Finite Group Databasebeta

← C2×C32×C5×D35 #20263170

Subgroups — C2×C32×C5×D35 #20263170

Order 6300.

288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C32×C5×D35C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C3×C5×D35C314yesmaximal, direct product factor
4C32×C52×C7C2211yescharacteristic, complemented, Hall
5C2×C32×D35C511yesmaximal, characteristic, direct product factor
6C2×C32×C5×D7—51nomaximal
7C2×C3×C52×C7C2×C314yescomplemented
8C3×C5×D35C2×C318yesdirect product factor
9C2×C32×C5×D5—71nomaximal, Hall
10C2×C5×D35C3211yescharacteristic, direct product factor, Hall
11C2×C32×C5×C7—22no—
12C2×C32×C5×C7D511yescharacteristic, complemented
13C2×C32×C5×C7C2×C511yescharacteristic, complemented
14C32×D35C2×C512yesdirect product factor
15C32×C5×D7—52no—
16C3×C52×C7C22×C314yescomplemented
17C2×C32×C52D711yescharacteristic, complemented
18C32×C5×D5—72no—
19C2×C3×D35C3×C514yesdirect product factor
20C2×C3×C5×D7—54no—
21C2×C52×C7C2×C3211yescharacteristic, complemented
22C5×D35C2×C3212yesdirect product factor
23C32×C5×C7—22no—
24C32×C5×C7C2×D511yescharacteristic, complemented
25C32×C5×C7C22×C511yescharacteristic, complemented
26C2×C3×C5×D5—74no—
27C2×C32×D7—51noHall
28C32×C52C2×D711yescharacteristic, complemented, Hall
29C2×C3×C5×C7—28no—
30C2×C3×C5×C7C3×D514yescomplemented
31C2×C3×C5×C7C2×C3×C514yescomplemented
32C3×D35C2×C3×C518yesdirect product factor
33C3×C5×D7—58no—
34C22×C32×C5—351no—
35C2×C32×D5—71no—
36C52×C7C22×C3211yescharacteristic, complemented, Hall
37C2×C3×C52C3×D714yescomplemented
38C3×C5×D5—78no—
39C2×D35C32×C511yescharacteristic, direct product factor
40C2×C5×D7—51no—
41C2×C32×C7C5×D511yescharacteristic, complemented
42C32×D7—52no—
43C3×C5×C7—28no—
44C3×C5×C7C2×C3×D514yescomplemented
45C3×C5×C7C22×C3×C514yescomplemented
46C2×C5×D5—71noHall
47C2×C32×C5—22no—
48C2×C32×C5—352no—
49C2×C32×C5C5×D711yescharacteristic, complemented
50C2×C32×C5D3511yescharacteristic, direct product factor
51C32×D5—72no—
52C2×C3×D7—54no—
53C3×C52C2×C3×D714yescomplemented
54C2×C5×C7—22no—
55C2×C5×C7C32×D511yescharacteristic, complemented
56C2×C5×C7C2×C32×C511yescharacteristic, complemented
57D35C2×C32×C512yesdirect product factor
58C5×D7—52no—
59C32×C7C2×C5×D511yescharacteristic, complemented, Hall
60C22×C3×C5—354no—
61C2×C3×D5—74no—
62C2×C52C32×D711yescharacteristic, complemented
63C5×D5—72no—
64C32×C5—22no—
65C32×C5C2×C5×D711yescharacteristic, complemented
66C32×C5C2×D3511yescharacteristic, direct product factor
67C2×C3×C7C3×C5×D514yescomplemented
68C3×D7—58no—
69C22×C32—351noHall
70C5×C7—22no—
71C5×C7C2×C32×D511yescharacteristic, complemented
72C5×C7C22×C32×C511yescharacteristic, complemented
73C2×C3×C5—28no—
74C2×C3×C5—358no—
75C2×C3×C5C3×C5×D714yescomplemented
76C2×C3×C5C3×D3514yesdirect product factor
77C3×D5—78no—
78C2×D7—51noHall
