Finite Group Databasebeta

← D5×C11×D155 #46802191

Subgroups — D5×C11×D155 #46802191

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D5×C11×C31C211yesmaximal, characteristic, complemented
2C5×C11×D155C211yesmaximal, characteristic, complemented
3C11×C5⋊D155C211yesmaximal, characteristic, complemented
4C52×C11×C31C2211yescharacteristic, complemented, Hall
5C2×C11×D155—51nomaximal
6D5×C11×D31—51nomaximal
7C11×D155—51no—
8C11×D155—51no—
9C11×D155—102no—
10C11×D155D511yescharacteristic, direct product factor
11D5×C11×C31D511yescharacteristic, complemented
12C5×C11×D31—51no—
13C2×C5×C11×C31—51no—
14D5×D155C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C11×C31—22no—
16C5×C11×C31C2×D511yescharacteristic, complemented
17C5×C11×C31C2×D511yescharacteristic, complemented
18C5⋊D155C2×C1111yescharacteristic, complemented
19C5×D155C2×C1111yescharacteristic, complemented
20C5×D5×C31C2×C1111yescharacteristic, complemented
21C2×C11×D31—251noHall
22D52×C11—311nomaximal, Hall
23C52×C31C22×C1111yescharacteristic, complemented, Hall
24C2×C11×C31—51no—
25C11×D31—51no—
26C11×D31—251no—
27C2×D155—51no—
28D5×D31—51no—
29C11×C5⋊D5—311no—
30C5×D5×C11—311no—
31C5×D5×C11D3111yescharacteristic, complemented
32C11×C31D5211yescharacteristic, complemented, Hall
33C2×C5×C31—51no—
34D155—51no—
35D155—51no—
36D155—102no—
37D155D5×C1111yescharacteristic, direct product factor
38C5×D31—51no—
39D5×C31D5×C1111yescharacteristic, complemented
40C52×C11C2×D3111yescharacteristic, complemented, Hall
41C2×D5×C11—1551no—
42C2×D5×C11—1551no—
43C5×C31—22no—
44C5×C31C2×D5×C1111yescharacteristic, complemented
45C5×C31C2×D5×C1111yescharacteristic, complemented
46C2×D31—251noHall
47C2×C5×C11—51no—
48C2×C5×C11—1551no—
49D5×C11—311no—
50D5×C11—3102no—
51D5×C11—1551no—
52D5×C11—1551no—
53D5×C11D15511yescharacteristic, direct product factor
54D52—311noHall
55C2×C31—51no—
56D31—51no—
57D31—251no—
58C5×C11—22no—
59C5×C11D5×D3111yescharacteristic, complemented
60C5×C11C2×D15511yescharacteristic, complemented
61C5⋊D5—311no—
62C5×D5—311no—
63C5×D5C11×D3111yescharacteristic, complemented
64C22×C11—7751noHall
65C31D52×C1111yescharacteristic, complemented, Sylow
66C52C2×C11×D3111yescharacteristic, complemented, Sylow
67C2×C11—51no—
68C2×C11—7751no—
69C2×C11—1551no—
70C2×D5—1551no—
71C2×D5—1551no—
72C11D5×D15511yescharacteristic, direct product factor, Sylow
73C2×C5—51no—
74C2×C5—1551no—
75D5—311no—
76D5—3102no—
77D5—1551no—
78D5—1551no—
79D5C11×D15511yescharacteristic, direct product factor
80C5—22no—
81C5D5×C11×D3111yescharacteristic, complemented
82C5C2×C11×D15511yescharacteristic, complemented
83C22—7751noSylow
84C2—51no—
85C2—7751no—
86C2—1551no—
subgroupG/H
center, hypercenterC11D5×D155
commutator, cosocle, hypocenterC52×C31C22×C11
FrattiniC1G
Fitting, socleC52×C11×C31C22
LCSG ▷ C52×C31
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C5×D5×C11×C31C2semidirect
2. C5×C11×D155C2semidirect
3. C11×C5⋊D155C2semidirect
4. C52×C11×C31C22semidirect
10. C11×D155D5direct (N × H)
11. D5×C11×C31D5semidirect
14. D5×D155C11direct (N × H)
16. C5×C11×C31C2×D5semidirect
17. C5×C11×C31C2×D5semidirect
18. C5⋊D155C2×C11semidirect
19. C5×D155C2×C11semidirect
20. C5×D5×C31C2×C11semidirect
23. C52×C31C22×C11semidirect
31. C5×D5×C11D31semidirect
32. C11×C31D52semidirect
37. D155D5×C11direct (N × H)
39. D5×C31D5×C11semidirect
40. C52×C11C2×D31semidirect
44. C5×C31C2×D5×C11semidirect
45. C5×C31C2×D5×C11semidirect
53. D5×C11D155direct (N × H)
59. C5×C11D5×D31semidirect
60. C5×C11C2×D155semidirect
63. C5×D5C11×D31semidirect
65. C31D52×C11semidirect
66. C52C2×C11×D31semidirect
72. C11D5×D155direct (N × H)
79. D5C11×D155direct (N × H)
81. C5D5×C11×D31semidirect
82. C5C2×C11×D155semidirect

Maximal subgroups

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

subgroupindex
C5×D5×C11×C312
C5×C11×D1552
C11×C5⋊D1552
C2×C11×D1555
D5×C11×D315
D5×D15511
D52×C1131