Finite Group Databasebeta

← #12077991

Subgroups — #12077991

Order 1280.

976 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×Q82C211yesmaximal, characteristic, complemented
2#10614944C211yesmaximal, characteristic
3#10614173C211yesmaximal, characteristic
4#10614172C211yesmaximal, characteristic
5#10602734C214yesmaximal, complemented
6#10602732C214yesmaximal, complemented
7#10602567C211yesmaximal, characteristic, complemented
8#10602415C211yesmaximal, characteristic, complemented
9#10602414C211yesmaximal, characteristic, complemented
10C5×Q82—22no—
11C5×Q82—22no—
12C5×Q82—22no—
13C5×Q82C2214yes—
14C2×C5×C4⋊Q8—22no—
15C2×C5×C4⋊Q8—21no—
16C2×C5×C4⋊Q8—21no—
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C4×C5×Q8—21no—
19C2×C4×C5×Q8—21no—
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×Q8C2211yescharacteristic
22C2×#4088—21no—
23#65811C2211yescharacteristic
24#65516—21no—
25#65516—22no—
26#65374C2212yes—
27#65372—22no—
28#65370C2212yes—
29#65320C2212yes—
30#65317—22no—
31#65316C2212yes—
32#65316C2212yes—
33C4×#688—22no—
34#65309C2212yes—
35#65257—21no—
36#65255—21no—
37#65214C2211yescharacteristic
38#65214C2211yescharacteristic
39#65213C2211yescharacteristic
40#64766C2214yes—
41Q8⋊#168C2214yes—
42Q8⋊#168C2214yes—
43#18768—51nomaximal, Sylow
44C22×C5×Q8—22no—
45C22×C5×Q8D411yescharacteristic
46C22×C5×Q8D411yescharacteristic
47C22×C5×Q8D412yes—
48C2×#709—21no—
49C5×C4⋊Q8—28no—
50C5×C4⋊Q8—24no—
51C5×C4⋊Q8—24no—
52C5×C4⋊Q8—28no—
53C5×C4⋊Q8—24no—
54C5×C4⋊Q8—24no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8D412yes—
58C5×C4⋊Q8C2312yes—
59C4×C5×Q8—24no—
60C4×C5×Q8—24no—
61C4×C5×Q8—24no—
62C4×C5×Q8—24no—
63C4×C5×Q8—21no—
64C4×C5×Q8—21no—
65C4×C5×Q8—21no—
66C4×C5×Q8—21no—
67C4×C5×Q8D412yes—
68C4×C5×Q8D412yes—
69C4×C5×Q8C2312yes—
70C4×C5×Q8C2312yes—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4D411yescharacteristic
78C2×C5×C4⋊C4D411yescharacteristic
79C2×C42×C5—22no—
80C2×C42×C5—21no—
81C2×C42×C5—21no—
82C2×C42×C5C2311yescharacteristic
83C2×#689—22no—
84#4088—44no—
85C2×#688—22no—
86C2×#688—22no—
87C2×#688—24no—
88#4076—21no—
89#4076—21no—
90C2×#681—21no—
91#4021—21no—
92#4020C2311yescharacteristic
93C4×D20—21no—
94C4×D20—21no—
95#4015C2311yescharacteristic
96#3967—22no—
97#3967—24no—
98C22⋊#168—21no—
99C22⋊#168—21no—
100#3942—22no—
101#3941—22no—
102#3941—22no—
103#3940—22no—
104C4⋊#168—21no—
105C4⋊#168—21no—
106C4⋊#168C2312yes—
107C4⋊#168C2312yes—
108C4×#168—21no—
109C4×#168C2312yes—
110C2×Q82D511yescharacteristic, complemented
111#3206—51no—
112#3103—51no—
113#3037—51no—
114#1645—54no—
115#1623—54no—
116#1548—51no—
117#1487—51no—
118#1479—51no—
119C2×C5×Q8—24no—
120C2×C5×Q8—28no—
121C2×C5×Q8—21no—
122C2×C5×Q8—21no—
123C2×C5×Q8—22no—
124C2×C5×Q8—22no—
125C2×C5×Q8—82no—
126C2×C5×Q8—84no—
127C2×C5×Q8SD1614yescomplemented
128C2×C5×Q8C2×D412yes—
129C2×C5×Q8C2×D412yes—
130C2×C5×Q8C2×D414yes—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5C2×D411yescharacteristic
137C22×C4×C5C2×D411yescharacteristic
138C22×C4×C5C2×D411yescharacteristic
139C2×C22⋊D5—41no—
140#709—42no—
141#709—42no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—21no—
145C2×C4×D5—41no—
146C2×Dic10—21no—
147C5×C4⋊C4—28no—
148C5×C4⋊C4—28no—
149C5×C4⋊C4—22no—
150C5×C4⋊C4—22no—
