Finite Group Databasebeta

← #12253790

Subgroups — #12253790

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3050C211yesmaximal, characteristic
2C2×#65484C211yesmaximal, characteristic, complemented
3C2×#65405C211yesmaximal, characteristic, complemented
4C22×#3944C211yesmaximal, characteristic, complemented
5#10602871C211yesmaximal, characteristic, complemented
6#10601876C212yesmaximal, complemented
7#10601874C212yesmaximal, complemented
8#10601867C212yesmaximal, complemented
9#10601865C212yesmaximal, complemented
10#10601447C211yesmaximal, characteristic, complemented
11#10601442C211yesmaximal, characteristic, complemented
12C2×C5×#135C2211yescharacteristic
13C23×C5×C8C2211yescharacteristic
14C5×#525—21no—
15C2×#4070—21no—
16C22×Dic20C2211yescharacteristic
17C5×#467C2211yescharacteristic
18C5×#467C2211yescharacteristic
19C5×#466C2211yescharacteristic
20C5×#466C2211yescharacteristic
21C5×#465—21no—
22C5×#465—21no—
23C5×#427C2211yescharacteristic
24C5×#416—21no—
25#65484—24no—
26C2×#3961C2212yescomplemented
27C2×#3959C2212yescomplemented
28#65405—21no—
29#65405—21no—
30#65405C2212yes—
31#65405C2212yes—
32C2×#3950C2211yescharacteristic
33C2×#3948—21no—
34C2×#3944—24no—
35C2×#3944C2211yescharacteristic
36C2×#3944C2212yes—
37C2×#3944C2211yescharacteristic
38C22×#672C2212yes—
39#64784C2212yescomplemented
40#64782C2212yescomplemented
41#64712C2212yescomplemented
42#64712C2212yescomplemented
43#64710C2212yescomplemented
44#64709C2212yescomplemented
45#33606—51nomaximal, Sylow
46C2×C5×#41—21no—
47C23×C4×C5D411yescharacteristic
48C22×Dic10—21no—
49C5×#135—22no—
50C5×#135—22no—
51C2×C5×Q16C2311yescharacteristic
52C2×C5×SD16—21no—
53C2×C5×D8C2311yescharacteristic
54C22×C5×C8—22no—
55C22×C5×C8—22no—
56C22×C5×C8D411yescharacteristic
57C22×C5×C8D411yescharacteristic
58C22×C5×C8D411yescharacteristic
59C22×C5×C8C2311yescharacteristic
60C22×C5×C8C2311yescharacteristic
61C22×C5×C8C2311yescharacteristic
62C5×#123—41no—
63C5×C22⋊Q8—21no—
64C5×C22⋊Q8—21no—
65C5×#121—21no—
66C5×#121—21no—
67C5×#120—41no—
68C4×C5×D4—41no—
69C4×C5×D4—41no—
70C5×#117—21no—
71C2×C22⋊Dic5—41no—
72C2×C4⋊Dic5—21no—
73#4070—22no—
74#4070—22no—
75#4070—41no—
76#4070—41no—
77C2×#683—41no—
78C2×Dic20—22no—
79C2×Dic20—22no—
80C2×Dic20—21no—
81C2×Dic20C2312yes—
82C5×#107C2311yescharacteristic
83C5×#107C2311yescharacteristic
84C5×#106—21no—
85C5×#103—21no—
86C5×#103—21no—
87C5×#102—21no—
88C5×#102—21no—
89#3961—24no—
90#3959—24no—
91#3950—21no—
92#3950C2312yes—
93#3948—22no—
94#3948—22no—
95#3944—22no—
96#3944—24no—
97#3944D414yescomplemented
98C2×#672—24no—
99C2×#672C2312yes—
100C2×#672C2312yes—
101C2×#510—51no—
102C22×M32—51no—
103#3050D511yescharacteristic
104C2×#467—51no—
105#2220—52no—
106#2219—52no—
107#2217—52no—
108#2216—52no—
109#2159—51no—
110#2141—51no—
111#2139—51no—
112C24×C5D811yescharacteristic
113C5×#41—42no—
114C5×#41—42no—
115C2×C5×Q8—21no—
116C2×C5×D4—21no—
117C2×C5×D4—41no—
118C2×C5×D4—41no—
119C2×C5×D4—41no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—41no—
123C22×C4×C5D811yescharacteristic
124C22×C4×C5D811yescharacteristic
125C22×C4×C5D811yescharacteristic
126C22×C4×C5C2×D411yescharacteristic
127C22×C4×C5C2×D411yescharacteristic
128C22×C4×C5C2×D411yescharacteristic
129C22×Dic5—41no—
130C22×Dic5—41no—
131C2×Dic10—22no—
132C2×Dic10—42no—
133C2×Dic10—42no—
134C2×Dic10—41no—
135C5×Q16—21no—
136C5×Q16—21no—
137C5×SD16—42no—
138C5×D8—21no—
139C5×D8—21no—
