Finite Group Databasebeta

← #12253779

Subgroups — #12253779

Order 1280.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3050C211yesmaximal, characteristic, complemented
2C2×#65482C211yesmaximal, characteristic, complemented
3C2×#65404C211yesmaximal, characteristic, complemented
4C22×#3944C211yesmaximal, characteristic, complemented
5#10602871C211yesmaximal, characteristic, complemented
6#10601877C212yesmaximal, complemented
7#10601875C212yesmaximal, complemented
8#10601866C212yesmaximal, complemented
9#10601864C212yesmaximal, complemented
10#10601445C211yesmaximal, characteristic, complemented
11#10601442C211yesmaximal, characteristic, complemented
12C2×C5×#135C2211yescharacteristic
13C23×C5×C8C2211yescharacteristic
14C5×#525—21no—
15C2×#4076—21no—
16C22×D40C2211yescharacteristic
17C5×#467C2211yescharacteristic, complemented
18C5×#467C2211yescharacteristic, complemented
19C5×#466C2211yescharacteristic, complemented
20C5×#466C2211yescharacteristic, complemented
21C5×#465—21no—
22C5×#465—21no—
23C5×#427C2211yescharacteristic
24C5×#416—21no—
25#65482—24no—
26C2×#3960C2212yescomplemented
27C2×#3958C2212yescomplemented
28#65404—21no—
29#65404—21no—
30#65404C2212yes—
31#65404C2212yes—
32C2×#3953—21no—
33C2×#3950C2211yescharacteristic
34C2×#3944—24no—
35C2×#3944C2211yescharacteristic
36C2×#3944C2211yescharacteristic
37C2×#3944C2212yescomplemented
38C22×#672C2212yescomplemented
39#64784C2212yescomplemented
40#64782C2212yescomplemented
41#64711C2212yescomplemented
42#64711C2212yescomplemented
43#64710C2212yescomplemented
44#64709C2212yescomplemented
45#33605—51nomaximal, Sylow
46C2×C5×#41—21no—
47C23×C4×C5D411yescharacteristic
48C22×C22⋊D5—41no—
49C22×D20—21no—
50C5×#135—22no—
51C5×#135—22no—
52C2×C5×Q16C2311yescharacteristic
53C2×C5×SD16—21no—
54C2×C5×D8C2311yescharacteristic
55C22×C5×C8—22no—
56C22×C5×C8—22no—
57C22×C5×C8D411yescharacteristic
58C22×C5×C8D411yescharacteristic
59C22×C5×C8D411yescharacteristic
60C22×C5×C8C2311yescharacteristic
61C22×C5×C8C2311yescharacteristic
62C22×C5×C8C2311yescharacteristic
63C5×#123—41no—
64C5×C22⋊Q8—21no—
65C5×C22⋊Q8—21no—
66C5×#121—21no—
67C5×#121—21no—
68C5×#120—41no—
69C4×C5×D4—41no—
70C4×C5×D4—41no—
71C5×#117—21no—
72#4076—22no—
73#4076—22no—
74#4076—41no—
75#4076—41no—
76C2×#685—41no—
77C2×C4⋊Dic5—21no—
78C2×D40—22no—
79C2×D40—22no—
80C2×D40—21no—
81C2×D40C2312yes—
82C5×#107C2311yescharacteristic
83C5×#107C2311yescharacteristic
84C5×#106—21no—
85C5×#103—21no—
86C5×#103—21no—
87C5×#102—21no—
88C5×#102—21no—
89#3960—24no—
90#3958—24no—
91#3953—22no—
92#3953—22no—
93#3950—21no—
94#3950C2312yes—
95#3944—22no—
96#3944—24no—
97#3944D414yescomplemented
98C2×#672—24no—
99C2×#672C2312yes—
100C2×#672C2312yes—
101C2×#509—51no—
102C22×M32—51no—
103#3050D511yescharacteristic, complemented
104C2×#466—51no—
105#2220—52no—
106#2218—52no—
107#2217—52no—
108#2215—52no—
109#2159—51no—
110#2140—51no—
111#2139—51no—
112C24×C5D811yescharacteristic
113C23×D5—41no—
114C5×#41—42no—
115C5×#41—42no—
116C2×C5×Q8—21no—
117C2×C5×D4—21no—
118C2×C5×D4—41no—
119C2×C5×D4—41no—
120C2×C5×D4—41no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—41no—
124C22×C4×C5D811yescharacteristic
125C22×C4×C5D811yescharacteristic
126C22×C4×C5D811yescharacteristic
127C22×C4×C5C2×D411yescharacteristic
128C22×C4×C5C2×D411yescharacteristic
129C22×C4×C5C2×D411yescharacteristic
130C2×C22⋊D5—42no—
131C2×C22⋊D5—42no—
132C2×C22⋊D5—84no—
133C22×Dic5—41no—
134C2×D20—22no—
135C2×D20—42no—
136C2×D20—42no—
137C2×D20—41no—
138C5×Q16—21no—
139C5×Q16—21no—
140C5×SD16—42no—
141C5×D8—21no—
142C5×D8—21no—
143C2×C5×C8—22no—
144C2×C5×C8—22no—
145C2×C5×C8—22no—
146C2×C5×C8—21no—
147C2×C5×C8—21no—
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C2×C5×C8C2×D412yes—
