Finite Group Databasebeta

← C5×D4×C5⋊D5 #14522913

Subgroups — C5×D4×C5⋊D5 #14522913

Order 2000.

624 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 122 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×C5×C5⋊D5C212yesmaximal, complemented
2C53×D4C211yesmaximal, characteristic, complemented
3C5×C22⋊(C5⋊D5)C212yesmaximal, complemented
4C5×C4⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
5C4×C5×C5⋊D5C211yesmaximal, characteristic, complemented
6C22×C53C2212yescomplemented
7C2×C5×C5⋊D5—24no—
8C2×C5×C5⋊D5C2211yescharacteristic
9C2×C5×C5⋊D5C2212yescomplemented
10C4×C53C2211yescharacteristic, complemented
11C5×#1039C2211yescharacteristic, complemented
12D4×C5⋊D5C511yesmaximal, characteristic, direct product factor
13C5×D4×D5—56nomaximal
14C2×C53—22no—
15C2×C53C2311yescharacteristic
16C5×C5⋊D5—22no—
17C5×C5⋊D5D412yesdirect product factor
18C22×C5⋊D5C2×C512yescomplemented
19C22×C5×D5—512no—
20C52×D4—212no—
21C52×D4D516yescomplemented
22C52×D4C2×C511yescharacteristic, complemented
23C22⋊(C5⋊D5)C2×C512yescomplemented
24C4⋊(C5⋊D5)C2×C511yescharacteristic, complemented
25C4×C5⋊D5C2×C511yescharacteristic, complemented
26C5×C22⋊D5—512no—
27C5×D20—56no—
28C4×C5×D5—56no—
29C53C2×D411yescharacteristic, complemented, Sylow
30C22×C52—224no—
31C22×C52C2×D5112yescomplemented
32C22×C52C22×C512yescomplemented
33C2×C5⋊D5—24no—
34C2×C5⋊D5C22×C511yescharacteristic
35C2×C5⋊D5C22×C512yescomplemented
36C2×C5×D5—56no—
37C2×C5×D5—512no—
38C2×C5×D5—1024no—
39C4×C52—212no—
40C4×C52C2×D516yescomplemented
41C4×C52C22×C511yescharacteristic, complemented
42#1039C22×C511yescharacteristic, complemented
43C5×Dic5—56no—
44C2×C5×D4—251no—
45D4×D5—56no—
46C2×C52—22no—
47C2×C52—212no—
48C2×C52—212no—
49C2×C52—424no—
50C2×C52C22×D516yes—
51C2×C52C23×C511yescharacteristic
52C5⋊D5—22no—
53C5⋊D5C5×D412yesdirect product factor
54C5×D5—512no—
55C5×D5—1012no—
56C23×C5—252no—
57C22×D5—512no—
58C5×D4—212no—
59C5×D4—252no—
60C5×D4—251no—
61C5×D4C5×D516yescomplemented
62C5×D4C5⋊D511yescharacteristic, direct product factor
63C2×C4×C5—251no—
64C22⋊D5—512no—
65D20—56no—
66C4×D5—56no—
67C52—212no—
68C52D4×D516yescomplemented
69C52C2×C5×D411yescharacteristic, complemented
70C22×C5—224no—
71C22×C5—251no—
72C22×C5—252no—
73C22×C5—504no—
74C22×C5C2×C5×D5112yescomplemented
75C22×C5C2×C5⋊D512yescomplemented
76C2×D5—56no—
77C2×D5—512no—
78C2×D5—1024no—
79C4×C5—212no—
80C4×C5—251no—
81C4×C5C2×C5×D516yescomplemented
82C4×C5C2×C5⋊D511yescharacteristic, complemented
83Dic5—56no—
84C2×D4—251noSylow
85C2×C5—212no—
86C2×C5—22no—
87C2×C5—212no—
88C2×C5—424no—
89C2×C5—252no—
90C2×C5—502no—
91C2×C5C22×C5×D516yes—
92C2×C5C22×C5⋊D511yescharacteristic
93D5—512no—
94D5—1012no—
95C23—252no—
96D4—252no—
97D4—251no—
98D4C5×C5⋊D511yescharacteristic, direct product factor
99C2×C4—251no—
100C5—212no—
101C5C5×D4×D516yescomplemented
102C5D4×C5⋊D511yescharacteristic, direct product factor
103C22—251no—
104C22—252no—
105C22—504no—
106C22C2×C5×C5⋊D512yescomplemented
107C4—251no—
108C4C2×C5×C5⋊D511yescharacteristic, complemented
109C2—22no—
110C2—252no—
111C2—502no—
112C2C22×C5×C5⋊D511yescharacteristic
subgroupG/H
centerC2×C5C22×C5⋊D5
commutator, cosocleC2×C52C23×C5
FrattiniC2C22×C5×C5⋊D5
FittingC53×D4C2
socleC2×C53C23
hypercenterC5×D4C5⋊D5
hypocenterC52C2×C5×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C5 ◁ C5×D4

Complements

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

NH ≅ G/Ntype
1. C22×C5×C5⋊D5C2semidirect
2. C53×D4C2semidirect
3. C5×C22⋊(C5⋊D5)C2semidirect
4. C5×C4⋊(C5⋊D5)C2semidirect
5. C4×C5×C5⋊D5C2semidirect
6. C22×C53C22semidirect
9. C2×C5×C5⋊D5C22semidirect
10. C4×C53C22semidirect
11. C5×#1039C22semidirect
12. D4×C5⋊D5C5direct (N × H)
17. C5×C5⋊D5D4direct (N × H)
18. C22×C5⋊D5C2×C5semidirect
21. C52×D4D5semidirect
22. C52×D4C2×C5semidirect
23. C22⋊(C5⋊D5)C2×C5semidirect
24. C4⋊(C5⋊D5)C2×C5semidirect
25. C4×C5⋊D5C2×C5semidirect
29. C53C2×D4semidirect
31. C22×C52C2×D5semidirect
32. C22×C52C22×C5semidirect
35. C2×C5⋊D5C22×C5semidirect
40. C4×C52C2×D5semidirect
41. C4×C52C22×C5semidirect
42. #1039C22×C5semidirect
53. C5⋊D5C5×D4direct (N × H)
61. C5×D4C5×D5semidirect
62. C5×D4C5⋊D5direct (N × H)
68. C52D4×D5semidirect
69. C52C2×C5×D4semidirect
74. C22×C5C2×C5×D5semidirect
75. C22×C5C2×C5⋊D5semidirect
81. C4×C5C2×C5×D5semidirect
82. C4×C5C2×C5⋊D5semidirect
98. D4C5×C5⋊D5direct (N × H)
101. C5C5×D4×D5semidirect
102. C5D4×C5⋊D5direct (N × H)
106. C22C2×C5×C5⋊D5semidirect
108. C4C2×C5×C5⋊D5semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C5⋊D52
C53×D42
C5×C22⋊(C5⋊D5)2
C5×C4⋊(C5⋊D5)2
C4×C5×C5⋊D52
D4×C5⋊D55
C5×D4×D55