Finite Group Databasebeta

← C3×#19152795 #30685656

Subgroups — C3×#19152795 #30685656

Order 17100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19×C52⋊C3C211yesmaximal, characteristic
2C3×C19⋊#1039C311yesmaximal, characteristic, complemented
3#19152795C313yesmaximal, direct product factor
4C3×C19×C52⋊C3C411yescharacteristic, complemented, Hall
5C2×C19×C52⋊C3C2×C313yes—
6C2×C3×C52×C19C2×C311yescharacteristic
7C19⋊#1039C3211yescharacteristic, complemented, Hall
8C3×C52×C19C3×C411yescharacteristic, complemented
9C19×C52⋊C3C3×C413yescomplemented
10C3×Dic95—152no—
11C2×C52×C19C2×C3211yescharacteristic
12C3×#1039⋊C3—191nomaximal, Hall
13C32×Dic19—251nomaximal, Hall
14C2×C3×C5×C19—32no—
15C52×C19C32×C411yescharacteristic, complemented, Hall
16C2×C3×C52⋊C3D1911yescharacteristic
17Dic95—152no—
18C2×C32×C19—251no—
19C3×#1039—191no—
20#1039⋊C3—193no—
21C3×C5×C19—32no—
22C3×Dic19—253no—
23C3×Dic19—751no—
24C3×C52⋊C3Dic1911yescharacteristic, complemented, Hall
25C2×C5×C19—32no—
26C32×C19—251noHall
27C2×C3×C52C3×D1911yescharacteristic
28C2×C52⋊C3C3×D1913yes—
29C2×C3×C19—253no—
30C2×C3×C19(C5⋊D5)⋊C311yescharacteristic
31#1039—191noHall
32C5×C19—32no—
33Dic19—751noHall
34C3×C52C3×Dic1911yescharacteristic, complemented
35C52⋊C3C3×Dic1913yescomplemented
36C3×Dic5—2852no—
37C3×C19—253no—
38C3×C19#1039⋊C311yescharacteristic, complemented
39C2×C52C32×D1911yescharacteristic
40C2×C19C3×(C5⋊D5)⋊C311yescharacteristic
41C32×C4—4751noHall
42C2×C3×C5—32no—
43C52C32×Dic1911yescharacteristic, complemented, Sylow
44Dic5—2852no—
45C19C3×#1039⋊C311yescharacteristic, complemented, Sylow
46C2×C32—251no—
47C3×C5—32no—
48C3×C4—14251no—
49C3×C4—4753no—
50C2×C5—32no—
51C32—251noSylow
52C2×C3—253no—
53C2×C3#1566813511yescharacteristic
54C5—32no—
55C4—14251noSylow
56C3—253no—
57C3#1915279511yescharacteristic, direct product factor
58C2C3×#1566813511yescharacteristic
subgroupG/H
center, hypercenterC2×C3#15668135
commutator, hypocenterC52×C19C32×C4
FrattiniC2C3×#15668135
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C19×C52⋊C3C2
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×C19⋊#1039C3semidirect
3. #19152795C3direct (N × H)
4. C3×C19×C52⋊C3C4semidirect
7. C19⋊#1039C32semidirect
8. C3×C52×C19C3×C4semidirect
9. C19×C52⋊C3C3×C4semidirect
15. C52×C19C32×C4semidirect
24. C3×C52⋊C3Dic19semidirect
34. C3×C52C3×Dic19semidirect
35. C52⋊C3C3×Dic19semidirect
38. C3×C19#1039⋊C3semidirect
43. C52C32×Dic19semidirect
45. C19C3×#1039⋊C3semidirect
57. C3#19152795direct (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⋊C32
C3×C19⋊#10393
#191527953
C3×#1039⋊C319
C32×Dic1925