Finite Group Databasebeta

← #13105708

Subgroups — #13105708

Order 1600.

944 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 212 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
3C4⋊C4×C5⋊D5C211yesmaximal, characteristic, complemented
4C5×#4039C212yesmaximal, complemented
5#11717039C212yesmaximal, complemented
6Dic5×D20C212yesmaximal, complemented
7C4×#6036C211yesmaximal, characteristic, complemented
8#11716997C214yesmaximal, complemented
9C22×D52C2212yes—
10C2×C4×C5⋊D5C2212yes—
11C2×C4×C5⋊D5C2211yescharacteristic
12C2×C5×D20C2212yes—
13C2×C4×C5×D5C2214yescomplemented
14C2×#6037C2212yes—
15C2×#6036C2211yescharacteristic
16C2×#6036C2211yescharacteristic
17C2×D5×Dic5C2214yescomplemented
18#87877C418yescomplemented
19C4×D52—28no—
20C52×C4⋊C4C2211yescharacteristic, complemented
21C4⋊#1039C2211yescharacteristic, complemented
22#87806C2212yescomplemented
23C5×#685C2214yescomplemented
24C4×C5×Dic5C2212yescomplemented
25#87778C2214yescomplemented
26Dic52C2212yescomplemented
27C4×D4×D5—52nomaximal
28C22×C5⋊D5C2311yescharacteristic
29C22×C5×D5C2314yes—
30C2×D52—24no—
31C2×D52—24no—
32C2×D52C2×C418yescomplemented
33C2×C4×C52C2312yes—
34C2×C4×C52C2311yescharacteristic
35C2×#1039C2312yes—
36C2×#1039C2311yescharacteristic
37C4×C5⋊D5—24no—
38C4×C5⋊D5C2×C414yescomplemented
39C2×C5×Dic5C2312yes—
40C2×C5×Dic5C2312yes—
41C5×D20C2×C418yescomplemented
42C4×C5×D5—28no—
43#6037C2×C418yescomplemented
44#6036—22no—
45#6036D414yescomplemented
46D5×Dic5—28no—
47C2×D4×D5—52no—
48C22×C4×D5—54no—
49C4×C5×D4—52no—
50D4×Dic5—52no—
51C4×C22⋊D5—54no—
52#4039D512yescomplemented
53D5×C4⋊C4—52no—
54D5×C4⋊C4—102no—
55#4027—54no—
56D5×C22⋊C4—54no—
57C4×D20—52no—
58C42×D5—52no—
59C22×C52C2411yescharacteristic
60C2×C5⋊D5C22×C412yes—
61C2×C5⋊D5C2×D412yes—
62C2×C5⋊D5#4112yes—
63C2×C5×D5—24no—
64C2×C5×D5—24no—
65C2×C5×D5C22×C418yescomplemented
66D52—216no—
67C4×C52—22no—
68C4×C52C22×C412yescomplemented
69#1039—22no—
70#1039C22×C412yescomplemented
71C5×Dic5—22no—
72C5×Dic5C2×D414yescomplemented
73C23×D5—54no—
74C2×C5×D4—52no—
75C22×C4×C5—54no—
76C2×C22⋊D5—54no—
77C22×Dic5—54no—
78D4×D5—516no—
79C2×D20C2×D512yes—
80C2×C4×D5—52no—
81C2×C4×D5—52no—
82C2×C4×D5—54no—
83C2×C4×D5—54no—
84C2×C4×D5—52no—
85C2×C4×D5—102no—
86C2×C4×D5—104no—
87C2×C4×D5—1016no—
88C2×C4×D5C2×D514yescomplemented
89C5×C4⋊C4—22no—
90C5×C4⋊C4C2×D512yescomplemented
91C5×C22⋊C4—54no—
92C42×C5—52no—
93C22⋊Dic5—54no—
94#685—54no—
95#685C2×D514yescomplemented
96C4⋊Dic5—52no—
97C4⋊Dic5—102no—
98#683—54no—
99#683—104no—
100C4×Dic5—52no—
101C4×Dic5—52no—
102C4×Dic5C2×D512yescomplemented
103C2×C4×D4—251noSylow
104C2×C52C23×C411yescharacteristic
105C2×C52C22×D411yescharacteristic
106C2×C52C2×#4111yescharacteristic
107C5⋊D5C4×D414yescomplemented
108C5×D5—28no—
109C23×C5—54no—
110C22×D5—52no—
111C22×D5—516no—
112C22×D5—102no—
113C22×D5—108no—
114C22×D5—108no—
115C22×D5C22×D514yes—
116C5×D4—58no—
117C2×C4×C5—22no—
118C2×C4×C5—24no—
119C2×C4×C5—52no—
120C2×C4×C5—52no—
121C2×C4×C5—108no—
122C2×C4×C5C22×D514yes—
123C2×C4×C5C22×D512yes—
124C22⋊D5—516no—
125C2×Dic5—52no—
126C2×Dic5—54no—
127C2×Dic5—102no—
128C2×Dic5—104no—
129C2×Dic5—108no—
130C2×Dic5C22×D512yes—
131C2×Dic5C22×D512yes—
132D20C4×D518yescomplemented
133C4×D5—28no—
134C4×D5—58no—
135C4×D5—58no—
136C4×D5—108no—
137C4×D5—104no—
