Finite Group Databasebeta

← #13105091

Subgroups — #13105091

Order 1600.

744 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 144 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×D20C211yesmaximal, characteristic, complemented
2C2×#87870C211yesmaximal, characteristic, complemented
3#11717195C211yesmaximal, characteristic, complemented
4C5×#4020C211yesmaximal, characteristic, complemented
5C5×#4018C211yesmaximal, characteristic, complemented
6#11717040C214yesmaximal, complemented
7#11717029C211yesmaximal, characteristic, complemented
8#11717005C214yesmaximal, complemented
9#11716979C211yesmaximal, characteristic, complemented
10C22×D52C2212yes—
11C2×C4⋊(C5⋊D5)C2211yescharacteristic
12C2×#6045C2211yescharacteristic, complemented
13C2×C5×D20C2211yescharacteristic
14C2×C5×D20C2211yescharacteristic, complemented
15C2×C5×D20C2214yescomplemented
16C2×C4×C5×D5C2211yescharacteristic
17C2×#6038C2212yes—
18C2×#6038C2214yescomplemented
19C2×#6037C2212yes—
20C2×D5×Dic5C2212yescomplemented
21D5×D20—24no—
22#87870—24no—
23C42×C52C2211yescharacteristic, complemented
24#87808C2214yescomplemented
25C5×#685C2212yes—
26C5×#683C2212yescomplemented
27C4×C5×Dic5C2211yescharacteristic, complemented
28#87778C2214yescomplemented
29#66049—51nomaximal
30#65859—51nomaximal
31C22×C5⋊D5C2312yes—
32C22×C5×D5C2312yes—
33C22×C5×D5C2312yes—
34C22×C5×D5C2311yescharacteristic
35C2×D52—24no—
36C2×D52—44no—
37C2×C4×C52C2312yes—
38C2×C4×C52C2311yescharacteristic
39C2×#1039C2312yes—
40C4⋊(C5⋊D5)—22no—
41#6045—22no—
42C2×C5×Dic5C2312yes—
43C2×C5×Dic5C2311yescharacteristic
44C5×D20—22no—
45C5×D20—22no—
46C5×D20—44no—
47C4×C5×D5D414yescomplemented
48#6038—24no—
49#6038—44no—
50#6037—24no—
51D5×Dic5—24no—
52C2×#711—51no—
53C2×D4×D5—51no—
54C2×#709—51no—
55C22×D20—51no—
56C5×#127—51no—
57C5×#117—51no—
58#4086—51no—
59#4085—54no—
60#4083—54no—
61#4082—51no—
62#4041—54no—
63#4028—54no—
64#4021—51no—
65#4021—51no—
66#4021—51no—
67#4021—102no—
68#4020—51no—
69#4020D511yescharacteristic, complemented
70#4018D511yescharacteristic, complemented
71C22×C52C2411yescharacteristic
72C2×C5⋊D5—22no—
73C2×C5⋊D5—24no—
74C2×C5×D5—22no—
75C2×C5×D5—22no—
76C2×C5×D5—22no—
77C2×C5×D5—24no—
78C2×C5×D5—24no—
79C2×C5×D5C2×D412yes—
80D52—48no—
81C4×C52—22no—
82C4×C52C2×D412yes—
83#1039—22no—
84C5×Dic5—22no—
85C5×Dic5C2×D412yes—
86C23×D5—52no—
87C23×D5—52no—
88C2×C5×D4—51no—
89C2×C5×D4—51no—
90C2×C5×D4—54no—
91C22×C4×C5—51no—
92C2×C22⋊D5—52no—
93C2×C22⋊D5—52no—
94C2×C22⋊D5—52no—
95C2×C22⋊D5—54no—
96C22×Dic5—52no—
97#711—104no—
98D4×D5—104no—
99#709—104no—
100C2×D20—52no—
101C2×D20—51no—
102C2×D20—51no—
103C2×D20—54no—
104C2×D20—102no—
105C2×D20—104no—
106C2×D20C2×D511yescharacteristic
107C2×D20C2×D511yescharacteristic, complemented
108C2×D20C2×D514yescomplemented
109C2×C4×D5—52no—
110C2×C4×D5C2×D511yescharacteristic
111C2×Dic10—51no—
112C2×Dic10—51no—
113C2×Dic10—102no—
114C5×C4⋊C4—52no—
115C5×C22⋊C4—52no—
116C42×C5—22no—
117C42×C5—51no—
118C42×C5C2×D511yescharacteristic, complemented
119C42×C5C2×D511yescharacteristic, complemented
120C22⋊Dic5—54no—
121#685—54no—
122#685—54no—
123#685—54no—
124#685—108no—
125#685C2×D512yes—
126#683C2×D512yescomplemented
127C4×Dic5C2×D511yescharacteristic, complemented
128#535—251noSylow
129C2×C52C22×D411yescharacteristic
130C2×C52H(5,𝔽2)12yes—
131C5⋊D5—42no—
132C5×D5—22no—
133C5×D5—42no—
134C5×D5—42no—
135C23×C5—51no—
136C23×C5—52no—
137C23×C5—52no—
138C22×D5—52no—
139C22×D5—52no—
140C22×D5—104no—
141C22×D5—104no—
142C22×D5—104no—
143C22×D5—204no—
144C22×D5—204no—
145C22×D5C22×D512yes—
146C22×D5C22×D512yes—
147C22×D5C22×D511yescharacteristic
148C5×D4—102no—
149C5×D4—102no—
150C5×D4—204no—
151C2×C4×C5—22no—
152C2×C4×C5—24no—
153C2×C4×C5—51no—
154C2×C4×C5—54no—
155C2×C4×C5—52no—
156C2×C4×C5C22×D512yes—
157C2×C4×C5C22×D512yes—
