Finite Group Databasebeta

← C2×C32×C5×C22⋊C4 #13088224

Subgroups — C2×C32×C5×C22⋊C4 #13088224

Order 1440.

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

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 456 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
1C24×C32×C5C211yesmaximal, characteristic
2C22×C32×C4×C5C212yesmaximal, complemented
3C32×C5×C22⋊C4C214yesmaximal, direct product factor
4C2×C3×C5×C22⋊C4C314yesmaximal, direct product factor
5C23×C32×C5—24no—
6C23×C32×C5C414yescomplemented
7C23×C32×C5C2212yes—
8C23×C32×C5C2211yescharacteristic
9C2×C32×C4×C5—24no—
10C2×C32×C4×C5C2214yescomplemented
11C2×C32×C22⋊C4C511yesmaximal, characteristic, direct product factor, Hall
12C24×C3×C5C2×C314yes—
13C22×C3×C4×C5C2×C318yescomplemented
14C3×C5×C22⋊C4C2×C3116yesdirect product factor
15C22×C32×C5—28no—
16C22×C32×C5—24no—
17C22×C32×C5C2×C412yes—
18C22×C32×C5C2×C414yescomplemented
19C22×C32×C5D414yes—
20C22×C32×C5C2311yescharacteristic
21C32×C4×C5—24no—
22C2×C5×C22⋊C4C3211yescharacteristic, direct product factor, Hall
23C24×C32C2×C511yescharacteristic
24C22×C32×C4C2×C512yescomplemented
25C32×C22⋊C4C2×C514yesdirect product factor
26C23×C3×C5—216no—
27C23×C3×C5C3×C4116yescomplemented
28C23×C3×C5C22×C318yes—
29C23×C3×C5C22×C314yes—
30C2×C3×C4×C5—216no—
31C2×C3×C4×C5C22×C3116yescomplemented
32C2×C3×C22⋊C4C3×C514yesdirect product factor
33C2×C32×C5—24no—
34C2×C32×C5C22⋊C414yesdirect product factor
35C2×C32×C5C22×C411yescharacteristic
36C2×C32×C5C2×D412yes—
37C24×C5C2×C3211yescharacteristic
38C22×C4×C5C2×C3212yescomplemented
39C5×C22⋊C4C2×C3214yesdirect product factor
40C23×C32—24no—
41C23×C32C4×C514yescomplemented
42C23×C32C22×C512yes—
43C23×C32C22×C511yescharacteristic
44C2×C32×C4—24no—
45C2×C32×C4C22×C514yescomplemented
46C22×C3×C5—232no—
47C22×C3×C5—216no—
48C22×C3×C5C2×C3×C418yes—
49C22×C3×C5C2×C3×C4116yescomplemented
50C22×C3×C5C3×D4116yes—
51C22×C3×C5C23×C314yes—
52C3×C4×C5—216no—
53C24×C3C2×C3×C514yes—
54C22×C3×C4C2×C3×C518yescomplemented
55C3×C22⋊C4C2×C3×C5116yesdirect product factor
56C32×C5C2×C22⋊C411yescharacteristic, direct product factor, Hall
57C23×C5—24no—
58C23×C5C32×C414yescomplemented
59C23×C5C22×C3212yes—
60C23×C5C22×C3211yescharacteristic
61C2×C4×C5—24no—
62C2×C4×C5C22×C3214yescomplemented
63C22×C32—28no—
64C22×C32—24no—
65C22×C32C2×C4×C512yes—
66C22×C32C2×C4×C514yescomplemented
67C22×C32C5×D414yes—
68C22×C32C23×C511yescharacteristic
69C32×C4—24no—
70C2×C22⋊C4C32×C511yescharacteristic, direct product factor, Sylow
71C2×C3×C5—216no—
72C2×C3×C5C3×C22⋊C4116yesdirect product factor
73C2×C3×C5C22×C3×C414yes—
74C2×C3×C5C2×C3×D418yes—
75C23×C3—216no—
76C23×C3C3×C4×C5116yescomplemented
77C23×C3C22×C3×C518yes—
78C23×C3C22×C3×C514yes—
79C2×C3×C4—216no—
80C2×C3×C4C22×C3×C5116yescomplemented
81C22×C5—28no—
82C22×C5—24no—
83C22×C5C2×C32×C412yes—
84C22×C5C2×C32×C414yescomplemented
85C22×C5C32×D414yes—
86C22×C5C23×C3211yescharacteristic
87C4×C5—24no—
88C2×C32—24no—
89C2×C32C5×C22⋊C414yesdirect product factor
90C2×C32C22×C4×C511yescharacteristic
