Finite Group Databasebeta

← C2×C3⋊#16811771 #35205804

Subgroups — C2×C3⋊#16811771 #35205804

Order 20460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊#16811771C212yesmaximal, direct product factor
2C2×C3×#13133721C211yesmaximal, characteristic, complemented
3C2×#16811771—31nomaximal, Hall
4C3×#13133721C2211yescharacteristic, complemented, Hall
5C2×C11×D93C511yesmaximal, characteristic, complemented, Hall
6#16811771—32no—
7C2×#13133721D311yescharacteristic, complemented
8C11×D93C2×C512yescomplemented
9C2×C3×C11×C31C2×C511yescharacteristic, complemented
10C2×C3⋊(D31⋊C5)—111nomaximal, Hall
11#13133721C2×D311yescharacteristic, complemented, Hall
12C2×C11×D31—31noHall
13C3×C11×C31C22×C511yescharacteristic, complemented, Hall
14C2×C3×ΓL(1,𝔽32)—111no—
15C3⋊(D31⋊C5)—112no—
16C2×C11×C31C5×D311yescharacteristic, complemented
17C11×D31—32no—
18C2×D3×C11⋊C5—311nomaximal, Hall
19C2×D31⋊C5—331noHall
20C3×ΓL(1,𝔽32)—111noHall
21C2×D93C11⋊C511yescharacteristic, complemented, Hall
22C11×C31C2×C5×D311yescharacteristic, complemented, Hall
23C2×C3×C11⋊C5—311no—
24D3×C11⋊C5—312no—
25C2×ΓL(1,𝔽32)—111no—
26D31⋊C5—332no—
27C22×C11⋊C5—931noHall
28C2×C3×C31C2×C11⋊C511yescharacteristic, complemented
29D93C2×C11⋊C512yescomplemented
30C3×C11⋊C5—311noHall
31ΓL(1,𝔽32)—111noHall
32C2×D3×C11—1551noHall
33C2×D31—31noHall
34C2×C11⋊C5—311no—
35C2×C11⋊C5—932no—
36C3×C31C22×C11⋊C511yescharacteristic, complemented, Hall
37C2×C3×C11D31⋊C511yescharacteristic, complemented
38D3×C11—1552no—
39C2×C31D3×C11⋊C511yescharacteristic, complemented
40D31—32no—
41C2×C5×D3—3411noHall
42C11⋊C5—311noHall
43C22×C11—4651noHall
44C3×C11C2×D31⋊C511yescharacteristic, complemented, Hall
45C31C2×D3×C11⋊C511yescharacteristic, complemented, Sylow
46C2×C3×C5—3411no—
47C5×D3—3412no—
48C2×C11—4652no—
49C2×C11C3⋊(D31⋊C5)11yescharacteristic, complemented
50C22×C5—10231noHall
51C3×C5—3411noHall
52C2×D3—1551noHall
53C11C2×C3⋊(D31⋊C5)11yescharacteristic, complemented, Sylow
54C2×C5—3411no—
55C2×C5—10232no—
56C2×C3#1681177111yescharacteristic, complemented
57D3—1552no—
58C5—3411noSylow
59C22—4651noSylow
60C3C2×#1681177111yescharacteristic, complemented, Sylow
61C2—4652no—
62C2C3⋊#1681177111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#16811771
commutator, cosocle, hypocenterC3×C11×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊#16811771C2direct (N × H)
2. C2×C3×#13133721C2semidirect
4. C3×#13133721C22semidirect
5. C2×C11×D93C5semidirect
7. C2×#13133721D3semidirect
8. C11×D93C2×C5semidirect
9. C2×C3×C11×C31C2×C5semidirect
11. #13133721C2×D3semidirect
13. C3×C11×C31C22×C5semidirect
16. C2×C11×C31C5×D3semidirect
21. C2×D93C11⋊C5semidirect
22. C11×C31C2×C5×D3semidirect
28. C2×C3×C31C2×C11⋊C5semidirect
29. D93C2×C11⋊C5semidirect
36. C3×C31C22×C11⋊C5semidirect
37. C2×C3×C11D31⋊C5semidirect
39. C2×C31D3×C11⋊C5semidirect
44. C3×C11C2×D31⋊C5semidirect
45. C31C2×D3×C11⋊C5semidirect
49. C2×C11C3⋊(D31⋊C5)semidirect
53. C11C2×C3⋊(D31⋊C5)semidirect
56. C2×C3#16811771semidirect
60. C3C2×#16811771semidirect
62. C2C3⋊#16811771direct (N × H)

Maximal subgroups

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

subgroupindex
C3⋊#168117712
C2×C3×#131337212
C2×#168117713
C2×C11×D935
C2×C3⋊(D31⋊C5)11
C2×D3×C11⋊C531