Finite Group Databasebeta

← C3×C4×C13⋊(C52⋊C3) #26043521

Subgroups — C3×C4×C13⋊(C52⋊C3) #26043521

Order 11700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13⋊(C52⋊C3)C211yesmaximal, characteristic
2C4×C13⋊(C52⋊C3)C313yesmaximal, direct product factor
3C3×C4×C52×C13C311yesmaximal, characteristic, complemented
4C3×C13⋊(C52⋊C3)C411yescharacteristic, direct product factor, Hall
5C2×C3×C52×C13C2×C311yescharacteristic
6C2×C13⋊(C52⋊C3)C2×C313yes—
7C4×C52×C13C3211yescharacteristic, complemented, Hall
8C3×C52×C13C3×C411yescharacteristic, complemented
9C13⋊(C52⋊C3)C3×C413yesdirect product factor
10C3×C4×C52⋊C3—131nomaximal, Hall
11C3×C4×C5×C13—32no—
12C2×C52×C13C2×C3211yescharacteristic
13C3×C4×C13⋊C3—251nomaximal, Hall
14C2×C3×C52⋊C3—131no—
15C2×C3×C5×C13—32no—
16C52×C13C32×C411yescharacteristic, complemented, Hall
17C3×C4×C52C13⋊C311yescharacteristic, complemented
18C4×C52⋊C3—133no—
19C4×C5×C13—32no—
20C2×C3×C13⋊C3—251no—
21C3×C52⋊C3—131noHall
22C3×C5×C13—32no—
23C3×C4×C13C52⋊C311yescharacteristic, complemented
24C4×C13⋊C3—253no—
25C2×C3×C52C2×C13⋊C311yescharacteristic
26C2×C52⋊C3—133no—
27C2×C5×C13—32no—
28C3×C13⋊C3—251noHall
29C4×C52C3×C13⋊C311yescharacteristic, complemented, Hall
30C2×C3×C13C2×C52⋊C311yescharacteristic
31C2×C13⋊C3—253no—
32C3×C52C4×C13⋊C311yescharacteristic, complemented
33C52⋊C3—133no—
34C5×C13—32no—
35C3×C4×C5—32no—
36C4×C13C3×C52⋊C311yescharacteristic, complemented, Hall
37C2×C52C2×C3×C13⋊C311yescharacteristic
38C3×C13C4×C52⋊C311yescharacteristic, complemented
39C13⋊C3—253no—
40C32×C4—3251noHall
41C2×C3×C5—32no—
42C2×C13C2×C3×C52⋊C311yescharacteristic
43C52C3×C4×C13⋊C311yescharacteristic, complemented, Sylow
44C4×C5—32no—
45C2×C32—3251no—
46C3×C5—32no—
47C13C3×C4×C52⋊C311yescharacteristic, complemented, Sylow
48C3×C4—3253no—
49C3×C4C13⋊(C52⋊C3)11yescharacteristic, direct product factor
50C2×C5—32no—
51C32—3251noSylow
52C2×C3—3253no—
53C2×C3C2×C13⋊(C52⋊C3)11yescharacteristic
54C5—32no—
55C4C3×C13⋊(C52⋊C3)11yescharacteristic, direct product factor, Sylow
56C3—3253no—
57C3C4×C13⋊(C52⋊C3)11yescharacteristic, direct product factor
58C2C2×C3×C13⋊(C52⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC3×C4C13⋊(C52⋊C3)
commutator, hypocenterC52×C13C32×C4
FrattiniC2C2×C3×C13⋊(C52⋊C3)
FittingC3×C4×C52×C13C3
socleC2×C3×C52×C13C2×C3
prime radicalC2×C3×C13⋊(C52⋊C3)C2
cosocleC2×C52×C13C2×C32
LCSG ▷ C52×C13
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C4×C13⋊(C52⋊C3)C3direct (N × H)
3. C3×C4×C52×C13C3semidirect
4. C3×C13⋊(C52⋊C3)C4direct (N × H)
7. C4×C52×C13C32semidirect
8. C3×C52×C13C3×C4semidirect
9. C13⋊(C52⋊C3)C3×C4direct (N × H)
16. C52×C13C32×C4semidirect
17. C3×C4×C52C13⋊C3semidirect
23. C3×C4×C13C52⋊C3semidirect
29. C4×C52C3×C13⋊C3semidirect
32. C3×C52C4×C13⋊C3semidirect
36. C4×C13C3×C52⋊C3semidirect
38. C3×C13C4×C52⋊C3semidirect
43. C52C3×C4×C13⋊C3semidirect
47. C13C3×C4×C52⋊C3semidirect
49. C3×C4C13⋊(C52⋊C3)direct (N × H)
55. C4C3×C13⋊(C52⋊C3)direct (N × H)
57. C3C4×C13⋊(C52⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C13⋊(C52⋊C3)2
C4×C13⋊(C52⋊C3)3
C3×C4×C52×C133
C3×C4×C52⋊C313
C3×C4×C13⋊C325