Finite Group Databasebeta

← C11⋊C5×D49⋊C3 #30633490

Subgroups — C11⋊C5×D49⋊C3 #30633490

Order 16170.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×C49⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11⋊C5×D49C311yesmaximal, characteristic, complemented, Hall
3C11×D49⋊C3C511yesmaximal, characteristic, complemented, Hall
4C49×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5AGL(1,𝔽7)×C11⋊C5—71nomaximal
6C11×C49⋊C3C2×C511yescharacteristic, complemented, Hall
7C5×D49⋊C3—111nomaximal, Hall
8ΓL(1,𝔽8)×C11⋊C5—71no—
9C11×D49C3×C511yescharacteristic, complemented, Hall
10D7×C11⋊C5—71no—
11C5×C49⋊C3—111noHall
12C11×C49C2×C3×C511yescharacteristic, complemented, Hall
13C5×D49—111noHall
14C11×AGL(1,𝔽7)—71no—
15C7×C11⋊C5AGL(1,𝔽7)11yescharacteristic
16C2×C3×C11⋊C5—491noHall
17D49⋊C3C11⋊C511yescharacteristic, direct product factor, Hall
18C5×C49—111noHall
19C11×ΓL(1,𝔽8)—71no—
20C5×AGL(1,𝔽7)—771no—
21C3×C11⋊C5—491noHall
22C11×D7—71no—
23C49⋊C3C2×C11⋊C511yescharacteristic, complemented, Hall
24C2×C11⋊C5—491noHall
25C5×ΓL(1,𝔽8)—771no—
26D49C3×C11⋊C511yescharacteristic, complemented, Hall
27C7×C11C5×AGL(1,𝔽7)11yescharacteristic
28C5×D7—771no—
29C2×C3×C11—491noHall
30C11⋊C5D49⋊C311yescharacteristic, direct product factor, Hall
31C49C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
32AGL(1,𝔽7)—71no—
33C5×C7—111no—
34C3×C11—491noHall
35C2×C3×C5—5391noHall
36C2×C11—491noHall
37ΓL(1,𝔽8)—71no—
38C3×C5—5391noHall
39D7—71no—
40C11C5×D49⋊C311yescharacteristic, complemented, Sylow
41C2×C5—5391noHall
42C7AGL(1,𝔽7)×C11⋊C511yescharacteristic
43C2×C3—491noHall
44C5—111noSylow
45C3—491noSylow
46C2—491noSylow
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7AGL(1,𝔽7)×C11⋊C5
socleC7×C11C5×AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C49⋊C3C2semidirect
2. C11⋊C5×D49C3semidirect
3. C11×D49⋊C3C5semidirect
4. C49×C11⋊C5C2×C3semidirect
6. C11×C49⋊C3C2×C5semidirect
9. C11×D49C3×C5semidirect
12. C11×C49C2×C3×C5semidirect
17. D49⋊C3C11⋊C5direct (N × H)
23. C49⋊C3C2×C11⋊C5semidirect
26. D49C3×C11⋊C5semidirect
30. C11⋊C5D49⋊C3direct (N × H)
31. C49C2×C3×C11⋊C5semidirect
40. C11C5×D49⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×C49⋊C32
C11⋊C5×D493
C11×D49⋊C35
AGL(1,𝔽7)×C11⋊C57
C5×D49⋊C311