Finite Group Databasebeta

← #12068517

Subgroups — #12068517

Order 1280.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611070C211yesmaximal, characteristic
2#10610781C211yesmaximal, characteristic
3#10610250C211yesmaximal, characteristic
4C5×#1569C211yesmaximal, characteristic, complemented
5#10601587C211yesmaximal, characteristic, complemented
6#10601284C211yesmaximal, characteristic, complemented
7#10600644C211yesmaximal, characteristic, complemented
8#10599368C211yesmaximal, characteristic, complemented
9#10599367C211yesmaximal, characteristic, complemented
10#10599365C211yesmaximal, characteristic, complemented
11#10599365C211yesmaximal, characteristic, complemented
12#10599328C211yesmaximal, characteristic, complemented
13#10599327C211yesmaximal, characteristic, complemented
14#10599326C211yesmaximal, characteristic, complemented
15#10599326C211yesmaximal, characteristic, complemented
16C4×#709C2211yescharacteristic
17C5×#432C2211yescharacteristic
18C5×#423C2211yescharacteristic
19C4×C5×M16C2211yescharacteristic
20#65418C412yes—
21#65417—21no—
22#65416—21no—
23#65408C412yes—
24#65215C2211yescharacteristic
25#65213C2211yescharacteristic
26C2×C4×#168C2211yescharacteristic
27#65126C2211yescharacteristic
28#65126C2211yescharacteristic
29#65125—21no—
30#65124C2211yescharacteristic
31#65124C2211yescharacteristic
32#65122C2211yescharacteristic
33#65122C2211yescharacteristic
34D5×C4⋊C8C2211yescharacteristic
35D5×C4⋊C8C2211yescharacteristic
36#65117—21no—
37#65018—21no—
38#65017—21no—
39#64998C412yes—
40#64998C412yes—
41#64995—21no—
42#64990—21no—
43#64974C2211yescharacteristic
44#64974C2211yescharacteristic
45#64974C2211yescharacteristic
46#64974C2211yescharacteristic
47C5×#335C2211yescharacteristic
48C5×#335C2211yescharacteristic
49C5×#334C2211yescharacteristic
50C5×#334C2211yescharacteristic
51#64700C2211yescharacteristic
52#64700C2211yescharacteristic
53#64699C2211yescharacteristic
54#64699C2211yescharacteristic
55#64699C2211yescharacteristic
56#64699C2211yescharacteristic
57#64699C2211yescharacteristic
58#64699C2211yescharacteristic
59#64678C2211yescharacteristic
60#64678C2211yescharacteristic
61#64677C2211yescharacteristic
62#64677C2211yescharacteristic
63#17825—51nomaximal, Sylow
64C2×#709C2×C411yescharacteristic
65C2×C5×M16—21no—
66C2×C5×M16C2×C412yes—
67C2×C42×C5C2311yescharacteristic
68C4×C22⋊D5D411yescharacteristic
69C4×C22⋊D5D411yescharacteristic
70C4×C22⋊D5Q811yescharacteristic
71C4×C22⋊D5Q811yescharacteristic
72#4072C2×C411yescharacteristic
73C2×#681—21no—
74C22×#168C2×C412yes—
75C2×#676—21no—
76C2×#676—21no—
77C2×C8×D5—21no—
78C2×C8×D5—21no—
79C4×D20D411yescharacteristic
80C4×D20Q811yescharacteristic
81#4018C2×C411yescharacteristic
82#4018C2×C411yescharacteristic
83C42×D5C2311yescharacteristic
84C42×D5C2311yescharacteristic
85C4×Dic10D411yescharacteristic
86C4×Dic10Q811yescharacteristic
87C5×C4⋊C8—21no—
88C5×C4⋊C8C2311yescharacteristic
89C5×C4⋊C8C2311yescharacteristic
90C5×C4⋊C8C2311yescharacteristic
91C5×C4⋊C8C2311yescharacteristic
92C5×C22⋊C8—21no—
