Finite Group Databasebeta

← #13032470

Subgroups — #13032470

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#704C211yesmaximal, characteristic
2#10617263C211yesmaximal, characteristic
3#10611903C211yesmaximal, characteristic
4C2×Q8⋊#170C211yesmaximal, characteristic
5#10604842C211yesmaximal, characteristic, complemented
6#10604840C211yesmaximal, characteristic, complemented
7#10604840C211yesmaximal, characteristic, complemented
8#10604838C211yesmaximal, characteristic, complemented
9#10604513C211yesmaximal, characteristic
10#10603982C211yesmaximal, characteristic, complemented
11#10603977C211yesmaximal, characteristic, complemented
12#10603976C211yesmaximal, characteristic, complemented
13#10603970C211yesmaximal, characteristic, complemented
14#10603897C211yesmaximal, characteristic
15#10603893C211yesmaximal, characteristic
16C2×Q8×Dic5C2211yescharacteristic
17#65956C2211yescharacteristic
18#65788—21no—
19#65788—21no—
20#65788C2211yescharacteristic
21#65788C2211yescharacteristic
22#65788C2211yescharacteristic
23Q8×#170C2211yescharacteristic
24Q8×#170C2211yescharacteristic
25Q8×#170C2211yescharacteristic
26#65758—21no—
27#65758C2211yescharacteristic
28C4×#704—21no—
29C4×#704C2211yescharacteristic
30C2×C4⋊#170C2211yescharacteristic
31C2×C4×#170C2211yescharacteristic
32#65709—21no—
33#65709C2211yescharacteristic
34#65707—21no—
35#65703C2211yescharacteristic
36#65696—21no—
37#65691—21no—
38C5×#451C411yescharacteristic
39#65517C411yescharacteristic
40Q16×Dic5C2211yescharacteristic
41Q16×Dic5C2211yescharacteristic
42#65471C411yescharacteristic
43#65471C411yescharacteristic
44#65333C411yescharacteristic
45#65083C411yescharacteristic
46#65083C411yescharacteristic
47#65079C2211yescharacteristic
48#65079C2211yescharacteristic
49#65011C411yescharacteristic
50#65007C2211yescharacteristic
51Q8⋊#170C2211yescharacteristic
52Q8⋊#170C2211yescharacteristic
53Q8⋊#170C2211yescharacteristic
54Q8⋊#170C2211yescharacteristic
55Q8⋊#170C2211yescharacteristic
56Q8⋊#170C2211yescharacteristic
57#64883C2211yescharacteristic
58#64883C2211yescharacteristic
59#64881C2211yescharacteristic
60#64881C2211yescharacteristic
61#170⋊C8C2211yescharacteristic
62#170⋊C8C2211yescharacteristic
63#64879C2211yescharacteristic
64#64879C2211yescharacteristic
65#64872C2211yescharacteristic
66#64872C2211yescharacteristic
67#18003—51nomaximal, Sylow
68C22×C5×Q8C2×C411yescharacteristic
69C2×#704—21no—
70C2×#704D411yescharacteristic
71C2×#704D411yescharacteristic
72C22×#170—21no—
73C22×#170—21no—
74C2×C5×Q16C2×C411yescharacteristic
75C2×C5×Q16C2×C411yescharacteristic
76C5×C22⋊Q8C2×C411yescharacteristic
77Q8×Dic5—21no—
78Q8×Dic5—21no—
79Q8×Dic5C2×C411yescharacteristic
80Q8×Dic5C2×C411yescharacteristic
81Q8×Dic5C2311yescharacteristic
82Q8×Dic5C2311yescharacteristic
83Q8×Dic5C2311yescharacteristic
84#4090C2×C411yescharacteristic
85C2×#689C2×C411yescharacteristic
86C2×#689C2×C411yescharacteristic
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5C2×C411yescharacteristic
89#4070C2×C411yescharacteristic
90C2×C4×Dic5—21no—
91C2×C4×Dic5C2311yescharacteristic
92#4035—21no—
93#4034C2×C411yescharacteristic
94#4033—21no—
95#4033C2311yescharacteristic
96#4024—21no—
97#4023—21no—
98#4004—21no—
99#4004—21no—
100#4004—21no—
101#4004—21no—
102#4004—21no—
103#4002—21no—
104#4002—21no—
105#4002—21no—
106#4002—21no—
107#4002D411yescharacteristic
108#4002D411yescharacteristic
109C4⋊#170—21no—
110C4⋊#170—21no—
111C4⋊#170—21no—
112C4⋊#170—21no—
113C4⋊#170—21no—
114C4⋊#170C2311yescharacteristic
115C4⋊#170C2311yescharacteristic
116C4⋊#170C2311yescharacteristic
117C4⋊#170C2311yescharacteristic
118C4×#170—21no—
119C4×#170—21no—
120C4×#170—21no—
121C4×#170—21no—
122C4×#170—21no—
123C4×#170C2311yescharacteristic
124C4×#170C2311yescharacteristic
125C4×#170C2311yescharacteristic
126C4×#170C2311yescharacteristic
127C5×#103C2×C411yescharacteristic
128C5×#103C2×C411yescharacteristic
129C5×C22⋊C8C2×C411yescharacteristic
130#3967C2×C411yescharacteristic
