Finite Group Databasebeta

← #13105382

Subgroups — #13105382

Order 1600.

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

normal subgroups only

This group has 822 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×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#6038C211yesmaximal, characteristic, complemented
3#11717202C211yesmaximal, characteristic, complemented
4C5×#4032C211yesmaximal, characteristic, complemented
5C5×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6#11717099C211yesmaximal, characteristic, complemented
7#11717084C211yesmaximal, characteristic, complemented
8#11717041C212yesmaximal, complemented
9#11717027C212yesmaximal, complemented
10#11717024C212yesmaximal, complemented
11#11717011C212yesmaximal, complemented
12C23×C5⋊D5C2211yescharacteristic, complemented
13C23×C5×D5C2211yescharacteristic
14C22×D52C2211yescharacteristic, complemented
15C2×C22⋊(C5⋊D5)C2211yescharacteristic
16C2×C4⋊(C5⋊D5)C2212yescomplemented
17C2×C5×C22⋊D5C2211yescharacteristic
18C22×C5×Dic5C2211yescharacteristic, complemented
19C2×C4×C5×D5C2212yescomplemented
20D5×C22⋊D5—24no—
21C2×#6038—24no—
22C2×#6038C2212yes—
23C2×#6038C2212yescomplemented
24C2×#6038C2211yescharacteristic, complemented
25C2×#6038C2212yescomplemented
26C2×#6037C2211yescharacteristic, complemented
27C2×D5×Dic5C2211yescharacteristic, complemented
28C52×C22⋊C4C2211yescharacteristic, complemented
29#87808C2212yescomplemented
30C5×C22⋊Dic5C2211yescharacteristic, complemented
31C5×#685C2212yescomplemented
32C5×#685C2212yescomplemented
33C5×C4⋊Dic5C2212yescomplemented
34#87780C2212yescomplemented
35#87779C2212yescomplemented
36#87779C2212yescomplemented
37#65987—51nomaximal
38#65827—51nomaximal
39C23×C52C2311yescharacteristic
40C22×C5⋊D5—22no—
41C22×C5⋊D5—42no—
42C22×C5⋊D5C2312yes—
43C22×C5⋊D5C2311yescharacteristic
44C22×C5×D5—42no—
45C22×C5×D5D414yescomplemented
46C22×C5×D5C2311yescharacteristic
47C22×C5×D5C2311yescharacteristic
48C22×C5×D5C2311yescharacteristic
49C2×D52—22no—
50C2×D52—42no—
51C2×C4×C52C2312yes—
52C22⋊(C5⋊D5)—22no—
53C2×#1039C2311yescharacteristic
54C4⋊(C5⋊D5)—42no—
55C5×C22⋊D5—22no—
56C2×C5×Dic5—22no—
57C2×C5×Dic5C2311yescharacteristic
58C2×C5×Dic5C2312yes—
59C2×C5×Dic5C2312yes—
60C4×C5×D5—42no—
61#6038—24no—
62#6038—24no—
63#6038—22no—
64#6038—42no—
65#6037—22no—
66D5×Dic5—22no—
67C22×C22⋊D5—51no—
68C22×C22⋊D5—51no—
69C2×D4×D5—51no—
70C22×D20—51no—
71C5×#123—51no—
72C2×C5×C22⋊C4—51no—
73#4083—51no—
74#4076—52no—
75#4076—52no—
76#4075—51no—
77#4041—52no—
78#4040—52no—
79#4032—51no—
80#4032—52no—
