Finite Group Databasebeta

← C2×C5×C3⋊D435 #39908237

Subgroups — C2×C5×C3⋊D435 #39908237

Order 26100.

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C3⋊D435C212yesmaximal, direct product factor
2C2×C32×C52×C29C211yesmaximal, characteristic, complemented
3C2×C5×D435—34nomaximal
4C32×C52×C29C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D87—51nomaximal
6C2×C3⋊D435C511yesmaximal, characteristic, direct product factor
7C5×D435—38no—
8C2×C3×C52×C29D314yescomplemented
9C2×C5×D145—91noHall
10C3⋊D435C2×C512yesdirect product factor
11C5×C3⋊D87—52no—
12C2×C32×C5×C29—22no—
13C2×C32×C5×C29D511yescharacteristic, complemented
14C2×C32×C5×C29C2×C511yescharacteristic, complemented
15C3×C52×C29C2×D314yescomplemented
16C2×D435—34no—
17C2×C5×D87—154no—
18C2×C52×C29C3⋊D311yescharacteristic, complemented
19C5×D145—92no—
20C32×C5×C29—22no—
21C32×C5×C29C2×D511yescharacteristic, complemented
22C32×C5×C29C22×C511yescharacteristic, complemented
23C2×C3⋊D87—51noHall
24C2×C5×C3⋊D15—291nomaximal, Hall
25C2×C3×C5×C29—28no—
26C2×C3×C5×C29C5×D314yescomplemented
27C2×C3×C5×C29D1514yescomplemented
28D435—38no—
29C5×D87—158no—
30C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
31C2×D145—91no—
32C2×C5×D29—451no—
33C2×C32×C29C5×D511yescharacteristic, complemented
34C3⋊D87—52no—
35C2×C32×C52D2911yescharacteristic, complemented
36C5×C3⋊D15—292no—
37C3×C5×C29—28no—
38C3×C5×C29C2×C5×D314yescomplemented
39C3×C5×C29C2×D1514yescomplemented
40C2×D87—154no—
41C2×C5×D15—874no—
42C2×C5×C29—22no—
43C2×C5×C29C5×C3⋊D311yescharacteristic, complemented
44C2×C5×C29C3⋊D1511yescharacteristic, complemented
45D145—92no—
46C5×D29—452no—
47C32×C29C2×C5×D511yescharacteristic, complemented, Hall
48C32×C52C2×D2911yescharacteristic, complemented, Hall
49C2×C3⋊D15—291no—
50C2×C5×C3⋊D3—1451no—
51C2×C3×C29C5×D1514yescomplemented
52D87—158no—
53C2×C3×C52D8714yescomplemented
54C5×D15—878no—
55C5×C29—22no—
56C5×C29C2×C5×C3⋊D311yescharacteristic, complemented
57C5×C29C2×C3⋊D1511yescharacteristic, complemented
58C2×D29—451noHall
59C2×C5×D5—2611noHall
60C2×C32×C5—22no—
61C2×C32×C5C5×D2911yescharacteristic, complemented
62C2×C32×C5D14511yescharacteristic, complemented
63C3⋊D15—292no—
64C5×C3⋊D3—1452no—
65C3×C29C2×C5×D1514yescomplemented
66C3×C52C2×D8714yescomplemented
67C2×D15—874no—
68C2×C5×D3—4354no—
69C2×C29C5×C3⋊D1511yescharacteristic, complemented
70D29—452no—
71C2×C52C3⋊D8711yescharacteristic, complemented
72C5×D5—2612no—
73C32×C5—22no—
74C32×C5C2×C5×D2911yescharacteristic, complemented
75C32×C5C2×D14511yescharacteristic, complemented
76C2×C3⋊D3—1451noHall
77C2×C3×C5—28no—
78C2×C3×C5C5×D8714yescomplemented
79C2×C3×C5D43514yescomplemented
80D15—878no—
81C5×D3—4358no—
82C29C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
83C52C2×C3⋊D8711yescharacteristic, complemented, Sylow
84C22×C5—13051no—
85C2×D5—2611no—
86C2×C32C5×D14511yescharacteristic, complemented
87C3⋊D3—1452no—
88C3×C5—28no—
89C3×C5C2×C5×D8714yescomplemented
90C3×C5C2×D43514yescomplemented
91C2×D3—4354no—
92C2×C5—22no—
93C2×C5—13052no—
94C2×C5C5×C3⋊D8711yescharacteristic, complemented
95C2×C5C3⋊D43511yescharacteristic, direct product factor
96D5—2612no—
97C32C2×C5×D14511yescharacteristic, complemented, Sylow
98C2×C3C5×D43514yescomplemented
99D3—4358no—
100C5—22no—
101C5C2×C3⋊D43511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D8711yescharacteristic, complemented
103C22—13051noSylow
104C3C2×C5×D43514yescomplemented
105C2—13052no—
106C2C5×C3⋊D43511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊D435
commutator, cosocle, hypocenterC32×C5×C29C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C29C2
LCSG ▷ C32×C5×C29
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D435C2direct (N × H)
2. C2×C32×C52×C29C2semidirect
4. C32×C52×C29C22semidirect
6. C2×C3⋊D435C5direct (N × H)
8. C2×C3×C52×C29D3semidirect
10. C3⋊D435C2×C5direct (N × H)
13. C2×C32×C5×C29D5semidirect
14. C2×C32×C5×C29C2×C5semidirect
15. C3×C52×C29C2×D3semidirect
18. C2×C52×C29C3⋊D3semidirect
21. C32×C5×C29C2×D5semidirect
22. C32×C5×C29C22×C5semidirect
26. C2×C3×C5×C29C5×D3semidirect
27. C2×C3×C5×C29D15semidirect
30. C52×C29C2×C3⋊D3semidirect
33. C2×C32×C29C5×D5semidirect
35. C2×C32×C52D29semidirect
38. C3×C5×C29C2×C5×D3semidirect
39. C3×C5×C29C2×D15semidirect
43. C2×C5×C29C5×C3⋊D3semidirect
44. C2×C5×C29C3⋊D15semidirect
47. C32×C29C2×C5×D5semidirect
48. C32×C52C2×D29semidirect
51. C2×C3×C29C5×D15semidirect
53. C2×C3×C52D87semidirect
56. C5×C29C2×C5×C3⋊D3semidirect
57. C5×C29C2×C3⋊D15semidirect
61. C2×C32×C5C5×D29semidirect
62. C2×C32×C5D145semidirect
65. C3×C29C2×C5×D15semidirect
66. C3×C52C2×D87semidirect
69. C2×C29C5×C3⋊D15semidirect
71. C2×C52C3⋊D87semidirect
74. C32×C5C2×C5×D29semidirect
75. C32×C5C2×D145semidirect
78. C2×C3×C5C5×D87semidirect
79. C2×C3×C5D435semidirect
82. C29C2×C5×C3⋊D15semidirect
83. C52C2×C3⋊D87semidirect
86. C2×C32C5×D145semidirect
89. C3×C5C2×C5×D87semidirect
90. C3×C5C2×D435semidirect
94. C2×C5C5×C3⋊D87semidirect
95. C2×C5C3⋊D435direct (N × H)
97. C32C2×C5×D145semidirect
98. C2×C3C5×D435semidirect
101. C5C2×C3⋊D435direct (N × H)
102. C5C2×C5×C3⋊D87semidirect
104. C3C2×C5×D435semidirect
106. C2C5×C3⋊D435direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C3⋊D4352
C2×C32×C52×C292
C2×C5×D4353
C2×C5×C3⋊D875
C2×C3⋊D4355
C2×C5×C3⋊D1529