Finite Group Databasebeta

← #13083701

Subgroups — #13083701

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D360C211yesmaximal, characteristic, complemented
2C9×D40C211yesmaximal, characteristic, complemented
3C5×C9⋊C16C211yesmaximal, characteristic, complemented
4#90938—31nomaximal
5D180—21no—
6C9×D20—21no—
7C5×C8×C9C2211yescharacteristic
8#63385—51nomaximal, Hall
9D120—31no—
10C3×D40D311yescharacteristic
11C5×C3⋊C16—31no—
12C2×D45—41no—
13C2×C9×D5—41no—
14C4×C5×C9D411yescharacteristic
15D80—91noHall
16C9×D8—51no—
17D72—51no—
18C9⋊C16D511yescharacteristic, complemented
19D60—61no—
20C3×D20—21no—
21C3×C5×C8C2×D311yescharacteristic
22#826—151no—
23C2×C5×C9D811yescharacteristic
24D45—81no—
25C9×D5—81no—
26D40—91no—
27D40D911yescharacteristic, complemented
28C5×C16—91no—
29D4×C9—101no—
30D36—101no—
31C8×C9C2×D511yescharacteristic
32C2×D15—121no—
33C2×C3×D5—41no—
34C3×C4×C5#6711yescharacteristic
35C3×D8—51no—
36D24—151no—
37C3⋊C16—31no—
38C5×C9D1611yescharacteristic, complemented, Hall
39D20—21no—
40D20—181no—
41C5×C8C2×D911yescharacteristic
42C22×C9—201no—
43C2×D9—201no—
44C4×C9D2011yescharacteristic
45D16—451noSylow
46C2×C3×C5#21311yescharacteristic
47D15—241no—
48C3×D5—81no—
49C3×D4—101no—
50D12—301no—
51C3×C8D3×D511yescharacteristic
52C2×D5—41no—
53C2×D5—361no—
54C4×C5#61111yescharacteristic
55C2×C9—401no—
56C2×C9D4011yescharacteristic
57D9—401no—
58D8—51no—
59D8—451no—
60C16—91no—
61C3×C5#82611yescharacteristic
62C22×C3—201no—
63C2×D3—601no—
64C3×C4#120211yescharacteristic
65C2×C5#367311yescharacteristic
66D5—81no—
67D5—721no—
68C9D8011yescharacteristic, complemented, Sylow
69D4—101no—
70D4—901no—
71C8D5×D911yescharacteristic
72C2×C3—401no—
73C2×C3#665311yescharacteristic
74D3—1201no—
75C5#6338511yescharacteristic, complemented, Sylow
76C22—201no—
77C22—1801no—
78C4#6708311yescharacteristic
79C3#9093811yescharacteristic
80C2—401no—
81C2—3601no—
82C2#1062354911yescharacteristic
subgroupG/H
centerC2#10623549
commutator, Fitting, cosocleC5×C8×C9C22
FrattiniC3×C8D3×D5
socleC2×C3×C5#213
hypercenterC8D5×D9
hypocenterC5×C9D16
LCSG ▷ C5×C8×C9 ▷ C4×C5×C9 ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. D360C2semidirect
2. C9×D40C2semidirect
3. C5×C9⋊C16C2semidirect
18. C9⋊C16D5semidirect
27. D40D9semidirect
38. C5×C9D16semidirect
68. C9D80semidirect
75. C5#63385semidirect

Maximal subgroups

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

subgroupindex
D3602
C9×D402
C5×C9⋊C162
#909383
#633855