Finite Group Databasebeta

← C2×C5×C7×C3⋊D15 #20263159

Subgroups — C2×C5×C7×C3⋊D15 #20263159

Order 6300.

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×C7×C3⋊D15C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C5×C7×D15—34nomaximal
4C32×C52×C7C2211yescharacteristic, complemented, Hall
5C2×C7×C3⋊D15C511yesmaximal, characteristic, direct product factor
6C2×C5×C7×C3⋊D3—51nomaximal
7C2×C3×C52×C7D314yescomplemented
8C5×C7×D15—38no—
9C2×C5×C3⋊D15C711yesmaximal, characteristic, direct product factor, Hall
10C2×C5×C7×D5—91noHall
11C2×C32×C5×C7—22no—
12C2×C32×C5×C7D511yescharacteristic, complemented
13C2×C32×C5×C7C2×C511yescharacteristic, complemented
14C7×C3⋊D15C2×C512yesdirect product factor
15C5×C7×C3⋊D3—52no—
16C3×C52×C7C2×D314yescomplemented
17C2×C32×C52C2×C711yescharacteristic, complemented
18C5×C3⋊D15C2×C712yesdirect product factor
19C2×C7×D15—34no—
20C2×C5×D3×C7—154no—
21C2×C52×C7C3⋊D311yescharacteristic, complemented
22C5×C7×D5—92no—
23C32×C5×C7—22no—
24C32×C5×C7C2×D511yescharacteristic, complemented
25C32×C5×C7C22×C511yescharacteristic, complemented
26C2×C5×D15—34no—
27C2×C7×C3⋊D3—51noHall
28C32×C52C22×C711yescharacteristic, complemented, Hall
29C2×C3×C5×C7—28no—
30C2×C3×C5×C7C5×D314yescomplemented
31C2×C3×C5×C7D1514yescomplemented
32C7×D15—38no—
33C5×D3×C7—158no—
34C2×C3⋊D15C5×C711yescharacteristic, direct product factor
35C2×C5×C3⋊D3—51no—
36C52×C7C2×C3⋊D311yescharacteristic, complemented, Hall
37C2×C3×C52D3×C714yescomplemented
38C5×D15—38no—
39C22×C5×C7—451no—
40C2×C7×D5—91no—
41C2×C32×C7C5×D511yescharacteristic, complemented
42C7×C3⋊D3—52no—
43C3×C5×C7—28no—
44C3×C5×C7C2×C5×D314yescomplemented
45C3×C5×C7C2×D1514yescomplemented
46C2×C5×D5—91noHall
47C2×C32×C5—22no—
48C2×C32×C5C7×D511yescharacteristic, complemented
49C2×C32×C5C2×C5×C711yescharacteristic, complemented
50C3⋊D15C2×C5×C712yesdirect product factor
51C5×C3⋊D3—52no—
52C2×D3×C7—154no—
53C3×C52C2×D3×C714yescomplemented
54C2×C5×C7—22no—
55C2×C5×C7—452no—
56C2×C5×C7C5×C3⋊D311yescharacteristic, complemented
57C2×C5×C7C3⋊D1511yescharacteristic, direct product factor
58C7×D5—92no—
59C32×C7C2×C5×D511yescharacteristic, complemented, Hall
60C2×D15—34no—
61C2×C5×D3—154no—
62C2×C52C7×C3⋊D311yescharacteristic, complemented
63C5×D5—92no—
64C32×C5—22no—
65C32×C5C2×C7×D511yescharacteristic, complemented
66C32×C5C22×C5×C711yescharacteristic, complemented
67C2×C3×C7C5×D1514yescomplemented
68D3×C7—158no—
69C2×C3⋊D3—51noHall
70C5×C7—22no—
71C5×C7C2×C5×C3⋊D311yescharacteristic, complemented
72C5×C7C2×C3⋊D1511yescharacteristic, direct product factor
73C2×C3×C5—28no—
74C2×C3×C5C5×D3×C714yescomplemented
75C2×C3×C5C7×D1514yescomplemented
76D15—38no—
77C5×D3—158no—
78C22×C7—451noHall
79C52C2×C7×C3⋊D311yescharacteristic, complemented, Sylow
80C3×C7C2×C5×D1514yescomplemented
81C22×C5—451no—
82C2×D5—91no—
83C2×C32C5×C7×D511yescharacteristic, complemented
84C3⋊D3—52no—
85C3×C5—28no—
86C3×C5C2×C5×D3×C714yescomplemented
87C3×C5C2×C7×D1514yescomplemented
88C2×C7—452no—
89C2×C7C5×C3⋊D1511yescharacteristic, direct product factor
90C2×D3—154no—
91C2×C5—22no—
92C2×C5—452no—
93C2×C5C5×C7×C3⋊D311yescharacteristic, complemented
94C2×C5C7×C3⋊D1511yescharacteristic, direct product factor
95D5—92no—
96C32C2×C5×C7×D511yescharacteristic, complemented, Sylow
97C7C2×C5×C3⋊D1511yescharacteristic, direct product factor, Sylow
98C2×C3C5×C7×D1514yescomplemented
99D3—158no—
100C5—22no—
101C5C2×C5×C7×C3⋊D311yescharacteristic, complemented
102C5C2×C7×C3⋊D1511yescharacteristic, direct product factor
103C22—451noSylow
104C3C2×C5×C7×D1514yescomplemented
105C2—452no—
106C2C5×C7×C3⋊D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C7C3⋊D15
commutator, hypocenterC32×C5C22×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C7

