Finite Group Databasebeta

← C9×#686 #10623575

Subgroups — C9×#686 #10623575

Order 720.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D4×C9C211yesmaximal, characteristic, complemented
2C9×D20C211yesmaximal, characteristic, complemented
3C9×#168C211yesmaximal, characteristic, complemented
4C3×#686C311yesmaximal, characteristic
5C22×C5×C9—21no—
6C2×C9×D5—21no—
7C4×C5×C9C2211yescharacteristic
8C9×D8—51nomaximal, Hall
9C3×C5×D4C2×C311yescharacteristic
10C3×D20C2×C311yescharacteristic
11C3×#168C2×C311yescharacteristic
12C2×C5×C9—41no—
13C2×C5×C9D411yescharacteristic
14C9×D5—41no—
15#686C911yescharacteristic, direct product factor, Hall
16D4×C9—51no—
17D4×C9D511yescharacteristic, complemented
18C8×C9—51no—
19C22×C3×C5—21no—
20C2×C3×D5—21no—
21C3×C4×C5C22×C311yescharacteristic
22C3×D8—51no—
23C5×C9D811yescharacteristic, complemented, Hall
24C5×D4C2×C911yescharacteristic, complemented
25D20C2×C911yescharacteristic, complemented
26#168C2×C911yescharacteristic, complemented
27C22×C9—21no—
28C22×C9—101no—
29C4×C9C2×D511yescharacteristic
30C2×C3×C5—41no—
31C2×C3×C5C3×D411yescharacteristic
32C3×D5—41no—
33C3×D4—51no—
34C3×D4C3×D511yescharacteristic
35C3×C8—51no—
36C22×C5—21no—
37C2×D5—21no—
38C4×C5C22×C911yescharacteristic
39C2×C9—41no—
40C2×C9—201no—
41C2×C9C22⋊D511yescharacteristic
42D8—51noSylow
43C3×C5C3×D811yescharacteristic
44C22×C3—21no—
45C22×C3—101no—
46C3×C4C2×C3×D511yescharacteristic
47C2×C5—41no—
48C2×C5D4×C911yescharacteristic
49D5—41no—
50C9#68611yescharacteristic, direct product factor, Sylow
51D4—51no—
52D4C9×D511yescharacteristic, complemented
53C8—51no—
54C2×C3—41no—
55C2×C3—201no—
56C2×C3C3×C22⋊D511yescharacteristic
57C5C9×D811yescharacteristic, complemented, Sylow
58C22—21no—
59C22—101no—
60C4C2×C9×D511yescharacteristic
61C3C3×#68611yescharacteristic
62C2—41no—
63C2—201no—
64C2C9×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C9C22⋊D5
commutatorC4×C5C22×C9
FrattiniC3×C4C2×C3×D5
FittingC5×D4×C9C2
socleC2×C3×C5C3×D4
prime radicalC3×#686C3
cosocleC3×C4×C5C22×C3
hypercenterD4×C9D5
hypocenterC5C9×D8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ D4×C9

Complements

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

NH ≅ G/Ntype
1. C5×D4×C9C2semidirect
2. C9×D20C2semidirect
3. C9×#168C2semidirect
15. #686C9direct (N × H)
17. D4×C9D5semidirect
23. C5×C9D8semidirect
24. C5×D4C2×C9semidirect
25. D20C2×C9semidirect
26. #168C2×C9semidirect
50. C9#686direct (N × H)
52. D4C9×D5semidirect
57. C5C9×D8semidirect

Maximal subgroups

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

subgroupindex
C5×D4×C92
C9×D202
C9×#1682
C3×#6863
C9×D85