Finite Group Databasebeta

← #13105092

Subgroups — #13105092

Order 1600.

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

normal subgroups only

This group has 776 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×#87874C211yesmaximal, characteristic, complemented
3#11717194C211yesmaximal, characteristic, complemented
4C5×#4021C211yesmaximal, characteristic, complemented
5C5×#4018C211yesmaximal, characteristic, complemented
6#11717041C214yesmaximal, complemented
7#11717029C211yesmaximal, characteristic, complemented
8#11717028C214yesmaximal, complemented
9#11716982C211yesmaximal, characteristic, complemented
10C22×D52C2212yes—
11C2×C4⋊(C5⋊D5)C2211yescharacteristic
12C2×C4⋊(C5⋊D5)C2211yescharacteristic, complemented
13C2×C4⋊(C5⋊D5)C2214yescomplemented
14C2×C5×D20C2211yescharacteristic
15C2×C4×C5×D5C2211yescharacteristic
16C2×C5×Dic10C2211yescharacteristic, complemented
17C2×#6038C2212yes—
18C2×#6038C2212yes—
19C2×#6038C2214yescomplemented
20C2×#6036C2212yescomplemented
21D5×D20—24no—
22#87874—24no—
23C42×C52C2211yescharacteristic, complemented
24C5×#685C2212yes—
25C5×#685C2214yescomplemented
26C5×#683C2212yescomplemented
27C4×C5×Dic5C2211yescharacteristic, complemented
28#87779C2214yescomplemented
29#66008—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
39C4⋊(C5⋊D5)—22no—
40C4⋊(C5⋊D5)—22no—
41C4⋊(C5⋊D5)—44no—
42C2×C5×Dic5C2312yes—
43C2×C5×Dic5C2312yes—
44C2×C5×Dic5C2311yescharacteristic
45C5×D20—22no—
46C4×C5×D5D414yescomplemented
47C5×Dic10—22no—
48#6038—24no—
49#6038—24no—
50#6038—44no—
51#6036—24no—
52C2×#713—51no—
53C2×D4×D5—51no—
54C2×#709—51no—
55C22×D20—51no—
56C5×#124—51no—
57C5×#117—51no—
58#4093—51no—
59#4086—51no—
60#4041—54no—
61#4030—54no—
62#4028—54no—
63#4028—54no—
64#4021—51no—
65#4021D511yescharacteristic, complemented
66#4020—51no—
67#4020—51no—
68#4020—51no—
69#4020—102no—
70#4018D511yescharacteristic, complemented
71C22×C52C2411yescharacteristic
72C2×C5⋊D5—22no—
73C2×C5⋊D5—22no—
74C2×C5⋊D5—24no—
75C2×C5⋊D5—24no—
76C2×C5×D5—22no—
77C2×C5×D5—22no—
78C2×C5×D5—24no—
79C2×C5×D5C2×D412yes—
80D52—48no—
81C4×C52—22no—
82C4×C52C2×D412yes—
83C5×Dic5—22no—
84C5×Dic5—22no—
85C5×Dic5C2×D412yes—
86C23×D5—52no—
87C23×D5—52no—
88C2×C5×Q8—51no—
89C2×C5×D4—51no—
90C22×C4×C5—51no—
91C2×C22⋊D5—52no—
92C2×C22⋊D5—52no—
93C2×C22⋊D5—54no—
94#713—104no—
95D4×D5—104no—
96#709—104no—
97C2×D20—52no—
98C2×D20—52no—
99C2×D20—51no—
100C2×D20—51no—
101C2×D20—51no—
102C2×D20—51no—
103C2×D20—54no—
104C2×D20—54no—
105C2×D20—54no—
106C2×D20—102no—
107C2×D20—102no—
108C2×D20—108no—
109C2×D20—104no—
110C2×D20C2×D511yescharacteristic
111C2×C4×D5—52no—
112C2×C4×D5—52no—
113C2×C4×D5C2×D511yescharacteristic
114C2×Dic10C2×D511yescharacteristic, complemented
115C5×C4⋊C4—52no—
116C5×C22⋊C4—52no—
117C5×C22⋊C4—54no—
118C42×C5—22no—
119C42×C5—51no—
120C42×C5C2×D511yescharacteristic, complemented
121C42×C5C2×D511yescharacteristic, complemented
122#685—54no—
123#685—54no—
124#685C2×D512yes—
125#685C2×D514yescomplemented
126#683C2×D512yescomplemented
127C4×Dic5C2×D511yescharacteristic, complemented
128#535—251noSylow
129C2×C52C22×D411yescharacteristic
130C2×C52H(5,𝔽2)12yes—
131C5⋊D5—42no—
132C5⋊D5—42no—
133C5×D5—22no—
134C5×D5—42no—
135C23×C5—51no—
136C23×C5—52no—
137C22×D5—52no—
138C22×D5—52no—
139C22×D5—52no—
140C22×D5—52no—
141C22×D5—104no—
142C22×D5—104no—
143C22×D5—104no—
144C22×D5—104no—
145C22×D5—204no—
146C22×D5—204no—
147C22×D5C22×D512yes—
148C22×D5C22×D511yescharacteristic
149C5×Q8—102no—
150C5×D4—102no—
151C2×C4×C5—24no—
152C2×C4×C5—22no—
153C2×C4×C5—51no—
154C2×C4×C5—54no—
155C2×C4×C5—52no—
156C2×C4×C5—52no—
157C2×C4×C5C22×D512yes—
158C2×C4×C5C22×D512yes—
159C2×C4×C5C22×D511yescharacteristic