93C5×#97—21no—
94C5×#97C2×C412yes—
95C4×C5×C8C2311yescharacteristic
96C4×C5×C8C2311yescharacteristic
97C22⋊#168—21no—
98#3952—21no—
99#3952—21no—
100#3952—21no—
101#3952—21no—
102#3952C2×C412yes—
103#3952C2×C412yes—
104#3952C2×C412yes—
105#3952C2×C412yes—
106#3947—21no—
107#3947—21no—
108#3946—21no—
109#3946—21no—
110#3946—21no—
111#3946—21no—
112#3946C2×C412yes—
113#3946C2×C412yes—
114#3946C2×C412yes—
115#3946C2×C412yes—
116C8×Dic5—21no—
117C8×Dic5—21no—
118C4⋊#168—21no—
119C4⋊#168C2311yescharacteristic
120C4⋊#168C2311yescharacteristic
121C4⋊#168C2311yescharacteristic
122C4⋊#168C2311yescharacteristic
123#3935—21no—
124C4×#168C2×C412yes—
125C4×#168C2311yescharacteristic
126C4×#168C2311yescharacteristic
127#2989—51no—
128#2989—51no—
129#2922—51no—
130#1574—51no—
131#1574—51no—
132#1573—51no—
133#1573—51no—
134#1572—51no—
135#1572—51no—
136#1571—51no—
137#1571—51no—
138#1569—51no—
139#1569D511yescharacteristic, complemented
140#1568—51no—
141#1567—51no—
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5C2×Q811yescharacteristic
145C2×C22⋊D5C4⋊C411yescharacteristic
146C2×C22⋊D5C4⋊C411yescharacteristic
147#709—42no—
148C2×D20C4⋊C411yescharacteristic
149C2×C4×D5C22×C411yescharacteristic
150C2×C4×D5C22×C411yescharacteristic
151C2×C4×D5C2×D411yescharacteristic
152C2×C4×D5C2×D411yescharacteristic
153C2×C4×D5C2×Q811yescharacteristic
154C2×C4×D5C2×Q811yescharacteristic
155C2×Dic10C4⋊C411yescharacteristic
156C5×M16—42no—
157C5×M16—81no—
158C2×C5×C8—21no—
159C2×C5×C8—21no—
160C2×C5×C8—21no—
161C2×C5×C8—21no—
162C2×C5×C8C22×C412yes—
163C2×C5×C8C22×C412yes—
164C42×C5C22×C411yescharacteristic
165C42×C5C2×D411yescharacteristic
166C42×C5C2×Q811yescharacteristic
167C42×C5C2411yescharacteristic
168C22⋊Dic5C4⋊C411yescharacteristic
169C22⋊Dic5C4⋊C411yescharacteristic
170#685C4⋊C411yescharacteristic
171#685C4⋊C411yescharacteristic
172#685C4⋊C411yescharacteristic
173#685C4⋊C411yescharacteristic
174C4⋊Dic5C4⋊C411yescharacteristic
175C4⋊Dic5C4⋊C411yescharacteristic
176#683C4⋊C411yescharacteristic
177#683C4⋊C411yescharacteristic
178#683C4⋊C411yescharacteristic
179#683C4⋊C411yescharacteristic
180C4×Dic5C22×C411yescharacteristic
181C4×Dic5C22×C411yescharacteristic
182C4×Dic5C2×D411yescharacteristic
183C4×Dic5C2×D411yescharacteristic
184C4×Dic5C2×Q811yescharacteristic
185C4×Dic5C2×Q811yescharacteristic
186#681—81no—
187C2×#168—21no—
188C2×#168—21no—
189C2×#168—21no—
190C2×#168—21no—
191C2×#168—42no—
192C2×#168C22×C412yes—
193C2×#168C22×C412yes—
194#676—81no—
195#676—81no—
196C8×D5—81no—
197C8×D5—81no—
198C4×#41—51no—
199#446—101no—
200#446—101no—
201#436—101no—
202#436—101no—
203#435—101no—
204#435—101no—
205#435—101no—
206#435—101no—
207#433—52no—
208#433—52no—
209#432—51no—
210#432—51no—
211#432—51no—
212#432C2×D511yescharacteristic
213#431—51no—
214#431—51no—
215#431—51no—
216#431—51no—
217#431—51no—
218#431—51no—
219#424—52no—
220#423—51no—
221#423—51no—
222#423—51no—
223#423C2×D511yescharacteristic
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226#408—52no—
