Finite Group Databasebeta

← #91118

Subgroups — #91118

Order 480.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×D4C211yesmaximal, characteristic
2#6719C212yesmaximal, complemented
3#3966—31nomaximal, Hall
4C23×C3×C5C411yescharacteristic, complemented
5C23×C3×C5C2211yescharacteristic
6C3×C5×D4—22no—
7C2×C3×C4×C5C411yescharacteristic, complemented
8C2×Dic15—22no—
9#834—51nomaximal, Hall
10C2×C5×D4D311yescharacteristic
11C22⋊Dic5—32no—
12C22×C3×C5—21no—
13C22×C3×C5—41no—
14C22×C3×C5—41no—
15C22×C3×C5C2×C411yescharacteristic
16C22×C3×C5D412yes—
17C3×C4×C5—21no—
18Dic15—42no—
19C2×C3×D4D511yescharacteristic
20#217—52no—
21C23×C5Dic311yescharacteristic, complemented
22C23×C5C2×D311yescharacteristic
23C5×D4—22no—
24C2×C4×C5Dic311yescharacteristic, complemented
25C2×Dic5—62no—
26#99—151noSylow
27C2×C3×C5—22no—
28C2×C3×C5—21no—
29C2×C3×C5—41no—
30C2×C3×C5C22⋊C411yescharacteristic
31C23×C3Dic511yescharacteristic, complemented
32C23×C3C2×D511yescharacteristic
33C3×D4—22no—
34C2×C3×C4Dic511yescharacteristic, complemented
35C2×Dic3—102no—
36C22×C5—21no—
37C22×C5—41no—
38C22×C5—41no—
39C22×C5C2×Dic311yescharacteristic
40C22×C5#6712yes—
41C4×C5—21no—
42Dic5—122no—
43C2×D4D1511yescharacteristic
44C22⋊C4—152no—
45C3×C5#9911yescharacteristic, complemented, Hall
46C22×C3—21no—
47C22×C3—41no—
48C22×C3—41no—
49C22×C3C2×Dic511yescharacteristic
50C22×C3C22⋊D512yes—
51C3×C4—21no—
52Dic3—202no—
53C2×C5—22no—
54C2×C5—21no—
55C2×C5—41no—
56C2×C5#21711yescharacteristic
57C23Dic1511yescharacteristic, complemented
58C23C2×D1511yescharacteristic
59D4—22no—
60C2×C4—302no—
61C2×C4Dic1511yescharacteristic, complemented
62C2×C3—22no—
63C2×C3—21no—
64C2×C3—41no—
65C2×C3C22⋊Dic511yescharacteristic
66C5#83411yescharacteristic, complemented, Sylow
67C22—21no—
68C22—41no—
69C22—41no—
70C22C2×Dic1511yescharacteristic
71C22#122012yes—
72C4—21no—
73C4—602no—
74C3#396611yescharacteristic, complemented, Sylow
75C2—22no—
76C2—21no—
77C2—41no—
78C2#671911yescharacteristic
subgroupG/H
centerC2#6719
commutatorC22×C3×C5C2×C4
FrattiniC23C2×D15
Fitting, prime radicalC2×C3×C5×D4C2
socleC2×C3×C5C22⋊C4
cosocleC23×C3×C5C22
hypercenterC2×D4D15
hypocenterC3×C5#99
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #6719C2semidirect
4. C23×C3×C5C4semidirect
7. C2×C3×C4×C5C4semidirect
21. C23×C5Dic3semidirect
24. C2×C4×C5Dic3semidirect
31. C23×C3Dic5semidirect
34. C2×C3×C4Dic5semidirect
45. C3×C5#99semidirect
57. C23Dic15semidirect
61. C2×C4Dic15semidirect
66. C5#834semidirect
74. C3#3966semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×D42
#67192
#39663
#8345