Finite Group Databasebeta

← D3×#11925890 #20300025

Subgroups — D3×#11925890 #20300025

Order 7260.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊#11925890C211yesmaximal, characteristic, complemented
2D3×#10597245C211yesmaximal, characteristic, complemented
3C3×#11925890C211yesmaximal, characteristic, complemented
4C2×#11925890—31nomaximal, Hall
5C3×#10597245C2211yescharacteristic, complemented, Hall
6D3×C11×D11—51nomaximal, Hall
7C2×#10597245—31no—
8#11925890—31no—
9#11925890D311yescharacteristic, direct product factor
10C11×D33—51no—
11D3×C112D511yescharacteristic, complemented
12C3×C11×D11—51no—
13#10597245C2×D311yescharacteristic, complemented, Hall
14C2×C11×D11—151noHall
15C3×C112C2×D511yescharacteristic, complemented, Hall
16D3×C11⋊C5—221no—
17C2×C112—31no—
18C11×D11—51no—
19C11×D11—151no—
20C3×C11⋊C5—221no—
21C2×D3×C11—551no—
22D3×D11—51no—
23C112D3×D511yescharacteristic, complemented, Sylow
24C2×C11⋊C5—661no—
25C2×C3×C11—551no—
26D33—51no—
27C3×D11—51no—
28D3×C11—21no—
29D3×C11—51no—
30D3×C11—51no—
31D3×C11—551no—
32D3×D5—1211nomaximal, Hall
33C11⋊C5—221no—
34C22×C11—1651no—
35C2×D11—151no—
36C3×C11—21no—
37C3×C11—51no—
38C3×C11—51no—
39D15—1211no—
40C3×D5—1211no—
41C5×D3—1211no—
42C2×C11—61no—
43C2×C11—151no—
44C2×C11—151no—
45C2×C11—551no—
46C2×C11—1651no—
47D11—51no—
48D11—151no—
49C2×D5—3631noHall
50C3×C5—1211noHall
51C2×D3—551noHall
52C11—21no—
53C11—51no—
54C11—51no—
55C2×C5—3631no—
56D5—3631no—
57D5—1211no—
58C2×C3—551no—
59D3—551no—
60D3#1192589011yescharacteristic, direct product factor
61C5—1211noSylow
62C22—1651noSylow
63C3C2×#1192589011yescharacteristic, complemented, Sylow
64C2—31no—
65C2—551no—
66C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterC3×#10597245C22
Fitting, socleC3×C112C2×D5
LCSG ▷ C3×#10597245
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊#11925890C2semidirect
2. D3×#10597245C2semidirect
3. C3×#11925890C2semidirect
5. C3×#10597245C22semidirect
9. #11925890D3direct (N × H)
11. D3×C112D5semidirect
13. #10597245C2×D3semidirect
15. C3×C112C2×D5semidirect
23. C112D3×D5semidirect
60. D3#11925890direct (N × H)
63. C3C2×#11925890semidirect