Finite Group Databasebeta

← C2×C5×D3×D4 #92078

Subgroups — C2×C5×D3×D4 #92078

Order 480.

472 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 194 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
1C23×C5×D3C212yesmaximal, complemented
2C2×C3×C5×D4C211yesmaximal, characteristic, complemented
3C2×C5×#67C212yesmaximal, complemented
4C5×D3×D4C218yesmaximal, direct product factor
5C2×C5×D12C211yesmaximal, characteristic, complemented
6C2×C4×C5×D3C211yesmaximal, characteristic, complemented
7C22×C5×D4—31nomaximal, Hall
8C23×C3×C5C2212yescomplemented
9C22×C5×D3—28no—
10C22×C5×D3C2211yescharacteristic
11C22×C5×D3C2218yescomplemented
12C22×C5×D3C2212yescomplemented
13C3×C5×D4C2214yescomplemented
14C2×C3×C4×C5C2211yescharacteristic, complemented
15C5×#67C2218yescomplemented
16C2×C5×Dic3C2211yescharacteristic, complemented
17C5×D12C2214yescomplemented
18C4×C5×D3C2214yescomplemented
19C2×D3×D4C511yesmaximal, characteristic, direct product factor, Hall
20C24×C5—32no—
21C2×C5×D4—32no—
22C2×C5×D4—38no—
23C2×C5×D4—31no—
24C2×C5×D4D311yescharacteristic, direct product factor
25C22×C4×C5—31no—
26C22×C3×C5—24no—
27C22×C3×C5C2311yescharacteristic
28C22×C3×C5C2314yescomplemented
29C2×C5×D3—24no—
30C2×C5×D3—216no—
31C2×C5×D3D414yesdirect product factor
32C2×C5×D3C2312yes—
33C2×C5×D3C2314yescomplemented
34C3×C4×C5C2312yescomplemented
35C5×Dic3C2312yescomplemented
36C23×D3C2×C512yescomplemented
37C2×C3×D4C2×C511yescharacteristic, complemented
38C2×#67C2×C512yescomplemented
39D3×D4C2×C518yesdirect product factor
40C2×D12C2×C511yescharacteristic, complemented
41C2×C4×D3C2×C511yescharacteristic, complemented
42C23×C5—31no—
43C23×C5—32no—
44C23×C5—38no—
45C23×C5—68no—
46C23×C5C2×D312yescomplemented
47C5×D4—38no—
48C5×D4—34no—
49C5×D4C2×D314yesdirect product factor
50C2×C4×C5—31no—
51C2×C4×C5—34no—
52C2×C4×C5C2×D311yescharacteristic, complemented
53C22×D4—31noSylow
54C2×C3×C5—24no—
55C2×C3×C5C2×D412yescomplemented
56C2×C3×C5C2411yescharacteristic
57C5×D3—24no—
58C5×D3C2×D414yesdirect product factor
59C23×C3C22×C512yescomplemented
60C22×D3—28no—
61C22×D3C22×C511yescharacteristic
62C22×D3C22×C518yescomplemented
63C22×D3C22×C512yescomplemented
64C3×D4C22×C514yescomplemented
65C2×C3×C4C22×C511yescharacteristic, complemented
66#67C22×C518yescomplemented
67C2×Dic3C22×C511yescharacteristic, complemented
68D12C22×C514yescomplemented
69C4×D3C22×C514yescomplemented
70C22×C5—24no—
71C22×C5—34no—
72C22×C5—32no—
73C22×C5—34no—
74C22×C5—616no—
75C22×C5—64no—
76C22×C5C22×D311yescharacteristic
77C22×C5C22×D314yescomplemented
78C4×C5—32no—
79C4×C5C22×D312yescomplemented
80C24—32no—
81C2×D4—32no—
82C2×D4—38no—
83C2×D4—31no—
84C2×D4C5×D311yescharacteristic, direct product factor
85C22×C4—31no—
86C3×C5C22×D411yescharacteristic, complemented, Hall
87C22×C3—24no—
88C22×C3C23×C511yescharacteristic
89C22×C3C23×C514yescomplemented
90C2×D3—24no—
91C2×D3—216no—
92C2×D3C5×D414yesdirect product factor
93C2×D3C23×C512yes—
94C2×D3C23×C514yescomplemented
