Finite Group Databasebeta

← C52×D4×D5 #14522903

Subgroups — C52×D4×D5 #14522903

Order 2000.

624 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 200 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
1C22×C52×D5C212yesmaximal, complemented
2C53×D4C211yesmaximal, characteristic, complemented
3C52×C22⋊D5C212yesmaximal, complemented
4C52×D20C211yesmaximal, characteristic, complemented
5C4×C52×D5C211yesmaximal, characteristic, complemented
6C22×C53C2212yescomplemented
7C2×C52×D5—24no—
8C2×C52×D5C2211yescharacteristic
9C2×C52×D5C2212yescomplemented
10C4×C53C2211yescharacteristic, complemented
11C52×Dic5C2211yescharacteristic, complemented
12C2×C52×D4—51nomaximal
13C5×D4×D5C516yesmaximal, direct product factor
14C2×C53—22no—
15C2×C53C2311yescharacteristic
16C52×D5—22no—
17C52×D5D412yesdirect product factor
18C23×C52—52no—
19C22×C5×D5C2×C5112yescomplemented
20C52×D4—212no—
21C52×D4—52no—
22C52×D4—51no—
23C52×D4D511yescharacteristic, direct product factor
24C52×D4C2×C516yescomplemented
25C2×C4×C52—51no—
26C5×C22⋊D5C2×C5112yescomplemented
27C5×D20C2×C516yescomplemented
28C4×C5×D5C2×C516yescomplemented
29C53C2×D411yescharacteristic, complemented, Sylow
30C22×C52—224no—
31C22×C52—51no—
32C22×C52—52no—
33C22×C52—104no—
34C22×C52C2×D512yescomplemented
35C22×C52C22×C5112yescomplemented
36C2×C5×D5—224no—
37C2×C5×D5C22×C516yes—
38C2×C5×D5C22×C5112yescomplemented
39C4×C52—212no—
40C4×C52—51no—
41C4×C52C2×D511yescharacteristic, complemented
42C4×C52C22×C516yescomplemented
43C5×Dic5C22×C516yescomplemented
44C2×C5×D4—56no—
45D4×D5C5211yescharacteristic, direct product factor
46C2×C52—22no—
47C2×C52—212no—
48C2×C52—212no—
49C2×C52—424no—
50C2×C52—52no—
51C2×C52—102no—
52C2×C52C22×D511yescharacteristic
53C2×C52C23×C516yes—
54C5×D5—212no—
55C5×D5C5×D4112yesdirect product factor
56C23×C5—512no—
57C22×D5C2×C5212yescomplemented
58C5×D4—212no—
59C5×D4—512no—
60C5×D4—56no—
61C5×D4C5×D516yesdirect product factor
62C5×D4C2×C5211yescharacteristic, complemented
63C2×C4×C5—56no—
64C22⋊D5C2×C5212yescomplemented
65D20C2×C5211yescharacteristic, complemented
66C4×D5C2×C5211yescharacteristic, complemented
67C52—212no—
68C52D4×D511yescharacteristic, direct product factor
69C52C2×C5×D416yescomplemented
70C22×C5—224no—
71C22×C5—56no—
72C22×C5—512no—
73C22×C5—1024no—
74C22×C5C2×C5×D5112yescomplemented
75C22×C5C22×C5212yescomplemented
76C2×D5—24no—
77C2×D5C22×C5211yescharacteristic
78C2×D5C22×C5212yescomplemented
79C4×C5—212no—
80C4×C5—56no—
81C4×C5C2×C5×D516yescomplemented
82C4×C5C22×C5211yescharacteristic, complemented
83Dic5C22×C5211yescharacteristic, complemented
84C2×D4—51noSylow
85C2×C5—212no—
86C2×C5—22no—
87C2×C5—212no—
88C2×C5—424no—
89C2×C5—512no—
90C2×C5—1012no—
91C2×C5C22×C5×D516yes—
92C2×C5C23×C5211yescharacteristic
93D5—22no—
94D5C52×D412yesdirect product factor
95C23—52no—
96D4—52no—
97D4—51no—
98D4C52×D511yescharacteristic, direct product factor
99C2×C4—51no—
100C5—212no—
101C5C5×D4×D516yesdirect product factor
102C5C2×C52×D411yescharacteristic, complemented
103C22—51no—
104C22—52no—
105C22—104no—
106C22C2×C52×D512yescomplemented
107C4—51no—
108C4C2×C52×D511yescharacteristic, complemented
109C2—22no—
110C2—52no—
111C2—102no—
112C2C22×C52×D511yescharacteristic
subgroupG/H
centerC2×C52C22×D5
commutator, cosocleC2×C5C23×C52
FrattiniC2C22×C52×D5
FittingC53×D4C2
socleC2×C53C23
hypercenterC52×D4D5
hypocenterC5C2×C52×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C52 ◁ C52×D4

Complements

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

NH ≅ G/Ntype
1. C22×C52×D5C2semidirect
2. C53×D4C2semidirect
3. C52×C22⋊D5C2semidirect
4. C52×D20C2semidirect
5. C4×C52×D5C2semidirect
6. C22×C53C22semidirect
9. C2×C52×D5C22semidirect
10. C4×C53C22semidirect
11. C52×Dic5C22semidirect
13. C5×D4×D5C5direct (N × H)
17. C52×D5D4direct (N × H)
19. C22×C5×D5C2×C5semidirect
23. C52×D4D5direct (N × H)
24. C52×D4C2×C5semidirect
26. C5×C22⋊D5C2×C5semidirect
27. C5×D20C2×C5semidirect
28. C4×C5×D5C2×C5semidirect
29. C53C2×D4semidirect
34. C22×C52C2×D5semidirect
35. C22×C52C22×C5semidirect
38. C2×C5×D5C22×C5semidirect
41. C4×C52C2×D5semidirect
42. C4×C52C22×C5semidirect
43. C5×Dic5C22×C5semidirect
45. D4×D5C52direct (N × H)
55. C5×D5C5×D4direct (N × H)
57. C22×D5C2×C52semidirect
61. C5×D4C5×D5direct (N × H)
62. C5×D4C2×C52semidirect
64. C22⋊D5C2×C52semidirect
65. D20C2×C52semidirect
66. C4×D5C2×C52semidirect
68. C52D4×D5direct (N × H)
69. C52C2×C5×D4semidirect
74. C22×C5C2×C5×D5semidirect
75. C22×C5C22×C52semidirect
78. C2×D5C22×C52semidirect
81. C4×C5C2×C5×D5semidirect
82. C4×C5C22×C52semidirect
83. Dic5C22×C52semidirect
94. D5C52×D4direct (N × H)
98. D4C52×D5direct (N × H)
101. C5C5×D4×D5direct (N × H)
102. C5C2×C52×D4semidirect
106. C22C2×C52×D5semidirect
108. C4C2×C52×D5semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C52×D52
C53×D42
C52×C22⋊D52
C52×D202
C4×C52×D52
C2×C52×D45
C5×D4×D55