158C2×C4×C5C22×D511yescharacteristic
159C2×C4×C5C22×D511yescharacteristic
160C22⋊D5—104no—
161C22⋊D5—104no—
162C22⋊D5—104no—
163C22⋊D5—204no—
164C2×Dic5—52no—
165C2×Dic5—52no—
166C2×Dic5—104no—
167C2×Dic5—104no—
168C2×Dic5C22×D512yes—
169C2×Dic5C22×D511yescharacteristic
170D20—22no—
171D20—22no—
172D20—44no—
173D20—104no—
174D20—102no—
175D20—102no—
176D20—204no—
177D20—204no—
178C4×D5—104no—
179C4×D5D2014yescomplemented
180Dic10—102no—
181Dic10—102no—
182Dic10—204no—
183C2×#41—251no—
184C22×D4—251no—
185#127—51no—
186#127—251no—
187#124—251no—
188#124—251no—
189#121—254no—
190#120—254no—
191#117—51no—
192C52#53511yescharacteristic, complemented, Sylow
193C22×C5—22no—
194C22×C5—52no—
195C22×C5—102no—
196C22×C5—102no—
197C22×C5—102no—
198C22×C5—104no—
199C22×C5—104no—
200C22×C5C23×D511yescharacteristic
201C22×C5C23×D511yescharacteristic
202C2×D5—22no—
203C2×D5—22no—
204C2×D5—22no—
205C2×D5—24no—
206C2×D5—24no—
207C2×D5—102no—
208C2×D5—102no—
209C2×D5—104no—
210C2×D5—104no—
211C2×D5—204no—
212C2×D5—208no—
213C2×D5—208no—
214C2×D5—208no—
215C2×D5C2×D2012yes—
216C4×C5—22no—
217C4×C5—22no—
218C4×C5—24no—
219C4×C5—44no—
220C4×C5—52no—
221C4×C5—102no—
222C4×C5C2×D2012yes—
223C4×C5D4×D512yes—
224Dic5—22no—
225Dic5—102no—
226Dic5—102no—
227Dic5—204no—
228Dic5C2×D2012yes—
229C24—252no—
230#41—504no—
231C2×Q8—251no—
232C2×D4—51no—
233C2×D4—51no—
234C2×D4—54no—
235C2×D4—252no—
236C2×D4—254no—
237C2×D4—252no—
238C2×D4—251no—
239C2×D4—504no—
240C22×C4—51no—
241C22×C4—252no—
242C4⋊C4—52no—
243C22⋊C4—52no—
244C22⋊C4—254no—
245C22⋊C4—254no—
246C42—51no—
247C42D5211yescharacteristic, complemented
248C2×C5—22no—
249C2×C5—24no—
250C2×C5—102no—
251C2×C5—202no—
252C2×C5—202no—
253C2×C5C22×D2011yescharacteristic
254C2×C5C2×D4×D511yescharacteristic
255C2×C5#414412yes—
256C2×C5#414912yes—
257D5—22no—
258D5—42no—
259D5—42no—
260D5—202no—
261D5—202no—
262D5—404no—
263C23—51no—
264C23—52no—
265C23—52no—
266C23—252no—
267C23—504no—
268C23—1004no—
269Q8—502no—
270D4—102no—
271D4—102no—
272D4—204no—
273D4—504no—
274D4—504no—
275D4—502no—
276D4—1004no—
277C2×C4—51no—
278C2×C4—54no—
279C2×C4—52no—
280C2×C4—252no—
281C2×C4—504no—
282C2×C4C2×D5212yes—
283C2×C4C2×D5211yescharacteristic
284C5—22no—
285C5#6585911yescharacteristic, complemented
286C5#6604911yescharacteristic, complemented
287C22—52no—
288C22—102no—
289C22—102no—
290C22—102no—
291C22—104no—
292C22—104no—
293C22—502no—
294C22—504no—
295C22—1008no—
296C22C22×D5211yescharacteristic
297C4—22no—
298C4—52no—
299C4—102no—
300C4—502no—
301C4D5×D2012yes—
302C2—102no—
303C2—202no—
304C2—202no—
305C2—1002no—
306C2C2×D5×D2011yescharacteristic
307C2#1171747212yes—
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC42×C52C22
hypercenterC42D52
hypocenterC52#535
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×D5×D20C2semidirect
2. C2×#87870C2semidirect
3. #11717195C2semidirect
4. C5×#4020C2semidirect
5. C5×#4018C2semidirect
6. #11717040C2semidirect
7. #11717029C2semidirect
8. #11717005C2semidirect
9. #11716979C2semidirect
12. C2×#6045C22semidirect
14. C2×C5×D20C22semidirect
15. C2×C5×D20C22semidirect
18. C2×#6038C22semidirect
20. C2×D5×Dic5C22semidirect
23. C42×C52C22semidirect
24. #87808C22semidirect
26. C5×#683C22semidirect
27. C4×C5×Dic5C22semidirect
28. #87778C22semidirect
47. C4×C5×D5D4semidirect
69. #4020D5semidirect
70. #4018D5semidirect
107. C2×D20C2×D5semidirect
108. C2×D20C2×D5semidirect
118. C42×C5C2×D5semidirect
119. C42×C5C2×D5semidirect
126. #683C2×D5semidirect
127. C4×Dic5C2×D5semidirect
179. C4×D5D20semidirect
192. C52#535semidirect
247. C42D52semidirect
285. C5#65859semidirect
286. C5#66049semidirect

Maximal subgroups

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

subgroupindex
C2×D5×D202
C2×#878702
#117171952
C5×#40202
C5×#40182
#117170402
#117170292
#117170052
#117169792
#660495
#658595