Finite Group Databasebeta

← C2×C3×C7×C3⋊(C5⋊D5) #20263163

Subgroups — C2×C3×C7×C3⋊(C5⋊D5) #20263163

Order 6300.

352 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 140 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
1C3×C7×C3⋊(C5⋊D5)C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C7×C3⋊(C5⋊D5)C311yesmaximal, characteristic, direct product factor
4C2×C3×C7×C5⋊D5—31nomaximal
5C32×C52×C7C2211yescharacteristic, complemented, Hall
6C2×C3×C7×D15—56nomaximal
7C2×C3×C52×C7—21no—
8C2×C3×C52×C7D311yescharacteristic, complemented
9C2×C3×C52×C7C2×C311yescharacteristic, complemented
10C7×C3⋊(C5⋊D5)C2×C312yesdirect product factor
11C3×C7×C5⋊D5—32no—
12C2×C3×C3⋊(C5⋊D5)C711yesmaximal, characteristic, direct product factor, Hall
13C2×C7×C5⋊D5—31noHall
14C2×C32×C5×C7D516yescomplemented
15C3×C7×D15—512no—
16C3×C52×C7—21no—
17C3×C52×C7C2×D311yescharacteristic, complemented
18C3×C52×C7C22×C311yescharacteristic, complemented
19C2×C32×C52C2×C711yescharacteristic, complemented
20C3×C3⋊(C5⋊D5)C2×C712yesdirect product factor
21C2×C7×D15—56no—
22C2×C3×C7×D5—156no—
23C2×C52×C7C3×D311yescharacteristic, complemented
24C7×C5⋊D5—32no—
25C32×C5×C7C2×D516yescomplemented
26C2×C3⋊(C5⋊D5)C3×C711yescharacteristic, direct product factor
27C2×C3×C5⋊D5—31no—
28C2×C3×D3×C7—251noHall
29C32×C52C22×C711yescharacteristic, complemented, Hall
30C2×C3×C5×C7—26no—
31C2×C3×C5×C7C3×D516yescomplemented
32C2×C3×C5×C7D1516yescomplemented
33C7×D15—512no—
34C3×C7×D5—1512no—
35C2×C3×D15—56no—
36C52×C7C2×C3×D311yescharacteristic, complemented, Hall
37C2×C3×C52—21no—
38C2×C3×C52D3×C711yescharacteristic, complemented
39C2×C3×C52C2×C3×C711yescharacteristic, complemented
40C3⋊(C5⋊D5)C2×C3×C712yesdirect product factor
41C3×C5⋊D5—32no—
42C2×C7×D5—156no—
43C2×C32×C7C5⋊D511yescharacteristic, complemented
44C3×D3×C7—252no—
45C3×C5×C7—26no—
46C3×C5×C7C2×C3×D516yescomplemented
47C3×C5×C7C2×D1516yescomplemented
48C2×C5⋊D5—31noHall
49C2×C32×C5C7×D516yescomplemented
50C3×D15—512no—
51C22×C3×C7—751no—
52C2×D3×C7—251no—
53C3×C52—21no—
54C3×C52C2×D3×C711yescharacteristic, complemented
55C3×C52C22×C3×C711yescharacteristic, complemented
56C2×C5×C7C3×D1516yescomplemented
57C7×D5—1512no—
58C32×C7C2×C5⋊D511yescharacteristic, complemented, Hall
59C2×D15—56no—
60C2×C3×D5—156no—
61C2×C52C3×D3×C711yescharacteristic, complemented
62C5⋊D5—32no—
63C32×C5C2×C7×D516yescomplemented
64C2×C3×C7—21no—
65C2×C3×C7—752no—
66C2×C3×C7C3×C5⋊D511yescharacteristic, complemented
67C2×C3×C7C3⋊(C5⋊D5)11yescharacteristic, direct product factor
68D3×C7—252no—
69C2×C3×D3—251noHall
70C5×C7C2×C3×D1516yescomplemented
71C2×C3×C5—26no—
72C2×C3×C5C3×C7×D516yescomplemented
73C2×C3×C5C7×D1516yescomplemented
74D15—512no—
75C3×D5—1512no—
76C22×C7—751noHall
77C52C2×C3×D3×C711yescharacteristic, complemented, Sylow
78C3×C7—21no—