151C5×C4⋊C4—22no—
152C5×C4⋊C4—22no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—22no—
156C5×C4⋊C4—22no—
157C5×C4⋊C4—22no—
158C5×C4⋊C4—22no—
159C5×C4⋊C4C2×D412yes—
160C5×C4⋊C4C2×D412yes—
161C42×C5—28no—
162C42×C5—22no—
163C42×C5—22no—
164C42×C5—22no—
165C42×C5—22no—
166C42×C5C2×D411yescharacteristic
167C42×C5C2×D411yescharacteristic
168C42×C5C2×D411yescharacteristic
169C42×C5C2411yescharacteristic
170#689—44no—
171#688—44no—
172#688—44no—
173#688—84no—
174#685—41no—
175#685—41no—
176C4⋊Dic5—21no—
177C4⋊Dic5—21no—
178#681—42no—
179C2×#168—22no—
180C2×#168—22no—
181C2×#168—22no—
182C2×#137—101no—
183Q82—22no—
184Q82—22no—
185Q82—22no—
186Q82C2×D514yes—
187#532—51no—
188C2×C4⋊Q8—22no—
189C2×C4⋊Q8—21no—
190C2×C4⋊Q8—21no—
191C2×C4⋊Q8C2×D511yescharacteristic
192C2×C4×Q8—21no—
193C2×C4×Q8—21no—
194C2×C4×Q8C2×D511yescharacteristic
195C2×C4×Q8C2×D511yescharacteristic
196#492—52no—
197#487—52no—
198#481—101no—
199#475—52no—
200#464—102no—
201#462—52no—
202#461—102no—
203#460—52no—
204#460—52no—
205#448—101no—
206#448—102no—
207C4×SD16—102no—
208#431—51no—
209#431—51no—
210#423—51no—
211#417—101no—
212#333—54no—
213Q8⋊C8—54no—
214Q8⋊C8—54no—
215C23×C5#12011yescharacteristic
216C22×D5—41no—
217C5×Q8—24no—
218C5×Q8—22no—
219C5×Q8—22no—
220C5×Q8—24no—
221C5×Q8—44no—
222C5×Q8—82no—
223C5×Q8—88no—
224C5×Q8C2×SD1614yes—
225C5×Q8#13714yescomplemented
226C2×C4×C5—24no—
227C2×C4×C5—22no—
228C2×C4×C5—22no—
229C2×C4×C5—24no—
230C2×C4×C5—22no—
231C2×C4×C5—24no—
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5—41no—
235C2×C4×C5—44no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5#12011yescharacteristic
239C2×C4×C5#12011yescharacteristic
240C2×C4×C5#12011yescharacteristic
241C2×C4×C5C2×SD1612yes—
242C2×C4×C5#13712yes—
243C2×C4×C5C22×D411yescharacteristic
244C2×C4×C5C22×D411yescharacteristic
245C2×C4×C5C22×D411yescharacteristic
246C22⋊D5—82no—
247C2×Dic5—41no—
248D20—42no—
249D20—41no—
250D20—42no—
251D20—41no—
252C4×D5—82no—
253Dic10—41no—
254Dic10—41no—
255#168—42no—
256#168—42no—
257#168—42no—
258C2×#41—101no—
259C22×Q8—22no—
260C22×Q8C22⋊D511yescharacteristic
261C22×Q8C22⋊D511yescharacteristic
262C22×Q8C22⋊D512yes—
263#137—204no—
264C2×Q16—102no—
265C2×SD16—102no—
266C2×SD16—102no—
267C2×SD16—104no—
268C2×M16—101no—
269C4⋊Q8—28no—
270C4⋊Q8—24no—
271C4⋊Q8—24no—
272C4⋊Q8—28no—
273C4⋊Q8—24no—
274C4⋊Q8—24no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—51no—
278C4⋊Q8C22⋊D512yes—
279C4⋊Q8C22×D512yes—
280#127—51no—
281#124—101no—
282#121—101no—
283#121—101no—
284C4×Q8—24no—
285C4×Q8—24no—
286C4×Q8—24no—
287C4×Q8—24no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8C22⋊D512yes—
293C4×Q8C22⋊D512yes—
294C4×Q8C22×D512yes—
295C4×Q8C22×D512yes—
296C4×D4—101no—
297C4×D4—101no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C22⋊D511yescharacteristic
305C2×C4⋊C4C22⋊D511yescharacteristic
306C2×C42—22no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42C22×D511yescharacteristic
310#106—102no—
311C4⋊C8—52no—
312C4⋊C8—52no—
313C4⋊C8—101no—
314C4⋊C8—101no—
315#103—102no—
316#103—104no—
317#103—102no—
318#102—102no—
319#102—102no—
320C22⋊C8—101no—
321C22⋊C8—101no—
322C4×C8—52no—
323C4×C8—101no—
324C22×C5—21no—
325C22×C5—21no—
326C22×C5#44812yes—
327C22×C5C2×#12011yescharacteristic
