Finite Group Databasebeta

← C2×C5×C8×C3⋊D3 #13088082

Subgroups — C2×C5×C8×C3⋊D3 #13088082

Order 1440.

456 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 186 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
1C2×C4×C5×C3⋊D3C211yesmaximal, characteristic
2C2×C32×C5×C8C211yesmaximal, characteristic, complemented
3C2×C5×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C5×C8×C3⋊D3C214yesmaximal, direct product factor
5C2×C5×D3×C8—34nomaximal
6C22×C5×C3⋊D3C411yescharacteristic
7C2×C32×C4×C5C2211yescharacteristic
8C2×C5×C3⋊Dic3C411yescharacteristic
9C4×C5×C3⋊D3C412yes—
10C4×C5×C3⋊D3C2212yes—
11C32×C5×C8C2212yescomplemented
12C5×C3⋊(C3⋊C8)C2212yescomplemented
13C2×C8×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
14C2×C4×C5×D3—34no—
15C2×C3×C5×C8D314yescomplemented
16C2×C5×C3⋊C8—34no—
17C5×D3×C8—316no—
18C22×C32×C5C2×C411yescharacteristic
19C2×C5×C3⋊D3C814yesdirect product factor
20C2×C5×C3⋊D3C2×C412yes—
21C32×C4×C5C2×C411yescharacteristic
22C32×C4×C5C2311yescharacteristic
23C5×C3⋊Dic3C2×C412yes—
24C22×C5×C8—91noHall
25C2×C4×C3⋊D3C2×C511yescharacteristic
26C2×C32×C8C2×C511yescharacteristic, complemented
27C2×C3⋊(C3⋊C8)C2×C511yescharacteristic, complemented
28C8×C3⋊D3C2×C514yesdirect product factor
29C22×C5×D3—34no—
30C2×C3×C4×C5C2×D314yes—
31C2×C5×Dic3—34no—
32C4×C5×D3—38no—
33C4×C5×D3—38no—
34C3×C5×C8C2×D318yescomplemented
35C5×C3⋊C8—38no—
36C2×D3×C8—34no—
37C2×C32×C5C2×C812yescomplemented
38C2×C32×C5C22×C411yescharacteristic
39C5×C3⋊D3C2×C814yesdirect product factor
40C22×C4×C5—91no—
41C2×C5×C8—91no—
42C2×C5×C8—94no—
43C2×C5×C8C3⋊D311yescharacteristic, direct product factor
44C22×C3⋊D3C4×C511yescharacteristic
45C2×C32×C4C22×C511yescharacteristic
46C2×C3⋊Dic3C4×C511yescharacteristic
47C4×C3⋊D3C4×C512yes—
48C4×C3⋊D3C22×C512yes—
49C32×C8C22×C512yescomplemented
50C3⋊(C3⋊C8)C22×C512yescomplemented
51C22×C3×C5C4×D314yes—
52C2×C5×D3—316no—
53C2×C5×D3—38no—
54C3×C4×C5C4×D314yes—
55C3×C4×C5C22×D314yes—
56C5×Dic3—38no—
57C2×C4×D3—34no—
58C2×C3×C8C5×D314yescomplemented
59C2×C3⋊C8—34no—
60D3×C8—316no—
61C32×C5C22×C811yescharacteristic, complemented, Hall
62C23×C5—91no—
63C2×C4×C5—91no—
64C2×C4×C5—92no—
65C2×C4×C5—92no—
66C2×C4×C5C2×C3⋊D311yescharacteristic
67C5×C8—92no—
68C5×C8C2×C3⋊D312yesdirect product factor
69C22×C32C2×C4×C511yescharacteristic
70C2×C3⋊D3C5×C814yesdirect product factor
71C2×C3⋊D3C2×C4×C512yes—
72C32×C4C2×C4×C511yescharacteristic
73C32×C4C23×C511yescharacteristic
74C3⋊Dic3C2×C4×C512yes—
75C22×C8—91noSylow
76C2×C3×C5D3×C818yescomplemented
77C2×C3×C5C2×C4×D314yes—
78C5×D3—316no—
79C22×D3—34no—
80C2×C3×C4C2×C5×D314yes—
81C2×Dic3—34no—
82C4×D3—38no—
83C4×D3—38no—
84C3×C8C2×C5×D318yescomplemented