81#4032D511yescharacteristic, complemented
82#4030—52no—
83#4028—51no—
84#4028—51no—
85#4028—51no—
86#4028—52no—
87#4028—52no—
88#4028—102no—
89D5×C22⋊C4D511yescharacteristic, complemented
90C22×C52—22no—
91C22×C52C2×D412yes—
92C22×C52C2411yescharacteristic
93C2×C5⋊D5—22no—
94C2×C5⋊D5—21no—
95C2×C5⋊D5—22no—
96C2×C5⋊D5—22no—
97C2×C5⋊D5—22no—
98C2×C5⋊D5—44no—
99C2×C5×D5—21no—
100C2×C5×D5—22no—
101C2×C5×D5—22no—
102C2×C5×D5—22no—
103C2×C5×D5—44no—
104C2×C5×D5C2×D412yes—
105C2×C5×D5C2×D412yes—
106D52—44no—
107C4×C52—22no—
108#1039—21no—
109C5×Dic5—21no—
110C5×Dic5—22no—
111C5×Dic5—22no—
112C24×C5—51no—
113C23×D5—51no—
114C23×D5—51no—
115C23×D5—51no—
116C23×D5—51no—
117C23×D5—102no—
118C23×D5C2×D511yescharacteristic
119C2×C5×D4—51no—
120C22×C4×C5—51no—
121C22×C4×C5—52no—
122C2×C22⋊D5—51no—
123C2×C22⋊D5—51no—
124C2×C22⋊D5—51no—
125C2×C22⋊D5—51no—
126C2×C22⋊D5—52no—
127C2×C22⋊D5—52no—
128C2×C22⋊D5—51no—
129C2×C22⋊D5—52no—
130C2×C22⋊D5—102no—
131C2×C22⋊D5—104no—
132C2×C22⋊D5—104no—
133C2×C22⋊D5C2×D511yescharacteristic
134C22×Dic5—51no—
135C22×Dic5C2×D511yescharacteristic, complemented
136D4×D5—104no—
137C2×D20—52no—
138C2×D20—52no—
139C2×D20—51no—
140C2×D20—52no—
141C2×D20—52no—
142C2×D20—52no—
143C2×D20—104no—
144C2×D20—104no—
145C2×C4×D5—51no—
146C2×C4×D5C2×D512yescomplemented
147C5×C4⋊C4—52no—
148C5×C22⋊C4—22no—
149C5×C22⋊C4—51no—
150C5×C22⋊C4—52no—
151C5×C22⋊C4—52no—
152C5×C22⋊C4C2×D511yescharacteristic, complemented
153C5×C22⋊C4C2×D511yescharacteristic, complemented
154C22⋊Dic5C2×D511yescharacteristic, complemented
155#685—52no—
156#685—52no—
157#685—52no—
158#685—52no—
159#685—52no—
160#685—52no—
161#685—104no—
162#685C2×D512yescomplemented
163#685C2×D512yescomplemented
164C4⋊Dic5—52no—
165C4⋊Dic5C2×D512yescomplemented
166#683—52no—
167#534—251noSylow
168C2×C52—22no—
169C2×C52C22×D411yescharacteristic
170C2×C52H(5,𝔽2)12yes—
171C5⋊D5—42no—
172C5⋊D5—41no—
173C5×D5—22no—
174C5×D5—22no—
175C5×D5—41no—
176C23×C5—22no—
177C23×C5—51no—
178C23×C5—51no—
179C23×C5—54no—
180C23×C5—51no—
181C23×C5—202no—
182C23×C5C22×D511yescharacteristic
183C23×C5C22×D511yescharacteristic
184C22×D5—42no—
185C22×D5—52no—
186C22×D5—51no—
187C22×D5—52no—
188C22×D5—51no—
189C22×D5—104no—
190C22×D5—102no—
191C22×D5—102no—
192C22×D5—102no—
193C22×D5—102no—
194C22×D5—102no—
195C22×D5—204no—
196C22×D5—202no—
197C22×D5—202no—
198C22×D5—202no—
199C22×D5—202no—
200C22×D5—208no—
201C22×D5D2014yescomplemented
202C22×D5C22×D511yescharacteristic
203C22×D5C22×D511yescharacteristic
204C22×D5C22×D511yescharacteristic
205C5×D4—102no—
