Finite Group Databasebeta

← C3×(C211⋊C3)⋊Dic5 #49183992

Subgroups — C3×(C211⋊C3)⋊Dic5 #49183992

Order 37980.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C211⋊C3C211yesmaximal, characteristic
2(C211⋊C3)⋊Dic5C313yesmaximal, direct product factor
3C3×Dic1055C311yesmaximal, characteristic, complemented
4C3×C5×C211⋊C3C411yescharacteristic, complemented, Hall
5C3×(C211⋊C3)⋊C4—51nomaximal, Hall
6C2×C5×C211⋊C3C2×C313yes—
7C2×C3×C5×C211C2×C311yescharacteristic
8Dic1055C3211yescharacteristic, complemented, Hall
9C2×C3×C211⋊C3D511yescharacteristic
10C3×C5×C211C3×C411yescharacteristic, complemented
11C5×C211⋊C3C3×C413yescomplemented
12C3×Dic211—51no—
13(C211⋊C3)⋊C4—53no—
14C2×C5×C211C2×C3211yescharacteristic
15C3×C211⋊C3Dic511yescharacteristic, complemented, Hall
16C2×C3×C211C3×D511yescharacteristic
17C2×C211⋊C3C3×D513yes—
18C5×C211C32×C411yescharacteristic, complemented, Hall
19Dic211—51noHall
20C3×C211C3×Dic511yescharacteristic, complemented
21C211⋊C3C3×Dic513yescomplemented
22C2×C211C32×D511yescharacteristic
23C211C32×Dic511yescharacteristic, complemented, Sylow
24C32×Dic5—2111nomaximal, Hall
25C2×C32×C5—2111no—
26C3×Dic5—2113no—
27C3×Dic5—2111no—
28C32×C5—2111noHall
29C32×C4—10551noHall
30C2×C3×C5—2113no—
31C2×C3×C5D211⋊C311yescharacteristic
32Dic5—2111noHall
33C2×C32—2111no—
34C3×C5—2113no—
35C3×C5(C211⋊C3)⋊C411yescharacteristic, complemented
36C3×C4—10553no—
37C3×C4—10551no—
38C2×C5C3×D211⋊C311yescharacteristic
39C32—2111noSylow
40C2×C3—2113no—
41C2×C3C5⋊(D211⋊C3)11yescharacteristic
42C5C3×(C211⋊C3)⋊C411yescharacteristic, complemented, Sylow
43C4—10551noSylow
44C3—2113no—
45C3(C211⋊C3)⋊Dic511yescharacteristic, direct product factor
46C2C3×C5⋊(D211⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C5⋊(D211⋊C3)
commutator, hypocenterC5×C211C32×C4
FrattiniC2C3×C5⋊(D211⋊C3)
Fitting, socleC2×C3×C5×C211C2×C3
prime radicalC2×C3×C5×C211⋊C3C2
cosocleC2×C5×C211C2×C32
LCSG ▷ C5×C211
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. (C211⋊C3)⋊Dic5C3direct (N × H)
3. C3×Dic1055C3semidirect
4. C3×C5×C211⋊C3C4semidirect
8. Dic1055C32semidirect
10. C3×C5×C211C3×C4semidirect
11. C5×C211⋊C3C3×C4semidirect
15. C3×C211⋊C3Dic5semidirect
18. C5×C211C32×C4semidirect
20. C3×C211C3×Dic5semidirect
21. C211⋊C3C3×Dic5semidirect
23. C211C32×Dic5semidirect
35. C3×C5(C211⋊C3)⋊C4semidirect
42. C5C3×(C211⋊C3)⋊C4semidirect
45. C3(C211⋊C3)⋊Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C211⋊C32
(C211⋊C3)⋊Dic53
C3×Dic10553
C3×(C211⋊C3)⋊C45
C32×Dic5211