Finite Group Databasebeta

← C2×C3×C52×D3×C7 #20263167

Subgroups — C2×C3×C52×D3×C7 #20263167

Order 6300.

352 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 224 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×C52×D3×C7C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C52×D3×C7C311yesmaximal, characteristic, direct product factor
4C22×C3×C52×C7—31nomaximal
5C32×C52×C7C2211yescharacteristic, complemented, Hall
6C2×C3×C5×D3×C7C516yesmaximal, direct product factor
7C2×C3×C52×C7—21no—
8C2×C3×C52×C7—32no—
9C2×C3×C52×C7D311yescharacteristic, direct product factor
10C2×C3×C52×C7C2×C311yescharacteristic, complemented
11C52×D3×C7C2×C312yesdirect product factor
12C2×C3×C52×D3C711yesmaximal, characteristic, direct product factor, Hall
13C22×C52×C7—31noHall
14C2×C32×C5×C7C2×C516yescomplemented
15C3×C5×D3×C7C2×C5112yesdirect product factor
16C3×C52×C7—21no—
17C3×C52×C7C2×D311yescharacteristic, direct product factor
18C3×C52×C7C22×C311yescharacteristic, complemented
19C2×C32×C52C2×C711yescharacteristic, complemented
20C3×C52×D3C2×C712yesdirect product factor
21C22×C3×C5×C7—36no—
22C2×C5×D3×C7C3×C516yesdirect product factor
23C2×C52×C7—32no—
24C2×C52×C7C3×D311yescharacteristic, direct product factor
25C32×C5×C7C22×C516yescomplemented
26C22×C3×C52—31no—
27C2×C52×D3C3×C711yescharacteristic, direct product factor
28C2×C3×D3×C7C5211yescharacteristic, direct product factor, Hall
29C32×C52C22×C711yescharacteristic, complemented, Hall
30C2×C3×C5×C7—26no—
31C2×C3×C5×C7—312no—
32C2×C3×C5×C7C5×D316yesdirect product factor
33C2×C3×C5×C7C2×C3×C516yescomplemented
34C5×D3×C7C2×C3×C5112yesdirect product factor
35C2×C3×C5×D3C5×C716yesdirect product factor
36C52×C7C2×C3×D311yescharacteristic, direct product factor, Hall
37C2×C3×C52—21no—
38C2×C3×C52—32no—
39C2×C3×C52D3×C711yescharacteristic, direct product factor
40C2×C3×C52C2×C3×C711yescharacteristic, complemented
41C52×D3C2×C3×C712yesdirect product factor
42C22×C5×C7—36no—
43C2×C32×C7C2×C5211yescharacteristic, complemented
44C3×D3×C7C2×C5212yesdirect product factor
45C3×C5×C7—26no—
46C3×C5×C7C2×C5×D316yesdirect product factor
47C3×C5×C7C22×C3×C516yescomplemented
48C22×C52—31noHall
49C2×C32×C5C2×C5×C716yescomplemented
50C3×C5×D3C2×C5×C7112yesdirect product factor
51C22×C3×C7—31no—
52C2×D3×C7C3×C5211yescharacteristic, direct product factor
53C3×C52—21no—
54C3×C52C2×D3×C711yescharacteristic, direct product factor
55C3×C52C22×C3×C711yescharacteristic, complemented
56C2×C5×C7—312no—
57C2×C5×C7C3×C5×D316yesdirect product factor
58C32×C7C22×C5211yescharacteristic, complemented, Hall
59C22×C3×C5—36no—
60C2×C5×D3C3×C5×C716yesdirect product factor
61C2×C52—32no—
62C2×C52C3×D3×C711yescharacteristic, direct product factor
63C32×C5C22×C5×C716yescomplemented
64C2×C3×C7—21no—
65C2×C3×C7—32no—
66C2×C3×C7C52×D311yescharacteristic, direct product factor
67C2×C3×C7C2×C3×C5211yescharacteristic, complemented
68D3×C7C2×C3×C5212yesdirect product factor
69C2×C3×D3C52×C711yescharacteristic, direct product factor, Hall
70C5×C7C2×C3×C5×D316yesdirect product factor
71C2×C3×C5—26no—
72C2×C3×C5—312no—
73C2×C3×C5C5×D3×C716yesdirect product factor
74C2×C3×C5C2×C3×C5×C716yescomplemented
75C5×D3C2×C3×C5×C7112yesdirect product factor
76C22×C7—31noHall
77C52C2×C3×D3×C711yescharacteristic, direct product factor, Sylow
78C3×C7—21no—
79C3×C7C2×C52×D311yescharacteristic, direct product factor
80C3×C7C22×C3×C5211yescharacteristic, complemented
81C22×C5—36no—
82C2×C32C2×C52×C711yescharacteristic, complemented
83C3×D3C2×C52×C712yesdirect product factor
84C3×C5—26no—
85C3×C5C2×C5×D3×C716yesdirect product factor
86C3×C5C22×C3×C5×C716yescomplemented
87C2×C7—32no—
88C2×C7C3×C52×D311yescharacteristic, direct product factor
89C22×C3—31no—
90C2×D3C3×C52×C711yescharacteristic, direct product factor
91C2×C5—312no—
92C2×C5C3×C5×D3×C716yesdirect product factor
93C32C22×C52×C711yescharacteristic, complemented, Sylow
94C7C2×C3×C52×D311yescharacteristic, direct product factor, Sylow
95C2×C3—21no—
96C2×C3—32no—
97C2×C3C52×D3×C711yescharacteristic, direct product factor
98C2×C3C2×C3×C52×C711yescharacteristic, complemented
99D3C2×C3×C52×C712yesdirect product factor
100C5C2×C3×C5×D3×C716yesdirect product factor
101C22—31noSylow
102C3—21no—
103C3C22×C3×C52×C711yescharacteristic, complemented
104C3C2×C52×D3×C711yescharacteristic, direct product factor
105C2—32no—
106C2C3×C52×D3×C711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C52×C7D3
commutator, hypocenterC3C22×C3×C52×C7
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C52×C7

