Finite Group Databasebeta

← C5×(C13⋊C3)⋊D49 #34062036

Subgroups — C5×(C13⋊C3)⋊D49 #34062036

Order 19110.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C13⋊C3×C49C211yesmaximal, characteristic, complemented, Hall
2C5×D637C311yesmaximal, characteristic, complemented, Hall
3(C13⋊C3)⋊D49C511yesmaximal, characteristic, direct product factor, Hall
4C5×C13×C49C2×C311yescharacteristic, complemented, Hall
5C5×(C13⋊C3)⋊D7—71nomaximal
6C13⋊C3×C49C2×C511yescharacteristic, complemented, Hall
7C3×C5×D49—131nomaximal, Hall
8C5×C7×C13⋊C3D711yescharacteristic
9D637C3×C511yescharacteristic, complemented, Hall
10C5×D91—71no—
11C3×C5×C49—131noHall
12C13×C49C2×C3×C511yescharacteristic, complemented, Hall
13(C13⋊C3)⋊D7—71no—
14C5×D49—131noHall
15C5×C7×C13C3×D711yescharacteristic
16C5×D13⋊C3—491noHall
17C3×D49—131noHall
18C7×C13⋊C3C5×D711yescharacteristic
19C5×C49D13⋊C311yescharacteristic, complemented, Hall
20C3×C5×D7—911no—
21C5×C13⋊C3D4911yescharacteristic, complemented, Hall
22D91—71no—
23C3×C49—131noHall
24C5×D13—491noHall
25C3×C5×C7—131no—
26D49—131noHall
27C7×C13C3×C5×D711yescharacteristic
28D13⋊C3—491noHall
29C5×D7—911no—
30C5×C13C3×D4911yescharacteristic, complemented, Hall
31C49C5×D13⋊C311yescharacteristic, complemented, Sylow
32C3×D7—911no—
33C13⋊C3C5×D4911yescharacteristic, complemented, Hall
34C5×C7(C13⋊C3)⋊D711yescharacteristic
35C2×C3×C5—6371noHall
36D13—491noHall
37C3×C7—131no—
38C3×C5—131noHall
39D7—911no—
40C13C3×C5×D4911yescharacteristic, complemented, Sylow
41C2×C5—6371noHall
42C7C5×(C13⋊C3)⋊D711yescharacteristic
43C2×C3—6371noHall
44C5(C13⋊C3)⋊D4911yescharacteristic, direct product factor, Sylow
45C3—131noSylow
46C2—6371noSylow
subgroupG/H
center, hypercenterC5(C13⋊C3)⋊D49
commutator, cosocle, hypocenterC13×C49C2×C3×C5
FrattiniC7C5×(C13⋊C3)⋊D7
FittingC5×C13×C49C2×C3
socleC5×C7×C13C3×D7
LCSG ▷ C13×C49
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C13⋊C3×C49C2semidirect
2. C5×D637C3semidirect
3. (C13⋊C3)⋊D49C5direct (N × H)
4. C5×C13×C49C2×C3semidirect
6. C13⋊C3×C49C2×C5semidirect
9. D637C3×C5semidirect
12. C13×C49C2×C3×C5semidirect
19. C5×C49D13⋊C3semidirect
21. C5×C13⋊C3D49semidirect
30. C5×C13C3×D49semidirect
31. C49C5×D13⋊C3semidirect
33. C13⋊C3C5×D49semidirect
40. C13C3×C5×D49semidirect
44. C5(C13⋊C3)⋊D49direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C13⋊C3×C492
C5×D6373
(C13⋊C3)⋊D495
C5×(C13⋊C3)⋊D77
C3×C5×D4913