Finite Group Databasebeta

← C3×#16839056 #26043500

Subgroups — C3×#16839056 #26043500

Order 11700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×C52⋊C3C211yesmaximal, characteristic
2C3×#13049918C311yesmaximal, characteristic, complemented
3#16839056C313yesmaximal, direct product factor
4C3×C13×C52⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C52×C13C2×C311yescharacteristic
6C2×C13×C52⋊C3C2×C313yes—
7#13049918C3211yescharacteristic, complemented, Hall
8C3×C52×C13C3×C411yescharacteristic, complemented
9C13×C52⋊C3C3×C413yescomplemented
10C3×#1039⋊C3—131nomaximal, Hall
11C3×Dic65—152no—
12C2×C52×C13C2×C3211yescharacteristic
13C32×Dic13—251nomaximal, Hall
14C2×C3×C52⋊C3D1311yescharacteristic
15C2×C3×C5×C13—32no—
16C52×C13C32×C411yescharacteristic, complemented, Hall
17C3×#1039—131no—
18#1039⋊C3—133no—
19Dic65—152no—
20C2×C32×C13—251no—
21C3×C52⋊C3Dic1311yescharacteristic, complemented, Hall
22C3×C5×C13—32no—
23C3×Dic13—253no—
24C3×Dic13—251no—
25C2×C3×C52C3×D1311yescharacteristic
26C2×C52⋊C3C3×D1313yes—
27C2×C5×C13—32no—
28C32×C13—251noHall
29#1039—131noHall
30C2×C3×C13—253no—
31C2×C3×C13(C5⋊D5)⋊C311yescharacteristic
32C3×C52C3×Dic1311yescharacteristic, complemented
33C52⋊C3C3×Dic1313yescomplemented
34C5×C13—32no—
35C3×Dic5—1952no—
36Dic13—251noHall
37C2×C52C32×D1311yescharacteristic
38C3×C13—253no—
39C3×C13#1039⋊C311yescharacteristic, complemented
40C32×C4—3251noHall
41C2×C3×C5—32no—
42C2×C13C3×(C5⋊D5)⋊C311yescharacteristic
43C52C32×Dic1311yescharacteristic, complemented, Sylow
44Dic5—1952no—
45C2×C32—251no—
46C3×C5—32no—
47C13C3×#1039⋊C311yescharacteristic, complemented, Sylow
48C3×C4—3253no—
49C3×C4—3251no—
50C2×C5—32no—
51C32—251noSylow
52C2×C3—253no—
53C2×C3#1451961311yescharacteristic
54C5—32no—
55C4—3251noSylow
56C3—253no—
57C3#1683905611yescharacteristic, direct product factor
58C2C3×#1451961311yescharacteristic
subgroupG/H
center, hypercenterC2×C3#14519613
commutator, hypocenterC52×C13C32×C4
FrattiniC2C3×#14519613
Fitting, socleC2×C3×C52×C13C2×C3
prime radicalC2×C3×C13×C52⋊C3C2
cosocleC2×C52×C13C2×C32
LCSG ▷ C52×C13
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×#13049918C3semidirect
3. #16839056C3direct (N × H)
4. C3×C13×C52⋊C3C4semidirect
7. #13049918C32semidirect
8. C3×C52×C13C3×C4semidirect
9. C13×C52⋊C3C3×C4semidirect
16. C52×C13C32×C4semidirect
21. C3×C52⋊C3Dic13semidirect
32. C3×C52C3×Dic13semidirect
33. C52⋊C3C3×Dic13semidirect
39. C3×C13#1039⋊C3semidirect
43. C52C32×Dic13semidirect
47. C13C3×#1039⋊C3semidirect
57. C3#16839056direct (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⋊C32
C3×#130499183
#168390563
C3×#1039⋊C313
C32×Dic1325