Finite Group Databasebeta

← C2×#11717231 #13107283

Subgroups — C2×#11717231 #13107283

Order 1600.

1192 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 235 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×#87902C211yesmaximal, characteristic, complemented
2C2×D4×C5⋊D5C211yesmaximal, characteristic, complemented
3C2×C52×D8C211yesmaximal, characteristic, complemented
4C2×#87810C211yesmaximal, characteristic, complemented
5C2×#87809C211yesmaximal, characteristic, complemented
6#11717231C218yesmaximal, direct product factor
7C2×#87800C211yesmaximal, characteristic, complemented
8C2×#87799C211yesmaximal, characteristic, complemented
9C23×C5⋊D5—21no—
10C2×C52×D4C2211yescharacteristic
11C2×C52×D4C2211yescharacteristic, complemented
12C2×C22⋊(C5⋊D5)—21no—
13C2×C22⋊(C5⋊D5)—21no—
14C22×#1039—21no—
15#87902—22no—
16#87902C2214yescomplemented
17D4×C5⋊D5—22no—
18D4×C5⋊D5C2214yescomplemented
19C2×C4⋊(C5⋊D5)C2211yescharacteristic
20C2×C4×C5⋊D5C2211yescharacteristic
21C2×#6045C2211yescharacteristic, complemented
22C52×D8C2214yescomplemented
23C2×C52×C8C2211yescharacteristic, complemented
24#87810C2214yescomplemented
25#87809C2214yescomplemented
26C2×#6029C2211yescharacteristic, complemented
27#87800C2214yescomplemented
28#87799C2214yescomplemented
29C2×#4057—56nomaximal
30C23×C52—21no—
31C23×C52—21no—
32C22×C5⋊D5—21no—
33C22×C5⋊D5—24no—
34C22×C5⋊D5—44no—
35C22×C5⋊D5D411yescharacteristic
36C52×D4—21no—
37C52×D4—21no—
38C52×D4C2312yes—
39C52×D4C2312yescomplemented
40C2×C4×C52C2311yescharacteristic
41C22⋊(C5⋊D5)—24no—
42C22⋊(C5⋊D5)—24no—
43C2×#1039—21no—
44C2×#1039—24no—
45C2×#1039D411yescharacteristic
46C4⋊(C5⋊D5)—21no—
47C4⋊(C5⋊D5)C2312yes—
48C4×C5⋊D5D412yes—
49C4×C5⋊D5C2312yes—
50#6045—21no—
51#6045C2312yescomplemented
52C52×C8C2312yescomplemented
53#6029C2312yescomplemented
54C2×#711—56no—
55C2×D4×D5—56no—
56C2×C5×D8D516yescomplemented
57C2×#687—56no—
58C2×#686—56no—
59#4057—548no—
60C2×#677—56no—
61C2×#676—56no—
62C22×C52—22no—
63C22×C52—22no—
64C22×C52—42no—
65C22×C52—42no—
66C22×C52C2×D411yescharacteristic
67C2×C5⋊D5—22no—
68C2×C5⋊D5—22no—
69C2×C5⋊D5—48no—
70C2×C5⋊D5—42no—
71C2×C5⋊D5C2×D412yes—
72C4×C52C2×D411yescharacteristic
73C4×C52C2411yescharacteristic
74#1039—22no—
75#1039C2×D412yes—
76C23×D5—106no—
77C2×C5×D4C2×D516yes—
78C2×C5×D4C2×D516yescomplemented
79C2×C22⋊D5—106no—
80C2×C22⋊D5—106no—
81C22×Dic5—106no—
82#711—524no—
83#711—1012no—
84D4×D5—524no—
85D4×D5—1012no—
86C2×D20—56no—
87C2×C4×D5—56no—
88C2×Dic10—56no—
89C5×D8C2×D5124yescomplemented
90C2×C5×C8C2×D516yescomplemented
91#687—524no—
92#686—524no—
93C2×#168—56no—
94#677—524no—
95#676—524no—
96C2×AGL(1,ℤ/8)—251noSylow
97C2×C52—42no—
98C2×C52—42no—
99C2×C52AGL(1,ℤ/8)12yescomplemented
100C2×C52C22×D411yescharacteristic
101C5⋊D5—22no—
102C5⋊D5—42no—
103C23×C5—26no—
104C23×C5—26no—
105C22×D5—56no—
106C22×D5—1024no—
107C22×D5—106no—
108C22×D5—2024no—
109C5×D4—26no—
110C5×D4—26no—
111C5×D4C22×D5112yes—
112C5×D4C22×D5112yescomplemented
113C2×C4×C5C22×D516yes—
114C22⋊D5—1024no—
115C22⋊D5—1024no—
116C2×Dic5—56no—
117C2×Dic5—1024no—
118C2×Dic5—106no—
119D20—512no—
120D20—106no—
121C4×D5—512no—
122C4×D5—512no—
123Dic10—512no—
124Dic10—106no—
125C5×C8C22×D5112yescomplemented
126#168—512no—