151C2×C5×C8C2×D411yescharacteristic
152C2×C5×C8C2×D411yescharacteristic
153C2×C5×C8C2×D411yescharacteristic
154C2×C5×C8#4112yes—
155C2×C5×C8C2411yescharacteristic
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—41no—
159C5×C4⋊C4—41no—
160C5×C22⋊C4—41no—
161C5×C22⋊C4—41no—
162C5×C22⋊C4—41no—
163C5×C22⋊C4—41no—
164C5×C22⋊C4—41no—
165C42×C5—41no—
166#685—42no—
167#685—42no—
168C4⋊Dic5—22no—
169C4⋊Dic5—41no—
170D40—22no—
171D40—22no—
172D40—42no—
173#672—22no—
174#672C2×D414yescomplemented
175C2×#135C2×D511yescharacteristic
176C22×D8—51no—
177C23×C8C2×D511yescharacteristic
178#525—21no—
179C2×#121—101no—
180#509—104no—
181C2×SD32—52no—
182C2×D16—52no—
183C2×M32—51no—
184C2×M32—51no—
185C2×M32—52no—
186C2×M32—104no—
187C22×C16—52no—
188#467C2×D511yescharacteristic, complemented
189#467C2×D511yescharacteristic, complemented
190#466—52no—
191#466—52no—
192#466—101no—
193#466—101no—
194#466C2×D511yescharacteristic, complemented
195#466C2×D511yescharacteristic, complemented
196#465—21no—
197#465—21no—
198#427C2×D511yescharacteristic
199C2×#107—51no—
200#416—21no—
201C2×#102—101no—
202#367—52no—
203#366—52no—
204#358—52no—
205#357—52no—
206#357—52no—
207#357—52no—
208C23×C5—22no—
209C23×C5—22no—
210C23×C5—41no—
211C23×C5—41no—
212C23×C5C2×D811yescharacteristic
213C23×C5C2×D811yescharacteristic
214C23×C5C2×D811yescharacteristic
215C22×D5—42no—
216C22×D5—82no—
217C22×D5—82no—
218C22×D5—82no—
219C5×Q8—41no—
220C5×Q8—41no—
221C5×D4—41no—
222C5×D4—41no—
223C5×D4—82no—
224C5×D4—82no—
225C5×D4—82no—
226C2×C4×C5—22no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—21no—
230C2×C4×C5—21no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—82no—
237C2×C4×C5#12112yes—
238C2×C4×C5C2×D811yescharacteristic
239C2×C4×C5C2×D811yescharacteristic
240C2×C4×C5C2×D811yescharacteristic
241C2×C4×C5#13512yes—
242C2×C4×C5C22×D411yescharacteristic
243C22⋊D5—84no—
244C22⋊D5—84no—
245C2×Dic5—42no—
246C2×Dic5—82no—
247D20—42no—
248D20—42no—
249D20—82no—
250C5×C8—21no—
251C5×C8—21no—
252C5×C8#12112yes—
253C5×C8C22×D411yescharacteristic
254C5×C8C2×#4111yescharacteristic
255C2×#41—21no—
256C22×D4—101no—
257C22×D4—201no—
258C23×C4C22⋊D511yescharacteristic
259#135—22no—
260#135—22no—
261C2×Q16C22×D511yescharacteristic
262C2×SD16—21no—
263C2×D8—52no—
264C2×D8—102no—
265C2×D8—102no—
266C2×D8—101no—
267C2×D8C22×D511yescharacteristic
268C22×C8—22no—
269C22×C8—22no—
270C22×C8C22⋊D511yescharacteristic
271C22×C8C22⋊D511yescharacteristic
272C22×C8C22⋊D511yescharacteristic
273C22×C8C22×D511yescharacteristic
274C22×C8C22×D511yescharacteristic
275C22×C8C22×D511yescharacteristic
276#123—41no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279#121—21no—
280#121—21no—
281#121—102no—
282#121—102no—
283#121—201no—
284#121—201no—
285#120—41no—
286C4×D4—41no—
287C4×D4—41no—
288#117—21no—
289C2×C4⋊C4—101no—
290C2×C22⋊C4—201no—
291SD32—104no—
292D16—104no—
293M32—54no—
294M32—104no—
295M32—102no—
296C2×C16—52no—
297C2×C16—52no—
298C2×C16—104no—
299#107—52no—
300#107—101no—
301#107C22×D511yescharacteristic
302#107C22×D511yescharacteristic
303#106—21no—
304#103—21no—
305#103—21no—
306#102—21no—
307#102—21no—
308#102—102no—
309#102—102no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—44no—
318C22×C5—81no—
319C22×C5—81no—
320C22×C5—81no—
321C22×C5#46612yes—
322C22×C5#50912yescomplemented
323C22×C5C22×D811yescharacteristic
324C2×D5—82no—
325C2×D5—82no—
326C2×D5—82no—
327C2×D5—164no—
328C4×C5—21no—
329C4×C5—21no—
330C4×C5—81no—
331C4×C5—81no—
332C4×C5—81no—
333C4×C5#46612yes—
334C4×C5C2×#12111yescharacteristic
335C4×C5C2×#13511yescharacteristic
336Dic5—82no—
337C24—201no—
338C24#68611yescharacteristic
339#41—42no—
340#41—42no—
