Finite Group Databasebeta

← C2×D5×#1044 #14522971

Subgroups — C2×D5×#1044 #14522971

Order 2000.

340 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 56 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
2C2×#92560C211yesmaximal, characteristic, complemented
3C2×C5×#1044C211yesmaximal, characteristic, complemented
4D5×#1044C214yesmaximal, direct product factor
5C2×C5⋊(C5⋊D5)C411yescharacteristic, complemented
6C2×C5×C5⋊D5C2211yescharacteristic
7C2×C52×D5C411yescharacteristic, complemented
8D5×C5⋊D5C412yescomplemented
9D5×C5⋊D5C2212yes—
10#92560C2212yescomplemented
11C5×#1044C2212yescomplemented
12C22×#1044—51nomaximal
13C2×D5×AGL(1,𝔽5)—52nomaximal
14C2×C53C2×C411yescharacteristic, complemented
15C5⋊(C5⋊D5)C2×C412yescomplemented
16C5×C5⋊D5C2×C411yescharacteristic, complemented
17C5×C5⋊D5C2311yescharacteristic
18C52×D5C2×C412yescomplemented
19C22×C5⋊D5—51no—
20C2×D52—52no—
21C2×D52—102no—
22C2×#1044—51no—
23C2×#1044—54no—
24C2×#1044D511yescharacteristic, direct product factor
25C2×#1042—52no—
26C2×C5×AGL(1,𝔽5)—52no—
27D5×AGL(1,𝔽5)—58no—
28C53C22×C411yescharacteristic, complemented, Sylow
29C22×C52—51no—
30C2×C5⋊D5—51no—
31C2×C5⋊D5—52no—
32C2×C5⋊D5—52no—
33C2×C5⋊D5—52no—
34C2×C5⋊D5—102no—
35C2×C5⋊D5—202no—
36C2×C5⋊D5—204no—
37C2×C5⋊D5C2×D511yescharacteristic
38C2×C5×D5—22no—
39C2×C5×D5—52no—
40C2×C5×D5—102no—
41C2×C5×D5AGL(1,𝔽5)12yescomplemented
42D52—54no—
43D52—54no—
44D52—104no—
45D52—104no—
46#1044—52no—
47#1044C2×D512yesdirect product factor
48#1042—54no—
49C5×AGL(1,𝔽5)—54no—
50C22×AGL(1,𝔽5)—252no—
51C2×C4×D5—251no—
52C2×C52—22no—
53C2×C52—44no—
54C2×C52—42no—
55C2×C52—52no—
56C2×C52C4×D511yescharacteristic, complemented
57C2×C52C2×AGL(1,𝔽5)12yescomplemented
58C5⋊D5—52no—
59C5⋊D5—54no—
60C5⋊D5—104no—
61C5⋊D5—204no—
62C5⋊D5—208no—
63C5⋊D5C4×D511yescharacteristic, complemented
64C5⋊D5C22×D511yescharacteristic
65C5×D5—24no—
66C5×D5—52no—
67C5×D5—52no—
68C5×D5—102no—
69C5×D5—102no—
70C5×D5C2×AGL(1,𝔽5)14yescomplemented
71C22×D5—252no—
72C22×D5—251no—
73C22×D5—502no—
74C2×AGL(1,𝔽5)—52no—
75C2×AGL(1,𝔽5)—258no—
76C2×AGL(1,𝔽5)—252no—
77C2×C4×C5—251no—
78C2×Dic5—251no—
79C4×D5—254no—
80C52—22no—
81C52—44no—
82C52—42no—
83C52C2×C4×D511yescharacteristic, complemented
84C52C22×AGL(1,𝔽5)12yescomplemented
85C22×C5—52no—
86C22×C5—102no—
87C22×C5—251no—
88C2×D5—52no—
89C2×D5—102no—
90C2×D5—254no—
91C2×D5—254no—
92C2×D5—252no—
93C2×D5—251no—
94C2×D5—252no—
95C2×D5—252no—
96C2×D5—504no—
97C2×D5—504no—
98C2×D5—502no—
99C2×D5—1002no—
100C2×D5—1004no—
101C2×D5#104411yescharacteristic, direct product factor
102AGL(1,𝔽5)—54no—
103AGL(1,𝔽5)—254no—
104C4×C5—252no—
105Dic5—252no—
106C22×C4—1251noSylow
107C2×C5—22no—
108C2×C5—44no—
109C2×C5—42no—
110C2×C5—54no—
111C2×C5—104no—
112C2×C5—251no—
113C2×C5—251no—
114C2×C5D5×AGL(1,𝔽5)12yescomplemented
115C2×C5C2×#104411yescharacteristic, complemented
116D5—52no—
117D5—52no—
118D5—102no—
119D5—102no—
120D5—254no—
121D5—252no—
122D5—504no—
123D5—1004no—
124D5—1008no—
125D5C2×#104412yesdirect product factor
126C23—1251no—
127C2×C4—251no—
128C2×C4—1254no—
129C2×C4—1251no—
130C5—22no—
131C5—44no—
132C5—42no—
133C5C2×D5×AGL(1,𝔽5)12yescomplemented
134C5C22×#104411yescharacteristic, complemented
135C22—51no—
136C22—251no—
137C22—1252no—
138C22—1252no—
139C22—1251no—
140C4—252no—
141C4—1252no—
142C2—52no—
143C2—251no—
144C2—251no—
145C2—1252no—
146C2D5×#104411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D5×#1044
commutator, hypocenterC53C22×C4
FrattiniC1G
Fitting, socleC2×C53C2×C4
prime radicalC2×D5×C5⋊D5C2
cosocleC5×C5⋊D5C23
LCSG ▷ C53
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C2×#92560C2semidirect
3. C2×C5×#1044C2semidirect
4. D5×#1044C2direct (N × H)
5. C2×C5⋊(C5⋊D5)C4semidirect
7. C2×C52×D5C4semidirect
8. D5×C5⋊D5C4semidirect
10. #92560C22semidirect
11. C5×#1044C22semidirect
14. C2×C53C2×C4semidirect
15. C5⋊(C5⋊D5)C2×C4semidirect
16. C5×C5⋊D5C2×C4semidirect
18. C52×D5C2×C4semidirect
24. C2×#1044D5direct (N × H)
28. C53C22×C4semidirect
41. C2×C5×D5AGL(1,𝔽5)semidirect
47. #1044C2×D5direct (N × H)
56. C2×C52C4×D5semidirect
57. C2×C52C2×AGL(1,𝔽5)semidirect
63. C5⋊D5C4×D5semidirect
70. C5×D5C2×AGL(1,𝔽5)semidirect
83. C52C2×C4×D5semidirect
84. C52C22×AGL(1,𝔽5)semidirect
101. C2×D5#1044direct (N × H)
114. C2×C5D5×AGL(1,𝔽5)semidirect
115. C2×C5C2×#1044semidirect
125. D5C2×#1044direct (N × H)
133. C5C2×D5×AGL(1,𝔽5)semidirect
134. C5C22×#1044semidirect
146. C2D5×#1044direct (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
C2×#925602
C2×C5×#10442
D5×#10442
C22×#10445
C2×D5×AGL(1,𝔽5)5