160C2×C4×C5C22×D511yescharacteristic
161C22⋊D5—104no—
162C22⋊D5—104no—
163C22⋊D5—204no—
164C2×Dic5C22×D512yes—
165C2×Dic5C22×D512yes—
166C2×Dic5C22×D511yescharacteristic
167D20—22no—
168D20—104no—
169D20—104no—
170D20—102no—
171D20—102no—
172D20—102no—
173D20—102no—
174D20—204no—
175D20—204no—
176D20—204no—
177D20—204no—
178D20—2016no—
179D20—204no—
180C4×D5—104no—
181C4×D5—104no—
182C4×D5D2014yescomplemented
183Dic10—22no—
184C2×#41—251no—
185C22×D4—251no—
186#127—251no—
187#127—251no—
188#124—51no—
189#124—251no—
190#121—254no—
191#120—254no—
192#117—51no—
193C52#53511yescharacteristic, complemented, Sylow
194C22×C5—22no—
195C22×C5—52no—
196C22×C5—102no—
197C22×C5—102no—
198C22×C5—104no—
199C22×C5C23×D511yescharacteristic
200C22×C5C23×D511yescharacteristic
201C2×D5—22no—
202C2×D5—22no—
203C2×D5—24no—
204C2×D5—102no—
205C2×D5—102no—
206C2×D5—102no—
207C2×D5—102no—
208C2×D5—104no—
209C2×D5—104no—
210C2×D5—104no—
211C2×D5—104no—
212C2×D5—204no—
213C2×D5—204no—
214C2×D5—208no—
215C2×D5—208no—
216C2×D5—208no—
217C2×D5—208no—
218C2×D5C2×D2012yes—
219C4×C5—28no—
220C4×C5—22no—
221C4×C5—22no—
222C4×C5—24no—
223C4×C5—52no—
224C4×C5—102no—
225C4×C5—102no—
226C4×C5C2×D2012yes—
227C4×C5D4×D512yes—
228Dic5—22no—
229Dic5—22no—
230Dic5C2×D2012yes—
231C24—252no—
232#41—504no—
233C2×Q8—51no—
234C2×D4—51no—
235C2×D4—252no—
236C2×D4—252no—
237C2×D4—254no—
238C2×D4—251no—
239C2×D4—251no—
240C2×D4—254no—
241C2×D4—504no—
242C22×C4—51no—
243C22×C4—252no—
244C4⋊C4—52no—
245C22⋊C4—52no—
246C22⋊C4—54no—
247C22⋊C4—254no—
248C42—51no—
249C42D5211yescharacteristic, complemented
250C2×C5—22no—
251C2×C5—24no—
252C2×C5—102no—
253C2×C5—202no—
254C2×C5C22×D2011yescharacteristic
255C2×C5C2×D4×D511yescharacteristic
256C2×C5#414912yes—
257C2×C5#414912yes—
258D5—22no—
259D5—42no—
260D5—202no—
261D5—202no—
262D5—202no—
263D5—202no—
264D5—404no—
265D5—404no—
266C23—51no—
267C23—52no—
268C23—252no—
269C23—252no—
270C23—504no—
271C23—1004no—
272Q8—102no—
273D4—102no—
274D4—504no—
275D4—504no—
276D4—502no—
277D4—502no—
278D4—1004no—
279D4—1004no—
280C2×C4—51no—
281C2×C4—54no—
282C2×C4—52no—
283C2×C4—52no—
284C2×C4—504no—
285C2×C4C2×D5212yes—
286C2×C4C2×D5211yescharacteristic
287C5—22no—
288C5#6585911yescharacteristic, complemented
289C5#6600811yescharacteristic, complemented
290C22—52no—
291C22—102no—
292C22—102no—
293C22—104no—
294C22—502no—
295C22—502no—
296C22—504no—
297C22—504no—
298C22—1008no—
299C22C22×D5211yescharacteristic
300C4—22no—
301C4—52no—
302C4—102no—
303C4—102no—
304C4D5×D2012yes—
305C2—102no—
306C2—202no—
307C2—1002no—
308C2—1002no—
309C2C2×D5×D2011yescharacteristic
310C2#1171747312yes—
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×#87874C2semidirect
3. #11717194C2semidirect
4. C5×#4021C2semidirect
5. C5×#4018C2semidirect
6. #11717041C2semidirect
7. #11717029C2semidirect
8. #11717028C2semidirect
9. #11716982C2semidirect
12. C2×C4⋊(C5⋊D5)C22semidirect
13. C2×C4⋊(C5⋊D5)C22semidirect
16. C2×C5×Dic10C22semidirect
19. C2×#6038C22semidirect
20. C2×#6036C22semidirect
23. C42×C52C22semidirect
25. C5×#685C22semidirect
26. C5×#683C22semidirect
27. C4×C5×Dic5C22semidirect
28. #87779C22semidirect
46. C4×C5×D5D4semidirect
65. #4021D5semidirect
70. #4018D5semidirect
114. C2×Dic10C2×D5semidirect
120. C42×C5C2×D5semidirect
121. C42×C5C2×D5semidirect
125. #685C2×D5semidirect
126. #683C2×D5semidirect
127. C4×Dic5C2×D5semidirect
182. C4×D5D20semidirect
193. C52#535semidirect
249. C42D52semidirect
288. C5#65859semidirect
289. C5#66008semidirect

Maximal subgroups

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

subgroupindex
C2×D5×D202
C2×#878742
#117171942
C5×#40212
C5×#40182
#117170412
#117170292
#117170282
#117169822
#660085
#658595