Finite Group Databasebeta

← C5×C3⋊((C11⋊C5)⋊D11) #31827656

Subgroups — C5×C3⋊((C11⋊C5)⋊D11) #31827656

Order 18150.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C5×(C11⋊C5)⋊D11—31nomaximal, Hall
3C5×C3⋊(C11⋊D11)C511yesmaximal, characteristic, complemented
4C3⋊((C11⋊C5)⋊D11)C515yesmaximal, direct product factor
5C5×C11×C11⋊C5D311yescharacteristic, complemented, Hall
6C3×C5×C112C2×C511yescharacteristic, complemented
7C3×C11×C11⋊C5C2×C515yescomplemented
8C52×D33—111nomaximal
9C5×C3⋊AGL(1,𝔽11)—111nomaximal
10C5×C11⋊D11—31no—
11(C11⋊C5)⋊D11—35no—
12C3×C52×C11—111no—
13C3×C5×C11⋊C5D1111yescharacteristic, complemented
14C3⋊(C11⋊D11)C5211yescharacteristic, complemented, Hall
15C5×C112C5×D311yescharacteristic, complemented
16C11×C11⋊C5C5×D315yescomplemented
17C52×D11—331no—
18C5×AGL(1,𝔽11)—331no—
19C3×C112C2×C5211yescharacteristic, complemented, Hall
20C5×D33—111no—
21C5×D33—115no—
22C5×D33—552no—
23C5×D33—551no—
24C3⋊AGL(1,𝔽11)—115no—
25C52×C11—111no—
26C5×C11⋊C5D3311yescharacteristic, complemented
27C11⋊D11—31noHall
28C3×C5×C11—52no—
29C3×C5×C11—115no—
30C3×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
31C3×C5×C11C5×D1111yescharacteristic, complemented
32C3×C11⋊C5C5×D1115yescomplemented
33C52×D3—1211noHall
34C112C52×D311yescharacteristic, complemented, Sylow
35C5×D11—331no—
36C5×D11—335no—
37C5×D11—1652no—
38C5×D11—1651no—
39AGL(1,𝔽11)—335no—
40C3×C52—111noHall
41D33—111no—
42D33—552no—
43D33—551no—
44C5×C11—52no—
45C5×C11—115no—
46C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
47C5×C11C5×D3311yescharacteristic, complemented
48C11⋊C5C5×D3315yescomplemented
49C2×C52—3631noHall
50C3×C11—52no—
51C3×C11C5×AGL(1,𝔽11)11yescharacteristic, complemented
52C3×C11C52×D1111yescharacteristic, complemented
53C5×D3—6051no—
54C5×D3—1215no—
55C52—111noSylow
56D11—331no—
57D11—1652no—
58D11—1651no—
59C3×C5—115no—
60C3×C5(C11⋊C5)⋊D1111yescharacteristic, complemented
61C11—52no—
62C11C5×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
63C11C52×D3311yescharacteristic, complemented
64C2×C5—18151no—
65C2×C5—3635no—
66D3—6051noHall
67C5—115no—
68C5C3⋊((C11⋊C5)⋊D11)11yescharacteristic, direct product factor
69C3C5×(C11⋊C5)⋊D1111yescharacteristic, complemented, Sylow
70C2—18151noSylow
subgroupG/H
center, hypercenterC5C3⋊((C11⋊C5)⋊D11)
commutator, cosocle, hypocenterC3×C112C2×C52
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C3×C112
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C11⋊C5C2semidirect
3. C5×C3⋊(C11⋊D11)C5semidirect
4. C3⋊((C11⋊C5)⋊D11)C5direct (N × H)
5. C5×C11×C11⋊C5D3semidirect
6. C3×C5×C112C2×C5semidirect
7. C3×C11×C11⋊C5C2×C5semidirect
13. C3×C5×C11⋊C5D11semidirect
14. C3⋊(C11⋊D11)C52semidirect
15. C5×C112C5×D3semidirect
16. C11×C11⋊C5C5×D3semidirect
19. C3×C112C2×C52semidirect
26. C5×C11⋊C5D33semidirect
30. C3×C5×C11AGL(1,𝔽11)semidirect
31. C3×C5×C11C5×D11semidirect
32. C3×C11⋊C5C5×D11semidirect
34. C112C52×D3semidirect
46. C5×C11C3⋊AGL(1,𝔽11)semidirect
47. C5×C11C5×D33semidirect
48. C11⋊C5C5×D33semidirect
51. C3×C11C5×AGL(1,𝔽11)semidirect
52. C3×C11C52×D11semidirect
60. C3×C5(C11⋊C5)⋊D11semidirect
62. C11C5×C3⋊AGL(1,𝔽11)semidirect
63. C11C52×D33semidirect
68. C5C3⋊((C11⋊C5)⋊D11)direct (N × H)
69. C3C5×(C11⋊C5)⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×C11⋊C52
C5×(C11⋊C5)⋊D113
C5×C3⋊(C11⋊D11)5
C3⋊((C11⋊C5)⋊D11)5
C52×D3311
C5×C3⋊AGL(1,𝔽11)11