Finite Group Databasebeta

← C2×C5×C29×C3⋊D15 #39908236

Subgroups — C2×C5×C29×C3⋊D15 #39908236

Order 26100.

288 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 108 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×C29×C3⋊D15C212yesmaximal, direct product factor
2C2×C32×C52×C29C211yesmaximal, characteristic, complemented
3C2×C5×C29×D15—34nomaximal
4C32×C52×C29C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D3×C29—51nomaximal
6C2×C29×C3⋊D15C511yesmaximal, characteristic, direct product factor
7C5×C29×D15—38no—
8C2×C3×C52×C29D314yescomplemented
9C2×C5×D5×C29—91noHall
10C29×C3⋊D15C2×C512yesdirect product factor
11C5×C3⋊D3×C29—52no—
12C2×C32×C5×C29—22no—
13C2×C32×C5×C29D511yescharacteristic, complemented
14C2×C32×C5×C29C2×C511yescharacteristic, complemented
15C3×C52×C29C2×D314yescomplemented
16C2×C29×D15—34no—
17C2×C5×D3×C29—154no—
18C2×C52×C29C3⋊D311yescharacteristic, complemented
19C5×D5×C29—92no—
20C32×C5×C29—22no—
21C32×C5×C29C2×D511yescharacteristic, complemented
22C32×C5×C29C22×C511yescharacteristic, complemented
23C2×C3⋊D3×C29—51noHall
24C2×C5×C3⋊D15C2911yesmaximal, characteristic, direct product factor, Hall
25C2×C3×C5×C29—28no—
26C2×C3×C5×C29C5×D314yescomplemented
27C2×C3×C5×C29D1514yescomplemented
28C29×D15—38no—
29C5×D3×C29—158no—
30C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
31C22×C5×C29—451no—
32C2×D5×C29—91no—
33C2×C32×C29C5×D511yescharacteristic, complemented
34C3⋊D3×C29—52no—
35C2×C32×C52C2×C2911yescharacteristic, complemented
36C5×C3⋊D15C2×C2912yesdirect product factor
37C3×C5×C29—28no—
38C3×C5×C29C2×C5×D314yescomplemented
39C3×C5×C29C2×D1514yescomplemented
40C2×D3×C29—154no—
41C2×C5×D15—34no—
42C2×C5×C29—22no—
43C2×C5×C29—452no—
44C2×C5×C29C5×C3⋊D311yescharacteristic, complemented
45C2×C5×C29C3⋊D1511yescharacteristic, direct product factor
46D5×C29—92no—
47C32×C29C2×C5×D511yescharacteristic, complemented, Hall
48C32×C52C22×C2911yescharacteristic, complemented, Hall
49C2×C3⋊D15C5×C2911yescharacteristic, direct product factor
50C2×C5×C3⋊D3—51no—
51C2×C3×C29C5×D1514yescomplemented
52D3×C29—158no—
53C2×C3×C52D3×C2914yescomplemented
54C5×D15—38no—
55C5×C29—22no—
56C5×C29C2×C5×C3⋊D311yescharacteristic, complemented
57C5×C29C2×C3⋊D1511yescharacteristic, direct product factor
58C22×C29—451noHall
59C2×C5×D5—91noHall
60C2×C32×C5—22no—
61C2×C32×C5D5×C2911yescharacteristic, complemented
62C2×C32×C5C2×C5×C2911yescharacteristic, complemented
63C3⋊D15C2×C5×C2912yesdirect product factor
64C5×C3⋊D3—52no—
65C3×C29C2×C5×D1514yescomplemented
66C3×C52C2×D3×C2914yescomplemented
67C2×D15—34no—
68C2×C5×D3—154no—
69C2×C29—452no—
70C2×C29C5×C3⋊D1511yescharacteristic, direct product factor
71C2×C52C3⋊D3×C2911yescharacteristic, complemented
72C5×D5—92no—
73C32×C5—22no—
74C32×C5C2×D5×C2911yescharacteristic, complemented
75C32×C5C22×C5×C2911yescharacteristic, complemented
76C2×C3⋊D3—51noHall
77C2×C3×C5—28no—
78C2×C3×C5C5×D3×C2914yescomplemented
79C2×C3×C5C29×D1514yescomplemented
80D15—38no—
81C5×D3—158no—
82C29C2×C5×C3⋊D1511yescharacteristic, direct product factor, Sylow
83C52C2×C3⋊D3×C2911yescharacteristic, complemented, Sylow
84C22×C5—451no—
85C2×D5—91no—
86C2×C32C5×D5×C2911yescharacteristic, complemented
87C3⋊D3—52no—
88C3×C5—28no—
89C3×C5C2×C5×D3×C2914yescomplemented
90C3×C5C2×C29×D1514yescomplemented
91C2×D3—154no—
92C2×C5—22no—
93C2×C5—452no—
94C2×C5C5×C3⋊D3×C2911yescharacteristic, complemented
95C2×C5C29×C3⋊D1511yescharacteristic, direct product factor
96D5—92no—
97C32C2×C5×D5×C2911yescharacteristic, complemented, Sylow
98C2×C3C5×C29×D1514yescomplemented
99D3—158no—
100C5—22no—
101C5C2×C29×C3⋊D1511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D3×C2911yescharacteristic, complemented
103C22—451noSylow
104C3C2×C5×C29×D1514yescomplemented
105C2—452no—
106C2C5×C29×C3⋊D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C29C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C5×C29
FrattiniC1G
Fitting, socleC2×C32×C52×C29C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C29

