Finite Group Databasebeta

← (#14523821⋊C3)⋊C5 #44544310

Subgroups — (#14523821⋊C3)⋊C5 #44544310

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1(C13⋊C3)⋊(D41⋊C5)C211yesmaximal, characteristic
2#14523821⋊C5C311yesmaximal, characteristic, complemented, Hall
3C13⋊C3×C41⋊C5C411yescharacteristic, complemented, Hall
4#14523821⋊C3C511yesmaximal, characteristic, complemented, Hall
5C13⋊(D41⋊C5)C2×C311yescharacteristic
6(C13⋊C3)⋊D41C2×C511yescharacteristic
7C13×C41⋊C5C3×C411yescharacteristic, complemented, Hall
8C3×#4223⋊C5—131nomaximal, Hall
9#14523821C3×C511yescharacteristic, complemented, Hall
10C13⋊C3×C41C4×C511yescharacteristic, complemented, Hall
11C3×D41⋊C5—131no—
12D533C2×C3×C511yescharacteristic
13#4223⋊C5—131noHall
14C5×AGL(1,𝔽13)—411nomaximal, Hall
15C3×C41⋊C5—131noHall
16C13×C41C3×C4×C511yescharacteristic, complemented, Hall
17C3×#4223—131noHall
18D41⋊C5—131no—
19C5×D13⋊C3—411no—
20C5×#261—411noHall
21C3×D41—131no—
22C41⋊C5AGL(1,𝔽13)11yescharacteristic, complemented, Hall
23C5×C13⋊C3—411noHall
24#4223—131noHall
25AGL(1,𝔽13)—411noHall
26C5×D13—411no—
27C3×C41—131noHall
28D41—131no—
29D13⋊C3—411no—
30C5×C13—411noHall
31C3×C4×C5—5331noHall
32#261—411noHall
33C41C5×AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
34C13⋊C3#4223⋊C511yescharacteristic, complemented, Hall
35C2×C3×C5—5331no—
36D13—411no—
37C4×C5—5331noHall
38C3×C5—5331noHall
39C13C3×#4223⋊C511yescharacteristic, complemented, Sylow
40C3×C4—5331noHall
41C2×C5—5331no—
42C2×C3—5331no—
43C5—411noSylow
44C4—5331noSylow
45C3—131noSylow
46C2—5331no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C41C3×C4×C5
prime radical(C13⋊C3)⋊(D41⋊C5)C2
cosocleD533C2×C3×C5
LCSG ▷ C13×C41
UCSC1

Complements

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

NH ≅ G/Ntype
2. #14523821⋊C5C3semidirect
3. C13⋊C3×C41⋊C5C4semidirect
4. #14523821⋊C3C5semidirect
7. C13×C41⋊C5C3×C4semidirect
9. #14523821C3×C5semidirect
10. C13⋊C3×C41C4×C5semidirect
16. C13×C41C3×C4×C5semidirect
22. C41⋊C5AGL(1,𝔽13)semidirect
33. C41C5×AGL(1,𝔽13)semidirect
34. C13⋊C3#4223⋊C5semidirect
39. C13C3×#4223⋊C5semidirect

Maximal subgroups

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

subgroupindex
(C13⋊C3)⋊(D41⋊C5)2
#14523821⋊C53
#14523821⋊C35
C3×#4223⋊C513
C5×AGL(1,𝔽13)41