Finite Group Databasebeta

← C2×C3⋊((C11⋊C5)⋊D31) #35205802

Subgroups — C2×C3⋊((C11⋊C5)⋊D31) #35205802

Order 20460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊((C11⋊C5)⋊D31)C212yesmaximal, direct product factor
2C2×C3×C31×C11⋊C5C211yesmaximal, characteristic, complemented
3C2×(C11⋊C5)⋊D31—31nomaximal, Hall
4C3×C31×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×D1023C511yesmaximal, characteristic, complemented, Hall
6(C11⋊C5)⋊D31—32no—
7C2×C31×C11⋊C5D311yescharacteristic, complemented
8D1023C2×C512yescomplemented
9C2×C3×C11×C31C2×C511yescharacteristic, complemented
10C2×C5×D93—111nomaximal, Hall
11C31×C11⋊C5C2×D311yescharacteristic, complemented, Hall
12C2×D341—31noHall
13C3×C11×C31C22×C511yescharacteristic, complemented, Hall
14C2×C3×C5×C31—111no—
15C5×D93—112no—
16C2×C11×C31C5×D311yescharacteristic, complemented
17D341—32no—
18C2×C3⋊AGL(1,𝔽11)—311nomaximal, Hall
19C2×C5×D31—331noHall
20C3×C5×C31—111noHall
21C2×D93—111noHall
22C11×C31C2×C5×D311yescharacteristic, complemented, Hall
23C2×C3×C11⋊C5D3111yescharacteristic, complemented
24C3⋊AGL(1,𝔽11)—312no—
25C2×C5×C31—111no—
26C5×D31—332no—
27C2×AGL(1,𝔽11)—931noHall
28C2×C3×C31AGL(1,𝔽11)11yescharacteristic, complemented
29D93—112no—
30C3×C11⋊C5C2×D3111yescharacteristic, complemented, Hall
31C5×C31—111noHall
32C2×D33—311noHall
33C2×D31—331noHall
34C2×C11⋊C5D9311yescharacteristic, complemented
35AGL(1,𝔽11)—932no—
36C3×C31C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
37C2×C3×C11C5×D3111yescharacteristic, complemented
38D33—312no—
39C2×C31C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
40D31—332no—
41C2×C5×D3—3411noHall
42C11⋊C5C2×D9311yescharacteristic, complemented, Hall
43C2×D11—931noHall
44C3×C11C2×C5×D3111yescharacteristic, complemented, Hall
45C31C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
46C2×C3×C5—111no—
47C5×D3—3412no—
48C2×C11C5×D9311yescharacteristic, complemented
49D11—932no—
50C22×C5—10231noHall
51C3×C5—111noHall
52C2×D3—3411noHall
53C11C2×C5×D9311yescharacteristic, complemented, Sylow
54C2×C5—111no—
55C2×C5—10232no—
56C2×C3(C11⋊C5)⋊D3111yescharacteristic, complemented
57D3—3412no—
58C5—111noSylow
59C22—10231noSylow
60C3C2×(C11⋊C5)⋊D3111yescharacteristic, complemented, Sylow
61C2—10232no—
62C2C3⋊((C11⋊C5)⋊D31)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊((C11⋊C5)⋊D31)
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⋊((C11⋊C5)⋊D31)C2direct (N × H)
2. C2×C3×C31×C11⋊C5C2semidirect
4. C3×C31×C11⋊C5C22semidirect
5. C2×D1023C5semidirect
7. C2×C31×C11⋊C5D3semidirect
8. D1023C2×C5semidirect
9. C2×C3×C11×C31C2×C5semidirect
11. C31×C11⋊C5C2×D3semidirect
13. C3×C11×C31C22×C5semidirect
16. C2×C11×C31C5×D3semidirect
22. C11×C31C2×C5×D3semidirect
23. C2×C3×C11⋊C5D31semidirect
28. C2×C3×C31AGL(1,𝔽11)semidirect
30. C3×C11⋊C5C2×D31semidirect
34. C2×C11⋊C5D93semidirect
36. C3×C31C2×AGL(1,𝔽11)semidirect
37. C2×C3×C11C5×D31semidirect
39. C2×C31C3⋊AGL(1,𝔽11)semidirect
42. C11⋊C5C2×D93semidirect
44. C3×C11C2×C5×D31semidirect
45. C31C2×C3⋊AGL(1,𝔽11)semidirect
48. C2×C11C5×D93semidirect
53. C11C2×C5×D93semidirect
56. C2×C3(C11⋊C5)⋊D31semidirect
60. C3C2×(C11⋊C5)⋊D31semidirect
62. C2C3⋊((C11⋊C5)⋊D31)direct (N × H)

Maximal subgroups

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

subgroupindex
C3⋊((C11⋊C5)⋊D31)2
C2×C3×C31×C11⋊C52
C2×(C11⋊C5)⋊D313
C2×D10235
C2×C5×D9311
C2×C3⋊AGL(1,𝔽11)31