79C3×C7C2×C3×C5⋊D511yescharacteristic, complemented
80C3×C7C2×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
81C2×D5—156no—
82C2×C32C7×C5⋊D511yescharacteristic, complemented
83C3×D3—252no—
84C3×C5—26no—
85C3×C5C2×C3×C7×D516yescomplemented
86C3×C5C2×C7×D1516yescomplemented
87C2×C7—752no—
88C2×C7C3×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
89C22×C3—751no—
90C2×D3—251no—
91C2×C5C3×C7×D1516yescomplemented
92D5—1512no—
93C32C2×C7×C5⋊D511yescharacteristic, complemented, Sylow
94C7C2×C3×C3⋊(C5⋊D5)11yescharacteristic, direct product factor, Sylow
95C2×C3—21no—
96C2×C3—752no—
97C2×C3C3×C7×C5⋊D511yescharacteristic, complemented
98C2×C3C7×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
99D3—252no—
100C5C2×C3×C7×D1516yescomplemented
101C22—751noSylow
102C3—21no—
103C3C2×C3×C7×C5⋊D511yescharacteristic, complemented
104C3C2×C7×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
105C2—752no—
106C2C3×C7×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C22×C3×C7
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C3×C52
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C3⋊(C5⋊D5)C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
3. C2×C7×C3⋊(C5⋊D5)C3direct (N × H)
5. C32×C52×C7C22semidirect
8. C2×C3×C52×C7D3semidirect
9. C2×C3×C52×C7C2×C3semidirect
10. C7×C3⋊(C5⋊D5)C2×C3direct (N × H)
12. C2×C3×C3⋊(C5⋊D5)C7direct (N × H)
14. C2×C32×C5×C7D5semidirect
17. C3×C52×C7C2×D3semidirect
18. C3×C52×C7C22×C3semidirect
19. C2×C32×C52C2×C7semidirect
20. C3×C3⋊(C5⋊D5)C2×C7direct (N × H)
23. C2×C52×C7C3×D3semidirect
25. C32×C5×C7C2×D5semidirect
26. C2×C3⋊(C5⋊D5)C3×C7direct (N × H)
29. C32×C52C22×C7semidirect
31. C2×C3×C5×C7C3×D5semidirect
32. C2×C3×C5×C7D15semidirect
36. C52×C7C2×C3×D3semidirect
38. C2×C3×C52D3×C7semidirect
39. C2×C3×C52C2×C3×C7semidirect
40. C3⋊(C5⋊D5)C2×C3×C7direct (N × H)
43. C2×C32×C7C5⋊D5semidirect
46. C3×C5×C7C2×C3×D5semidirect
47. C3×C5×C7C2×D15semidirect
49. C2×C32×C5C7×D5semidirect
54. C3×C52C2×D3×C7semidirect
55. C3×C52C22×C3×C7semidirect
56. C2×C5×C7C3×D15semidirect
58. C32×C7C2×C5⋊D5semidirect
61. C2×C52C3×D3×C7semidirect
63. C32×C5C2×C7×D5semidirect
66. C2×C3×C7C3×C5⋊D5semidirect
67. C2×C3×C7C3⋊(C5⋊D5)direct (N × H)
70. C5×C7C2×C3×D15semidirect
72. C2×C3×C5C3×C7×D5semidirect
73. C2×C3×C5C7×D15semidirect
77. C52C2×C3×D3×C7semidirect
79. C3×C7C2×C3×C5⋊D5semidirect
80. C3×C7C2×C3⋊(C5⋊D5)direct (N × H)
82. C2×C32C7×C5⋊D5semidirect
85. C3×C5C2×C3×C7×D5semidirect
86. C3×C5C2×C7×D15semidirect
88. C2×C7C3×C3⋊(C5⋊D5)direct (N × H)
91. C2×C5C3×C7×D15semidirect
93. C32C2×C7×C5⋊D5semidirect
94. C7C2×C3×C3⋊(C5⋊D5)direct (N × H)
97. C2×C3C3×C7×C5⋊D5semidirect
98. C2×C3C7×C3⋊(C5⋊D5)direct (N × H)
100. C5C2×C3×C7×D15semidirect
103. C3C2×C3×C7×C5⋊D5semidirect
104. C3C2×C7×C3⋊(C5⋊D5)direct (N × H)
106. C2C3×C7×C3⋊(C5⋊D5)direct (N × H)