328C2×D5—81no—
329C2×D5—81no—
330C2×D5—81no—
331C4×C5—24no—
332C4×C5—24no—
333C4×C5—21no—
334C4×C5—21no—
335C4×C5—21no—
336C4×C5—44no—
337C4×C5—42no—
338C4×C5—42no—
339C4×C5#44812yes—
340C4×C5C22×SD1611yescharacteristic
341C4×C5C2×#13711yescharacteristic
342C4×C5C2×#13712yes—
343Dic5—81no—
344#41—202no—
345#41—202no—
346C2×Q8—24no—
347C2×Q8—28no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—82no—
353C2×Q8—84no—
354C2×Q8—101no—
355C2×Q8#68814yescomplemented
356C2×Q8C2×C22⋊D512yes—
357C2×Q8C2×C22⋊D512yes—
358C2×Q8C2×C22⋊D514yes—
359C2×D4—101no—
360C2×D4—101no—
361C2×D4—101no—
362C2×D4—201no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—201no—
369C22×C4C2×C22⋊D511yescharacteristic
370C22×C4C2×C22⋊D511yescharacteristic
371C22×C4C2×C22⋊D511yescharacteristic
372Q16—204no—
373SD16—204no—
374SD16—204no—
375SD16—404no—
376M16—202no—
377C2×C8—102no—
378C2×C8—102no—
379C2×C8—102no—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—101no—
393C4⋊C4—101no—
394C4⋊C4C2×C22⋊D512yes—
395C4⋊C4C2×C22⋊D512yes—
396C22⋊C4—201no—
397C22⋊C4—201no—
398C42—28no—
399C42—22no—
400C42—22no—
401C42—22no—
402C42—22no—
403C42C2×C22⋊D511yescharacteristic
404C42C2×C22⋊D511yescharacteristic
405C42C2×C22⋊D511yescharacteristic
406C42C23×D511yescharacteristic
407C2×C5—22no—
408C2×C5C2×#44811yescharacteristic
409C2×C5#300411yescharacteristic
410C2×C5#301911yescharacteristic
411D5—161no—
412C23—201no—
413C23#409911yescharacteristic
414Q8—24no—
415Q8—22no—
416Q8—22no—
417Q8—24no—
418Q8—44no—
419Q8—82no—
420Q8—88no—
421Q8—201no—
422Q8—201no—
423Q8C2×#68814yes—
424Q8#408814yescomplemented
425D4—202no—
426D4—201no—
427D4—202no—
428D4—201no—
429D4—402no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—201no—
443C2×C4—402no—
444C2×C4C2×#68812yes—
445C2×C4#408812yes—
446C2×C4#409911yescharacteristic
447C2×C4#409911yescharacteristic
448C2×C4#409911yescharacteristic
449C2×C4C22×C22⋊D511yescharacteristic
450C2×C4C22×C22⋊D511yescharacteristic
451C2×C4C22×C22⋊D511yescharacteristic
452C8—202no—
453C8—202no—
454C8—202no—
455C5#1876811yescharacteristic, complemented, Sylow
456C22—21no—
457C22—21no—
458C22—401no—
459C22—401no—
460C22—401no—
461C22#6551612yes—
462C22C2×#409911yescharacteristic
463C4—21no—
464C4—21no—
465C4—24no—
466C4—24no—
467C4—21no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—401no—
472C4#6551612yes—
473C4C22×#68811yescharacteristic
474C4C2×#408811yescharacteristic
475C4C2×#408812yes—
476C2—22no—
477C2—801no—
478C2C2×#6551611yescharacteristic
479C2#1061579011yescharacteristic
480C2#1061583511yescharacteristic
subgroupG/H
centerC22C2×#4099
commutator, cosocleC42×C5C24
FrattiniC42C23×D5
FittingC2×C5×Q82C2
socleC22×C5C2×#120
prime radical#65811C22
hypercenterC2×Q82D5
hypocenterC5#18768
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. C2×C5×Q82C2semidirect
5. #10602734C2semidirect
6. #10602732C2semidirect
7. #10602567C2semidirect
8. #10602415C2semidirect
9. #10602414C2semidirect
110. C2×Q82D5semidirect
127. C2×C5×Q8SD16semidirect
225. C5×Q8#137semidirect
355. C2×Q8#688semidirect
424. Q8#4088semidirect
455. C5#18768semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q822
#106149442
#106141732
#106141722
#106027342
#106027322
#106025672
#106024152
#106024142
#187685