227C4×M16C2×D511yescharacteristic
228C2×C4×C8—51no—
229#335—51no—
230#335—51no—
231#335—51no—
232#335—51no—
233#335—51no—
234#335—51no—
235#335—51no—
236#335—51no—
237#335C2×D511yescharacteristic
238#335C2×D511yescharacteristic
239#334—51no—
240#334—51no—
241#334—51no—
242#334—51no—
243#334C2×D511yescharacteristic
244#334C2×D511yescharacteristic
245C23×C5C2×C4⋊C411yescharacteristic
246C22×D5C2×C4⋊C411yescharacteristic
247C22×D5C2×C4⋊C411yescharacteristic
248C2×C4×C5—22no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—41no—
252C2×C4×C5C2×C4⋊C411yescharacteristic
253C2×C4×C5C2×C4⋊C411yescharacteristic
254C2×C4×C5C2×C4⋊C411yescharacteristic
255C2×C4×C5C23×C411yescharacteristic
256C2×C4×C5C22×D411yescharacteristic
257C2×C4×C5C22×Q811yescharacteristic
258C22⋊D5—41no—
259C22⋊D5—41no—
260C2×Dic5C2×C4⋊C411yescharacteristic
261C2×Dic5C2×C4⋊C411yescharacteristic
262C2×Dic5C2×C4⋊C411yescharacteristic
263C2×Dic5C2×C4⋊C411yescharacteristic
264C2×Dic5C2×C4⋊C411yescharacteristic
265C2×Dic5C2×C4⋊C411yescharacteristic
266D20—41no—
267C4×D5—22no—
268C4×D5—22no—
269C4×D5—21no—
270C4×D5—21no—
271C4×D5—21no—
272C4×D5—21no—
273C4×D5—41no—
274C4×D5—41no—
275Dic10—41no—
276C5×C8—22no—
277C5×C8—22no—
278C5×C8—41no—
279C5×C8—41no—
280C5×C8—41no—
281C5×C8—41no—
282#168—22no—
283#168—22no—
284#168—41no—
285#168—41no—
286#168—41no—
287#168—41no—
288C2×#41—51no—
289C2×M16—21no—
290C2×M16—101no—
291C2×M16—101no—
292C2×M16—101no—
293C2×M16C4×D512yes—
294C22×C8—52no—
295C22×C8—101no—
296C22×C8—101no—
297C4×Q8—51no—
298C4×Q8—51no—
299C4×D4—51no—
300C4×D4—51no—
301C4×D4—51no—
302C4×D4—51no—
303C4×D4—51no—
304C4×D4—51no—
305#117—51no—
306#117—51no—
307#117—51no—
308C2×C42—51no—
309C2×C42—51no—
310C2×C42C22×D511yescharacteristic
311C4⋊C8—21no—
312C4⋊C8—52no—
313C4⋊C8—52no—
314C4⋊C8—52no—
315C4⋊C8—52no—
316C4⋊C8—51no—
317C4⋊C8—51no—
318C4⋊C8—51no—
319C4⋊C8—51no—
320C4⋊C8—101no—
321C4⋊C8—101no—
322C4⋊C8—101no—
323C4⋊C8—101no—
324C4⋊C8—101no—
325C4⋊C8C22×D511yescharacteristic
326C4⋊C8C22×D511yescharacteristic
327C4⋊C8C22×D511yescharacteristic
328C4⋊C8C22×D511yescharacteristic
329C22⋊C8—21no—
330C22⋊C8—52no—
331C22⋊C8—52no—
332C22⋊C8—52no—
333C22⋊C8—52no—
334C22⋊C8—101no—
335C22⋊C8—101no—
336C22⋊C8—101no—
337C22⋊C8—101no—
338C22⋊C8—101no—
339#97—21no—
340#97—101no—
341#97—101no—
342#97—101no—
343#97C4×D512yes—
344C4×C8—52no—
345C4×C8—51no—
346C4×C8—51no—
347C4×C8—101no—
348C4×C8—101no—
349C4×C8C22×D511yescharacteristic
350C4×C8C22×D511yescharacteristic
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5C22×C4⋊C411yescharacteristic
355C2×D5—21no—
356C2×D5—21no—
357C2×D5—21no—
358C2×D5—21no—
359C2×D5—21no—
360C2×D5—21no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—21no—
364C4×C5—21no—
365C4×C5#56812yes—
366C4×C5#57611yescharacteristic
367C4×C5#57811yescharacteristic
368Dic5—21no—
369Dic5—21no—
370Dic5—21no—
371Dic5—21no—
372Dic5—21no—
373Dic5—21no—
374#41—202no—
375C2×Q8—51no—
376C2×D4—51no—
377C2×D4—51no—
378C2×D4—51no—
379C22×C4—51no—
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—51no—
