Finite Group Databasebeta

← C3×(C11⋊C5)⋊(D19⋊C3) #34037849

Subgroups — C3×(C11⋊C5)⋊(D19⋊C3) #34037849

Order 18810.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C19⋊C3C211yesmaximal, characteristic, complemented, Hall
2(C11⋊C5)⋊(D19⋊C3)C313yesmaximal, direct product factor
3C3×C19⋊AGL(1,𝔽11)C311yesmaximal, characteristic, complemented
4C3×C11⋊(D19⋊C3)C511yesmaximal, characteristic, complemented, Hall
5C11⋊C5×C19⋊C3C2×C313yescomplemented
6C3×C19×C11⋊C5C2×C311yescharacteristic, complemented
7C19⋊AGL(1,𝔽11)C3211yescharacteristic, complemented, Hall
8C3×C11×C19⋊C3C2×C511yescharacteristic, complemented, Hall
9C3×C5×D19⋊C3—111nomaximal, Hall
10C3×D209C3×C511yescharacteristic, complemented
11C11⋊(D19⋊C3)C3×C513yescomplemented
12C19×C11⋊C5C2×C3211yescharacteristic, complemented, Hall
13C32×AGL(1,𝔽11)—191nomaximal, Hall
14C3×C5×C19⋊C3—111noHall
15C3×C11×C19C2×C3×C511yescharacteristic, complemented
16C11×C19⋊C3C2×C3×C513yescomplemented
17C3×C5×D19—111no—
18C5×D19⋊C3—113no—
19C32×C11⋊C5—191noHall
20D209C32×C511yescharacteristic, complemented, Hall
21C3×D19⋊C3—111noHall
22C3×AGL(1,𝔽11)—193no—
23C3×AGL(1,𝔽11)—571no—
24C3×C5×C19—111no—
25C5×C19⋊C3—113no—
26C11×C19C2×C32×C511yescharacteristic, complemented, Hall
27C32×D11—191noHall
28C5×D19—111noHall
29C3×C19⋊C3AGL(1,𝔽11)11yescharacteristic, complemented, Hall
30C3×C11⋊C5—193no—
31C3×C11⋊C5D19⋊C311yescharacteristic, complemented
32C3×D19—111no—
33D19⋊C3—113no—
34AGL(1,𝔽11)—571noHall
35C32×C11—191noHall
36C5×C19—111noHall
37C2×C32×C5—2091noHall
38C3×D11—191no—
39C3×D11—193no—
40C3×C19C3×AGL(1,𝔽11)11yescharacteristic, complemented
41C19⋊C3C3×AGL(1,𝔽11)13yescomplemented
42C11⋊C5C3×D19⋊C311yescharacteristic, complemented, Hall
43C32×C5—2091noHall
44D19—111noHall
45C3×C11—193no—
46C3×C11C5×D19⋊C311yescharacteristic, complemented
47C2×C3×C5—6271no—
48C2×C3×C5—2093no—
49D11—191noHall
50C19C32×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
51C2×C32—2091noHall
52C3×C5—111no—
53C3×C5—2093no—
54C11C3×C5×D19⋊C311yescharacteristic, complemented, Sylow
55C2×C5—6271noHall
56C32—191noSylow
57C2×C3—6271no—
58C2×C3—2093no—
59C5—111noSylow
60C3—193no—
61C3(C11⋊C5)⋊(D19⋊C3)11yescharacteristic, direct product factor
62C2—6271noSylow
subgroupG/H
center, hypercenterC3(C11⋊C5)⋊(D19⋊C3)
commutator, cosocle, hypocenterC11×C19C2×C32×C5
FrattiniC1G
Fitting, socleC3×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C19⋊C3C2semidirect
2. (C11⋊C5)⋊(D19⋊C3)C3direct (N × H)
3. C3×C19⋊AGL(1,𝔽11)C3semidirect
4. C3×C11⋊(D19⋊C3)C5semidirect
5. C11⋊C5×C19⋊C3C2×C3semidirect
6. C3×C19×C11⋊C5C2×C3semidirect
7. C19⋊AGL(1,𝔽11)C32semidirect
8. C3×C11×C19⋊C3C2×C5semidirect
10. C3×D209C3×C5semidirect
11. C11⋊(D19⋊C3)C3×C5semidirect
12. C19×C11⋊C5C2×C32semidirect
15. C3×C11×C19C2×C3×C5semidirect
16. C11×C19⋊C3C2×C3×C5semidirect
20. D209C32×C5semidirect
26. C11×C19C2×C32×C5semidirect
29. C3×C19⋊C3AGL(1,𝔽11)semidirect
31. C3×C11⋊C5D19⋊C3semidirect
40. C3×C19C3×AGL(1,𝔽11)semidirect
41. C19⋊C3C3×AGL(1,𝔽11)semidirect
42. C11⋊C5C3×D19⋊C3semidirect
46. C3×C11C5×D19⋊C3semidirect
50. C19C32×AGL(1,𝔽11)semidirect
54. C11C3×C5×D19⋊C3semidirect
61. C3(C11⋊C5)⋊(D19⋊C3)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×C19⋊C32
(C11⋊C5)⋊(D19⋊C3)3
C3×C19⋊AGL(1,𝔽11)3
C3×C11⋊(D19⋊C3)5
C3×C5×D19⋊C311
C32×AGL(1,𝔽11)19