79C52C2×C32×D711yescharacteristic, complemented, Sylow
80C3×C7C2×C3×C5×D514yescomplemented
81C22×C5—351no—
82C2×D5—71no—
83C2×C32—352no—
84C2×C32C5×D3511yescharacteristic, direct product factor
85C3×C5—28no—
86C3×C5C2×C3×C5×D714yescomplemented
87C3×C5C2×C3×D3514yesdirect product factor
88C2×C7C32×C5×D511yescharacteristic, complemented
89D7—52no—
90C22×C3—354no—
91C2×C5—22no—
92C2×C5—352no—
93C2×C5C32×C5×D711yescharacteristic, complemented
94C2×C5C32×D3511yescharacteristic, direct product factor
95D5—72no—
96C32C2×C5×D3511yescharacteristic, direct product factor, Sylow
97C7C2×C32×C5×D511yescharacteristic, complemented, Sylow
98C2×C3—358no—
99C2×C3C3×C5×D3514yesdirect product factor
100C5—22no—
101C5C2×C32×C5×D711yescharacteristic, complemented
102C5C2×C32×D3511yescharacteristic, direct product factor
103C22—351noSylow
104C3C2×C3×C5×D3514yesdirect product factor
105C2—352no—
106C2C32×C5×D3511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5D35
commutator, hypocenterC5×C7C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D35C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
3. C2×C3×C5×D35C3direct (N × H)
4. C32×C52×C7C22semidirect
5. C2×C32×D35C5direct (N × H)
7. C2×C3×C52×C7C2×C3semidirect
8. C3×C5×D35C2×C3direct (N × H)
10. C2×C5×D35C32direct (N × H)
12. C2×C32×C5×C7D5semidirect
13. C2×C32×C5×C7C2×C5semidirect
14. C32×D35C2×C5direct (N × H)
16. C3×C52×C7C22×C3semidirect
17. C2×C32×C52D7semidirect
19. C2×C3×D35C3×C5direct (N × H)
21. C2×C52×C7C2×C32semidirect
22. C5×D35C2×C32direct (N × H)
24. C32×C5×C7C2×D5semidirect
25. C32×C5×C7C22×C5semidirect
28. C32×C52C2×D7semidirect
30. C2×C3×C5×C7C3×D5semidirect
31. C2×C3×C5×C7C2×C3×C5semidirect
32. C3×D35C2×C3×C5direct (N × H)
36. C52×C7C22×C32semidirect
37. C2×C3×C52C3×D7semidirect
39. C2×D35C32×C5direct (N × H)
41. C2×C32×C7C5×D5semidirect
44. C3×C5×C7C2×C3×D5semidirect
45. C3×C5×C7C22×C3×C5semidirect
49. C2×C32×C5C5×D7semidirect
50. C2×C32×C5D35direct (N × H)
53. C3×C52C2×C3×D7semidirect
55. C2×C5×C7C32×D5semidirect
56. C2×C5×C7C2×C32×C5semidirect
57. D35C2×C32×C5direct (N × H)
59. C32×C7C2×C5×D5semidirect
62. C2×C52C32×D7semidirect
65. C32×C5C2×C5×D7semidirect
66. C32×C5C2×D35direct (N × H)
67. C2×C3×C7C3×C5×D5semidirect
71. C5×C7C2×C32×D5semidirect
72. C5×C7C22×C32×C5semidirect
75. C2×C3×C5C3×C5×D7semidirect
76. C2×C3×C5C3×D35direct (N × H)
79. C52C2×C32×D7semidirect
80. C3×C7C2×C3×C5×D5semidirect
84. C2×C32C5×D35direct (N × H)
86. C3×C5C2×C3×C5×D7semidirect
87. C3×C5C2×C3×D35direct (N × H)
88. C2×C7C32×C5×D5semidirect
93. C2×C5C32×C5×D7semidirect
94. C2×C5C32×D35direct (N × H)
96. C32C2×C5×D35direct (N × H)
97. C7C2×C32×C5×D5semidirect
99. C2×C3C3×C5×D35direct (N × H)
101. C5C2×C32×C5×D7semidirect
102. C5C2×C32×D35direct (N × H)
104. C3C2×C3×C5×D35direct (N × H)
106. C2C32×C5×D35direct (N × H)