Complements

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

NH ≅ G/Ntype
1. C5×C29×C3⋊D15C2direct (N × H)
2. C2×C32×C52×C29C2semidirect
4. C32×C52×C29C22semidirect
6. C2×C29×C3⋊D15C5direct (N × H)
8. C2×C3×C52×C29D3semidirect
10. C29×C3⋊D15C2×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
24. C2×C5×C3⋊D15C29direct (N × H)
26. C2×C3×C5×C29C5×D3semidirect
27. C2×C3×C5×C29D15semidirect
30. C52×C29C2×C3⋊D3semidirect
33. C2×C32×C29C5×D5semidirect
35. C2×C32×C52C2×C29semidirect
36. C5×C3⋊D15C2×C29direct (N × H)
38. C3×C5×C29C2×C5×D3semidirect
39. C3×C5×C29C2×D15semidirect
44. C2×C5×C29C5×C3⋊D3semidirect
45. C2×C5×C29C3⋊D15direct (N × H)
47. C32×C29C2×C5×D5semidirect
48. C32×C52C22×C29semidirect
49. C2×C3⋊D15C5×C29direct (N × H)
51. C2×C3×C29C5×D15semidirect
53. C2×C3×C52D3×C29semidirect
56. C5×C29C2×C5×C3⋊D3semidirect
57. C5×C29C2×C3⋊D15direct (N × H)
61. C2×C32×C5D5×C29semidirect
62. C2×C32×C5C2×C5×C29semidirect
63. C3⋊D15C2×C5×C29direct (N × H)
65. C3×C29C2×C5×D15semidirect
66. C3×C52C2×D3×C29semidirect
70. C2×C29C5×C3⋊D15direct (N × H)
71. C2×C52C3⋊D3×C29semidirect
74. C32×C5C2×D5×C29semidirect
75. C32×C5C22×C5×C29semidirect
78. C2×C3×C5C5×D3×C29semidirect
79. C2×C3×C5C29×D15semidirect
82. C29C2×C5×C3⋊D15direct (N × H)
83. C52C2×C3⋊D3×C29semidirect
86. C2×C32C5×D5×C29semidirect
89. C3×C5C2×C5×D3×C29semidirect
90. C3×C5C2×C29×D15semidirect
94. C2×C5C5×C3⋊D3×C29semidirect
95. C2×C5C29×C3⋊D15direct (N × H)
97. C32C2×C5×D5×C29semidirect
98. C2×C3C5×C29×D15semidirect
101. C5C2×C29×C3⋊D15direct (N × H)
102. C5C2×C5×C3⋊D3×C29semidirect
104. C3C2×C5×C29×D15semidirect
106. C2C5×C29×C3⋊D15direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C29×C3⋊D152
C2×C32×C52×C292
C2×C5×C29×D153
C2×C5×C3⋊D3×C295
C2×C29×C3⋊D155
C2×C5×C3⋊D1529