131#3967C2×C411yescharacteristic
132#3967C2×C411yescharacteristic
133#3967C2×C411yescharacteristic
134C22⋊#168C2×C411yescharacteristic
135#3950C2×C411yescharacteristic
136#3950C2×C411yescharacteristic
137#3948C2×C411yescharacteristic
138#3948C2×C411yescharacteristic
139#3946C2×C411yescharacteristic
140#3946C2×C411yescharacteristic
141C8×Dic5C2311yescharacteristic
142C8×Dic5C2311yescharacteristic
143#3939C2×C411yescharacteristic
144#3939C2×C411yescharacteristic
145#3104—51no—
146Q8×M16—51no—
147#2962—51no—
148#1593—51no—
149#1593—51no—
150#1587—51no—
151#1587—51no—
152#1587—51no—
153#1587—51no—
154#1579—51no—
155#1579—51no—
156#1570—51no—
157#1493—51no—
158C2×Q8⋊C8—51no—
159#1451—51no—
160C2×C5×Q8—21no—
161C2×C5×Q8—22no—
162C2×C5×Q8—41no—
163C2×C5×Q8C22×C411yescharacteristic
164C2×C5×Q8C22×C411yescharacteristic
165C2×C5×Q8C22×C411yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5C22×C411yescharacteristic
168C22×Dic5—21no—
169C22×Dic5C2×D411yescharacteristic
170C22×Dic5#4111yescharacteristic
171C2×Dic10—21no—
172C2×Dic10C22×C411yescharacteristic
173#704—22no—
174#704—22no—
175#704—42no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—42no—
183C2×#170—42no—
184C2×#170C2×D411yescharacteristic
185C2×#170C2×D411yescharacteristic
186C2×#170C2×D411yescharacteristic
187C2×#170C2×D411yescharacteristic
188C5×Q16—22no—
189C5×Q16—41no—
190C2×C5×C8C22×C411yescharacteristic
191C2×C5×C8C22×C411yescharacteristic
192C5×C4⋊C4—21no—
193C5×C4⋊C4C22×C411yescharacteristic
194C5×C22⋊C4—21no—
195C22⋊Dic5—21no—
196#689—22no—
197#689—41no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5C22×C411yescharacteristic
205C4⋊Dic5C22×C411yescharacteristic
206C4⋊Dic5C22×C411yescharacteristic
207#683—21no—
208#683—21no—
209#683—21no—
210#683—21no—
211#683—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—21no—
217C4×Dic5—21no—
218C4×Dic5C22×C411yescharacteristic
219C4×Dic5C2×D411yescharacteristic
220C4×Dic5#4111yescharacteristic
221C4×Dic5C2411yescharacteristic
222C2×#168C22×C411yescharacteristic
223C2×#168C22×C411yescharacteristic
224#533—51no—
225C2×C4×Q8—51no—
226#484—51no—
227#484—51no—
228#477—51no—
229#477—51no—
230#462—51no—
231#462—51no—
232#451—51no—
233#451AGL(1,𝔽5)11yescharacteristic
234#446—51no—
235#446—51no—
236#446—51no—
237#446—51no—
238#446—101no—
239#446—101no—
240#446—101no—
241#446—101no—
242C8×Q8—51no—
243C8×Q8—51no—
244C8×Q8—51no—
245C8×Q8—51no—
246C4×Q16—51no—
247C4×Q16—51no—
248C4×Q16—51no—
249C4×Q16—51no—
250#431—51no—
251#424—101no—
252#423—51no—
253#423—101no—
254C2×C4⋊C8—51no—
255#405—101no—
256C4×M16—51no—
257C4×M16—101no—
258C2×C4×C8—51no—
259#334—51no—
260#334—51no—
261#334—51no—
262#334—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269Q8⋊C8—51no—
270Q8⋊C8—51no—
271#322—51no—
272#322—51no—
273#322—51no—
274#322—51no—
275C23×C5C4×D411yescharacteristic
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8—42no—
282C5×Q8#13112yes—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—42no—
290C2×C4×C5C4×D411yescharacteristic
291C2×C4×C5C23×C411yescharacteristic
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—41no—
297C2×Dic5—81no—
298C2×Dic5C4×D411yescharacteristic
299C2×Dic5C4×D411yescharacteristic
300C2×Dic5#13712yes—
301C2×Dic5#13712yes—
302C2×Dic5C22×D411yescharacteristic
303C2×Dic5C2×#4111yescharacteristic
304Dic10—21no—
305Dic10—21no—
306Dic10—81no—
307#170—22no—
308#170—21no—
309#170—21no—
310#170—21no—
311#170—21no—
312#170—41no—
313#170—41no—
314#170—41no—
315#170—41no—
316#170—41no—
317C5×C8—21no—
318C5×C8—21no—
319#168—21no—
320#168—21no—
321C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
322C2×Q16—51no—
323C2×Q16—51no—
324C2×Q16C2×AGL(1,𝔽5)11yescharacteristic
325C2×Q16C2×AGL(1,𝔽5)11yescharacteristic
326C2×M16—51no—
327C2×M16—51no—
328C2×M16—101no—
329C22×C8—101no—
330C22×C8—101no—
331C4⋊Q8—51no—
332C4⋊Q8—51no—
333#125—101no—
334C22⋊Q8—51no—
335C22⋊Q8—101no—
336C22⋊Q8C2×AGL(1,𝔽5)11yescharacteristic
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8—51no—
343C4×Q8—101no—
