C11C2×C3×C11⋊C511yescharacteristic, complemented
51D11C2×C3×C11⋊C512yescomplemented
52C22×C5—1211noHall
53C3×C5—1211noHall
54C22×C3—111noHall
55C11—101no—
56C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
57C11C22×C3×C11⋊C511yescharacteristic, complemented
58C2×C5—1212no—
59C2×C5—1211no—
60C2×C3—112no—
61C2×C3#1192589811yescharacteristic, direct product factor
62C5—1211noSylow
63C22—111noSylow
64C3C2×#1192589811yescharacteristic, direct product factor, Sylow
65C2—112no—
66C2C3×#1192589811yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3#11925898
commutator, hypocenterC112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#10597244C2semidirect
2. C3×#11925898C2direct (N × H)
3. C2×#11925898C3direct (N × H)
4. C3×#10597244C22semidirect
5. C2×C3×C11×D11C5semidirect
6. C2×#10597244C2×C3semidirect
7. #11925898C2×C3direct (N × H)
8. C2×C3×C112C2×C5semidirect
9. C3×C11×D11C2×C5semidirect
12. #10597244C22×C3semidirect
13. C2×C11×D11C3×C5semidirect
14. C3×C112C22×C5semidirect
19. C2×C112C2×C3×C5semidirect
20. C11×D11C2×C3×C5semidirect
26. C2×C3×D11C11⋊C5semidirect
27. C112C22×C3×C5semidirect
34. C2×C3×C11AGL(1,𝔽11)semidirect
35. C2×C3×C11C2×C11⋊C5semidirect
36. C3×D11C2×C11⋊C5semidirect
41. C2×D11C3×C11⋊C5semidirect
43. C3×C11C2×AGL(1,𝔽11)semidirect
44. C3×C11C22×C11⋊C5semidirect
49. C2×C11C3×AGL(1,𝔽11)semidirect
50. C2×C11C2×C3×C11⋊C5semidirect
51. D11C2×C3×C11⋊C5semidirect
56. C11C2×C3×AGL(1,𝔽11)semidirect
57. C11C22×C3×C11⋊C5semidirect
61. C2×C3#11925898direct (N × H)
64. C3C2×#11925898direct (N × H)
66. C2C3×#11925898direct (N × H)