341C2×Q8—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—102no—
347C2×D4—202no—
348C2×D4—202no—
349C2×D4—202no—
350C2×D4—201no—
351C2×D4—202no—
352C2×D4—404no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—41no—
356C22×C4—201no—
357C22×C4#68611yescharacteristic
358C22×C4#68611yescharacteristic
359C22×C4#68611yescharacteristic
360C22×C4C2×C22⋊D511yescharacteristic
361C22×C4C2×C22⋊D511yescharacteristic
362C22×C4C2×C22⋊D511yescharacteristic
363Q16—21no—
364Q16—21no—
365SD16—42no—
366D8—21no—
367D8—21no—
368D8—102no—
369D8—102no—
370D8—202no—
371C2×C8—22no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8D4×D512yes—
379C2×C8#71112yes—
380C2×C8C2×C22⋊D511yescharacteristic
381C2×C8C2×C22⋊D511yescharacteristic
382C2×C8C2×C22⋊D511yescharacteristic
383C2×C8C23×D511yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—102no—
389C4⋊C4—201no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—202no—
396C22⋊C4—202no—
397C42—41no—
398C16—54no—
399C16—102no—
400C2×C5—22no—
401C2×C5—22no—
402C2×C5—41no—
403C2×C5—161no—
404C2×C5C2×#46611yescharacteristic
405C2×C5C2×#50911yescharacteristic
406C2×C5#341411yescharacteristic
407D5—162no—
408C23—22no—
409C23—22no—
410C23—41no—
411C23—41no—
412C23—202no—
413C23—402no—
414C23—402no—
415C23—402no—
416C23C2×#68611yescharacteristic
417C23C2×#68611yescharacteristic
418C23C2×#68611yescharacteristic
419Q8—41no—
420Q8—41no—
421D4—41no—
422D4—41no—
423D4—82no—
424D4—82no—
425D4—82no—
426D4—202no—
427D4—202no—
428D4—404no—
429D4—404no—
430D4—402no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—82no—
442C2×C4—202no—
443C2×C4—402no—
444C2×C4C2×#68611yescharacteristic
445C2×C4C2×#68611yescharacteristic
446C2×C4C2×#68611yescharacteristic
447C2×C4#408512yes—
448C2×C4#409612yes—
449C2×C4C22×C22⋊D511yescharacteristic
450C8—21no—
451C8—21no—
452C8#408512yes—
453C8C2×D4×D511yescharacteristic
454C8C2×#71111yescharacteristic
455C5#3360511yescharacteristic, complemented, Sylow
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—402no—
468C22—402no—
469C22—402no—
470C22—804no—
471C22#6532712yes—
472C22#6548212yescomplemented
473C22C22×#68611yescharacteristic
474C4—21no—
475C4—21no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—402no—
480C4#6532712yes—
481C4C2×#408511yescharacteristic
482C4C2×#409611yescharacteristic
483C2—22no—
484C2—22no—
485C2—41no—
486C2—161no—
487C2—802no—
488C2C2×#6532711yescharacteristic
489C2C2×#6548211yescharacteristic
490C2#1061562511yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
FittingC5×#3050C2
socleC22×C5C22×D8
hypercenter#3050D5
hypocenterC5#33605
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C5×#3050C2semidirect
2. C2×#65482C2semidirect
3. C2×#65404C2semidirect
4. C22×#3944C2semidirect
5. #10602871C2semidirect
6. #10601877C2semidirect
7. #10601875C2semidirect
8. #10601866C2semidirect
9. #10601864C2semidirect
10. #10601445C2semidirect
11. #10601442C2semidirect
17. C5×#467C22semidirect
18. C5×#467C22semidirect
19. C5×#466C22semidirect
20. C5×#466C22semidirect
26. C2×#3960C22semidirect
27. C2×#3958C22semidirect
37. C2×#3944C22semidirect
38. C22×#672C22semidirect
39. #64784C22semidirect
40. #64782C22semidirect
41. #64711C22semidirect
42. #64711C22semidirect
43. #64710C22semidirect
44. #64709C22semidirect
97. #3944D4semidirect
103. #3050D5semidirect
174. #672C2×D4semidirect
188. #467C2×D5semidirect
189. #467C2×D5semidirect
194. #466C2×D5semidirect
195. #466C2×D5semidirect
322. C22×C5#509semidirect
455. C5#33605semidirect
472. C22#65482semidirect

Maximal subgroups

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

subgroupindex
C5×#30502
C2×#654822
C2×#654042
C22×#39442
#106028712
#106018772
#106018752
#106018662
#106018642
#106014452
#106014422
#336055