Finite Group Databasebeta

← C3×Dic19⋊(C52⋊C3) #30685657

Subgroups — C3×Dic19⋊(C52⋊C3) #30685657

Order 17100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19⋊(C52⋊C3)C211yesmaximal, characteristic
2C3×C52×Dic19C311yesmaximal, characteristic, complemented
3Dic19⋊(C52⋊C3)C313yesmaximal, direct product factor
4C3×C19⋊(C52⋊C3)C411yescharacteristic, complemented, Hall
5C2×C19⋊(C52⋊C3)C2×C313yes—
6C2×C3×C52×C19C2×C311yescharacteristic
7C52×Dic19C3211yescharacteristic, complemented, Hall
8C3×C52×C19C3×C411yescharacteristic, complemented
9C19⋊(C52⋊C3)C3×C413yescomplemented
10C3×C5×Dic19—32no—
11C2×C52×C19C2×C3211yescharacteristic
12C3×C4×C52⋊C3—191nomaximal, Hall
13C3×(C19⋊C3)⋊C4—251nomaximal, Hall
14C2×C3×C5×C19—32no—
15C52×C19C32×C411yescharacteristic, complemented, Hall
16C2×C3×C52⋊C3—191no—
17C5×Dic19—32no—
18C2×C3×C19⋊C3—251no—
19C3×C4×C52—571no—
20C4×C52⋊C3—193no—
21C3×C5×C19—32no—
22C3×Dic19C52⋊C311yescharacteristic, complemented
23(C19⋊C3)⋊C4—253no—
24C3×C52⋊C3—191noHall
25C2×C5×C19—32no—
26C3×C19⋊C3—251noHall
27C2×C3×C52D19⋊C311yescharacteristic
28C2×C52⋊C3—193no—
29C2×C3×C19C2×C52⋊C311yescharacteristic
30C2×C19⋊C3—253no—
31C4×C52—571noHall
32C5×C19—32no—
33Dic19C3×C52⋊C311yescharacteristic, complemented, Hall
34C3×C52(C19⋊C3)⋊C411yescharacteristic, complemented
35C52⋊C3—193no—
36C3×C4×C5—572no—
37C3×C19C4×C52⋊C311yescharacteristic, complemented
38C19⋊C3—253no—
39C2×C52C3×D19⋊C311yescharacteristic
40C2×C19C2×C3×C52⋊C311yescharacteristic
41C32×C4—4751noHall
42C2×C3×C5—32no—
43C52C3×(C19⋊C3)⋊C411yescharacteristic, complemented, Sylow
44C4×C5—572no—
45C19C3×C4×C52⋊C311yescharacteristic, complemented, Sylow
46C2×C32—4751no—
47C3×C5—32no—
48C3×C4—571no—
49C3×C4—4753no—
50C2×C5—32no—
51C32—4751noSylow
52C2×C3—4753no—
53C2×C3D19⋊(C52⋊C3)11yescharacteristic
54C5—32no—
55C4—571noSylow
56C3—4753no—
57C3Dic19⋊(C52⋊C3)11yescharacteristic, direct product factor
58C2C3×D19⋊(C52⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3D19⋊(C52⋊C3)
commutator, hypocenterC52×C19C32×C4
FrattiniC2C3×D19⋊(C52⋊C3)
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C19⋊(C52⋊C3)C2
cosocleC2×C52×C19C2×C32
LCSG ▷ C52×C19
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C52×Dic19C3semidirect
3. Dic19⋊(C52⋊C3)C3direct (N × H)
4. C3×C19⋊(C52⋊C3)C4semidirect
7. C52×Dic19C32semidirect
8. C3×C52×C19C3×C4semidirect
9. C19⋊(C52⋊C3)C3×C4semidirect
15. C52×C19C32×C4semidirect
22. C3×Dic19C52⋊C3semidirect
33. Dic19C3×C52⋊C3semidirect
34. C3×C52(C19⋊C3)⋊C4semidirect
37. C3×C19C4×C52⋊C3semidirect
43. C52C3×(C19⋊C3)⋊C4semidirect
45. C19C3×C4×C52⋊C3semidirect
57. C3Dic19⋊(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×C19⋊(C52⋊C3)2
C3×C52×Dic193
Dic19⋊(C52⋊C3)3
C3×C4×C52⋊C319
C3×(C19⋊C3)⋊C425