206C2×C4×C5—24no—
207C2×C4×C5—52no—
208C2×C4×C5—52no—
209C2×C4×C5—51no—
210C2×C4×C5—102no—
211C2×C4×C5—202no—
212C2×C4×C5C22×D512yes—
213C2×C4×C5C22×D512yes—
214C22⋊D5—22no—
215C22⋊D5—104no—
216C22⋊D5—104no—
217C22⋊D5—102no—
218C22⋊D5—102no—
219C22⋊D5—102no—
220C22⋊D5—102no—
221C22⋊D5—102no—
222C22⋊D5—204no—
223C22⋊D5—202no—
224C2×Dic5—22no—
225C2×Dic5—51no—
226C2×Dic5—51no—
227C2×Dic5—102no—
228C2×Dic5—102no—
229C2×Dic5C22×D512yes—
230C2×Dic5C22×D512yes—
231C2×Dic5C22×D511yescharacteristic
232D20—104no—
233D20—104no—
234D20—102no—
235D20—202no—
236D20—202no—
237D20—208no—
238D20—202no—
239C4×D5—42no—
240C4×D5—102no—
241C22×D4—251no—
242C22×D4—251no—
243#123—51no—
244#123—252no—
245#123—251no—
246#121—252no—
247#121—252no—
248#120—252no—
249#120—251no—
250#120—251no—
251C2×C22⋊C4—51no—
252C52#53411yescharacteristic, complemented, Sylow
253C22×C5—22no—
254C22×C5—22no—
255C22×C5—24no—
256C22×C5—22no—
257C22×C5—44no—
258C22×C5—52no—
259C22×C5—52no—
260C22×C5—102no—
261C22×C5—102no—
262C22×C5—101no—
263C22×C5—102no—
264C22×C5—204no—
265C22×C5C2×D2012yes—
266C22×C5D4×D512yes—
267C22×C5C23×D511yescharacteristic
268C22×C5C23×D511yescharacteristic
269C2×D5—22no—
270C2×D5—22no—
271C2×D5—21no—
272C2×D5—22no—
273C2×D5—44no—
274C2×D5—108no—
275C2×D5—102no—
276C2×D5—101no—
277C2×D5—102no—
278C2×D5—101no—
279C2×D5—102no—
280C2×D5—102no—
281C2×D5—102no—
282C2×D5—102no—
283C2×D5—102no—
284C2×D5—102no—
285C2×D5—204no—
286C2×D5—204no—
287C2×D5—204no—
288C2×D5—202no—
289C2×D5—204no—
290C2×D5—204no—
291C2×D5—204no—
292C2×D5—204no—
293C2×D5—2016no—
294C2×D5C2×D2012yes—
295C2×D5C2×D2012yes—
296C4×C5—22no—
297C4×C5—22no—
298C4×C5—44no—
299C4×C5—101no—
300C4×C5—102no—
301C4×C5—102no—
302Dic5—22no—
303Dic5—21no—
304Dic5—22no—
305Dic5—101no—
306Dic5—101no—
307Dic5—202no—
308C24—51no—
309C24—251no—
310C24—251no—
311C2×D4—51no—
312C2×D4—252no—
313C2×D4—252no—
314C2×D4—251no—
315C2×D4—252no—
316C2×D4—251no—
317C2×D4—251no—
318C2×D4—252no—
319C2×D4—504no—
320C2×D4—504no—
321C22×C4—51no—
322C22×C4—52no—
323C22×C4—251no—
324C4⋊C4—52no—
325C4⋊C4—252no—
326C22⋊C4—51no—
327C22⋊C4—52no—
328C22⋊C4—52no—
329C22⋊C4—252no—
330C22⋊C4—252no—
331C22⋊C4—252no—
332C22⋊C4D5211yescharacteristic, complemented
333C2×C5—22no—
334C2×C5—22no—
335C2×C5—22no—
336C2×C5—24no—
337C2×C5—44no—
338C2×C5—102no—
339C2×C5—102no—
340C2×C5—201no—
341C2×C5C22×D2011yescharacteristic
342C2×C5C2×D4×D511yescharacteristic
343C2×C5#414412yes—
344C2×C5#414912yes—
345D5—22no—
346D5—22no—
347D5—41no—
348D5—208no—
349D5—202no—
350D5—201no—
351D5—202no—
352D5—201no—
