Finite Group Databasebeta

← D15⋊D203 #27131811

Subgroups — D15⋊D203 #27131811

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C29×D15C211yesmaximal, characteristic, complemented
2C5×D609C211yesmaximal, characteristic, complemented
3C3×D1015C211yesmaximal, characteristic, complemented
4D5×D203—31nomaximal, Hall
5C3×C5×C7×C29C2211yescharacteristic, complemented, Hall
6D3×D203—51nomaximal, Hall
7D1015D311yescharacteristic, complemented
8C7×D5×C29—31no—
9C5×D203—31no—
10D15⋊D29—71nomaximal, Hall
11D609D511yescharacteristic, complemented
12D3×C7×C29—51no—
13C3×D203—51no—
14C5×C7×C29C2×D311yescharacteristic, complemented, Hall
15C29×D15D711yescharacteristic, complemented
16C5×D87—71no—
17C3×D145—71no—
18C2×D203—151noHall
19C3×C7×C29C2×D511yescharacteristic, complemented, Hall
20D5×D29—211noHall
21C3×C5×C29C2×D711yescharacteristic, complemented, Hall
22D15⋊D7—291nomaximal, Hall
23C2×C7×C29—151no—
24D203—31no—
25D203—51no—
26D3×D29—351noHall
27D145—71no—
28C5×D29—211no—
29D5×C29—31no—
30C7×D15D2911yescharacteristic, complemented
31C5×D21—291no—
32C3×D35—291no—
33C7×C29D3×D511yescharacteristic, complemented, Hall
34D87—71no—
35C3×D29—351no—
36D3×C29—51no—
37C5×C29D3×D711yescharacteristic, complemented, Hall
38D5×D7—871noHall
39C2×D29—1051noHall
40C3×C5×C7C2×D2911yescharacteristic, complemented, Hall
41C3×C29D5×D711yescharacteristic, complemented, Hall
42D3×D7—1451noHall
43D35—291no—
44C5×D7—871no—
45C7×D5—31no—
46D3×D5—2031noHall
47C2×C29—151no—
48D29—211no—
49D29—351no—
50D21—291no—
51C3×D7—1451no—
52D3×C7—51no—
53C5×C7D3×D2911yescharacteristic, complemented, Hall
54D15D20311yescharacteristic, complemented
55C3×D5—2031no—
56C5×D3—2031no—
57C29D15⋊D711yescharacteristic, complemented, Sylow
58C2×D7—4351noHall
59C3×C7D5×D2911yescharacteristic, complemented, Hall
60C2×D5—6091noHall
61C3×C5C2×D20311yescharacteristic, complemented, Hall
62C2×C7—151no—
63D7—871no—
64D7—1451no—
65C2×D3—10151noHall
66C2×C5—6091no—
67D5—31no—
68D5—2031no—
69C7D15⋊D2911yescharacteristic, complemented, Sylow
70C2×C3—10151no—
71D3—51no—
72D3—2031no—
73C5D3×D20311yescharacteristic, complemented, Sylow
74C22—30451noSylow
75C3D5×D20311yescharacteristic, complemented, Sylow
76C2—151no—
77C2—6091no—
78C2—10151no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C29C22
LCSG ▷ C3×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7×C29×D15C2semidirect
2. C5×D609C2semidirect
3. C3×D1015C2semidirect
5. C3×C5×C7×C29C22semidirect
7. D1015D3semidirect
11. D609D5semidirect
14. C5×C7×C29C2×D3semidirect
15. C29×D15D7semidirect
19. C3×C7×C29C2×D5semidirect
21. C3×C5×C29C2×D7semidirect
30. C7×D15D29semidirect
33. C7×C29D3×D5semidirect
37. C5×C29D3×D7semidirect
40. C3×C5×C7C2×D29semidirect
41. C3×C29D5×D7semidirect
53. C5×C7D3×D29semidirect
54. D15D203semidirect
57. C29D15⋊D7semidirect
59. C3×C7D5×D29semidirect
61. C3×C5C2×D203semidirect
69. C7D15⋊D29semidirect
73. C5D3×D203semidirect
75. C3D5×D203semidirect