Finite Group Databasebeta

← C5×C11×(C3⋊D3)⋊D19 #49178702

Subgroups — C5×C11×(C3⋊D3)⋊D19 #49178702

Order 37620.

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×D57C212yesmaximal, complemented
2C5×C11×C3⋊D3×C19C211yesmaximal, characteristic, complemented
3C5×D3×C11×D19—32nomaximal
4C32×C5×C11×C19C2211yescharacteristic, complemented, Hall
5C11×(C3⋊D3)⋊D19C511yesmaximal, characteristic, direct product factor, Hall
6C5×C11×D57D312yescomplemented
7C5×D3×C11×C19—32no—
8C5×D3×C11×C19—61no—
9C3×C5×C11×D19—32no—
10C2×C5×C11×D19—91noHall
11C11×C3⋊D3×C19C2×C511yescharacteristic, complemented
12C3×C11×D57C2×C512yescomplemented
13C5×(C3⋊D3)⋊D19C1111yesmaximal, characteristic, direct product factor, Hall
14C3×C5×C11×C19—21no—
15C3×C5×C11×C19C2×D312yescomplemented
16D3×C11×D19—32no—
17C5×C11×D19—32no—
18C2×C5×C11×C19—91no—
19C5×D32×C11—191nomaximal, Hall
20C32×C11×C19C22×C511yescharacteristic, complemented, Hall
21C5×C3⋊D3×C19C2×C1111yescharacteristic, complemented
22C3×C5×D57C2×C1112yescomplemented
23C11×D57C5×D312yescomplemented
24D3×C11×C19—32no—
25D3×C11×C19—61no—
26C3×C11×D19—32no—
27C5×D3×D19—32no—
28C5×C11×C19D3211yescharacteristic, complemented, Hall
29C5×C11×C3⋊D3D1911yescharacteristic, complemented
30C3×C5×D3×C11—192no—
31C32×C5×C19C22×C1111yescharacteristic, complemented, Hall
32C2×C11×D19—91noHall
33(C3⋊D3)⋊D19C5×C1111yescharacteristic, direct product factor, Hall
34C2×C5×D3×C11—572no—
35C3×C11×C19—21no—
36C3×C11×C19C2×C5×D312yescomplemented
37C5×D57D3×C1112yescomplemented
38C5×D3×C19—32no—
39C5×D3×C19—61no—
40C3×C5×D19—32no—
41C32×C5×C11C2×D1911yescharacteristic, complemented, Hall
42C2×C11×C19—91no—
43C11×D19—32no—
44D32×C11—191noHall
45C2×C5×D19—91noHall
46C3⋊D3×C19C2×C5×C1111yescharacteristic, complemented
47C3×D57C2×C5×C1112yescomplemented
48C2×C3×C5×C11—572no—
49C5×D3×C11—32no—
50C5×D3×C11—61no—
51C5×D3×C11—192no—
52C3×C5×C19—21no—
53C3×C5×C19C2×D3×C1112yescomplemented
54D3×D19—32no—
55C22×C5×C11—1711noHall
56C11×C19C5×D3211yescharacteristic, complemented, Hall
57C11×C3⋊D3C5×D1911yescharacteristic, complemented
58C3×D3×C11—192no—
59C2×C5×C19—91no—
60C5×D19—32no—
61C5×D32—191noHall
62C32×C19C22×C5×C1111yescharacteristic, complemented, Hall
63C3×C5×C11—21no—
64C3×C5×C11D3×D1912yescomplemented
65C2×D3×C11—572no—
66D57C5×D3×C1112yescomplemented
67C3×D19—32no—
68D3×C19—32no—
69D3×C19—61no—
70C2×C5×C11—91no—
71C2×C5×C11—572no—
72C32×C11C2×C5×D1911yescharacteristic, complemented, Hall
73C5×C19D32×C1111yescharacteristic, complemented, Hall
74C5×C3⋊D3C11×D1911yescharacteristic, complemented
75C3×C5×D3—192no—
76C2×D19—91noHall
77C2×C3×C11—572no—
78D3×C11—32no—
79D3×C11—61no—
80D3×C11—192no—
