Finite Group Databasebeta

← C2×C5×#6038 #14522858

Subgroups — C2×C5×#6038 #14522858

Order 2000.

416 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 80 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⋊D5C211yesmaximal, characteristic, complemented
2C22×C52×D5C211yesmaximal, characteristic, complemented
3C2×C52×Dic5C211yesmaximal, characteristic, complemented
4C5×#6038C214yesmaximal, direct product factor
5C22×C53C2211yescharacteristic
6C2×C5×C5⋊D5—22no—
7C2×C5×C5⋊D5C2212yescomplemented
8C2×C52×D5—22no—
9C2×C52×D5C2212yescomplemented
10C52×Dic5C2212yescomplemented
11C2×C5×C22⋊D5—51nomaximal
12C2×C5×D20—51nomaximal
13C2×#6038C511yesmaximal, characteristic, direct product factor
14C2×C53D412yescomplemented
15C2×C53C2311yescharacteristic
16C5×C5⋊D5—22no—
17C52×D5—22no—
18C23×C52—51no—
19C22×C5⋊D5C2×C511yescharacteristic, complemented
20C22×C5×D5—22no—
21C22×C5×D5—51no—
22C22×C5×D5—51no—
23C22×C5×D5—102no—
24C22×C5×D5D511yescharacteristic, complemented
25C22×C5×D5C2×C511yescharacteristic, complemented
26C2×C4×C52—51no—
27C5×C22⋊D5—54no—
28C2×C5×Dic5—22no—
29C2×C5×Dic5D511yescharacteristic, complemented
30C2×C5×Dic5C2×C511yescharacteristic, complemented
31C5×D20—54no—
32#6038C2×C514yesdirect product factor
33C53C2×D411yescharacteristic, complemented, Sylow
34C22×C52—22no—
35C22×C52—22no—
36C22×C52—22no—
37C22×C52—44no—
38C22×C52—52no—
39C22×C52—102no—
40C22×C52C2×D511yescharacteristic
41C22×C52C2×D511yescharacteristic
42C22×C52C22×C511yescharacteristic
43C2×C5⋊D5—22no—
44C2×C5⋊D5C22×C512yescomplemented
45C2×C5×D5—28no—
46C2×C5×D5—24no—
47C2×C5×D5—22no—
48C2×C5×D5—22no—
49C2×C5×D5—52no—
50C2×C5×D5—52no—
51C2×C5×D5—104no—
52C2×C5×D5—108no—
53C2×C5×D5—102no—
54C2×C5×D5—102no—
55C2×C5×D5C2×D512yescomplemented
56C2×C5×D5C22×C512yescomplemented
57C4×C52—52no—
58C5×Dic5—24no—
59C5×Dic5C2×D512yescomplemented
60C5×Dic5C22×C512yescomplemented
61C2×C5×D4—251no—
62C2×C22⋊D5—51no—
63C2×D20—51no—
64C2×C52—24no—
65C2×C52—24no—
66C2×C52—24no—
67C2×C52—22no—
68C2×C52—22no—
69C2×C52—22no—
70C2×C52—48no—
71C2×C52—44no—
72C2×C52—102no—
73C2×C52D2012yescomplemented
74C2×C52C22⋊D512yescomplemented
75C2×C52C5×D412yescomplemented
76C2×C52C22×D511yescharacteristic
77C2×C52C22×D511yescharacteristic
78C2×C52C23×C511yescharacteristic
79C5⋊D5—22no—
80C5×D5—28no—
81C5×D5—22no—
82C5×D5—22no—
83C5×D5—108no—
84C5×D5—102no—
85C5×D5—102no—
86C23×C5—51no—
87C23×C5—51no—
88C23×C5—102no—
89C23×C5—251no—
90C22×D5—51no—
91C22×D5—51no—
92C22×D5—102no—
93C22×D5C5×D511yescharacteristic, complemented
94C5×D4—254no—
95C2×C4×C5—51no—
96C2×C4×C5—51no—
97C2×C4×C5—102no—
98C22⋊D5—54no—
99C2×Dic5C5×D511yescharacteristic, complemented
100D20—54no—
101C52—22no—
102C52—22no—
103C52—22no—
104C52—44no—
105C52C2×D2011yescharacteristic, complemented
106C52C2×C22⋊D511yescharacteristic, complemented
107C52C2×C5×D411yescharacteristic, complemented