95C3×C4C23×C512yescomplemented
96Dic3C23×C512yescomplemented
97C2×C5—24no—
98C2×C5—34no—
99C2×C5—64no—
100C2×C5D3×D412yesdirect product factor
101C2×C5C23×D311yescharacteristic
102C23—31no—
103C23—32no—
104C23—38no—
105C23—68no—
106C23C2×C5×D312yescomplemented
107D4—38no—
108D4—34no—
109D4C2×C5×D314yesdirect product factor
110C2×C4—31no—
111C2×C4—34no—
112C2×C4C2×C5×D311yescharacteristic, complemented
113C2×C3—24no—
114C2×C3C2×C5×D412yescomplemented
115C2×C3C24×C511yescharacteristic
116D3—24no—
117D3C2×C5×D414yesdirect product factor
118C5C2×D3×D411yescharacteristic, direct product factor, Sylow
119C22—24no—
120C22—34no—
121C22—32no—
122C22—34no—
123C22—616no—
124C22—64no—
125C22C22×C5×D311yescharacteristic
126C22C22×C5×D314yescomplemented
127C4—32no—
128C4C22×C5×D312yescomplemented
129C3C22×C5×D411yescharacteristic, complemented, Sylow
130C2—24no—
131C2—34no—
132C2—64no—
133C2C5×D3×D412yesdirect product factor
134C2C23×C5×D311yescharacteristic
subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC2×C3C24×C5
FrattiniC2C23×C5×D3
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×C5×D4D3
hypocenterC3C22×C5×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
1. C23×C5×D3C2semidirect
2. C2×C3×C5×D4C2semidirect
3. C2×C5×#67C2semidirect
4. C5×D3×D4C2direct (N × H)
5. C2×C5×D12C2semidirect
6. C2×C4×C5×D3C2semidirect
8. C23×C3×C5C22semidirect
11. C22×C5×D3C22semidirect
12. C22×C5×D3C22semidirect
13. C3×C5×D4C22semidirect
14. C2×C3×C4×C5C22semidirect
15. C5×#67C22semidirect
16. C2×C5×Dic3C22semidirect
17. C5×D12C22semidirect
18. C4×C5×D3C22semidirect
19. C2×D3×D4C5direct (N × H)
24. C2×C5×D4D3direct (N × H)
28. C22×C3×C5C23semidirect
31. C2×C5×D3D4direct (N × H)
33. C2×C5×D3C23semidirect
34. C3×C4×C5C23semidirect
35. C5×Dic3C23semidirect
36. C23×D3C2×C5semidirect
37. C2×C3×D4C2×C5semidirect
38. C2×#67C2×C5semidirect
39. D3×D4C2×C5direct (N × H)
40. C2×D12C2×C5semidirect
41. C2×C4×D3C2×C5semidirect
46. C23×C5C2×D3semidirect
49. C5×D4C2×D3direct (N × H)
52. C2×C4×C5C2×D3semidirect
55. C2×C3×C5C2×D4semidirect
58. C5×D3C2×D4direct (N × H)
59. C23×C3C22×C5semidirect
62. C22×D3C22×C5semidirect
63. C22×D3C22×C5semidirect
64. C3×D4C22×C5semidirect
65. C2×C3×C4C22×C5semidirect
66. #67C22×C5semidirect
67. C2×Dic3C22×C5semidirect
68. D12C22×C5semidirect
69. C4×D3C22×C5semidirect
77. C22×C5C22×D3semidirect
79. C4×C5C22×D3semidirect
84. C2×D4C5×D3direct (N × H)
86. C3×C5C22×D4semidirect
89. C22×C3C23×C5semidirect
92. C2×D3C5×D4direct (N × H)
94. C2×D3C23×C5semidirect
95. C3×C4C23×C5semidirect
96. Dic3C23×C5semidirect
100. C2×C5D3×D4direct (N × H)
106. C23C2×C5×D3semidirect
109. D4C2×C5×D3direct (N × H)
112. C2×C4C2×C5×D3semidirect
114. C2×C3C2×C5×D4semidirect
117. D3C2×C5×D4direct (N × H)
118. C5C2×D3×D4direct (N × H)
126. C22C22×C5×D3semidirect
128. C4C22×C5×D3semidirect
129. C3C22×C5×D4semidirect
133. C2C5×D3×D4direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×D32
C2×C3×C5×D42
C2×C5×#672
C5×D3×D42
C2×C5×D122
C2×C4×C5×D32
C22×C5×D43
C2×D3×D45