Finite Group Databasebeta

← C5×C7×C9⋊#1181 #49141265

Subgroups — C5×C7×C9⋊#1181 #49141265

Order 36540.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C7×C9×D29C211yesmaximal, characteristic
2C5×C7×C3⋊#1181—31nomaximal
3C5×C7×C9×C29C411yescharacteristic, complemented, Hall
4C7×C9⋊#1181C511yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C7×D29D311yescharacteristic
6C5×C9⋊#1181C711yesmaximal, characteristic, direct product factor, Hall
7C5×C7×#1181—91noHall
8C7×C9×D29C2×C511yescharacteristic
9C3×C5×C7×C29Dic311yescharacteristic
10C5×C9×D29C2×C711yescharacteristic
11C7×C3⋊#1181—31no—
12C5×C7×D29D911yescharacteristic
13C7×C9×C29C4×C511yescharacteristic, complemented, Hall
14C5×C3⋊#1181—31no—
15C5×C9×C29C4×C711yescharacteristic, complemented, Hall
16C5×C7×Dic9—291nomaximal, Hall
17C3×C7×D29C5×D311yescharacteristic
18C9⋊#1181C5×C711yescharacteristic, direct product factor, Hall
19C5×C7×C29Dic911yescharacteristic, complemented, Hall
20C3×C5×D29D3×C711yescharacteristic
21C7×#1181—91noHall
22C2×C5×C7×C9—291no—
23C3×C7×C29C5×Dic311yescharacteristic
24C5×#1181—91noHall
25C9×D29C2×C5×C711yescharacteristic
26C3×C5×C29C7×Dic311yescharacteristic
27C5×C7×Dic3—871no—
28C7×D29C5×D911yescharacteristic
29C3⋊#1181—31no—
30C5×C7×C9#118111yescharacteristic, complemented, Hall
31C5×D29C7×D911yescharacteristic
32C9×C29C4×C5×C711yescharacteristic, complemented, Hall
33C7×Dic9—291noHall
34C2×C3×C5×C7—291no—
35C7×C29C5×Dic911yescharacteristic, complemented, Hall
36C5×Dic9—291noHall
37C3×D29C5×D3×C711yescharacteristic
38C5×C29C7×Dic911yescharacteristic, complemented, Hall
39C4×C5×C7—2611noHall
40C2×C7×C9—291no—
41#1181—91noHall
42C3×C5×C7C3⋊#118111yescharacteristic
43C2×C5×C9—291no—
44C3×C29C5×C7×Dic311yescharacteristic
45C7×Dic3—871no—
46C2×C5×C7—291no—
47C7×C9C5×#118111yescharacteristic, complemented, Hall
48C5×Dic3—871no—
49D29C5×C7×D911yescharacteristic
50C5×C9C7×#118111yescharacteristic, complemented, Hall
51C2×C3×C7—291no—
52Dic9—291noHall
53C5×C7C9⋊#118111yescharacteristic, direct product factor, Hall
54C2×C3×C5—291no—
55C29C5×C7×Dic911yescharacteristic, complemented, Sylow
56C4×C7—2611noHall
57C3×C7C5×C3⋊#118111yescharacteristic
58C4×C5—2611noHall
59C2×C9—291no—
60C3×C5C7×C3⋊#118111yescharacteristic
61C2×C7—291no—
62Dic3—871no—
63C2×C5—291no—
64C9C5×C7×#118111yescharacteristic, complemented, Sylow
65C7C5×C9⋊#118111yescharacteristic, direct product factor, Sylow
66C2×C3—291no—
67C5C7×C9⋊#118111yescharacteristic, direct product factor, Sylow
68C4—2611noSylow
69C3C5×C7×C3⋊#118111yescharacteristic
70C2—291no—
subgroupG/H
center, hypercenterC5×C7C9⋊#1181
commutator, hypocenterC9×C29C4×C5×C7
FrattiniC3C5×C7×C3⋊#1181
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29Dic3
prime radicalC3×C5×C7×D29D3
cosocleC9×D29C2×C5×C7
LCSG ▷ C9×C29
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
3. C5×C7×C9×C29C4semidirect
4. C7×C9⋊#1181C5direct (N × H)
6. C5×C9⋊#1181C7direct (N × H)
13. C7×C9×C29C4×C5semidirect
15. C5×C9×C29C4×C7semidirect
18. C9⋊#1181C5×C7direct (N × H)
19. C5×C7×C29Dic9semidirect
30. C5×C7×C9#1181semidirect
32. C9×C29C4×C5×C7semidirect
35. C7×C29C5×Dic9semidirect
38. C5×C29C7×Dic9semidirect
47. C7×C9C5×#1181semidirect
50. C5×C9C7×#1181semidirect
53. C5×C7C9⋊#1181direct (N × H)
55. C29C5×C7×Dic9semidirect
64. C9C5×C7×#1181semidirect
65. C7C5×C9⋊#1181direct (N × H)
67. C5C7×C9⋊#1181direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×C9×D292
C5×C7×C3⋊#11813
C7×C9⋊#11815
C5×C9⋊#11817
C5×C7×Dic929