Finite Group Databasebeta

← C5×C7×C3⋊(C3⋊#1181) #49141630

Subgroups — C5×C7×C3⋊(C3⋊#1181) #49141630

Order 36540.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C7×D29C211yesmaximal, characteristic
2C5×C7×C3⋊#1181—34nomaximal
3C32×C5×C7×C29C411yescharacteristic, complemented, Hall
4C7×C3⋊(C3⋊#1181)C511yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C7×D29D314yes—
6C5×C3⋊(C3⋊#1181)C711yesmaximal, characteristic, direct product factor, Hall
7C5×C7×#1181—91noHall
8C32×C7×D29C2×C511yescharacteristic
9C3×C5×C7×C29Dic314yescomplemented
10C32×C5×D29C2×C711yescharacteristic
11C7×C3⋊#1181—34no—
12C5×C7×D29C3⋊D311yescharacteristic
13C32×C7×C29C4×C511yescharacteristic, complemented, Hall
14C5×C3⋊#1181—34no—
15C32×C5×C29C4×C711yescharacteristic, complemented, Hall
16C5×C7×C3⋊Dic3—291nomaximal, Hall
17C3×C7×D29C5×D314yes—
18C3⋊(C3⋊#1181)C5×C711yescharacteristic, direct product factor, Hall
19C5×C7×C29C3⋊Dic311yescharacteristic, complemented, Hall
20C3×C5×D29D3×C714yes—
21C7×#1181—91noHall
22C2×C32×C5×C7—291no—
23C3×C7×C29C5×Dic314yescomplemented
24C5×#1181—91noHall
25C32×D29C2×C5×C711yescharacteristic
26C3×C5×C29C7×Dic314yescomplemented
27C5×C7×Dic3—874no—
28C7×D29C5×C3⋊D311yescharacteristic
29C3⋊#1181—34no—
30C32×C5×C7#118111yescharacteristic, complemented, Hall
31C5×D29C7×C3⋊D311yescharacteristic
32C32×C29C4×C5×C711yescharacteristic, complemented, Hall
33C7×C3⋊Dic3—291noHall
34C2×C3×C5×C7—294no—
35C7×C29C5×C3⋊Dic311yescharacteristic, complemented, Hall
36C5×C3⋊Dic3—291noHall
37C3×D29C5×D3×C714yes—
38C5×C29C7×C3⋊Dic311yescharacteristic, complemented, Hall
39C4×C5×C7—2611noHall
40C2×C32×C7—291no—
41#1181—91noHall
42C3×C5×C7C3⋊#118114yescomplemented
43C2×C32×C5—291no—
44C3×C29C5×C7×Dic314yescomplemented
45C7×Dic3—874no—
46C2×C5×C7—291no—
47C32×C7C5×#118111yescharacteristic, complemented, Hall
48C5×Dic3—874no—
49D29C5×C7×C3⋊D311yescharacteristic
50C32×C5C7×#118111yescharacteristic, complemented, Hall
51C2×C3×C7—294no—
52C3⋊Dic3—291noHall
53C5×C7C3⋊(C3⋊#1181)11yescharacteristic, direct product factor, Hall
54C2×C3×C5—294no—
55C29C5×C7×C3⋊Dic311yescharacteristic, complemented, Sylow
56C4×C7—2611noHall
57C3×C7C5×C3⋊#118114yescomplemented
58C4×C5—2611noHall
59C2×C32—291no—
60C3×C5C7×C3⋊#118114yescomplemented
61C2×C7—291no—
62Dic3—874no—
63C2×C5—291no—
64C32C5×C7×#118111yescharacteristic, complemented, Sylow
65C7C5×C3⋊(C3⋊#1181)11yescharacteristic, direct product factor, Sylow
66C2×C3—294no—
67C5C7×C3⋊(C3⋊#1181)11yescharacteristic, direct product factor, Sylow
68C4—2611noSylow
69C3C5×C7×C3⋊#118114yescomplemented
70C2—291no—
subgroupG/H
center, hypercenterC5×C7C3⋊(C3⋊#1181)
commutator, hypocenterC32×C29C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C5×C7×D29C2
cosocleC32×D29C2×C5×C7
LCSG ▷ C32×C29
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
3. C32×C5×C7×C29C4semidirect
4. C7×C3⋊(C3⋊#1181)C5direct (N × H)
6. C5×C3⋊(C3⋊#1181)C7direct (N × H)
9. C3×C5×C7×C29Dic3semidirect
13. C32×C7×C29C4×C5semidirect
15. C32×C5×C29C4×C7semidirect
18. C3⋊(C3⋊#1181)C5×C7direct (N × H)
19. C5×C7×C29C3⋊Dic3semidirect
23. C3×C7×C29C5×Dic3semidirect
26. C3×C5×C29C7×Dic3semidirect
30. C32×C5×C7#1181semidirect
32. C32×C29C4×C5×C7semidirect
35. C7×C29C5×C3⋊Dic3semidirect
38. C5×C29C7×C3⋊Dic3semidirect
42. C3×C5×C7C3⋊#1181semidirect
44. C3×C29C5×C7×Dic3semidirect
47. C32×C7C5×#1181semidirect
50. C32×C5C7×#1181semidirect
53. C5×C7C3⋊(C3⋊#1181)direct (N × H)
55. C29C5×C7×C3⋊Dic3semidirect
57. C3×C7C5×C3⋊#1181semidirect
60. C3×C5C7×C3⋊#1181semidirect
64. C32C5×C7×#1181semidirect
65. C7C5×C3⋊(C3⋊#1181)direct (N × H)
67. C5C7×C3⋊(C3⋊#1181)direct (N × H)
69. C3C5×C7×C3⋊#1181semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C5×C7×C3⋊#11813
C7×C3⋊(C3⋊#1181)5
C5×C3⋊(C3⋊#1181)7
C5×C7×C3⋊Dic329