344C4×Q8—101no—
345C4×Q8—101no—
346#117—101no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—101no—
349C2×C42—51no—
350C2×C42—101no—
351#107—51no—
352#107—51no—
353#107—51no—
354#107—51no—
355C4⋊C8—51no—
356C4⋊C8—51no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8—101no—
370C4⋊C8—101no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#103—51no—
377#103C2×AGL(1,𝔽5)11yescharacteristic
378#103C2×AGL(1,𝔽5)11yescharacteristic
379C22⋊C8—51no—
380C22⋊C8C2×AGL(1,𝔽5)11yescharacteristic
381#97—51no—
382#97—51no—
383#97—101no—
384#97—101no—
385#97—101no—
386#97—101no—
387C4×C8—51no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C4×C8—101no—
398C22×C5—21no—
399C22×C5—21no—
400C22×C5#44112yes—
401C22×C5C2×C4×D411yescharacteristic
402C4×C5—21no—
403C4×C5—22no—
404C4×C5—41no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5C2×#13111yescharacteristic
408C4×C5#56811yescharacteristic
409Dic5—21no—
410Dic5—21no—
411Dic5—41no—
412Dic5—41no—
413Dic5—41no—
414Dic5—41no—
415Dic5#44112yes—
416Dic5C2×#13711yescharacteristic
417Dic5C2×#13711yescharacteristic
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8—51no—
422C2×Q8—101no—
423C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
424C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
425C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
426C22×C4—21no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—101no—
430C22×C4C22×AGL(1,𝔽5)11yescharacteristic
431Q16—22no—
432Q16—41no—
433Q16—102no—
434Q16—201no—
435M16—102no—
436M16—102no—
437M16—202no—
438C2×C8—51no—
439C2×C8—51no—
440C2×C8—51no—
441C2×C8—51no—
442C2×C8—51no—
443C2×C8—51no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—202no—
451C2×C8—202no—
452C2×C8C22×AGL(1,𝔽5)11yescharacteristic
453C2×C8C22×AGL(1,𝔽5)11yescharacteristic
454C4⋊C4—21no—
455C4⋊C4—51no—
456C4⋊C4—51no—
457C4⋊C4—51no—
458C4⋊C4—101no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—101no—
472C42—51no—
473C42—51no—
474C42—51no—
475C42—51no—
476C42—101no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42—101no—
482C2×C5—22no—
483C2×C5#293311yescharacteristic
484C2×C5C2×#44111yescharacteristic
485C2×C5#295611yescharacteristic
486C23D4×AGL(1,𝔽5)11yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—42no—
493Q8—101no—
494Q8—101no—
495Q8—401no—
496Q8#413112yes—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—42no—
504C2×C4—52no—
505C2×C4—52no—
506C2×C4—51no—
507C2×C4—51no—
508C2×C4—51no—
509C2×C4—51no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—201no—
515C2×C4—401no—
516C2×C4D4×AGL(1,𝔽5)11yescharacteristic
517C2×C4C23×AGL(1,𝔽5)11yescharacteristic
518C8—21no—
519C8—21no—
520C8—101no—
521C8—101no—
522C8—101no—
523C8—101no—
524C8—102no—
525C8—101no—
526C8—101no—
527C8—201no—
528C8—201no—
529C8—201no—
530C8—201no—
531C8—201no—
532C5#1800311yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22#6573912yes—
536C22C2×D4×AGL(1,𝔽5)11yescharacteristic
537C4—21no—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—51no—
543C4—51no—
544C4—52no—
545C4—101no—
546C4—101no—
547C4—201no—
548C4—201no—
549C4—201no—
550C4—201no—
551C4C2×#413111yescharacteristic
552C4#6625611yescharacteristic
553C2—22no—
554C2#1061721711yescharacteristic
555C2C2×#6573911yescharacteristic
556C2#1061745311yescharacteristic
subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#451C4
socleC22×C5C2×C4×D4
prime radicalC23×C5C4×D4
cosocleC4×Dic5C24
hypercenter#451AGL(1,𝔽5)
hypocenterC5#18003
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #10604842C2semidirect
6. #10604840C2semidirect
7. #10604840C2semidirect
8. #10604838C2semidirect
10. #10603982C2semidirect
11. #10603977C2semidirect
12. #10603976C2semidirect
13. #10603970C2semidirect
532. C5#18003semidirect

Maximal subgroups

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

subgroupindex
Q8×#7042
#106172632
#106119032
C2×Q8⋊#1702
#106048422
#106048402
#106048382
#106045132
#106039822
#106039772
#106039762
#106039702
#106038972
#106038932
#180035