127C2×#41—251no—
128C22×D4—251no—
129AGL(1,ℤ/8)—258no—
130C2×SD16—251no—
131C2×SD16—251no—
132C2×D8—251no—
133C2×D8C5⋊D511yescharacteristic, complemented
134C2×M16—251no—
135C52C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
136C22×C5—212no—
137C22×C5—212no—
138C22×C5—412no—
139C22×C5—412no—
140C22×C5D4×D516yes—
141C2×D5—512no—
142C2×D5—1012no—
143C2×D5—1012no—
144C2×D5—2048no—
145C2×D5—2012no—
146C4×C5D4×D516yes—
147C4×C5C23×D516yes—
148Dic5—512no—
149Dic5—1012no—
150C24—501no—
151#41—254no—
152#41—502no—
153C2×Q8—251no—
154C2×D4—254no—
155C2×D4—251no—
156C2×D4—502no—
157C2×D4—501no—
158C2×D4—501no—
159C2×D4C2×C5⋊D511yescharacteristic
160C2×D4C2×C5⋊D511yescharacteristic, complemented
161C22×C4—251no—
162C22×C4—501no—
163SD16—254no—
164SD16—254no—
165D8—254no—
166D8C2×C5⋊D514yescomplemented
167M16—254no—
168C2×C8—251no—
169C2×C8C2×C5⋊D511yescharacteristic, complemented
170C2×C5—412no—
171C2×C5—412no—
172C2×C5#4057112yescomplemented
173C2×C5C2×D4×D516yes—
174D5—1012no—
175D5—2012no—
176C23—21no—
177C23—21no—
178C23—251no—
179C23—504no—
180C23—501no—
181C23—1004no—
182Q8—252no—
183Q8—501no—
184D4—21no—
185D4—21no—
186D4—252no—
187D4—504no—
188D4—504no—
189D4—501no—
190D4C22×C5⋊D512yes—
191D4C22×C5⋊D512yescomplemented
192C2×C4—251no—
193C2×C4—252no—
194C2×C4—252no—
195C2×C4—504no—
196C2×C4—501no—
197C2×C4C22×C5⋊D511yescharacteristic
198C8—252no—
199C8C22×C5⋊D512yescomplemented
200C5C2×#405716yescomplemented
201C22—22no—
202C22—22no—
203C22—42no—
204C22—42no—
205C22—252no—
206C22—502no—
207C22—502no—
208C22—1008no—
209C22—1002no—
210C22D4×C5⋊D511yescharacteristic
211C4—252no—
212C4—502no—
213C4D4×C5⋊D511yescharacteristic
214C4C23×C5⋊D511yescharacteristic
215C2—42no—
216C2—42no—
217C2—502no—
218C2—1002no—
219C2#1171723112yesdirect product factor
220C2C2×D4×C5⋊D511yescharacteristic
subgroupG/H
centerC22D4×C5⋊D5
commutator, cosocleC4×C52C24
FrattiniC4C23×C5⋊D5
FittingC2×C52×D8C2
socleC22×C52C2×D4
hypercenterC2×D8C5⋊D5
hypocenterC52C2×AGL(1,ℤ/8)
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#87902C2semidirect
2. C2×D4×C5⋊D5C2semidirect
3. C2×C52×D8C2semidirect
4. C2×#87810C2semidirect
5. C2×#87809C2semidirect
6. #11717231C2direct (N × H)
7. C2×#87800C2semidirect
8. C2×#87799C2semidirect
11. C2×C52×D4C22semidirect
16. #87902C22semidirect
18. D4×C5⋊D5C22semidirect
21. C2×#6045C22semidirect
22. C52×D8C22semidirect
23. C2×C52×C8C22semidirect
24. #87810C22semidirect
25. #87809C22semidirect
26. C2×#6029C22semidirect
27. #87800C22semidirect
28. #87799C22semidirect
39. C52×D4C23semidirect
51. #6045C23semidirect
52. C52×C8C23semidirect
53. #6029C23semidirect
56. C2×C5×D8D5semidirect
78. C2×C5×D4C2×D5semidirect
89. C5×D8C2×D5semidirect
90. C2×C5×C8C2×D5semidirect
99. C2×C52AGL(1,ℤ/8)semidirect
112. C5×D4C22×D5semidirect
125. C5×C8C22×D5semidirect
133. C2×D8C5⋊D5semidirect
135. C52C2×AGL(1,ℤ/8)semidirect
160. C2×D4C2×C5⋊D5semidirect
166. D8C2×C5⋊D5semidirect
169. C2×C8C2×C5⋊D5semidirect
172. C2×C5#4057semidirect
191. D4C22×C5⋊D5semidirect
199. C8C22×C5⋊D5semidirect
200. C5C2×#4057semidirect
219. C2#11717231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#879022
C2×D4×C5⋊D52
C2×C52×D82
C2×#878102
C2×#878092
#117172312
C2×#878002
C2×#877992
C2×#40575