Finite Group Databasebeta

← C2×C3×C52×D21 #20263166

Subgroups — C2×C3×C52×D21 #20263166

Order 6300.

352 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 176 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×D21C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C52×D21C311yesmaximal, characteristic, direct product factor
4C2×C3×C52×D7—31nomaximal
5C32×C52×C7C2211yescharacteristic, complemented, Hall
6C2×C3×C5×D21C516yesmaximal, direct product factor
7C2×C3×C52×C7—21no—
8C2×C3×C52×C7D311yescharacteristic, complemented
9C2×C3×C52×C7C2×C311yescharacteristic, complemented
10C52×D21C2×C312yesdirect product factor
11C3×C52×D7—32no—
12C2×C3×C52×D3—71nomaximal, Hall
13C2×C52×D7—31noHall
14C2×C32×C5×C7C2×C516yescomplemented
15C3×C5×D21C2×C5112yesdirect product factor
16C3×C52×C7—21no—
17C3×C52×C7C2×D311yescharacteristic, complemented
18C3×C52×C7C22×C311yescharacteristic, complemented
19C2×C32×C52D711yescharacteristic, complemented
20C3×C52×D3—72no—
21C2×C5×D21C3×C516yesdirect product factor
22C2×C3×C5×D7—36no—
23C2×C52×C7C3×D311yescharacteristic, complemented
24C52×D7—32no—
25C32×C5×C7C22×C516yescomplemented
26C22×C3×C52—211no—
27C2×C52×D3—71no—
28C2×C3×D21C5211yescharacteristic, direct product factor, Hall
29C32×C52C2×D711yescharacteristic, complemented, Hall
30C2×C3×C5×C7—26no—
31C2×C3×C5×C7C5×D316yescomplemented
32C2×C3×C5×C7C2×C3×C516yescomplemented
33C5×D21C2×C3×C5112yesdirect product factor
34C3×C5×D7—312no—
35C2×C3×C5×D3—76no—
36C52×C7C2×C3×D311yescharacteristic, complemented, Hall
37C2×C3×C52—21no—
38C2×C3×C52—212no—
39C2×C3×C52C3×D711yescharacteristic, complemented
40C2×C3×C52D2111yescharacteristic, direct product factor
41C52×D3—72no—
42C2×C5×D7—36no—
43C2×C32×C7C2×C5211yescharacteristic, complemented
44C3×D21C2×C5212yesdirect product factor
45C3×C5×C7—26no—
46C3×C5×C7C2×C5×D316yescomplemented
47C3×C5×C7C22×C3×C516yescomplemented
48C22×C52—211noHall
49C2×C32×C5C5×D716yescomplemented
50C3×C5×D3—712no—
51C2×D21C3×C5211yescharacteristic, direct product factor
52C2×C3×D7—31no—
53C3×C52—21no—
54C3×C52C2×C3×D711yescharacteristic, complemented
55C3×C52C2×D2111yescharacteristic, direct product factor
56C2×C5×C7C3×C5×D316yescomplemented
57C5×D7—312no—
58C32×C7C22×C5211yescharacteristic, complemented, Hall
59C22×C3×C5—216no—
60C2×C5×D3—76no—
61C2×C52—212no—
62C2×C52C3×D2111yescharacteristic, direct product factor
63C32×C5C2×C5×D716yescomplemented
64C2×C3×C7—21no—
65C2×C3×C7C52×D311yescharacteristic, complemented
66C2×C3×C7C2×C3×C5211yescharacteristic, complemented
67D21C2×C3×C5212yesdirect product factor
68C3×D7—32no—
69C2×C3×D3—71noHall
70C5×C7C2×C3×C5×D316yescomplemented
71C2×C3×C5—26no—
72C2×C3×C5—2112no—
73C2×C3×C5C3×C5×D716yescomplemented
74C2×C3×C5C5×D2116yesdirect product factor
75C5×D3—712no—
76C2×D7—31noHall
77C52C2×C3×D2111yescharacteristic, direct product factor, Sylow
78C3×C7—21no—
