Finite Group Databasebeta

← D15⋊D129 #21440940

Subgroups — D15⋊D129 #21440940

Order 7740.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C3⋊D129C211yesmaximal, characteristic, complemented
2C3×D645C211yesmaximal, characteristic, complemented
3C3×D15×C43C211yesmaximal, characteristic, complemented
4D15⋊D43—31nomaximal
5D5×D129—31nomaximal
6C32×C5×C43C2211yescharacteristic, complemented, Hall
7D3×D129—51nomaximal, Hall
8D645D311yescharacteristic, complemented
9D15×C43D311yescharacteristic, complemented
10C5×D129—31no—
11C5×D129—31no—
12C5×D129—61no—
13C3×D215—31no—
14C3×D5×C43—31no—
15D5×D43—91noHall
16C3⋊D129D511yescharacteristic, complemented
17C3×D129—51no—
18C3×D3×C43—51no—
19C3×C5×C43—21no—
20C3×C5×C43C2×D311yescharacteristic, complemented
21C3×C5×C43C2×D311yescharacteristic, complemented
22C2×D129—151no—
23D3×D43—151no—
24D215—31no—
25C5×D43—91no—
26D5×C43—31no—
27C32×C43C2×D511yescharacteristic, complemented, Hall
28C2×C3×C43—151no—
29D129—31no—
30D129—31no—
31D129—51no—
32D129—61no—
33C3×D43—151no—
34D3×C43—51no—
35C5×C43D3211yescharacteristic, complemented, Hall
36(C3⋊D3)⋊D5—431nomaximal, Hall
37C2×D43—451noHall
38C3×C43—21no—
39C3×C43D3×D511yescharacteristic, complemented
40C3×C43D3×D511yescharacteristic, complemented
41C5×C3⋊D3—431no—
42C3×D15—431no—
43C3×D15D4311yescharacteristic, complemented
44C2×C43—151no—
45D43—91no—
46D43—151no—
47D3×D5—1291no—
48D3×D5—1291no—
49C32×C5C2×D4311yescharacteristic, complemented, Hall
50C43(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
51D32—2151noHall
52D15—431no—
53D15D12911yescharacteristic, complemented
54C3×D5—31no—
55C3×D5—1291no—
56C5×D3—2581no—
57C5×D3—1291no—
58C5×D3—1291no—
59C2×D5—3871noHall
60C3⋊D3—431no—
61C3×D3—51no—
62C3×D3—2151no—
63C3×C5—21no—
64C3×C5D3×D4311yescharacteristic, complemented
65C3×C5C2×D12911yescharacteristic, complemented
66C2×D3—6451no—
67C2×D3—6451no—
68C2×C5—3871no—
69D5—31no—
70D5—1291no—
71C32D5×D4311yescharacteristic, complemented, Sylow
72C2×C3—151no—
73C2×C3—6451no—
74D3—2581no—
75D3—51no—
76D3—1291no—
77D3—1291no—
78D3—2151no—
79C5D3×D12911yescharacteristic, complemented, Sylow
80C22—19351noSylow
81C3—21no—
82C3D5×D12911yescharacteristic, complemented
83C3D15⋊D4311yescharacteristic, complemented
84C2—151no—
85C2—3871no—
86C2—6451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C43C22
LCSG ▷ C32×C5×C43
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D129C2semidirect
2. C3×D645C2semidirect
3. C3×D15×C43C2semidirect
6. C32×C5×C43C22semidirect
8. D645D3semidirect
9. D15×C43D3semidirect
16. C3⋊D129D5semidirect
20. C3×C5×C43C2×D3semidirect
21. C3×C5×C43C2×D3semidirect
27. C32×C43C2×D5semidirect
35. C5×C43D32semidirect
39. C3×C43D3×D5semidirect
40. C3×C43D3×D5semidirect
43. C3×D15D43semidirect
49. C32×C5C2×D43semidirect
50. C43(C3⋊D3)⋊D5semidirect
53. D15D129semidirect
64. C3×C5D3×D43semidirect
65. C3×C5C2×D129semidirect
71. C32D5×D43semidirect
79. C5D3×D129semidirect
82. C3D5×D129semidirect
83. C3D15⋊D43semidirect