140C2×C5×C8—22no—
141C2×C5×C8—22no—
142C2×C5×C8—22no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8C2×D412yes—
148C2×C5×C8C2×D411yescharacteristic
149C2×C5×C8C2×D411yescharacteristic
150C2×C5×C8C2×D411yescharacteristic
151C2×C5×C8#4112yes—
152C2×C5×C8C2411yescharacteristic
153C5×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—41no—
156C5×C4⋊C4—41no—
157C5×C22⋊C4—41no—
158C5×C22⋊C4—41no—
159C5×C22⋊C4—41no—
160C5×C22⋊C4—41no—
161C5×C22⋊C4—41no—
162C42×C5—41no—
163C22⋊Dic5—42no—
164C22⋊Dic5—42no—
165C4⋊Dic5—22no—
166C4⋊Dic5—41no—
167#683—42no—
168#683—42no—
169Dic20—22no—
170Dic20—22no—
171Dic20—42no—
172#672—22no—
173#672C2×D414yes—
174C2×#135C2×D511yescharacteristic
175C22×Q16—51no—
176C23×C8C2×D511yescharacteristic
177#525—21no—
178C2×C22⋊Q8—101no—
179#510—104no—
180C2×Q32—52no—
181C2×SD32—52no—
182C2×M32—51no—
183C2×M32—51no—
184C2×M32—52no—
185C2×M32—104no—
186C22×C16—52no—
187#467—52no—
188#467—52no—
189#467—101no—
190#467—101no—
191#467C2×D511yescharacteristic
192#467C2×D511yescharacteristic
193#466C2×D511yescharacteristic
194#466C2×D511yescharacteristic
195#465—21no—
196#465—21no—
197#427C2×D511yescharacteristic
198C2×#107—51no—
199#416—21no—
200C2×#103—101no—
201#367—52no—
202#366—52no—
203#358—52no—
204#358—52no—
205#358—52no—
206#357—52no—
207C23×C5—22no—
208C23×C5—22no—
209C23×C5—41no—
210C23×C5—41no—
211C23×C5C2×D811yescharacteristic
212C23×C5C2×D811yescharacteristic
213C23×C5C2×D811yescharacteristic
214C5×Q8—41no—
215C5×Q8—41no—
216C5×D4—41no—
217C5×D4—41no—
218C5×D4—82no—
219C5×D4—82no—
220C5×D4—82no—
221C2×C4×C5—22no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—82no—
232C2×C4×C5#12112yes—
233C2×C4×C5C2×D811yescharacteristic
234C2×C4×C5C2×D811yescharacteristic
235C2×C4×C5C2×D811yescharacteristic
236C2×C4×C5#13512yes—
237C2×C4×C5C22×D411yescharacteristic
238C2×Dic5—42no—
239C2×Dic5—42no—
240C2×Dic5—82no—
241C2×Dic5—82no—
242Dic10—42no—
243Dic10—42no—
244Dic10—82no—
245C5×C8—21no—
246C5×C8—21no—
247C5×C8#12112yes—
248C5×C8C22×D411yescharacteristic
249C5×C8C2×#4111yescharacteristic
250C2×#41—21no—
251C22×Q8—101no—
252C23×C4C22⋊D511yescharacteristic
253#135—22no—
254#135—22no—
255C2×Q16—52no—
256C2×Q16—102no—
257C2×Q16—102no—
258C2×Q16—101no—
259C2×Q16C22×D511yescharacteristic
260C2×SD16—21no—
261C2×D8C22×D511yescharacteristic
262C22×C8—22no—
263C22×C8—22no—
264C22×C8C22⋊D511yescharacteristic
265C22×C8C22⋊D511yescharacteristic
266C22×C8C22⋊D511yescharacteristic
267C22×C8C22×D511yescharacteristic
268C22×C8C22×D511yescharacteristic
269C22×C8C22×D511yescharacteristic
270#123—41no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—102no—
274C22⋊Q8—102no—
275C22⋊Q8—201no—
276C22⋊Q8—201no—
277#121—21no—
278#121—21no—
279#120—41no—
280C4×D4—41no—
281C4×D4—41no—
282#117—21no—
283C2×C4⋊C4—101no—
284C2×C4⋊C4—201no—
285C2×C22⋊C4—201no—
286Q32—104no—
287SD32—104no—
288M32—54no—
289M32—104no—
290M32—102no—
291C2×C16—52no—
292C2×C16—52no—
293C2×C16—104no—
294#107—52no—
295#107—101no—
296#107C22×D511yescharacteristic
297#107C22×D511yescharacteristic
298#106—21no—
299#103—21no—
300#103—21no—
301#103—102no—
302#103—102no—
303#102—21no—
304#102—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—44no—
313C22×C5—81no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5#46612yes—
317C22×C5#51012yescomplemented
318C22×C5C22×D811yescharacteristic
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—81no—
322C4×C5—81no—
