Finite Group Databasebeta

← C4×C13×(C31⋊C3)⋊C5 #37563708

Subgroups — C4×C13×(C31⋊C3)⋊C5 #37563708

Order 24180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×(C31⋊C3)⋊C5C211yesmaximal, characteristic
2C4×C13×ΓL(1,𝔽32)C311yesmaximal, characteristic, complemented, Hall
3C13×(C31⋊C3)⋊C5C411yescharacteristic, direct product factor, Hall
4C4×C13×C31⋊C3C511yesmaximal, characteristic, complemented, Hall
5C2×C13×ΓL(1,𝔽32)C2×C311yescharacteristic
6C2×C13×C31⋊C3C2×C511yescharacteristic
7C13×ΓL(1,𝔽32)C3×C411yescharacteristic, complemented, Hall
8C4×(C31⋊C3)⋊C5C1311yesmaximal, characteristic, direct product factor, Hall
9C4×C13×C31C3×C511yescharacteristic, complemented, Hall
10C13×C31⋊C3C4×C511yescharacteristic, complemented, Hall
11C2×(C31⋊C3)⋊C5C2×C1311yescharacteristic
12C2×C13×C31C2×C3×C511yescharacteristic
13C3×C4×C5×C13—311nomaximal, Hall
14C4×ΓL(1,𝔽32)C3×C1311yescharacteristic, complemented, Hall
15(C31⋊C3)⋊C5C4×C1311yescharacteristic, direct product factor, Hall
16C13×C31C3×C4×C511yescharacteristic, complemented, Hall
17C2×C3×C5×C13—311no—
18C4×C31⋊C3C5×C1311yescharacteristic, complemented, Hall
19C2×ΓL(1,𝔽32)C2×C3×C1311yescharacteristic
20C4×C5×C13—311noHall
21C3×C5×C13—311noHall
22C2×C31⋊C3C2×C5×C1311yescharacteristic
23C3×C4×C13—311noHall
24ΓL(1,𝔽32)C3×C4×C1311yescharacteristic, complemented, Hall
25C2×C5×C13—311no—
26C4×C31C3×C5×C1311yescharacteristic, complemented, Hall
27C31⋊C3C4×C5×C1311yescharacteristic, complemented, Hall
28C2×C3×C13—311no—
29C5×C13—311noHall
30C2×C31C2×C3×C5×C1311yescharacteristic
31C3×C4×C5—311noHall
32C4×C13(C31⋊C3)⋊C511yescharacteristic, direct product factor, Hall
33C3×C13—311noHall
34C31C3×C4×C5×C1311yescharacteristic, complemented, Sylow
35C2×C3×C5—311no—
36C2×C13C2×(C31⋊C3)⋊C511yescharacteristic
37C4×C5—311noHall
38C3×C5—311noHall
39C13C4×(C31⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
40C3×C4—311noHall
41C2×C5—311no—
42C2×C3—311no—
43C5—311noSylow
44C4C13×(C31⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
45C3—311noSylow
46C2C2×C13×(C31⋊C3)⋊C511yescharacteristic
subgroupG/H
center, hypercenterC4×C13(C31⋊C3)⋊C5
commutator, hypocenterC31C3×C4×C5×C13
FrattiniC2C2×C13×(C31⋊C3)⋊C5
FittingC4×C13×C31C3×C5
socleC2×C13×C31C2×C3×C5
prime radicalC2×C13×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C3×C5×C13
LCSG ▷ C31
UCSC1 ◁ C4×C13

Complements

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

NH ≅ G/Ntype
2. C4×C13×ΓL(1,𝔽32)C3semidirect
3. C13×(C31⋊C3)⋊C5C4direct (N × H)
4. C4×C13×C31⋊C3C5semidirect
7. C13×ΓL(1,𝔽32)C3×C4semidirect
8. C4×(C31⋊C3)⋊C5C13direct (N × H)
9. C4×C13×C31C3×C5semidirect
10. C13×C31⋊C3C4×C5semidirect
14. C4×ΓL(1,𝔽32)C3×C13semidirect
15. (C31⋊C3)⋊C5C4×C13direct (N × H)
16. C13×C31C3×C4×C5semidirect
18. C4×C31⋊C3C5×C13semidirect
24. ΓL(1,𝔽32)C3×C4×C13semidirect
26. C4×C31C3×C5×C13semidirect
27. C31⋊C3C4×C5×C13semidirect
32. C4×C13(C31⋊C3)⋊C5direct (N × H)
34. C31C3×C4×C5×C13semidirect
39. C13C4×(C31⋊C3)⋊C5direct (N × H)
44. C4C13×(C31⋊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×C13×(C31⋊C3)⋊C52
C4×C13×ΓL(1,𝔽32)3
C4×C13×C31⋊C35
C4×(C31⋊C3)⋊C513
C3×C4×C5×C1331