Finite Group Databasebeta

← C4×#87877 #13105086

Subgroups — C4×#87877 #13105086

Order 1600.

960 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 214 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×#87877C211yesmaximal, characteristic
2C2×C4×D52C212yesmaximal, complemented
3C42×C5⋊D5C211yesmaximal, characteristic, complemented
4C4×C5×D20C212yesmaximal, complemented
5#11717039C212yesmaximal, complemented
6#11717020C212yesmaximal, complemented
7C4×#6037C212yesmaximal, complemented
8#11717018C211yesmaximal, characteristic, complemented
9#11717017C212yesmaximal, complemented
10C22×D52C2212yes—
11C2×C4×C5⋊D5C2211yescharacteristic
12C2×C4×C5⋊D5C2211yescharacteristic
13C2×C4×C5⋊D5C2211yescharacteristic
14C2×C5×D20C2212yes—
15C2×C4×C5×D5C2214yescomplemented
16C2×#6037C2212yes—
17C2×#6036C2212yes—
18C2×D5×Dic5C2214yescomplemented
19#87877C418yesdirect product factor
20C4×D52—28no—
21C42×C52C2211yescharacteristic, complemented
22C4×#1039C2211yescharacteristic, complemented
23C4×#1039C2211yescharacteristic, complemented
24C4×#1039C2211yescharacteristic, complemented
25C5×#685C2214yescomplemented
26C5×C4⋊Dic5C2212yescomplemented
27#87781C2212yescomplemented
28#87778C2214yescomplemented
29C4×D4×D5—52nomaximal
30C22×C5⋊D5C2311yescharacteristic
31C22×C5×D5C2314yes—
32C2×D52—24no—
33C2×D52—24no—
34C2×D52C2×C418yescomplemented
35C2×C4×C52C2311yescharacteristic
36C2×C4×C52C2311yescharacteristic
37C2×C4×C52C2311yescharacteristic
38C2×#1039C2311yescharacteristic
39C2×#1039C2311yescharacteristic
40C2×#1039C2311yescharacteristic
41C4×C5⋊D5—22no—
42C4×C5⋊D5C2×C414yescomplemented
43C4×C5⋊D5D414yescomplemented
44C2×C5×Dic5C2314yes—
45C5×D20C2×C418yescomplemented
46C4×C5×D5—28no—
47#6037C2×C418yescomplemented
48#6036—24no—
49D5×Dic5—28no—
50C2×D4×D5—52no—
51C22×C4×D5—54no—
52C4×C5×D4—52no—
53D4×Dic5—52no—
54C4×C22⋊D5—54no—
55#4039—52no—
56D5×C4⋊C4—52no—
57#4027—54no—
58D5×C22⋊C4—54no—
59C4×D20D512yescomplemented
60C42×D5—52no—
61C42×D5—102no—
62C22×C52C2411yescharacteristic
63C2×C5⋊D5C22×C412yes—
64C2×C5⋊D5C2×D412yes—
65C2×C5⋊D5#4112yes—
66C2×C5×D5—24no—
67C2×C5×D5—24no—
68C2×C5×D5C22×C418yescomplemented
69D52—216no—
70C4×C52—21no—
71C4×C52C22×C412yescomplemented
72C4×C52C2×D412yescomplemented
73#1039—21no—
74#1039C22×C412yescomplemented
75#1039C2×D412yescomplemented
76C5×Dic5—24no—
77C23×D5—54no—
78C2×C5×D4—52no—
79C22×C4×C5—54no—
80C2×C22⋊D5—54no—
81C22×Dic5—54no—
82D4×D5—516no—
83C2×D20C2×D512yes—
84C2×C4×D5—52no—
85C2×C4×D5—52no—
86C2×C4×D5—54no—
87C2×C4×D5—52no—
88C2×C4×D5—54no—
89C2×C4×D5—102no—
90C2×C4×D5—102no—
91C2×C4×D5—102no—
92C2×C4×D5—1016no—
93C2×C4×D5C2×D514yescomplemented
94C5×C4⋊C4—52no—
95C5×C22⋊C4—54no—
96C42×C5—22no—
97C42×C5C2×D512yescomplemented
98C22⋊Dic5—54no—
99#685—54no—
100#685C2×D514yescomplemented
101C4⋊Dic5C2×D512yescomplemented
102#683—54no—
103C4×Dic5—52no—
104C4×Dic5—52no—
105C4×Dic5—52no—
106C4×Dic5—102no—
107C4×Dic5—102no—
108C4×Dic5—102no—
109C2×C4×D4—251noSylow
110C2×C52C23×C411yescharacteristic
111C2×C52C22×D411yescharacteristic
112C2×C52C2×#4111yescharacteristic
113C5⋊D5C4×D414yescomplemented
114C5×D5—28no—
115C23×C5—54no—
116C22×D5—52no—
117C22×D5—516no—
118C22×D5—102no—
119C22×D5—108no—
120C22×D5—108no—
121C22×D5C22×D514yes—
122C5×D4—58no—
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—54no—
127C2×C4×C5—108no—
128C2×C4×C5C22×D512yes—
129C2×C4×C5C22×D512yes—
130C2×C4×C5C22×D512yes—
131C22⋊D5—516no—
132C2×Dic5—52no—
133C2×Dic5—52no—
134C2×Dic5—52no—
135C2×Dic5—102no—
136C2×Dic5—102no—
137C2×Dic5—102no—
138C2×Dic5—108no—
139C2×Dic5C22×D514yes—
140D20C4×D518yescomplemented
141C4×D5—28no—
142C4×D5—58no—