138C4×D5—108no—
139C4×D5—108no—
140C4×D5—208no—
141C22×D4—251no—
142C23×C4—252no—
143C4×D4—52no—
144C4×D4—252no—
145C4×D4—254no—
146C2×C4⋊C4—251no—
147C2×C22⋊C4—252no—
148C2×C42—251no—
149C52C2×C4×D411yescharacteristic, complemented, Sylow
150C22×C5—22no—
151C22×C5—58no—
152C22×C5—104no—
153C22×C5—104no—
154C22×C5C23×D512yes—
155C2×D5—24no—
156C2×D5—24no—
157C2×D5—54no—
158C2×D5—54no—
159C2×D5—54no—
160C2×D5—104no—
161C2×D5—104no—
162C2×D5—104no—
163C2×D5—1032no—
164C2×D5C2×C4×D518yescomplemented
165C4×C5—24no—
166C4×C5—24no—
167C4×C5—44no—
168C4×C5—54no—
169C4×C5—102no—
170C4×C5C2×C4×D514yescomplemented
171Dic5—22no—
172Dic5—54no—
173Dic5—104no—
174Dic5—104no—
175Dic5—204no—
176Dic5D4×D514yescomplemented
177C24—252no—
178C2×D4—52no—
179C2×D4—258no—
180C2×D4—252no—
181C22×C4—54no—
182C22×C4—251no—
183C22×C4—251no—
184C22×C4—254no—
185C22×C4—251no—
186C22×C4—252no—
187C22×C4—508no—
188C4⋊C4—252no—
189C4⋊C4—251no—
190C4⋊C4D5211yescharacteristic, complemented
191C22⋊C4—54no—
192C22⋊C4—254no—
193C42—52no—
194C42—252no—
195C2×C5—22no—
196C2×C5—22no—
197C2×C5—22no—
198C2×C5—108no—
199C2×C5C22×C4×D512yes—
200C2×C5C2×D4×D512yes—
201C2×C5D5×#4112yes—
202D5—28no—
203D5—58no—
204D5—108no—
205C23—54no—
206C23—258no—
207C23—251no—
208C23—504no—
209C23—504no—
210D4—58no—
211D4—258no—
212C2×C4—52no—
213C2×C4—52no—
214C2×C4—108no—
215C2×C4—254no—
216C2×C4—251no—
217C2×C4—254no—
218C2×C4—252no—
219C2×C4—504no—
220C2×C4—508no—
221C2×C4—502no—
222C2×C4C2×D5212yes—
223C2×C4C2×D5211yescharacteristic
224C5—22no—
225C5C4×D4×D512yescomplemented
226C22—58no—
227C22—104no—
228C22—104no—
229C22—252no—
230C22—252no—
231C22—252no—
232C22—5016no—
233C22C22×D5211yescharacteristic
234C4—22no—
235C4—54no—
236C4—102no—
237C4—252no—
238C4—502no—
239C4C4×D5212yescomplemented
240C2—108no—
241C2—254no—
242C2C2×C4×D5211yescharacteristic
243C2D4×D5211yescharacteristic
244C2#1171748411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutatorC2×C52C23×C4
FittingC52×C4⋊C4C22
socle, cosocleC22×C52C24
prime radicalC2×#87877C2
hypercenterC4⋊C4D52
hypocenterC52C2×C4×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D52C2semidirect
3. C4⋊C4×C5⋊D5C2semidirect
4. C5×#4039C2semidirect
5. #11717039C2semidirect
6. Dic5×D20C2semidirect
7. C4×#6036C2semidirect
8. #11716997C2semidirect
13. C2×C4×C5×D5C22semidirect
17. C2×D5×Dic5C22semidirect
18. #87877C4semidirect
20. C52×C4⋊C4C22semidirect
21. C4⋊#1039C22semidirect
22. #87806C22semidirect
23. C5×#685C22semidirect
24. C4×C5×Dic5C22semidirect
25. #87778C22semidirect
26. Dic52C22semidirect
32. C2×D52C2×C4semidirect
38. C4×C5⋊D5C2×C4semidirect
41. C5×D20C2×C4semidirect
43. #6037C2×C4semidirect
45. #6036D4semidirect
52. #4039D5semidirect
65. C2×C5×D5C22×C4semidirect
68. C4×C52C22×C4semidirect
70. #1039C22×C4semidirect
72. C5×Dic5C2×D4semidirect
88. C2×C4×D5C2×D5semidirect
90. C5×C4⋊C4C2×D5semidirect
95. #685C2×D5semidirect
102. C4×Dic5C2×D5semidirect
107. C5⋊D5C4×D4semidirect
132. D20C4×D5semidirect
149. C52C2×C4×D4semidirect
164. C2×D5C2×C4×D5semidirect
170. C4×C5C2×C4×D5semidirect
176. Dic5D4×D5semidirect
190. C4⋊C4D52semidirect
225. C5C4×D4×D5semidirect
239. C4C4×D52semidirect

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
C4⋊C4×C5⋊D52
C5×#40392
#117170392
Dic5×D202
C4×#60362
#117169972
C4×D4×D55