Finite Group Databasebeta

← C3×C3⋊(C19⋊#1043) #30685877

Subgroups — C3×C3⋊(C19⋊#1043) #30685877

Order 17100.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C19×C5⋊D5C211yesmaximal, characteristic
2C3⋊(C19⋊#1043)C311yesmaximal, characteristic, direct product factor
3C3×C19⋊#1043—31nomaximal
4C32×C52×C19C411yescharacteristic, complemented, Hall
5C3×C3⋊(C19⋊AGL(1,𝔽5))—56nomaximal
6C3×C19×C5⋊D5—21no—
7C3×C19×C5⋊D5D311yescharacteristic
8C3×C19×C5⋊D5C2×C311yescharacteristic
9C19⋊#1043—31noHall
10C32×D5×C19—56no—
11C3×C52×C19—21no—
12C3×C52×C19Dic311yescharacteristic, complemented
13C3×C52×C19C3×C411yescharacteristic, complemented
14C3⋊(C19⋊AGL(1,𝔽5))—56no—
15C3×C19⋊AGL(1,𝔽5)—156no—
16C19×C5⋊D5C3×D311yescharacteristic
17C3×C3⋊#1043—191nomaximal, Hall
18C32×C5×C19AGL(1,𝔽5)16yescomplemented
19C3×Dic57—251noHall
20C3×D5×C19—56no—
21C3×D5×C19—56no—
22C3×D5×C19—106no—
23C52×C19C3×Dic311yescharacteristic, complemented, Hall
24C32×C5⋊D5D1911yescharacteristic
25C19⋊AGL(1,𝔽5)—156no—
26C2×C32×C19—251no—
27C3⋊#1043—191no—
28C3×#1043—571no—
29C3×C5×C19—26no—
30C3×C5×C19C3×AGL(1,𝔽5)16yescomplemented
31C3×C5×C19ΓL(1,𝔽16)16yescomplemented
32Dic57—251no—
33C3×Dic19—751no—
34C32×C52Dic1911yescharacteristic, complemented, Hall
35D5×C19—56no—
36C3×ΓL(1,𝔽16)—956no—
37C32×C19#104311yescharacteristic, complemented, Hall
38C3×C5⋊D5—21no—
39C3×C5⋊D5C3×D1911yescharacteristic
40C3×C5⋊D5D5711yescharacteristic
41C2×C3×C19—251no—
42C2×C3×C19—251no—
43C2×C3×C19—501no—
44#1043—571noHall
45C5×C19C3×ΓL(1,𝔽16)16yescomplemented
46C32×D5—56no—
47Dic19—751noHall
48C3×C52—21no—
49C3×C52C3×Dic1911yescharacteristic, complemented
50C3×C52Dic5711yescharacteristic, complemented
51ΓL(1,𝔽16)—956no—
52C3×AGL(1,𝔽5)—2856no—
53C3×C19—21no—
54C3×C19C3×#104311yescharacteristic, complemented
55C3×C19C3⋊#104311yescharacteristic, complemented
56C5⋊D5C3×D5711yescharacteristic
57C32×C5C19⋊AGL(1,𝔽5)16yescomplemented
58C2×C19—251no—
59C3×Dic3—4751noHall
60C3×D5—56no—
61C3×D5—56no—
62C3×D5—106no—
63C52C3×Dic5711yescharacteristic, complemented, Sylow
64AGL(1,𝔽5)—2856no—
65C19C3×C3⋊#104311yescharacteristic, complemented, Sylow
66C2×C32—251no—
67C3×C5—26no—
68C3×C5C3×C19⋊AGL(1,𝔽5)16yescomplemented
69C3×C5C3⋊(C19⋊AGL(1,𝔽5))16yescomplemented
70C3×C4—14251no—
71Dic3—4751no—
72D5—56no—
73C32C19⋊#104311yescharacteristic, complemented, Sylow
74C2×C3—251no—
75C2×C3—251no—
76C2×C3—501no—
77C5C3×C3⋊(C19⋊AGL(1,𝔽5))16yescomplemented
78C4—14251noSylow
79C3—21no—
80C3C3×C19⋊#104311yescharacteristic, complemented
81C3C3⋊(C19⋊#1043)11yescharacteristic, direct product factor
82C2—251no—
subgroupG/H
center, hypercenterC3C3⋊(C19⋊#1043)
commutator, hypocenterC3×C52×C19C3×C4
FrattiniC1G
Fitting, socleC32×C52×C19C4
prime radicalC32×C19×C5⋊D5C2
cosocleC3×C19×C5⋊D5C2×C3
LCSG ▷ C3×C52×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C19⋊#1043)C3direct (N × H)
4. C32×C52×C19C4semidirect
12. C3×C52×C19Dic3semidirect
13. C3×C52×C19C3×C4semidirect
18. C32×C5×C19AGL(1,𝔽5)semidirect
23. C52×C19C3×Dic3semidirect
30. C3×C5×C19C3×AGL(1,𝔽5)semidirect
31. C3×C5×C19ΓL(1,𝔽16)semidirect
34. C32×C52Dic19semidirect
37. C32×C19#1043semidirect
45. C5×C19C3×ΓL(1,𝔽16)semidirect
49. C3×C52C3×Dic19semidirect
50. C3×C52Dic57semidirect
54. C3×C19C3×#1043semidirect
55. C3×C19C3⋊#1043semidirect
57. C32×C5C19⋊AGL(1,𝔽5)semidirect
63. C52C3×Dic57semidirect
65. C19C3×C3⋊#1043semidirect
68. C3×C5C3×C19⋊AGL(1,𝔽5)semidirect
69. C3×C5C3⋊(C19⋊AGL(1,𝔽5))semidirect
73. C32C19⋊#1043semidirect
77. C5C3×C3⋊(C19⋊AGL(1,𝔽5))semidirect
80. C3C3×C19⋊#1043semidirect
81. C3C3⋊(C19⋊#1043)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C19×C5⋊D52
C3⋊(C19⋊#1043)3
C3×C19⋊#10433
C3×C3⋊(C19⋊AGL(1,𝔽5))5
C3×C3⋊#104319