79C3×C7C2×C52×D311yescharacteristic, complemented
80C3×C7C22×C3×C5211yescharacteristic, complemented
81C22×C5—216no—
82C2×C32C52×D711yescharacteristic, complemented
83C3×D3—72no—
84C3×C5—26no—
85C3×C5C2×C3×C5×D716yescomplemented
86C3×C5C2×C5×D2116yesdirect product factor
87C2×C7C3×C52×D311yescharacteristic, complemented
88D7—32no—
89C22×C3—211no—
90C2×D3—71no—
91C2×C5—2112no—
92C2×C5C3×C5×D2116yesdirect product factor
93C32C2×C52×D711yescharacteristic, complemented, Sylow
94C7C2×C3×C52×D311yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—212no—
97C2×C3C3×C52×D711yescharacteristic, complemented
98C2×C3C52×D2111yescharacteristic, direct product factor
99D3—72no—
100C5C2×C3×C5×D2116yesdirect product factor
101C22—211noSylow
102C3—21no—
103C3C2×C3×C52×D711yescharacteristic, complemented
104C3C2×C52×D2111yescharacteristic, direct product factor
105C2—212no—
106C2C3×C52×D2111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C52D21
commutator, hypocenterC3×C7C22×C3×C52
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C3×C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×D21C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
3. C2×C52×D21C3direct (N × H)
5. C32×C52×C7C22semidirect
6. C2×C3×C5×D21C5direct (N × H)
8. C2×C3×C52×C7D3semidirect
9. C2×C3×C52×C7C2×C3semidirect
10. C52×D21C2×C3direct (N × H)
14. C2×C32×C5×C7C2×C5semidirect
15. C3×C5×D21C2×C5direct (N × H)
17. C3×C52×C7C2×D3semidirect
18. C3×C52×C7C22×C3semidirect
19. C2×C32×C52D7semidirect
21. C2×C5×D21C3×C5direct (N × H)
23. C2×C52×C7C3×D3semidirect
25. C32×C5×C7C22×C5semidirect
28. C2×C3×D21C52direct (N × H)
29. C32×C52C2×D7semidirect
31. C2×C3×C5×C7C5×D3semidirect
32. C2×C3×C5×C7C2×C3×C5semidirect
33. C5×D21C2×C3×C5direct (N × H)
36. C52×C7C2×C3×D3semidirect
39. C2×C3×C52C3×D7semidirect
40. C2×C3×C52D21direct (N × H)
43. C2×C32×C7C2×C52semidirect
44. C3×D21C2×C52direct (N × H)
46. C3×C5×C7C2×C5×D3semidirect
47. C3×C5×C7C22×C3×C5semidirect
49. C2×C32×C5C5×D7semidirect
51. C2×D21C3×C52direct (N × H)
54. C3×C52C2×C3×D7semidirect
55. C3×C52C2×D21direct (N × H)
56. C2×C5×C7C3×C5×D3semidirect
58. C32×C7C22×C52semidirect
62. C2×C52C3×D21direct (N × H)
63. C32×C5C2×C5×D7semidirect
65. C2×C3×C7C52×D3semidirect
66. C2×C3×C7C2×C3×C52semidirect
67. D21C2×C3×C52direct (N × H)
70. C5×C7C2×C3×C5×D3semidirect
73. C2×C3×C5C3×C5×D7semidirect
74. C2×C3×C5C5×D21direct (N × H)
77. C52C2×C3×D21direct (N × H)
79. C3×C7C2×C52×D3semidirect
80. C3×C7C22×C3×C52semidirect
82. C2×C32C52×D7semidirect
85. C3×C5C2×C3×C5×D7semidirect
86. C3×C5C2×C5×D21direct (N × H)
87. C2×C7C3×C52×D3semidirect
92. C2×C5C3×C5×D21direct (N × H)
93. C32C2×C52×D7semidirect
94. C7C2×C3×C52×D3semidirect
97. C2×C3C3×C52×D7semidirect
98. C2×C3C52×D21direct (N × H)
100. C5C2×C3×C5×D21direct (N × H)
103. C3C2×C3×C52×D7semidirect
104. C3C2×C52×D21direct (N × H)
106. C2C3×C52×D21direct (N × H)