85C3⋊C8—38no—
86C22×C5—94no—
87C22×C5—92no—
88C22×C5C4×C3⋊D311yescharacteristic
89C4×C5—92no—
90C4×C5C4×C3⋊D311yescharacteristic
91C4×C5C22×C3⋊D311yescharacteristic
92C2×C32C2×C5×C812yescomplemented
93C2×C32C22×C4×C511yescharacteristic
94C3⋊D3C2×C5×C814yesdirect product factor
95C22×C4—91no—
96C2×C8—91no—
97C2×C8—94no—
98C2×C8C5×C3⋊D311yescharacteristic, direct product factor
99C3×C5C2×D3×C814yescomplemented
100C22×C3C4×C5×D314yes—
101C2×D3—316no—
102C2×D3—38no—
103C3×C4C4×C5×D314yes—
104C3×C4C22×C5×D314yes—
105Dic3—38no—
106C2×C5—94no—
107C2×C5C8×C3⋊D312yesdirect product factor
108C2×C5C2×C4×C3⋊D311yescharacteristic
109C32C22×C5×C811yescharacteristic, complemented, Sylow
110C23—91no—
111C2×C4—91no—
112C2×C4—92no—
113C2×C4—92no—
114C2×C4C2×C5×C3⋊D311yescharacteristic
115C8—92no—
116C8C2×C5×C3⋊D312yesdirect product factor
117C2×C3C5×D3×C818yescomplemented
118C2×C3C2×C4×C5×D314yes—
119D3—316no—
120C5C2×C8×C3⋊D311yescharacteristic, direct product factor, Sylow
121C22—92no—
122C22—94no—
123C22C4×C5×C3⋊D311yescharacteristic
124C4—92no—
125C4C4×C5×C3⋊D311yescharacteristic
126C4C22×C5×C3⋊D311yescharacteristic
127C3C2×C5×D3×C814yescomplemented
128C2—94no—
129C2C5×C8×C3⋊D312yesdirect product factor
130C2C2×C4×C5×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2×C5×C8C3⋊D3
commutator, hypocenterC32C22×C5×C8
FrattiniC4C22×C5×C3⋊D3
FittingC2×C32×C5×C8C2
socleC22×C32×C5C2×C4
prime radicalC22×C5×C3⋊D3C4
cosocleC32×C4C23×C5
LCSG ▷ C32
UCSC1 ◁ C2×C5×C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C5×C8C2semidirect
3. C2×C5×C3⋊(C3⋊C8)C2semidirect
4. C5×C8×C3⋊D3C2direct (N × H)
11. C32×C5×C8C22semidirect
12. C5×C3⋊(C3⋊C8)C22semidirect
13. C2×C8×C3⋊D3C5direct (N × H)
15. C2×C3×C5×C8D3semidirect
19. C2×C5×C3⋊D3C8direct (N × H)
26. C2×C32×C8C2×C5semidirect
27. C2×C3⋊(C3⋊C8)C2×C5semidirect
28. C8×C3⋊D3C2×C5direct (N × H)
34. C3×C5×C8C2×D3semidirect
37. C2×C32×C5C2×C8semidirect
39. C5×C3⋊D3C2×C8direct (N × H)
43. C2×C5×C8C3⋊D3direct (N × H)
49. C32×C8C22×C5semidirect
50. C3⋊(C3⋊C8)C22×C5semidirect
58. C2×C3×C8C5×D3semidirect
61. C32×C5C22×C8semidirect
68. C5×C8C2×C3⋊D3direct (N × H)
70. C2×C3⋊D3C5×C8direct (N × H)
76. C2×C3×C5D3×C8semidirect
84. C3×C8C2×C5×D3semidirect
92. C2×C32C2×C5×C8semidirect
94. C3⋊D3C2×C5×C8direct (N × H)
98. C2×C8C5×C3⋊D3direct (N × H)
99. C3×C5C2×D3×C8semidirect
107. C2×C5C8×C3⋊D3direct (N × H)
109. C32C22×C5×C8semidirect
116. C8C2×C5×C3⋊D3direct (N × H)
117. C2×C3C5×D3×C8semidirect
120. C5C2×C8×C3⋊D3direct (N × H)
127. C3C2×C5×D3×C8semidirect
129. C2C5×C8×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C5×C3⋊D32
C2×C32×C5×C82
C2×C5×C3⋊(C3⋊C8)2
C5×C8×C3⋊D32
C2×C5×D3×C83
C2×C8×C3⋊D35