Finite Group Databasebeta

← C5×C11⋊(D49⋊C3) #30633484

Subgroups — C5×C11⋊(D49⋊C3) #30633484

Order 16170.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C49⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5×D539C311yesmaximal, characteristic, complemented, Hall
3C11⋊(D49⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
4C5×C11×C49C2×C311yescharacteristic, complemented, Hall
5C5×C11⋊AGL(1,𝔽7)—71nomaximal
6C11×C49⋊C3C2×C511yescharacteristic, complemented, Hall
7C5×D49⋊C3—111nomaximal, Hall
8C5×C11×ΓL(1,𝔽8)—71no—
9D539C3×C511yescharacteristic, complemented, Hall
10C5×D77—71no—
11C5×C49⋊C3D1111yescharacteristic, complemented, Hall
12C11×C49C2×C3×C511yescharacteristic, complemented, Hall
13C5×D49—111noHall
14C11⋊AGL(1,𝔽7)—71no—
15C5×C7×C11AGL(1,𝔽7)11yescharacteristic
16C3×C5×D11—491noHall
17D49⋊C3—111noHall
18C5×C49C3×D1111yescharacteristic, complemented, Hall
19C11×ΓL(1,𝔽8)—71no—
20C5×AGL(1,𝔽7)—771no—
21C3×C5×C11—491noHall
22D77—71no—
23C49⋊C3C5×D1111yescharacteristic, complemented, Hall
24C5×D11—491noHall
25C5×ΓL(1,𝔽8)—71no—
26D49—111noHall
27C7×C11C5×AGL(1,𝔽7)11yescharacteristic
28C5×D7—771no—
29C3×D11—491noHall
30C5×C11D49⋊C311yescharacteristic, complemented, Hall
31C49C3×C5×D1111yescharacteristic, complemented, Sylow
32AGL(1,𝔽7)—771no—
33C5×C7C11⋊AGL(1,𝔽7)11yescharacteristic
34C3×C11—491noHall
35C2×C3×C5—5391noHall
36D11—491noHall
37ΓL(1,𝔽8)—71no—
38C3×C5—491noHall
39D7—771no—
40C11C5×D49⋊C311yescharacteristic, complemented, Sylow
41C2×C5—5391noHall
42C7C5×C11⋊AGL(1,𝔽7)11yescharacteristic
43C2×C3—5391noHall
44C5C11⋊(D49⋊C3)11yescharacteristic, direct product factor, Sylow
45C3—491noSylow
46C2—5391noSylow
subgroupG/H
center, hypercenterC5C11⋊(D49⋊C3)
commutator, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7C5×C11⋊AGL(1,𝔽7)
FittingC5×C11×C49C2×C3
socleC5×C7×C11AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C11×C49⋊C3C2semidirect
2. C5×D539C3semidirect
3. C11⋊(D49⋊C3)C5direct (N × H)
4. C5×C11×C49C2×C3semidirect
6. C11×C49⋊C3C2×C5semidirect
9. D539C3×C5semidirect
11. C5×C49⋊C3D11semidirect
12. C11×C49C2×C3×C5semidirect
18. C5×C49C3×D11semidirect
23. C49⋊C3C5×D11semidirect
30. C5×C11D49⋊C3semidirect
31. C49C3×C5×D11semidirect
40. C11C5×D49⋊C3semidirect
44. C5C11⋊(D49⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×C49⋊C32
C5×D5393
C11⋊(D49⋊C3)5
C5×C11⋊AGL(1,𝔽7)7
C5×D49⋊C311