353D5—402no—
354C23—51no—
355C23—51no—
356C23—54no—
357C23—51no—
358C23—202no—
359C23—252no—
360C23—251no—
361C23—502no—
362C23—502no—
363C23—1002no—
364C23—1002no—
365C23C2×D5211yescharacteristic
366D4—102no—
367D4—504no—
368D4—504no—
369D4—502no—
370D4—502no—
371D4—502no—
372D4—1002no—
373D4—1002no—
374C2×C4—52no—
375C2×C4—52no—
376C2×C4—51no—
377C2×C4—102no—
378C2×C4—202no—
379C2×C4—251no—
380C2×C4—502no—
381C2×C4C2×D5212yes—
382C5—22no—
383C5#6582711yescharacteristic, complemented
384C5#6598711yescharacteristic, complemented
385C22—22no—
386C22—52no—
387C22—52no—
388C22—102no—
389C22—102no—
390C22—101no—
391C22—102no—
392C22—204no—
393C22—502no—
394C22—501no—
395C22—502no—
396C22—502no—
397C22—502no—
398C22—1004no—
399C22—1004no—
400C22D5×D2012yes—
401C22C22×D5211yescharacteristic
402C4—22no—
403C4—102no—
404C4—101no—
405C4—102no—
406C4—501no—
407C2—22no—
408C2—102no—
409C2—102no—
410C2—201no—
411C2—1002no—
412C2—1001no—
413C2C2×D5×D2011yescharacteristic
414C2#1171747912yes—
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C22⋊C4C22
hypercenterC22⋊C4D52
hypocenterC52#534
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D5×C22⋊D5C2semidirect
2. C22×#6038C2semidirect
3. #11717202C2semidirect
4. C5×#4032C2semidirect
5. C5×D5×C22⋊C4C2semidirect
6. #11717099C2semidirect
7. #11717084C2semidirect
8. #11717041C2semidirect
9. #11717027C2semidirect
10. #11717024C2semidirect
11. #11717011C2semidirect
12. C23×C5⋊D5C22semidirect
14. C22×D52C22semidirect
16. C2×C4⋊(C5⋊D5)C22semidirect
18. C22×C5×Dic5C22semidirect
19. C2×C4×C5×D5C22semidirect
23. C2×#6038C22semidirect
24. C2×#6038C22semidirect
25. C2×#6038C22semidirect
26. C2×#6037C22semidirect
27. C2×D5×Dic5C22semidirect
28. C52×C22⋊C4C22semidirect
29. #87808C22semidirect
30. C5×C22⋊Dic5C22semidirect
31. C5×#685C22semidirect
32. C5×#685C22semidirect
33. C5×C4⋊Dic5C22semidirect
34. #87780C22semidirect
35. #87779C22semidirect
36. #87779C22semidirect
45. C22×C5×D5D4semidirect
81. #4032D5semidirect
89. D5×C22⋊C4D5semidirect
135. C22×Dic5C2×D5semidirect
146. C2×C4×D5C2×D5semidirect
152. C5×C22⋊C4C2×D5semidirect
153. C5×C22⋊C4C2×D5semidirect
154. C22⋊Dic5C2×D5semidirect
162. #685C2×D5semidirect
163. #685C2×D5semidirect
165. C4⋊Dic5C2×D5semidirect
201. C22×D5D20semidirect
252. C52#534semidirect
332. C22⋊C4D52semidirect
383. C5#65827semidirect
384. C5#65987semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊D52
C22×#60382
#117172022
C5×#40322
C5×D5×C22⋊C42
#117170992
#117170842
#117170412
#117170272
#117170242
#117170112
#659875
#658275