Finite Group Databasebeta

← C5×D8×C3⋊D3 #13088093

Subgroups — C5×D8×C3⋊D3 #13088093

Order 1440.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C5×D4×C3⋊D3C212yesmaximal, complemented
2C32×C5×D8C211yesmaximal, characteristic, complemented
3C5×#3753C212yesmaximal, complemented
4C5×#3745C211yesmaximal, characteristic, complemented
5C5×C8×C3⋊D3C211yesmaximal, characteristic, complemented
6C5×D3×D8—34nomaximal
7C22×C5×C3⋊D3—22no—
8C32×C5×D4C2212yescomplemented
9C5×#638—22no—
10C5×C4⋊(C3⋊D3)C2212yescomplemented
11C4×C5×C3⋊D3C2211yescharacteristic
12C32×C5×C8C2211yescharacteristic, complemented
13C5×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
14D8×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
15C5×D3×D4—38no—
16C3×C5×D8D314yescomplemented
17C5×#213—38no—
18C5×D24—34no—
19C5×D3×C8—34no—
20C22×C32×C5—22no—
21C2×C5×C3⋊D3—22no—
22C2×C5×C3⋊D3—44no—
23C2×C5×C3⋊D3D411yescharacteristic
24C32×C4×C5C2311yescharacteristic
25C5×C3⋊Dic3D411yescharacteristic
26C2×C5×D8—91noHall
27D4×C3⋊D3C2×C512yescomplemented
28C32×D8C2×C511yescharacteristic, complemented
29#3753C2×C512yescomplemented
30#3745C2×C511yescharacteristic, complemented
31C8×C3⋊D3C2×C511yescharacteristic, complemented
32C22×C5×D3—68no—
33C3×C5×D4C2×D318yescomplemented
34C5×#67—68no—
35C5×D12—38no—
36C4×C5×D3—34no—
37C3×C5×C8C2×D314yescomplemented
38C5×C3⋊C8—34no—
39D3×D8—34no—
40C2×C32×C5—42no—
41C2×C32×C5C2×D411yescharacteristic
42C5×C3⋊D3—42no—
43C5×C3⋊D3D812yesdirect product factor
44C2×C5×D4—92no—
45C5×D8—92no—
46C5×D8—91no—
47C5×D8C3⋊D311yescharacteristic, direct product factor
48C2×C5×C8—91no—
49C22×C3⋊D3—22no—
50C32×D4C22×C512yescomplemented
51#638—22no—
52C4⋊(C3⋊D3)C22×C512yescomplemented
53C4×C3⋊D3C22×C511yescharacteristic
54C32×C8C22×C511yescharacteristic, complemented
55C3⋊(C3⋊C8)C22×C511yescharacteristic, complemented
56C22×C3×C5—28no—
57C2×C5×D3—34no—
58C2×C5×D3—68no—
59C2×C5×D3—1216no—
60C3×C4×C5C22×D314yes—
61C5×Dic3—34no—
62D3×D4—38no—
63C3×D8C5×D314yescomplemented
64#213—38no—
65D24—34no—
66D3×C8—34no—
67C32×C5C2×D811yescharacteristic, complemented, Hall
68C23×C5—182no—
69C5×D4—92no—
70C5×D4—182no—
71C5×D4C2×C3⋊D312yescomplemented
72C2×C4×C5—91no—
73C5×C8—91no—
74C5×C8C2×C3⋊D311yescharacteristic, complemented
75C22×C32—22no—
76C2×C3⋊D3—22no—
77C2×C3⋊D3—44no—
78C2×C3⋊D3C5×D411yescharacteristic
79C32×C4C23×C511yescharacteristic
80C3⋊Dic3C5×D411yescharacteristic
81C2×D8—91noSylow
82C2×C3×C5—48no—
83C2×C3×C5D3×D414yes—
84C5×D3—38no—
85C5×D3—128no—
86C22×D3—68no—
87C3×D4C2×C5×D318yescomplemented
88#67—68no—
89D12—38no—
90C4×D3—34no—
91C3×C8C2×C5×D314yescomplemented
92C3⋊C8—34no—
93C22×C5—22no—
94C22×C5—91no—
95C22×C5—182no—
96C22×C5—364no—
97C4×C5—91no—
98C4×C5C22×C3⋊D311yescharacteristic
99C2×C32—42no—
100C2×C32C2×C5×D411yescharacteristic
101C3⋊D3—42no—
102C3⋊D3C5×D812yesdirect product factor
103C2×D4—92no—
104D8—92no—
105D8—91no—
106D8C5×C3⋊D311yescharacteristic, direct product factor
107C2×C8—91no—
108C3×C5D3×D814yescomplemented
109C22×C3—28no—
110C2×D3—34no—
111C2×D3—68no—
112C2×D3—1216no—
113C3×C4C22×C5×D314yes—
114Dic3—34no—
115C2×C5—42no—
116C2×C5—92no—
117C2×C5—362no—
118C2×C5D4×C3⋊D311yescharacteristic
119C32C2×C5×D811yescharacteristic, complemented, Sylow
120C23—182no—
121D4—92no—
122D4—182no—
123D4C2×C5×C3⋊D312yescomplemented
124C2×C4—91no—
125C8—91no—
126C8C2×C5×C3⋊D311yescharacteristic, complemented
127C2×C3—48no—
128C2×C3C5×D3×D414yes—
129D3—38no—
130D3—128no—
131C5D8×C3⋊D311yescharacteristic, direct product factor, Sylow
132C22—22no—
133C22—91no—
134C22—182no—
135C22—364no—
136C4—91no—
137C4C22×C5×C3⋊D311yescharacteristic
138C3C5×D3×D814yescomplemented
139C2—42no—
140C2—92no—
141C2—362no—
142C2C5×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C5D4×C3⋊D3
commutator, cosocleC32×C4C23×C5
FrattiniC4C22×C5×C3⋊D3
FittingC32×C5×D8C2
socleC2×C32×C5C2×D4
hypercenterC5×D8C3⋊D3
hypocenterC32C2×C5×D8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D8