143C4×D5—58no—
144C4×D5—108no—
145C4×D5—108no—
146C4×D5—108no—
147C4×D5—108no—
148C4×D5—104no—
149C4×D5—108no—
150C22×D4—251no—
151C23×C4—252no—
152C4×D4—52no—
153C4×D4—252no—
154C4×D4—252no—
155C4×D4—252no—
156C2×C4⋊C4—251no—
157C2×C22⋊C4—252no—
158C2×C42—251no—
159C52C2×C4×D411yescharacteristic, complemented, Sylow
160C22×C5—22no—
161C22×C5—58no—
162C22×C5—104no—
163C22×C5—104no—
164C22×C5C23×D512yes—
165C2×D5—24no—
166C2×D5—24no—
167C2×D5—54no—
168C2×D5—54no—
169C2×D5—54no—
170C2×D5—104no—
171C2×D5—104no—
172C2×D5—104no—
173C2×D5—1032no—
174C2×D5C2×C4×D518yescomplemented
175C4×C5—24no—
176C4×C5—22no—
177C4×C5—24no—
178C4×C5—24no—
179C4×C5—104no—
180C4×C5C2×C4×D514yescomplemented
181C4×C5D4×D514yescomplemented
182Dic5—24no—
183Dic5—54no—
184Dic5—54no—
185Dic5—104no—
186Dic5—104no—
187Dic5—104no—
188Dic5—102no—
189C24—252no—
190C2×D4—52no—
191C2×D4—258no—
192C2×D4—252no—
193C22×C4—54no—
194C22×C4—252no—
195C22×C4—254no—
196C22×C4—251no—
197C22×C4—251no—
198C22×C4—251no—
199C22×C4—508no—
200C4⋊C4—52no—
201C4⋊C4—252no—
202C22⋊C4—54no—
203C22⋊C4—254no—
204C42—251no—
205C42—251no—
206C42—251no—
207C42D5211yescharacteristic, complemented
208C2×C5—22no—
209C2×C5—22no—
210C2×C5—22no—
211C2×C5—108no—
212C2×C5C22×C4×D512yes—
213C2×C5C2×D4×D512yes—
214C2×C5D5×#4112yes—
215D5—28no—
216D5—58no—
217D5—108no—
218C23—54no—
219C23—258no—
220C23—251no—
221C23—504no—
222C23—504no—
223D4—58no—
224D4—258no—
225C2×C4—54no—
226C2×C4—108no—
227C2×C4—251no—
228C2×C4—251no—
229C2×C4—254no—
230C2×C4—254no—
231C2×C4—251no—
232C2×C4—502no—
233C2×C4—504no—
234C2×C4—508no—
235C2×C4C2×D5211yescharacteristic
236C2×C4C2×D5211yescharacteristic
237C2×C4C2×D5211yescharacteristic
238C5—22no—
239C5C4×D4×D512yescomplemented
240C22—58no—
241C22—104no—
242C22—104no—
243C22—252no—
244C22—252no—
245C22—252no—
246C22—5016no—
247C22C22×D5211yescharacteristic
248C4—21no—
249C4—104no—
250C4—252no—
251C4—252no—
252C4—501no—
253C4C4×D5212yescomplemented
254C4#8787712yesdirect product factor
255C2—108no—
256C2—254no—
257C2C2×C4×D5211yescharacteristic
258C2C2×#8787711yescharacteristic
259C2#1171747111yescharacteristic
subgroupG/H
centerC2×C4C2×D52
commutatorC2×C52C23×C4
FrattiniC22C22×D52
FittingC42×C52C22
socle, cosocleC22×C52C24
prime radicalC2×#87877C2
hypercenterC42D52
hypocenterC52C2×C4×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×D52C2semidirect
3. C42×C5⋊D5C2semidirect
4. C4×C5×D20C2semidirect
5. #11717039C2semidirect
6. #11717020C2semidirect
7. C4×#6037C2semidirect
8. #11717018C2semidirect
9. #11717017C2semidirect
15. C2×C4×C5×D5C22semidirect
18. C2×D5×Dic5C22semidirect
19. #87877C4direct (N × H)
21. C42×C52C22semidirect
22. C4×#1039C22semidirect
23. C4×#1039C22semidirect
24. C4×#1039C22semidirect
25. C5×#685C22semidirect
26. C5×C4⋊Dic5C22semidirect
27. #87781C22semidirect
28. #87778C22semidirect
34. C2×D52C2×C4semidirect
42. C4×C5⋊D5C2×C4semidirect
43. C4×C5⋊D5D4semidirect
45. C5×D20C2×C4semidirect
47. #6037C2×C4semidirect
59. C4×D20D5semidirect
68. C2×C5×D5C22×C4semidirect
71. C4×C52C22×C4semidirect
72. C4×C52C2×D4semidirect
74. #1039C22×C4semidirect
75. #1039C2×D4semidirect
93. C2×C4×D5C2×D5semidirect
97. C42×C5C2×D5semidirect
100. #685C2×D5semidirect
101. C4⋊Dic5C2×D5semidirect
113. C5⋊D5C4×D4semidirect
140. D20C4×D5semidirect
159. C52C2×C4×D4semidirect
174. C2×D5C2×C4×D5semidirect
180. C4×C5C2×C4×D5semidirect
181. C4×C5D4×D5semidirect
207. C42D52semidirect
239. C5C4×D4×D5semidirect
253. C4C4×D52semidirect
254. C4#87877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#878772
C2×C4×D522
C42×C5⋊D52
C4×C5×D202
#117170392
#117170202
C4×#60372
#117170182
#117170172
C4×D4×D55