81C2×C5×D3—572no—
82C3×C19—21no—
83C3×C19C2×C5×D3×C1112yescomplemented
84C5×C11(C3⋊D3)⋊D1911yescharacteristic, direct product factor, Hall
85C32×C5C2×C11×D1911yescharacteristic, complemented, Hall
86C22×C11—1711noHall
87C2×C19—91no—
88D19—32no—
89D32—191noHall
90C3×C11—21no—
91C3×C11C5×D3×D1912yescomplemented
92C2×C3×C5—572no—
93C5×D3—32no—
94C5×D3—61no—
95C5×D3—192no—
96C2×C11—91no—
97C2×C11—572no—
98C22×C5—1711noHall
99C19C5×D32×C1111yescharacteristic, complemented, Sylow
100C3⋊D3C5×C11×D1911yescharacteristic, complemented
101C3×D3—192no—
102C3×C5—21no—
103C3×C5D3×C11×D1912yescomplemented
104C2×D3—572no—
105C11C5×(C3⋊D3)⋊D1911yescharacteristic, direct product factor, Sylow
106C2×C5—91no—
107C2×C5—572no—
108C32C2×C5×C11×D1911yescharacteristic, complemented, Sylow
109C2×C3—572no—
110D3—32no—
111D3—61no—
112D3—192no—
113C5C11×(C3⋊D3)⋊D1911yescharacteristic, direct product factor, Sylow
114C22—1711noSylow
115C3—21no—
116C3C5×D3×C11×D1912yescomplemented
117C2—91no—
118C2—572no—
subgroupG/H
center, hypercenterC5×C11(C3⋊D3)⋊D19
commutator, cosocle, hypocenterC32×C19C22×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C32×C19
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×D57C2semidirect
2. C5×C11×C3⋊D3×C19C2semidirect
4. C32×C5×C11×C19C22semidirect
5. C11×(C3⋊D3)⋊D19C5direct (N × H)
6. C5×C11×D57D3semidirect
11. C11×C3⋊D3×C19C2×C5semidirect
12. C3×C11×D57C2×C5semidirect
13. C5×(C3⋊D3)⋊D19C11direct (N × H)
15. C3×C5×C11×C19C2×D3semidirect
20. C32×C11×C19C22×C5semidirect
21. C5×C3⋊D3×C19C2×C11semidirect
22. C3×C5×D57C2×C11semidirect
23. C11×D57C5×D3semidirect
28. C5×C11×C19D32semidirect
29. C5×C11×C3⋊D3D19semidirect
31. C32×C5×C19C22×C11semidirect
33. (C3⋊D3)⋊D19C5×C11direct (N × H)
36. C3×C11×C19C2×C5×D3semidirect
37. C5×D57D3×C11semidirect
41. C32×C5×C11C2×D19semidirect
46. C3⋊D3×C19C2×C5×C11semidirect
47. C3×D57C2×C5×C11semidirect
53. C3×C5×C19C2×D3×C11semidirect
56. C11×C19C5×D32semidirect
57. C11×C3⋊D3C5×D19semidirect
62. C32×C19C22×C5×C11semidirect
64. C3×C5×C11D3×D19semidirect
66. D57C5×D3×C11semidirect
72. C32×C11C2×C5×D19semidirect
73. C5×C19D32×C11semidirect
74. C5×C3⋊D3C11×D19semidirect
83. C3×C19C2×C5×D3×C11semidirect
84. C5×C11(C3⋊D3)⋊D19direct (N × H)
85. C32×C5C2×C11×D19semidirect
91. C3×C11C5×D3×D19semidirect
99. C19C5×D32×C11semidirect
100. C3⋊D3C5×C11×D19semidirect
103. C3×C5D3×C11×D19semidirect
105. C11C5×(C3⋊D3)⋊D19direct (N × H)
108. C32C2×C5×C11×D19semidirect
113. C5C11×(C3⋊D3)⋊D19direct (N × H)
116. C3C5×D3×C11×D19semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×D572
C5×C11×C3⋊D3×C192
C5×D3×C11×D193
C11×(C3⋊D3)⋊D195
C5×(C3⋊D3)⋊D1911
C5×D32×C1119