Complements

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

NH ≅ G/Ntype
1. C3×C52×D3×C7C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
3. C2×C52×D3×C7C3direct (N × H)
5. C32×C52×C7C22semidirect
6. C2×C3×C5×D3×C7C5direct (N × H)
9. C2×C3×C52×C7D3direct (N × H)
10. C2×C3×C52×C7C2×C3semidirect
11. C52×D3×C7C2×C3direct (N × H)
12. C2×C3×C52×D3C7direct (N × H)
14. C2×C32×C5×C7C2×C5semidirect
15. C3×C5×D3×C7C2×C5direct (N × H)
17. C3×C52×C7C2×D3direct (N × H)
18. C3×C52×C7C22×C3semidirect
19. C2×C32×C52C2×C7semidirect
20. C3×C52×D3C2×C7direct (N × H)
22. C2×C5×D3×C7C3×C5direct (N × H)
24. C2×C52×C7C3×D3direct (N × H)
25. C32×C5×C7C22×C5semidirect
27. C2×C52×D3C3×C7direct (N × H)
28. C2×C3×D3×C7C52direct (N × H)
29. C32×C52C22×C7semidirect
32. C2×C3×C5×C7C5×D3direct (N × H)
33. C2×C3×C5×C7C2×C3×C5semidirect
34. C5×D3×C7C2×C3×C5direct (N × H)
35. C2×C3×C5×D3C5×C7direct (N × H)
36. C52×C7C2×C3×D3direct (N × H)
39. C2×C3×C52D3×C7direct (N × H)
40. C2×C3×C52C2×C3×C7semidirect
41. C52×D3C2×C3×C7direct (N × H)
43. C2×C32×C7C2×C52semidirect
44. C3×D3×C7C2×C52direct (N × H)
46. C3×C5×C7C2×C5×D3direct (N × H)
47. C3×C5×C7C22×C3×C5semidirect
49. C2×C32×C5C2×C5×C7semidirect
50. C3×C5×D3C2×C5×C7direct (N × H)
52. C2×D3×C7C3×C52direct (N × H)
54. C3×C52C2×D3×C7direct (N × H)
55. C3×C52C22×C3×C7semidirect
57. C2×C5×C7C3×C5×D3direct (N × H)
58. C32×C7C22×C52semidirect
60. C2×C5×D3C3×C5×C7direct (N × H)
62. C2×C52C3×D3×C7direct (N × H)
63. C32×C5C22×C5×C7semidirect
66. C2×C3×C7C52×D3direct (N × H)
67. C2×C3×C7C2×C3×C52semidirect
68. D3×C7C2×C3×C52direct (N × H)
69. C2×C3×D3C52×C7direct (N × H)
70. C5×C7C2×C3×C5×D3direct (N × H)
73. C2×C3×C5C5×D3×C7direct (N × H)
74. C2×C3×C5C2×C3×C5×C7semidirect
75. C5×D3C2×C3×C5×C7direct (N × H)
77. C52C2×C3×D3×C7direct (N × H)
79. C3×C7C2×C52×D3direct (N × H)
80. C3×C7C22×C3×C52semidirect
82. C2×C32C2×C52×C7semidirect
83. C3×D3C2×C52×C7direct (N × H)
85. C3×C5C2×C5×D3×C7direct (N × H)
86. C3×C5C22×C3×C5×C7semidirect
88. C2×C7C3×C52×D3direct (N × H)
90. C2×D3C3×C52×C7direct (N × H)
92. C2×C5C3×C5×D3×C7direct (N × H)
93. C32C22×C52×C7semidirect
94. C7C2×C3×C52×D3direct (N × H)
97. C2×C3C52×D3×C7direct (N × H)
98. C2×C3C2×C3×C52×C7semidirect
99. D3C2×C3×C52×C7direct (N × H)
100. C5C2×C3×C5×D3×C7direct (N × H)
103. C3C22×C3×C52×C7semidirect
104. C3C2×C52×D3×C7direct (N × H)
106. C2C3×C52×D3×C7direct (N × H)