Finite Group Databasebeta

← #13083869

Subgroups — #13083869

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C9×D8C211yesmaximal, characteristic, complemented
2D360C211yesmaximal, characteristic, complemented
3C9⋊#672C211yesmaximal, characteristic, complemented
4#91110—31nomaximal
5C5×D4×C9—21no—
6D180—21no—
7C5×C8×C9C2211yescharacteristic
8#63385—51nomaximal, Hall
9C3×C5×D8D311yescharacteristic
10D120—31no—
11C3⋊#672—31no—
12C22×C5×C9—41no—
13C2×D45—41no—
14C4×C5×C9D411yescharacteristic
15#3958—91noHall
16C9×D8D511yescharacteristic, complemented
17D72—51no—
18C9⋊C16—51no—
19C3×C5×D4—21no—
20D60—61no—
21C3×C5×C8C2×D311yescharacteristic
22#826—151no—
23C2×C5×C9—81no—
24C2×C5×C9D811yescharacteristic
25D45—81no—
26C5×D8D911yescharacteristic, complemented
27D40—91no—
28#672—91no—
29D4×C9—21no—
30D36—101no—
31C8×C9C2×D511yescharacteristic
32C22×C3×C5—41no—
33C2×D15—121no—
34C3×C4×C5#6711yescharacteristic
35C3×D8D1511yescharacteristic
36D24—151no—
37C3⋊C16—151no—
38C5×C9D1611yescharacteristic, complemented, Hall
39C5×D4—21no—
40D20—181no—
41C5×C8C2×D911yescharacteristic
42C22×C9—41no—
43C2×D9—201no—
44C4×C9C22⋊D511yescharacteristic
45D16—451noSylow
46C2×C3×C5—81no—
47C2×C3×C5#21311yescharacteristic
48D15—241no—
49C3×D4—21no—
50D12—301no—
51C3×C8C2×D1511yescharacteristic
52C22×C5—41no—
53C2×D5—361no—
54C4×C5#61111yescharacteristic
55C2×C9—81no—
56C2×C9#68611yescharacteristic
57D9—401no—
58D8—451no—
59D8D4511yescharacteristic, complemented
60C16—451no—
61C3×C5#82611yescharacteristic
62C22×C3—41no—
63C2×D3—601no—
64C3×C4#122011yescharacteristic
65C2×C5—81no—
66C2×C5#367311yescharacteristic
67D5—721no—
68C9#395811yescharacteristic, complemented, Sylow
69D4—21no—
70D4—901no—
71C8C2×D4511yescharacteristic
72C2×C3—81no—
73C2×C3#671511yescharacteristic
74D3—1201no—
75C5#6338511yescharacteristic, complemented, Sylow
76C22—41no—
77C22—1801no—
78C4#6709911yescharacteristic
79C3#9111011yescharacteristic
80C2—81no—
81C2—3601no—
82C2#1062360811yescharacteristic
subgroupG/H
centerC2#10623608
commutator, cosocleC5×C8×C9C22
FrattiniC3×C8C2×D15
FittingC5×C9×D8C2
socleC2×C3×C5#213
hypercenterD8D45
hypocenterC5×C9D16
LCSG ▷ C5×C8×C9 ▷ C4×C5×C9 ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

Complements

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

NH ≅ G/Ntype
1. C5×C9×D8C2semidirect
2. D360C2semidirect
3. C9⋊#672C2semidirect
16. C9×D8D5semidirect
26. C5×D8D9semidirect
38. C5×C9D16semidirect
59. D8D45semidirect
68. C9#3958semidirect
75. C5#63385semidirect

Maximal subgroups

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

subgroupindex
C5×C9×D82
D3602
C9⋊#6722
#911103
#633855