Finite Group Databasebeta

← D145⋊D15 #22576489

Subgroups — D145⋊D15 #22576489

Order 8700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C5×D435C211yesmaximal, characteristic, complemented
3C3×C5×D145C211yesmaximal, characteristic, complemented
4(C5⋊D5)⋊D29—31nomaximal, Hall
5C3×C52×C29C2211yescharacteristic, complemented, Hall
6D15⋊D29—51nomaximal
7D15×D29—51nomaximal
8C29×C5⋊D5—31no—
9C5×D145—31no—
10C5×D145D311yescharacteristic, complemented
11D435D511yescharacteristic, complemented
12C29×D15—51no—
13C29×D15—51no—
14C29×D15—102no—
15C5×D87—51no—
16C3×D145D511yescharacteristic, complemented
17C3×C5×D29—51no—
18C52×C29C2×D311yescharacteristic, complemented, Hall
19D5×D29—151no—
20D5×D29—151no—
21C3×C5×C29—22no—
22C3×C5×C29C2×D511yescharacteristic, complemented
23C3×C5×C29C2×D511yescharacteristic, complemented
24D3×D29—251noHall
25D5×D15—291nomaximal, Hall
26D145—31no—
27D145D1511yescharacteristic, complemented
28C5×D29—51no—
29C5×D29—151no—
30D5×C29—151no—
31D5×C29—151no—
32D5×C29—302no—
33D87—51no—
34C3×D29—51no—
35D3×C29—251no—
36C3⋊(C5⋊D5)D2911yescharacteristic, complemented
37C5×D15—291no—
38C3×C5×D5—291no—
39C5×C29—22no—
40C5×C29D3×D511yescharacteristic, complemented
41C5×C29C2×D1511yescharacteristic, complemented
42C2×D29—751noHall
43D52—871noHall
44C3×C29D5211yescharacteristic, complemented, Hall
45C3×C52C2×D2911yescharacteristic, complemented, Hall
46C2×D15—1451no—
47D3×D5—1451no—
48C2×C29—751no—
49D29—51no—
50D29—151no—
51C5⋊D5—31no—
52C5×D5—291no—
53C5×D5—871no—
54C2×C3×C5—1451no—
55D15—51no—
56D15—51no—
57D15—102no—
58D15—291no—
59C3×D5—291no—
60C5×D3—1451no—
61C29D5×D1511yescharacteristic, complemented, Sylow
62C52D3×D2911yescharacteristic, complemented, Sylow
63C2×D5—4351no—
64C2×D5—4351no—
65C3×C5—22no—
66C3×C5D5×D2911yescharacteristic, complemented
67C3×C5D5×D2911yescharacteristic, complemented
68C2×D3—7251noHall
69C2×C5—1451no—
70C2×C5—4351no—
71D5—151no—
72D5—151no—
73D5—291no—
74D5—302no—
75D5—871no—
76C2×C3—1451no—
77D3—251no—
78D3—1451no—
79C5—22no—
80C5D15×D2911yescharacteristic, complemented
81C5D15⋊D2911yescharacteristic, complemented
82C22—21751noSylow
83C3(C5⋊D5)⋊D2911yescharacteristic, complemented, Sylow
84C2—751no—
85C2—1451no—
86C2—4351no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C29C22
LCSG ▷ C3×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C29×C3⋊(C5⋊D5)C2semidirect
2. C5×D435C2semidirect
3. C3×C5×D145C2semidirect
5. C3×C52×C29C22semidirect
10. C5×D145D3semidirect
11. D435D5semidirect
16. C3×D145D5semidirect
18. C52×C29C2×D3semidirect
22. C3×C5×C29C2×D5semidirect
23. C3×C5×C29C2×D5semidirect
27. D145D15semidirect
36. C3⋊(C5⋊D5)D29semidirect
40. C5×C29D3×D5semidirect
41. C5×C29C2×D15semidirect
44. C3×C29D52semidirect
45. C3×C52C2×D29semidirect
61. C29D5×D15semidirect
62. C52D3×D29semidirect
66. C3×C5D5×D29semidirect
67. C3×C5D5×D29semidirect
80. C5D15×D29semidirect
81. C5D15⋊D29semidirect
83. C3(C5⋊D5)⋊D29semidirect