Finite Group Databasebeta

← C4×D5×C5⋊D5 #14522872

Subgroups — C4×D5×C5⋊D5 #14522872

Order 2000.

624 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×D5×C5⋊D5C211yesmaximal, characteristic
2C4×C5⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C4×C5×C5⋊D5C211yesmaximal, characteristic, complemented
4C4×C52×D5C211yesmaximal, characteristic, complemented
5#11758751C211yesmaximal, characteristic, complemented
6Dic5×C5⋊D5C211yesmaximal, characteristic, complemented
7D5×#1039C211yesmaximal, characteristic, complemented
8C2×C5⋊(C5⋊D5)C2211yescharacteristic
9C2×C5×C5⋊D5C2211yescharacteristic
10C2×C52×D5C2211yescharacteristic
11D5×C5⋊D5C414yesdirect product factor
12C4×C53C2211yescharacteristic, complemented
13#92553C2211yescharacteristic, complemented
14C5×#1039C2211yescharacteristic, complemented
15C52×Dic5C2211yescharacteristic, complemented
16C2×C4×C5⋊D5—51nomaximal
17C4×D52—56nomaximal
18C2×C53C2311yescharacteristic
19C5⋊(C5⋊D5)C2×C412yescomplemented
20C5×C5⋊D5C2×C412yescomplemented
21C52×D5C2×C412yescomplemented
22C22×C5⋊D5—51no—
23C2×D52—56no—
24C2×C4×C52—51no—
25C2×#1039—51no—
26C4×C5⋊D5—51no—
27C4×C5⋊D5—51no—
28C4×C5⋊D5—56no—
29C4×C5⋊D5—51no—
30C4×C5⋊D5—1012no—
31C4×C5⋊D5D511yescharacteristic, direct product factor
32C4×C5×D5—56no—
33C4×C5×D5D516yescomplemented
34#6036—56no—
35D5×Dic5—56no—
36D5×Dic5—56no—
37C53C22×C411yescharacteristic, complemented, Sylow
38C22×C52—51no—
39C2×C5⋊D5—51no—
40C2×C5⋊D5—56no—
41C2×C5⋊D5—54no—
42C2×C5⋊D5—1012no—
43C2×C5⋊D5C2×D511yescharacteristic
44C2×C5×D5—56no—
45C2×C5×D5C2×D516yes—
46D52—524no—
47C4×C52—212no—
48C4×C52—51no—
49C4×C52C2×D516yescomplemented
50C4×C52C2×D511yescharacteristic, complemented
51#1039—51no—
52#1039—56no—
53#1039—1012no—
54#1039C2×D511yescharacteristic, complemented
55C5×Dic5—56no—
56C5×Dic5C2×D516yescomplemented
57C2×C4×D5—256no—
58C2×C4×D5—251no—
59C2×C52—212no—
60C2×C52—52no—
61C2×C52C22×D516yes—
62C2×C52C22×D511yescharacteristic
63C5⋊D5—52no—
64C5⋊D5—512no—
65C5⋊D5—1024no—
66C5⋊D5C4×D512yesdirect product factor
67C5×D5—512no—
68C5×D5C4×D5112yescomplemented
69C22×D5—256no—
70C22×D5—251no—
71C2×C4×C5—56no—
72C2×C4×C5—251no—
73C2×Dic5—256no—
74C2×Dic5—251no—
75C4×D5—56no—
76C4×D5—256no—
77C4×D5—256no—
78C4×D5—251no—
79C4×D5—256no—
80C4×D5—251no—
81C4×D5—251no—
82C4×D5—5012no—
83C4×D5C5⋊D511yescharacteristic, direct product factor
84C52—212no—
85C52C2×C4×D516yescomplemented
86C52C2×C4×D511yescharacteristic, complemented
87C22×C5—56no—
88C22×C5—251no—
89C2×D5—56no—
90C2×D5—2524no—
91C2×D5—256no—
92C2×D5—251no—
93C2×D5—254no—
94C2×D5—5012no—
95C2×D5C2×C5⋊D511yescharacteristic
96C4×C5—212no—
97C4×C5—56no—
98C4×C5—251no—
99C4×C5D5216yescomplemented
100C4×C5C2×C5⋊D511yescharacteristic, complemented
101Dic5—56no—
102Dic5—256no—
103Dic5—251no—
104Dic5—5012no—
105Dic5C2×C5⋊D511yescharacteristic, complemented
106C22×C4—1251noSylow
107C2×C5—212no—
108C2×C5—512no—
109C2×C5—252no—
110C2×C5C2×D5216yes—
111C2×C5C22×C5⋊D511yescharacteristic
112D5—512no—
113D5—2512no—
114D5—252no—
115D5—5024no—
116D5C4×C5⋊D512yesdirect product factor
117C23—1251no—
118C2×C4—51no—
119C2×C4—251no—
120C2×C4—1251no—
121C2×C4—1251no—
122C2×C4—1251no—
123C2×C4—1251no—
124C5—212no—
125C5C4×D5216yescomplemented
126C5C2×C4×C5⋊D511yescharacteristic, complemented
127C22—51no—
128C22—251no—
129C22—1254no—
130C22—1251no—
131C4—51no—
132C4—251no—
133C4—1251no—
134C4D5×C5⋊D511yescharacteristic, direct product factor
135C2—52no—
136C2—252no—
137C2—1252no—
138C2C2×D5×C5⋊D511yescharacteristic
subgroupG/H
center, hypercenterC4D5×C5⋊D5
commutator, hypocenterC53C22×C4
FrattiniC2C2×D5×C5⋊D5
FittingC4×C53C22
socle, cosocleC2×C53C23
prime radicalC2×D5×C5⋊D5C2
LCSG ▷ C53
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C5⋊(C5⋊D5)C2semidirect
3. C4×C5×C5⋊D5C2semidirect
4. C4×C52×D5C2semidirect
5. #11758751C2semidirect
6. Dic5×C5⋊D5C2semidirect
7. D5×#1039C2semidirect
11. D5×C5⋊D5C4direct (N × H)
12. C4×C53C22semidirect
13. #92553C22semidirect
14. C5×#1039C22semidirect
15. C52×Dic5C22semidirect
19. C5⋊(C5⋊D5)C2×C4semidirect
20. C5×C5⋊D5C2×C4semidirect
21. C52×D5C2×C4semidirect
31. C4×C5⋊D5D5direct (N × H)
33. C4×C5×D5D5semidirect
37. C53C22×C4semidirect
49. C4×C52C2×D5semidirect
50. C4×C52C2×D5semidirect
54. #1039C2×D5semidirect
56. C5×Dic5C2×D5semidirect
66. C5⋊D5C4×D5direct (N × H)
68. C5×D5C4×D5semidirect
83. C4×D5C5⋊D5direct (N × H)
85. C52C2×C4×D5semidirect
86. C52C2×C4×D5semidirect
99. C4×C5D52semidirect
100. C4×C5C2×C5⋊D5semidirect
105. Dic5C2×C5⋊D5semidirect
116. D5C4×C5⋊D5direct (N × H)
125. C5C4×D52semidirect
126. C5C2×C4×C5⋊D5semidirect
134. C4D5×C5⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C5⋊D52
C4×C5⋊(C5⋊D5)2
C4×C5×C5⋊D52
C4×C52×D52
#117587512
Dic5×C5⋊D52
D5×#10392
C2×C4×C5⋊D55
C4×D525