Finite Group Databasebeta

← C3×D5×D93 #19150146

Subgroups — C3×D5×D93 #19150146

Order 5580.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D465C211yesmaximal, characteristic, complemented
2C3×C5×D93C211yesmaximal, characteristic, complemented
3C32×D5×C31C211yesmaximal, characteristic, complemented
4D5×D93C311yesmaximal, characteristic, direct product factor
5C3×D5×D31—31nomaximal
6C32×C5×C31C2211yescharacteristic, complemented, Hall
7C2×C3×D93—51nomaximal, Hall
8D465C2×C311yescharacteristic, complemented
9C5×D93C2×C311yescharacteristic, complemented
10C3×D155—31no—
11C3×D5×C31—21no—
12C3×D5×C31D311yescharacteristic, complemented
13C3×D5×C31C2×C311yescharacteristic, complemented
14C3×C5×D31—31no—
15D5×D31—31noHall
16C2×C32×C31—51no—
17C3×D93—51no—
18C3×D93D511yescharacteristic, direct product factor
19C3×C5×C31—21no—
20C3×C5×C31C2×D311yescharacteristic, complemented
21C3×C5×C31C22×C311yescharacteristic, complemented
22C2×D93—51no—
23C2×C3×D31—151no—
24D155—31no—
25C5×D31—31no—
26D5×C31C3×D311yescharacteristic, complemented
27C32×C31C2×D511yescharacteristic, complemented, Hall
28C2×C3×C31—51no—
29C2×C3×C31—51no—
30C2×C3×C31—101no—
31D93—51no—
32D93C3×D511yescharacteristic, direct product factor
33C3×D31—31no—
34C3×D31—151no—
35C3×D3×D5—311nomaximal, Hall
36C5×C31C2×C3×D311yescharacteristic, complemented, Hall
37C2×D31—151noHall
38C3×C31—21no—
39C3×C31D3×D511yescharacteristic, complemented
40C3×C31C2×C3×D511yescharacteristic, complemented
41C3×D15—311no—
42C3×C5×D3—311no—
43C32×D5D3111yescharacteristic, complemented
44C2×C31—51no—
45D31—31no—
46D31—151no—
47C2×C3×D5—931no—
48D3×D5—311no—
49C32×C5C2×D3111yescharacteristic, complemented, Hall
50C2×C3×D3—1551noHall
51C31C3×D3×D511yescharacteristic, complemented, Sylow
52C2×C3×C5—931no—
53D15—311no—
54C3×D5—21no—
55C3×D5—931no—
56C3×D5C3×D3111yescharacteristic, complemented
57C3×D5D9311yescharacteristic, direct product factor
58C5×D3—311no—
59C2×D5—931noHall
60C2×C32—51no—
61C3×D3—311no—
62C3×D3—1551no—
63C3×C5—21no—
64C3×C5C2×C3×D3111yescharacteristic, complemented
65C3×C5C2×D9311yescharacteristic, complemented
66C22×C3—4651no—
67C2×D3—1551no—
68C2×C5—931no—
69D5—931no—
70D5C3×D9311yescharacteristic, direct product factor
71C32D5×D3111yescharacteristic, complemented, Sylow
72C2×C3—51no—
73C2×C3—51no—
74C2×C3—101no—
75C2×C3—931no—
76C2×C3—4651no—
77D3—311no—
78D3—1551no—
79C5C2×C3×D9311yescharacteristic, complemented, Sylow
80C22—4651noSylow
81C3—21no—
82C3C3×D5×D3111yescharacteristic, complemented
83C3D5×D9311yescharacteristic, direct product factor
84C2—51no—
85C2—931no—
86C2—4651no—
subgroupG/H
center, hypercenterC3D5×D93
commutator, hypocenterC3×C5×C31C22×C3
FrattiniC1G
Fitting, socleC32×C5×C31C22
LCSG ▷ C3×C5×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D465C2semidirect
2. C3×C5×D93C2semidirect
3. C32×D5×C31C2semidirect
4. D5×D93C3direct (N × H)
6. C32×C5×C31C22semidirect
8. D465C2×C3semidirect
9. C5×D93C2×C3semidirect
12. C3×D5×C31D3semidirect
13. C3×D5×C31C2×C3semidirect
18. C3×D93D5direct (N × H)
20. C3×C5×C31C2×D3semidirect
21. C3×C5×C31C22×C3semidirect
26. D5×C31C3×D3semidirect
27. C32×C31C2×D5semidirect
32. D93C3×D5direct (N × H)
36. C5×C31C2×C3×D3semidirect
39. C3×C31D3×D5semidirect
40. C3×C31C2×C3×D5semidirect
43. C32×D5D31semidirect
49. C32×C5C2×D31semidirect
51. C31C3×D3×D5semidirect
56. C3×D5C3×D31semidirect
57. C3×D5D93direct (N × H)
64. C3×C5C2×C3×D31semidirect
65. C3×C5C2×D93semidirect
70. D5C3×D93direct (N × H)
71. C32D5×D31semidirect
79. C5C2×C3×D93semidirect
82. C3C3×D5×D31semidirect
83. C3D5×D93direct (N × H)