108C22×C5—22no—
109C22×C5—22no—
110C22×C5—22no—
111C22×C5—44no—
112C22×C5—52no—
113C22×C5—52no—
114C22×C5—104no—
115C22×C5—108no—
116C22×C5—102no—
117C22×C5—102no—
118C22×C5—252no—
119C22×C5—502no—
120C22×C5D5211yescharacteristic
121C22×C5C2×C5×D511yescharacteristic
122C22×C5C2×C5×D511yescharacteristic
123C2×D5—22no—
124C2×D5—52no—
125C2×D5—52no—
126C2×D5—104no—
127C2×D5—108no—
128C2×D5—102no—
129C2×D5—102no—
130C2×D5C2×C5×D512yescomplemented
131C4×C5—52no—
132C4×C5—52no—
133C4×C5—104no—
134Dic5C2×C5×D512yescomplemented
135C2×D4—251noSylow
136C2×C5—24no—
137C2×C5—24no—
138C2×C5—24no—
139C2×C5—22no—
140C2×C5—22no—
141C2×C5—22no—
142C2×C5—48no—
143C2×C5—44no—
144C2×C5—108no—
145C2×C5—102no—
146C2×C5—102no—
147C2×C5—502no—
148C2×C5#603812yesdirect product factor
149C2×C5C5×D2012yescomplemented
150C2×C5C5×C22⋊D512yescomplemented
151C2×C5C2×D5211yescharacteristic
152C2×C5C22×C5×D511yescharacteristic
153C2×C5C22×C5×D511yescharacteristic
154D5—22no—
155D5—108no—
156D5—102no—
157D5—102no—
158C23—51no—
159C23—251no—
160D4—254no—
161C2×C4—51no—
162C5—22no—
163C5—22no—
164C5—22no—
165C5—44no—
166C5C2×#603811yescharacteristic, direct product factor
167C5C2×C5×D2011yescharacteristic, complemented
168C5C2×C5×C22⋊D511yescharacteristic, complemented
169C22—52no—
170C22—102no—
171C22—252no—
172C22—502no—
173C22C5×D5211yescharacteristic
174C4—52no—
175C2—102no—
176C2—502no—
177C2C5×#603812yesdirect product factor
178C2C2×C5×D5211yescharacteristic
subgroupG/H
center, hypercenterC22×C5D52
commutator, cosocleC2×C52C23×C5
FrattiniC2C2×C5×D52
Fitting, socleC22×C53C22
hypocenterC52C2×C5×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C22×C5×C5⋊D5C2semidirect
2. C22×C52×D5C2semidirect
3. C2×C52×Dic5C2semidirect
4. C5×#6038C2direct (N × H)
7. C2×C5×C5⋊D5C22semidirect
9. C2×C52×D5C22semidirect
10. C52×Dic5C22semidirect
13. C2×#6038C5direct (N × H)
14. C2×C53D4semidirect
19. C22×C5⋊D5C2×C5semidirect
24. C22×C5×D5D5semidirect
25. C22×C5×D5C2×C5semidirect
29. C2×C5×Dic5D5semidirect
30. C2×C5×Dic5C2×C5semidirect
32. #6038C2×C5direct (N × H)
33. C53C2×D4semidirect
44. C2×C5⋊D5C22×C5semidirect
55. C2×C5×D5C2×D5semidirect
56. C2×C5×D5C22×C5semidirect
59. C5×Dic5C2×D5semidirect
60. C5×Dic5C22×C5semidirect
73. C2×C52D20semidirect
74. C2×C52C22⋊D5semidirect
75. C2×C52C5×D4semidirect
93. C22×D5C5×D5semidirect
99. C2×Dic5C5×D5semidirect
105. C52C2×D20semidirect
106. C52C2×C22⋊D5semidirect
107. C52C2×C5×D4semidirect
130. C2×D5C2×C5×D5semidirect
134. Dic5C2×C5×D5semidirect
148. C2×C5#6038direct (N × H)
149. C2×C5C5×D20semidirect
150. C2×C5C5×C22⋊D5semidirect
166. C5C2×#6038direct (N × H)
167. C5C2×C5×D20semidirect
168. C5C2×C5×C22⋊D5semidirect
177. C2C5×#6038direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C5⋊D52
C22×C52×D52
C2×C52×Dic52
C5×#60382
C2×C5×C22⋊D55
C2×C5×D205
C2×#60385