Finite Group Databasebeta

← C2×C4×C5×A4 #92050

Subgroups — C2×C4×C5×A4 #92050

Order 480.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×A4C211yesmaximal, characteristic
2C4×C5×A4C212yesmaximal, direct product factor
3C23×C4×C5C311yesmaximal, characteristic, complemented, Hall
4C2×C5×A4C412yesdirect product factor
5C2×C5×A4C2211yescharacteristic
6C2×C3×C4×C5—41nomaximal
7C2×C4×A4C511yesmaximal, characteristic, direct product factor, Hall
8C24×C5C2×C311yescharacteristic
9C22×C4×C5—31no—
10C22×C4×C5—31no—
11C22×C4×C5—32no—
12C22×C4×C5C2×C312yescomplemented
13C22×C3×C5—41no—
14C5×A4C2×C411yescharacteristic, direct product factor
15C3×C4×C5—42no—
16C22×A4C2×C511yescharacteristic
17C4×A4C2×C512yesdirect product factor
18C23×C5—31no—
19C23×C5—32no—
20C23×C5—31no—
21C23×C5C3×C412yescomplemented
22C23×C5C22×C311yescharacteristic
23C2×C4×C5—32no—
24C2×C4×C5—31no—
25C2×C4×C5—32no—
26C2×C4×C5—32no—
27C2×C4×C5—32no—
28C2×C4×C5A411yescharacteristic, direct product factor
29C23×C4C3×C511yescharacteristic, complemented, Sylow
30C2×C3×C5—42no—
31C2×C3×C5—41no—
32C2×A4C4×C512yesdirect product factor
33C2×A4C22×C511yescharacteristic
34C2×C3×C4—41no—
35C22×C5—32no—
36C22×C5—31no—
37C22×C5—32no—
38C22×C5—32no—
39C22×C5—32no—
40C22×C5—31no—
41C22×C5—31no—
42C22×C5C2×C3×C411yescharacteristic, complemented
43C22×C5C2×A411yescharacteristic
44C4×C5—32no—
45C4×C5C2×A412yesdirect product factor
46C24C2×C3×C511yescharacteristic
47C22×C4—31no—
48C22×C4—31no—
49C22×C4—32no—
50C22×C4C2×C3×C512yescomplemented
51C3×C5—41noHall
52C22×C3—41no—
53A4C2×C4×C511yescharacteristic, direct product factor
54C3×C4—42no—
55C2×C5—32no—
56C2×C5—31no—
57C2×C5—31no—
58C2×C5C4×A412yesdirect product factor
59C2×C5C22×A411yescharacteristic
60C23—31no—
61C23—32no—
62C23—31no—
63C23C3×C4×C512yescomplemented
64C23C22×C3×C511yescharacteristic
65C2×C4—32no—
66C2×C4—31no—
67C2×C4—32no—
68C2×C4—32no—
69C2×C4—32no—
70C2×C4C5×A411yescharacteristic, direct product factor
71C2×C3—42no—
72C2×C3—41no—
73C5C2×C4×A411yescharacteristic, direct product factor, Sylow
74C22—32no—
75C22—31no—
76C22—32no—
77C22—32no—
78C22—32no—
79C22—31no—
80C22—31no—
81C22C2×C3×C4×C511yescharacteristic, complemented
82C22C2×C5×A411yescharacteristic
83C4—32no—
84C4C2×C5×A412yesdirect product factor
85C3—41noSylow
86C2—31no—
87C2—32no—
88C2—31no—
89C2C4×C5×A412yesdirect product factor
90C2C22×C5×A411yescharacteristic
subgroupG/H
center, hypercenterC2×C4×C5A4
commutator, hypocenterC22C2×C3×C4×C5
FrattiniC2C22×C5×A4
FittingC23×C4×C5C3
socleC24×C5C2×C3
prime radicalC22×C5×A4C2
cosocleC23C22×C3×C5
LCSG ▷ C22
UCSC1 ◁ C2×C4×C5

Complements

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

NH ≅ G/Ntype
2. C4×C5×A4C2direct (N × H)
3. C23×C4×C5C3semidirect
4. C2×C5×A4C4direct (N × H)
7. C2×C4×A4C5direct (N × H)
12. C22×C4×C5C2×C3semidirect
14. C5×A4C2×C4direct (N × H)
17. C4×A4C2×C5direct (N × H)
21. C23×C5C3×C4semidirect
28. C2×C4×C5A4direct (N × H)
29. C23×C4C3×C5semidirect
32. C2×A4C4×C5direct (N × H)
42. C22×C5C2×C3×C4semidirect
45. C4×C5C2×A4direct (N × H)
50. C22×C4C2×C3×C5semidirect
53. A4C2×C4×C5direct (N × H)
58. C2×C5C4×A4direct (N × H)
63. C23C3×C4×C5semidirect
70. C2×C4C5×A4direct (N × H)
73. C5C2×C4×A4direct (N × H)
81. C22C2×C3×C4×C5semidirect
84. C4C2×C5×A4direct (N × H)
89. C2C4×C5×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×A42
C4×C5×A42
C23×C4×C53
C2×C3×C4×C54
C2×C4×A45