323C4×C5—81no—
324C4×C5#46612yes—
325C4×C5C2×#12111yescharacteristic
326C4×C5C2×#13511yescharacteristic
327Dic5—82no—
328Dic5—82no—
329C24#68611yescharacteristic
330#41—42no—
331#41—42no—
332C2×Q8—21no—
333C2×Q8—102no—
334C2×Q8—201no—
335C2×Q8—202no—
336C2×Q8—202no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—41no—
344C22×C4—201no—
345C22×C4—201no—
346C22×C4#68611yescharacteristic
347C22×C4#68611yescharacteristic
348C22×C4#68611yescharacteristic
349C22×C4C2×C22⋊D511yescharacteristic
350C22×C4C2×C22⋊D511yescharacteristic
351C22×C4C2×C22⋊D511yescharacteristic
352Q16—21no—
353Q16—21no—
354Q16—102no—
355Q16—102no—
356Q16—202no—
357SD16—42no—
358D8—21no—
359D8—21no—
360C2×C8—22no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8D4×D512yes—
368C2×C8#71112yes—
369C2×C8C2×C22⋊D511yescharacteristic
370C2×C8C2×C22⋊D511yescharacteristic
371C2×C8C2×C22⋊D511yescharacteristic
372C2×C8C23×D511yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—102no—
378C4⋊C4—201no—
379C4⋊C4—202no—
380C4⋊C4—202no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—202no—
387C22⋊C4—202no—
388C42—41no—
389C16—54no—
390C16—102no—
391C2×C5—22no—
392C2×C5—22no—
393C2×C5—41no—
394C2×C5—161no—
395C2×C5C2×#46611yescharacteristic
396C2×C5C2×#51011yescharacteristic
397C2×C5#341411yescharacteristic
398C23—22no—
399C23—22no—
400C23—41no—
401C23—41no—
402C23C2×#68611yescharacteristic
403C23C2×#68611yescharacteristic
404C23C2×#68611yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—202no—
408Q8—202no—
409Q8—402no—
410D4—41no—
411D4—41no—
412D4—82no—
413D4—82no—
414D4—82no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—82no—
426C2×C4—202no—
427C2×C4—202no—
428C2×C4—402no—
429C2×C4—402no—
430C2×C4C2×#68611yescharacteristic
431C2×C4C2×#68611yescharacteristic
432C2×C4C2×#68611yescharacteristic
433C2×C4#408512yes—
434C2×C4#409612yes—
435C2×C4C22×C22⋊D511yescharacteristic
436C8—21no—
437C8—21no—
438C8#408512yes—
439C8C2×D4×D511yescharacteristic
440C8C2×#71111yescharacteristic
441C5#3360611yescharacteristic, complemented, Sylow
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22#6532712yes—
454C22#6548412yescomplemented
455C22C22×#68611yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—402no—
462C4—402no—
463C4#6532712yes—
464C4C2×#408511yescharacteristic
465C4C2×#409611yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—161no—
470C2C2×#6532711yescharacteristic
471C2#1061562511yescharacteristic
472C2C2×#6548411yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
Fitting, prime radicalC5×#3050C2
socleC22×C5C22×D8
hypercenter#3050D5
hypocenterC5#33606
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
2. C2×#65484C2semidirect
3. C2×#65405C2semidirect
4. C22×#3944C2semidirect
5. #10602871C2semidirect
6. #10601876C2semidirect
7. #10601874C2semidirect
8. #10601867C2semidirect
9. #10601865C2semidirect
10. #10601447C2semidirect
11. #10601442C2semidirect
26. C2×#3961C22semidirect
27. C2×#3959C22semidirect
39. #64784C22semidirect
40. #64782C22semidirect
41. #64712C22semidirect
42. #64712C22semidirect
43. #64710C22semidirect
44. #64709C22semidirect
97. #3944D4semidirect
317. C22×C5#510semidirect
441. C5#33606semidirect
454. C22#65484semidirect

Maximal subgroups

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

subgroupindex
C5×#30502
C2×#654842
C2×#654052
C22×#39442
#106028712
#106018762
#106018742
#106018672
#106018652
#106014472
#106014422
#336065