Complements

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

NH ≅ G/Ntype
1. C5×D4×C3⋊D3C2semidirect
2. C32×C5×D8C2semidirect
3. C5×#3753C2semidirect
4. C5×#3745C2semidirect
5. C5×C8×C3⋊D3C2semidirect
8. C32×C5×D4C22semidirect
10. C5×C4⋊(C3⋊D3)C22semidirect
12. C32×C5×C8C22semidirect
13. C5×C3⋊(C3⋊C8)C22semidirect
14. D8×C3⋊D3C5direct (N × H)
16. C3×C5×D8D3semidirect
27. D4×C3⋊D3C2×C5semidirect
28. C32×D8C2×C5semidirect
29. #3753C2×C5semidirect
30. #3745C2×C5semidirect
31. C8×C3⋊D3C2×C5semidirect
33. C3×C5×D4C2×D3semidirect
37. C3×C5×C8C2×D3semidirect
43. C5×C3⋊D3D8direct (N × H)
47. C5×D8C3⋊D3direct (N × H)
50. C32×D4C22×C5semidirect
52. C4⋊(C3⋊D3)C22×C5semidirect
54. C32×C8C22×C5semidirect
55. C3⋊(C3⋊C8)C22×C5semidirect
63. C3×D8C5×D3semidirect
67. C32×C5C2×D8semidirect
71. C5×D4C2×C3⋊D3semidirect
74. C5×C8C2×C3⋊D3semidirect
87. C3×D4C2×C5×D3semidirect
91. C3×C8C2×C5×D3semidirect
102. C3⋊D3C5×D8direct (N × H)
106. D8C5×C3⋊D3direct (N × H)
108. C3×C5D3×D8semidirect
119. C32C2×C5×D8semidirect
123. D4C2×C5×C3⋊D3semidirect
126. C8C2×C5×C3⋊D3semidirect
131. C5D8×C3⋊D3direct (N × H)
138. C3C5×D3×D8semidirect

Maximal subgroups

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

subgroupindex
C5×D4×C3⋊D32
C32×C5×D82
C5×#37532
C5×#37452
C5×C8×C3⋊D32
C5×D3×D83
D8×C3⋊D35