383C22×C4—51no—
384C22×C4—51no—
385C22×C4C2×C4×D511yescharacteristic
386C22×C4D4×D511yescharacteristic
387C22×C4Q8×D511yescharacteristic
388M16—42no—
389M16—81no—
390M16—401no—
391M16—401no—
392M16—401no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—52no—
398C2×C8—52no—
399C2×C8—101no—
400C2×C8—101no—
401C2×C8—101no—
402C2×C8—101no—
403C2×C8—202no—
404C2×C8—401no—
405C2×C8—401no—
406C2×C8C2×C4×D512yes—
407C2×C8C2×C4×D512yes—
408C4⋊C4—51no—
409C4⋊C4—51no—
410C4⋊C4—51no—
411C4⋊C4—51no—
412C4⋊C4—51no—
413C4⋊C4—51no—
414C22⋊C4—51no—
415C22⋊C4—51no—
416C22⋊C4—51no—
417C22⋊C4—51no—
418C22⋊C4—51no—
419C22⋊C4—51no—
420C42—51no—
421C42—51no—
422C42—51no—
423C42—51no—
424C42—51no—
425C42—51no—
426C42C2×C4×D511yescharacteristic
427C42D4×D511yescharacteristic
428C42Q8×D511yescharacteristic
429C42C23×D511yescharacteristic
430C2×C5—41no—
431C2×C5#290511yescharacteristic
432C2×C5#291311yescharacteristic
433C2×C5#291611yescharacteristic
434D5—41no—
435D5—41no—
436C23—51no—
437C23—51no—
438C23D5×C4⋊C411yescharacteristic
439Q8—201no—
440D4—201no—
441D4—201no—
442D4—201no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—51no—
448C2×C4—51no—
449C2×C4—51no—
450C2×C4—51no—
451C2×C4—51no—
452C2×C4—51no—
453C2×C4—102no—
454C2×C4—102no—
455C2×C4—101no—
456C2×C4—101no—
457C2×C4—101no—
458C2×C4—101no—
459C2×C4—201no—
460C2×C4—201no—
461C2×C4D5×C4⋊C411yescharacteristic
462C2×C4D5×C4⋊C411yescharacteristic
463C2×C4D5×C4⋊C411yescharacteristic
464C2×C4C22×C4×D511yescharacteristic
465C2×C4C2×D4×D511yescharacteristic
466C2×C4C2×Q8×D511yescharacteristic
467C8—22no—
468C8—22no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—102no—
474C8—102no—
475C8—201no—
476C8—201no—
477C8—201no—
478C8—201no—
479C5#1782511yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—21no—
483C22—101no—
484C22—101no—
485C22—101no—
486C22—101no—
487C22—101no—
488C22—101no—
489C22C2×D5×C4⋊C411yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—101no—
495C4—101no—
496C4—101no—
497C4—101no—
498C4—101no—
499C4—101no—
500C4#6607912yes—
501C4#6610811yescharacteristic
502C4#6611311yescharacteristic
503C2—41no—
504C2—201no—
505C2—201no—
506C2#1061077911yescharacteristic
507C2#1061094111yescharacteristic
508C2#1061099111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1569C2
socleC22×C5C22×C4⋊C4
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenter#1569D5
hypocenterC5#17825
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. C5×#1569C2semidirect
5. #10601587C2semidirect
6. #10601284C2semidirect
7. #10600644C2semidirect
8. #10599368C2semidirect
9. #10599367C2semidirect
10. #10599365C2semidirect
11. #10599365C2semidirect
12. #10599328C2semidirect
13. #10599327C2semidirect
14. #10599326C2semidirect
15. #10599326C2semidirect
139. #1569D5semidirect
479. C5#17825semidirect

Maximal subgroups

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

subgroupindex
#106110702
#106107812
#106102502
C5×#15692
#106015872
#106012842
#106006442
#105993682
#105993672
#105993652
#105993282
#105993272
#105993262
#178255