Finite Group Databasebeta

← C3×C4×(C181⋊C3)⋊C5 #45656409

Subgroups — C3×C4×(C181⋊C3)⋊C5 #45656409

Order 32580.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C181⋊C3)⋊C5C211yesmaximal, characteristic
2C4×(C181⋊C3)⋊C5C313yesmaximal, direct product factor
3C3×C4×C181⋊C5C311yesmaximal, characteristic, complemented
4C3×(C181⋊C3)⋊C5C411yescharacteristic, direct product factor, Hall
5C3×C4×C181⋊C3C511yesmaximal, characteristic, complemented, Hall
6C2×(C181⋊C3)⋊C5C2×C313yes—
7C2×C3×C181⋊C5C2×C311yescharacteristic
8C4×C181⋊C5C3211yescharacteristic, complemented, Hall
9C2×C3×C181⋊C3C2×C511yescharacteristic
10C3×C181⋊C5C3×C411yescharacteristic, complemented
11(C181⋊C3)⋊C5C3×C413yesdirect product factor
12C4×C181⋊C3C3×C513yescomplemented
13C3×C4×C181C3×C511yescharacteristic, complemented
14C2×C181⋊C5C2×C3211yescharacteristic
15C3×C181⋊C3C4×C511yescharacteristic, complemented, Hall
16C2×C3×C181C2×C3×C511yescharacteristic
17C2×C181⋊C3C2×C3×C513yes—
18C181⋊C5C32×C411yescharacteristic, complemented, Hall
19C4×C181C32×C511yescharacteristic, complemented, Hall
20C3×C181C3×C4×C511yescharacteristic, complemented
21C181⋊C3C3×C4×C513yescomplemented
22C2×C181C2×C32×C511yescharacteristic
23C181C32×C4×C511yescharacteristic, complemented, Sylow
24C32×C4×C5—1811nomaximal, Hall
25C2×C32×C5—1811no—
26C3×C4×C5—1813no—
27C3×C4×C5—1811no—
28C32×C5—1811noHall
29C32×C4—1811noHall
30C2×C3×C5—1813no—
31C2×C3×C5—1811no—
32C4×C5—1811noHall
33C2×C32—1811no—
34C3×C5—1813no—
35C3×C5—1811no—
36C3×C4—1813no—
37C3×C4(C181⋊C3)⋊C511yescharacteristic, direct product factor
38C2×C5—1811no—
39C32—1811noSylow
40C2×C3—1813no—
41C2×C3C2×(C181⋊C3)⋊C511yescharacteristic
42C5—1811noSylow
43C4C3×(C181⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
44C3—1813no—
45C3C4×(C181⋊C3)⋊C511yescharacteristic, direct product factor
46C2C2×C3×(C181⋊C3)⋊C511yescharacteristic
subgroupG/H
center, hypercenterC3×C4(C181⋊C3)⋊C5
commutator, hypocenterC181C32×C4×C5
FrattiniC2C2×C3×(C181⋊C3)⋊C5
FittingC3×C4×C181C3×C5
socleC2×C3×C181C2×C3×C5
prime radicalC2×C3×(C181⋊C3)⋊C5C2
cosocleC2×C181C2×C32×C5
LCSG ▷ C181
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C4×(C181⋊C3)⋊C5C3direct (N × H)
3. C3×C4×C181⋊C5C3semidirect
4. C3×(C181⋊C3)⋊C5C4direct (N × H)
5. C3×C4×C181⋊C3C5semidirect
8. C4×C181⋊C5C32semidirect
10. C3×C181⋊C5C3×C4semidirect
11. (C181⋊C3)⋊C5C3×C4direct (N × H)
12. C4×C181⋊C3C3×C5semidirect
13. C3×C4×C181C3×C5semidirect
15. C3×C181⋊C3C4×C5semidirect
18. C181⋊C5C32×C4semidirect
19. C4×C181C32×C5semidirect
20. C3×C181C3×C4×C5semidirect
21. C181⋊C3C3×C4×C5semidirect
23. C181C32×C4×C5semidirect
37. C3×C4(C181⋊C3)⋊C5direct (N × H)
43. C4C3×(C181⋊C3)⋊C5direct (N × H)
45. C3C4×(C181⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C181⋊C3)⋊C52
C4×(C181⋊C3)⋊C53
C3×C4×C181⋊C53
C3×C4×C181⋊C35
C32×C4×C5181