Finite Group Databasebeta

← C5×#63769 #13086321

Subgroups — C5×#63769 #13086321

Order 1440.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C4⋊#157C212yesmaximal
2C5×C8×C3⋊D3C211yesmaximal, characteristic
3C2×C5×#157—22no—
4C4×C5×C3⋊D3C2211yescharacteristic
5C32×C5×C8C411yescharacteristic, complemented
6C5×C3⋊(C3⋊C8)C411yescharacteristic, complemented
7#63769C511yesmaximal, characteristic, direct product factor, Hall
8C5×D3×C8—62no—
9C2×C5×C3⋊D3D411yescharacteristic
10C5×#157—42no—
11C32×C4×C5C2×C411yescharacteristic
12C5×C3⋊Dic3Q811yescharacteristic
13C5×#107—91nomaximal, Hall
14C4⋊#157C2×C512yes—
15C8×C3⋊D3C2×C511yescharacteristic
16C4×C5×D3—62no—
17C3×C5×C8—22no—
18C5×C3⋊C8—62no—
19C2×C32×C5C4⋊C411yescharacteristic
20C5×C3⋊D3D811yescharacteristic
21C5×C3⋊D3Q1611yescharacteristic
22C2×C5×C8—91no—
23C5×C4⋊C4—92no—
24C2×#157—22no—
25C4×C3⋊D3C22×C511yescharacteristic
26C32×C8C4×C511yescharacteristic, complemented
27C3⋊(C3⋊C8)C4×C511yescharacteristic, complemented
28C2×C5×D3—62no—
29C3×C4×C5—22no—
30C5×Dic3—62no—
31D3×C8—62no—
32C32×C5#10711yescharacteristic, complemented, Hall
33C2×C4×C5—91no—
34C2×C4×C5—182no—
35C5×C8—91no—
36C5×C8#15711yescharacteristic, complemented
37C2×C3⋊D3C5×D411yescharacteristic
38#157—42no—
39C32×C4C2×C4×C511yescharacteristic
40C3⋊Dic3C5×Q811yescharacteristic
41#107—91noSylow
42C2×C3×C5—22no—
43C5×D3—62no—
44C5×D3—62no—
45C4×D3—62no—
46C3×C8—22no—
47C3⋊C8—62no—
48C22×C5—91no—
49C4×C5—91no—
50C4×C5—362no—
51C4×C5C2×#15711yescharacteristic
52C2×C32C5×C4⋊C411yescharacteristic
53C3⋊D3C5×D811yescharacteristic
54C3⋊D3C5×Q1611yescharacteristic
55C2×C8—91no—
56C4⋊C4—92no—
57C3×C5—22no—
58C2×D3—62no—
59C3×C4—22no—
60Dic3—62no—
61C2×C5—91no—
62C2×C5—91no—
63C2×C5C4⋊#15711yescharacteristic
64C32C5×#10711yescharacteristic, complemented, Sylow
65C2×C4—91no—
66C2×C4—182no—
67C8—91no—
68C8C5×#15711yescharacteristic, complemented
69C2×C3—22no—
70D3—62no—
71D3—62no—
72C5#6376911yescharacteristic, direct product factor, Sylow
73C22—91no—
74C4—91no—
75C4—362no—
76C4C2×C5×#15711yescharacteristic
77C3—22no—
78C2—91no—
79C2—91no—
80C2C5×C4⋊#15711yescharacteristic
subgroupG/H
centerC2×C5C4⋊#157
commutatorC32×C4C2×C4×C5
FrattiniC4C2×C5×#157
FittingC32×C5×C8C4
socleC2×C32×C5C4⋊C4
prime radicalC2×C5×C3⋊D3D4
cosocleC4×C3⋊D3C22×C5
hypercenterC5×C8#157
hypocenterC32C5×#107
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8

Complements

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

NH ≅ G/Ntype
5. C32×C5×C8C4semidirect
6. C5×C3⋊(C3⋊C8)C4semidirect
7. #63769C5direct (N × H)
26. C32×C8C4×C5semidirect
27. C3⋊(C3⋊C8)C4×C5semidirect
32. C32×C5#107semidirect
36. C5×C8#157semidirect
64. C32C5×#107semidirect
68. C8C5×#157semidirect
72. C5#63769direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C4⋊#1572
C5×C8×C3⋊D32
#637695
C5×#1079