Finite Group Databasebeta

← C13×(C19⋊C3)⋊Dic5 #28414751

Subgroups — C13×(C19⋊C3)⋊Dic5 #28414751

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C13×C19⋊C3C211yesmaximal, characteristic
2C13×Dic95C311yesmaximal, characteristic, complemented, Hall
3C5×C13×C19⋊C3C411yescharacteristic, complemented, Hall
4C13×(C19⋊C3)⋊C4—51nomaximal, Hall
5C2×C5×C13×C19C2×C311yescharacteristic
6C2×C13×C19⋊C3D511yescharacteristic
7C5×C13×C19C3×C411yescharacteristic, complemented, Hall
8(C19⋊C3)⋊Dic5C1311yesmaximal, characteristic, direct product factor, Hall
9C13×Dic19—51noHall
10C3×C13×Dic5—191nomaximal, Hall
11C13×C19⋊C3Dic511yescharacteristic, complemented, Hall
12C2×C5×C19⋊C3C2×C1311yescharacteristic
13C2×C13×C19C3×D511yescharacteristic
14C2×C3×C5×C13—191no—
15Dic95C3×C1311yescharacteristic, complemented, Hall
16C5×C19⋊C3C4×C1311yescharacteristic, complemented, Hall
17C13×Dic5—191noHall
18C13×C19C3×Dic511yescharacteristic, complemented, Hall
19(C19⋊C3)⋊C4—51noHall
20C3×C5×C13—191noHall
21C2×C5×C19C2×C3×C1311yescharacteristic
22C3×C4×C13—951noHall
23C2×C5×C13D19⋊C311yescharacteristic
24C2×C19⋊C3D5×C1311yescharacteristic
25C5×C19C3×C4×C1311yescharacteristic, complemented, Hall
26C2×C3×C13—191no—
27Dic19—51noHall
28C5×C13(C19⋊C3)⋊C411yescharacteristic, complemented, Hall
29C3×Dic5—191noHall
30C19⋊C3C13×Dic511yescharacteristic, complemented, Hall
31C4×C13—951noHall
32C3×C13—191noHall
33C2×C19C3×D5×C1311yescharacteristic
34C2×C3×C5—191no—
35C2×C13C5⋊(D19⋊C3)11yescharacteristic
36Dic5—191noHall
37C19C3×C13×Dic511yescharacteristic, complemented, Sylow
38C3×C5—191noHall
39C13(C19⋊C3)⋊Dic511yescharacteristic, direct product factor, Sylow
40C3×C4—951noHall
41C2×C5C13×D19⋊C311yescharacteristic
42C2×C3—191no—
43C5C13×(C19⋊C3)⋊C411yescharacteristic, complemented, Sylow
44C4—951noSylow
45C3—191noSylow
46C2C13×C5⋊(D19⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C13C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C3×C4×C13
FrattiniC2C13×C5⋊(D19⋊C3)
Fitting, socleC2×C5×C13×C19C2×C3
prime radicalC2×C5×C13×C19⋊C3C2
cosocleC2×C5×C19C2×C3×C13
LCSG ▷ C5×C19
UCSC1 ◁ C2×C13

Complements

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

NH ≅ G/Ntype
2. C13×Dic95C3semidirect
3. C5×C13×C19⋊C3C4semidirect
7. C5×C13×C19C3×C4semidirect
8. (C19⋊C3)⋊Dic5C13direct (N × H)
11. C13×C19⋊C3Dic5semidirect
15. Dic95C3×C13semidirect
16. C5×C19⋊C3C4×C13semidirect
18. C13×C19C3×Dic5semidirect
25. C5×C19C3×C4×C13semidirect
28. C5×C13(C19⋊C3)⋊C4semidirect
30. C19⋊C3C13×Dic5semidirect
37. C19C3×C13×Dic5semidirect
39. C13(C19⋊C3)⋊Dic5direct (N × H)
43. C5C13×(C19⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C13×C19⋊C32
C13×Dic953
C13×(C19⋊C3)⋊C45
(C19⋊C3)⋊Dic513
C3×C13×Dic519