91C2×C32C2×C5×D412yes—
92C24C2×C32×C511yescharacteristic
93C22×C4C2×C32×C512yescomplemented
94C22⋊C4C2×C32×C514yesdirect product factor
95C3×C5C2×C3×C22⋊C414yesdirect product factor
96C22×C3—232no—
97C22×C3—216no—
98C22×C3C2×C3×C4×C518yes—
99C22×C3C2×C3×C4×C5116yescomplemented
100C22×C3C3×C5×D4116yes—
101C22×C3C23×C3×C514yes—
102C3×C4—216no—
103C2×C5—24no—
104C2×C5C32×C22⋊C414yesdirect product factor
105C2×C5C22×C32×C411yescharacteristic
106C2×C5C2×C32×D412yes—
107C32C2×C5×C22⋊C411yescharacteristic, direct product factor, Sylow
108C23—24no—
109C23C32×C4×C514yescomplemented
110C23C22×C32×C512yes—
111C23C22×C32×C511yescharacteristic
112C2×C4—24no—
113C2×C4C22×C32×C514yescomplemented
114C2×C3—216no—
115C2×C3C3×C5×C22⋊C4116yesdirect product factor
116C2×C3C22×C3×C4×C514yes—
117C2×C3C2×C3×C5×D418yes—
118C5C2×C32×C22⋊C411yescharacteristic, direct product factor, Sylow
119C22—24no—
120C22—28no—
121C22C2×C32×C4×C512yes—
122C22C2×C32×C4×C514yescomplemented
123C22C32×C5×D414yes—
124C22C23×C32×C511yescharacteristic
125C4—24no—
126C3C2×C3×C5×C22⋊C414yesdirect product factor
127C2—24no—
128C2C32×C5×C22⋊C414yesdirect product factor
129C2C22×C32×C4×C511yescharacteristic
130C2C2×C32×C5×D412yes—
subgroupG/H
center, socleC23×C32×C5C22
commutatorC2C22×C32×C4×C5
Frattini, cosocleC22C23×C32×C5
prime radicalC24×C32×C5C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C32×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C32×C4×C5C2semidirect
3. C32×C5×C22⋊C4C2direct (N × H)
4. C2×C3×C5×C22⋊C4C3direct (N × H)
6. C23×C32×C5C4semidirect
10. C2×C32×C4×C5C22semidirect
11. C2×C32×C22⋊C4C5direct (N × H)
13. C22×C3×C4×C5C2×C3semidirect
14. C3×C5×C22⋊C4C2×C3direct (N × H)
18. C22×C32×C5C2×C4semidirect
22. C2×C5×C22⋊C4C32direct (N × H)
24. C22×C32×C4C2×C5semidirect
25. C32×C22⋊C4C2×C5direct (N × H)
27. C23×C3×C5C3×C4semidirect
31. C2×C3×C4×C5C22×C3semidirect
32. C2×C3×C22⋊C4C3×C5direct (N × H)
34. C2×C32×C5C22⋊C4direct (N × H)
38. C22×C4×C5C2×C32semidirect
39. C5×C22⋊C4C2×C32direct (N × H)
41. C23×C32C4×C5semidirect
45. C2×C32×C4C22×C5semidirect
49. C22×C3×C5C2×C3×C4semidirect
54. C22×C3×C4C2×C3×C5semidirect
55. C3×C22⋊C4C2×C3×C5direct (N × H)
56. C32×C5C2×C22⋊C4direct (N × H)
58. C23×C5C32×C4semidirect
62. C2×C4×C5C22×C32semidirect
66. C22×C32C2×C4×C5semidirect
70. C2×C22⋊C4C32×C5direct (N × H)
72. C2×C3×C5C3×C22⋊C4direct (N × H)
76. C23×C3C3×C4×C5semidirect
80. C2×C3×C4C22×C3×C5semidirect
84. C22×C5C2×C32×C4semidirect
89. C2×C32C5×C22⋊C4direct (N × H)
93. C22×C4C2×C32×C5semidirect
94. C22⋊C4C2×C32×C5direct (N × H)
95. C3×C5C2×C3×C22⋊C4direct (N × H)
99. C22×C3C2×C3×C4×C5semidirect
104. C2×C5C32×C22⋊C4direct (N × H)
107. C32C2×C5×C22⋊C4direct (N × H)
109. C23C32×C4×C5semidirect
113. C2×C4C22×C32×C5semidirect
115. C2×C3C3×C5×C22⋊C4direct (N × H)
118. C5C2×C32×C22⋊C4direct (N × H)
122. C22C2×C32×C4×C5semidirect
126. C3C2×C3×C5×C22⋊C4direct (N × H)
128. C2C32×C5×C22⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C32×C52
C22×C32×C4×C52
C32×C5×C22⋊C42
C2×C3×C5×C22⋊C43
C2×C32×C22⋊C45