Complements

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

NH ≅ G/Ntype
1. C5×C7×C3⋊D15C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
4. C32×C52×C7C22semidirect
5. C2×C7×C3⋊D15C5direct (N × H)
7. C2×C3×C52×C7D3semidirect
9. C2×C5×C3⋊D15C7direct (N × H)
12. C2×C32×C5×C7D5semidirect
13. C2×C32×C5×C7C2×C5semidirect
14. C7×C3⋊D15C2×C5direct (N × H)
16. C3×C52×C7C2×D3semidirect
17. C2×C32×C52C2×C7semidirect
18. C5×C3⋊D15C2×C7direct (N × H)
21. C2×C52×C7C3⋊D3semidirect
24. C32×C5×C7C2×D5semidirect
25. C32×C5×C7C22×C5semidirect
28. C32×C52C22×C7semidirect
30. C2×C3×C5×C7C5×D3semidirect
31. C2×C3×C5×C7D15semidirect
34. C2×C3⋊D15C5×C7direct (N × H)
36. C52×C7C2×C3⋊D3semidirect
37. C2×C3×C52D3×C7semidirect
41. C2×C32×C7C5×D5semidirect
44. C3×C5×C7C2×C5×D3semidirect
45. C3×C5×C7C2×D15semidirect
48. C2×C32×C5C7×D5semidirect
49. C2×C32×C5C2×C5×C7semidirect
50. C3⋊D15C2×C5×C7direct (N × H)
53. C3×C52C2×D3×C7semidirect
56. C2×C5×C7C5×C3⋊D3semidirect
57. C2×C5×C7C3⋊D15direct (N × H)
59. C32×C7C2×C5×D5semidirect
62. C2×C52C7×C3⋊D3semidirect
65. C32×C5C2×C7×D5semidirect
66. C32×C5C22×C5×C7semidirect
67. C2×C3×C7C5×D15semidirect
71. C5×C7C2×C5×C3⋊D3semidirect
72. C5×C7C2×C3⋊D15direct (N × H)
74. C2×C3×C5C5×D3×C7semidirect
75. C2×C3×C5C7×D15semidirect
79. C52C2×C7×C3⋊D3semidirect
80. C3×C7C2×C5×D15semidirect
83. C2×C32C5×C7×D5semidirect
86. C3×C5C2×C5×D3×C7semidirect
87. C3×C5C2×C7×D15semidirect
89. C2×C7C5×C3⋊D15direct (N × H)
93. C2×C5C5×C7×C3⋊D3semidirect
94. C2×C5C7×C3⋊D15direct (N × H)
96. C32C2×C5×C7×D5semidirect
97. C7C2×C5×C3⋊D15direct (N × H)
98. C2×C3C5×C7×D15semidirect
101. C5C2×C5×C7×C3⋊D3semidirect
102. C5C2×C7×C3⋊D15direct (N × H)
104. C3C2×C5×C7×D15semidirect
106. C2C5×C7×C3⋊D15direct (N × H)