Finite Group Databasebeta

← C5×C3⋊#11925895 #31827652

Subgroups — C5×C3⋊#11925895 #31827652

Order 18150.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#10597243C211yesmaximal, characteristic, complemented, Hall
2C5×#11925895—31nomaximal, Hall
3C5×C11×D33C511yesmaximal, characteristic, complemented
4C3⋊#11925895C515yesmaximal, direct product factor
5C5×#10597243D311yescharacteristic, complemented, Hall
6C3×C5×C112C2×C511yescharacteristic, complemented
7C3×#10597243C2×C515yescomplemented
8C5×C3⋊AGL(1,𝔽11)—111nomaximal
9C5×D3×C11⋊C5—111nomaximal
10C5×C11×D11—31no—
11#11925895—35no—
12C3×C5×C11⋊C5—111no—
13C3×C5×C11⋊C5—111no—
14C3×C5×C11⋊C5—225no—
15C11×D33C5211yescharacteristic, complemented, Hall
16C5×C112C5×D311yescharacteristic, complemented
17#10597243C5×D315yescomplemented
18C2×C5×C11⋊C5—331no—
19C5×AGL(1,𝔽11)—331no—
20C3×C112C2×C5211yescharacteristic, complemented, Hall
21C5×D33C11⋊C511yescharacteristic, complemented
22C5×D3×C11—551no—
23C3⋊AGL(1,𝔽11)—115no—
24D3×C11⋊C5—115no—
25C5×C11⋊C5—111no—
26C5×C11⋊C5—111no—
27C5×C11⋊C5—225no—
28C11×D11—31noHall
29C3×C5×C11—25no—
30C3×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
31C3×C5×C11C2×C11⋊C511yescharacteristic, complemented
32C3×C11⋊C5—115no—
33C3×C11⋊C5—115no—
34C3×C11⋊C5—2225no—
35C52×D3—1211noHall
36C112C52×D311yescharacteristic, complemented, Sylow
37C2×C5×C11—1651no—
38C5×D11—31no—
39C2×C11⋊C5—335no—
40AGL(1,𝔽11)—335no—
41C3×C52—1211noHall
42D33C5×C11⋊C511yescharacteristic, complemented
43D3×C11—551no—
44C5×C11—25no—
45C5×C11D3×C11⋊C511yescharacteristic, complemented
46C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
47C11⋊C5—115no—
48C11⋊C5—115no—
49C11⋊C5—2225no—
50C2×C52—3631noHall
51C3×C11—25no—
52C3×C11C5×AGL(1,𝔽11)11yescharacteristic, complemented
53C3×C11C2×C5×C11⋊C511yescharacteristic, complemented
54C5×D3—551no—
55C5×D3—1215no—
56C52—1211noSylow
57C2×C11—1651no—
58D11—31no—
59C3×C5—1215no—
60C3×C5#1192589511yescharacteristic, complemented
61C11—25no—
62C11C5×D3×C11⋊C511yescharacteristic, complemented
63C11C5×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
64C2×C5—3635no—
65C2×C5—1651no—
66D3—551noHall
67C5—1215no—
68C5C3⋊#1192589511yescharacteristic, direct product factor
69C3C5×#1192589511yescharacteristic, complemented, Sylow
70C2—1651noSylow
subgroupG/H
center, hypercenterC5C3⋊#11925895
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×#10597243C2semidirect
3. C5×C11×D33C5semidirect
4. C3⋊#11925895C5direct (N × H)
5. C5×#10597243D3semidirect
6. C3×C5×C112C2×C5semidirect
7. C3×#10597243C2×C5semidirect
15. C11×D33C52semidirect
16. C5×C112C5×D3semidirect
17. #10597243C5×D3semidirect
20. C3×C112C2×C52semidirect
21. C5×D33C11⋊C5semidirect
30. C3×C5×C11AGL(1,𝔽11)semidirect
31. C3×C5×C11C2×C11⋊C5semidirect
36. C112C52×D3semidirect
42. D33C5×C11⋊C5semidirect
45. C5×C11D3×C11⋊C5semidirect
46. C5×C11C3⋊AGL(1,𝔽11)semidirect
52. C3×C11C5×AGL(1,𝔽11)semidirect
53. C3×C11C2×C5×C11⋊C5semidirect
60. C3×C5#11925895semidirect
62. C11C5×D3×C11⋊C5semidirect
63. C11C5×C3⋊AGL(1,𝔽11)semidirect
68. C5C3⋊#11925895direct (N × H)
69. C3C5×#11925895semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#105972432
C5×#119258953
C5×C11×D335
C3⋊#119258955
C5×C3⋊AGL(1,𝔽11)11
C5×D3×C11⋊C511