Finite Group Databasebeta

← #12158117

Subgroups — #12158117

Order 1280.

774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2441C211yesmaximal, characteristic
2C2×#65353C211yesmaximal, characteristic, complemented
3C2×#65284C211yesmaximal, characteristic
4#10605226C211yesmaximal, characteristic
5#10602532C211yesmaximal, characteristic, complemented
6#10602369C211yesmaximal, characteristic
7#10600413C211yesmaximal, characteristic, complemented
8#10600411C211yesmaximal, characteristic, complemented
9#10600402C211yesmaximal, characteristic, complemented
10#10600399C211yesmaximal, characteristic, complemented
11#10600371C211yesmaximal, characteristic, complemented
12#10600363C211yesmaximal, characteristic, complemented
13#10600306C211yesmaximal, characteristic
14#10600298C211yesmaximal, characteristic
15#10600241C211yesmaximal, characteristic
16C2×C5×#125C2211yescharacteristic
17C2×C5×#117C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×#681C2211yescharacteristic
20C2×#4016C2211yescharacteristic
21C5×#399—21no—
22C5×#396—21no—
23C5×#389—21no—
24C5×#389C2211yescharacteristic
25C5×#389C2211yescharacteristic
26C5×#387—21no—
27C5×#384C2211yescharacteristic
28C5×#380C2211yescharacteristic
29C4×C5×C22⋊C4C2211yescharacteristic
30#65501C2211yescharacteristic
31C2×C22⋊#168C2211yescharacteristic
32#65353—24no—
33#65284—24no—
34C2×#3940C2211yescharacteristic
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C2×#3939C2211yescharacteristic
42C2×#3939C2211yescharacteristic
43C2×#3939C2211yescharacteristic
44#65235—21no—
45#65231—21no—
46#65225C2211yescharacteristic
47#65217C2211yescharacteristic
48#65217C2211yescharacteristic
49C2×#3935C2211yescharacteristic
50C2×C4×#168C2211yescharacteristic
51#64949—21no—
52#64946—21no—
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64744C2211yescharacteristic
60#64744C2211yescharacteristic
61#26075—51nomaximal, Sylow
62C23×C4×C5C2311yescharacteristic
63C23×Dic5—21no—
64C5×#125—22no—
65C5×#125—41no—
66C5×#117—22no—
67C5×#117—41no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4D411yescharacteristic
81C2×C5×C22⋊C4D411yescharacteristic
82C2×C42×C5—21no—
83C2×C42×C5C2311yescharacteristic
84C2×C42×C5C2311yescharacteristic
85C2×C22⋊Dic5—21no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5—41no—
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96C2×#683—21no—
97C2×#681—22no—
98C2×#681—22no—
99C2×#681Q814yes—
100C22×#168C2311yescharacteristic
101C22×#168C2311yescharacteristic
102C22×#168C2311yescharacteristic
103C22×#168C2311yescharacteristic
104#4016—22no—
105#4016—41no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95D411yescharacteristic
110C5×#95D411yescharacteristic
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116C22⋊#168Q814yes—
117#3940—22no—
118#3940—22no—
119#3940—22no—
120#3940—22no—
121#3940—22no—
122#3940—41no—
123#3939—22no—
124#3939—22no—
125#3939—41no—
126#3939D414yes—
127#3935—22no—
128C4×#168—22no—
129C2×#499—51no—
130C2×#428—51no—
131#2442—51no—
132#2441D511yescharacteristic
133#2085—51no—
134#2084—51no—
135#2059—51no—
136#2059—51no—
137#1943—51no—
138#1941—51no—
139#1854—51no—
140#1853—51no—
141#1847—51no—
142#1809—51no—
143#1753—51no—
144C24×C5C2×D411yescharacteristic
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×Q812yes—
159C22×C4×C5C2×Q812yes—
160C22×C4×C5C2411yescharacteristic
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—42no—
166C22×Dic5—42no—
167C22×Dic5—81no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—42no—
176C5×C4⋊C4—42no—
177C5×C4⋊C4—42no—
178C5×C4⋊C4—42no—
179C5×C4⋊C4—81no—
180C5×C4⋊C4—81no—
181C5×C4⋊C4C2×D412yes—
182C5×C22⋊C4—41no—
183C5×C22⋊C4—41no—
184C5×C22⋊C4—42no—
185C5×C22⋊C4—81no—
186C42×C5—21no—
187C42×C5—21no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5—42no—
191C22⋊Dic5—42no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—42no—
200C4⋊Dic5C2×D412yes—
201#683—42no—
202#683—42no—
203#683—81no—
204#683—81no—
205#681—28no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168C2×D412yes—
213C2×#168C2×Q812yes—
214C2×#168C2×Q812yes—
215C2×#168C2×Q812yes—
216C2×#168C2×Q812yes—
217C2×#168#4112yes—
218C22×M16—51no—
219C2×#125—51no—
220C2×#125C2×D511yescharacteristic
221C2×#117C2×D511yescharacteristic
222C22×C4⋊C4—51no—
223#499—104no—
224#428—104no—
225C2×#107—51no—
226C2×#107—51no—
227C2×#107—51no—
228C2×#107—51no—
229C2×#106—51no—
230C2×#106—51no—
231C2×#106—51no—
232C2×#106—51no—
233C2×#106—51no—
234C2×#106—51no—
235C2×C22⋊C8—51no—
236C2×#97—51no—
237C2×C4×C8—51no—
238#400—101no—
239#399—21no—
240#398—101no—
241#396—21no—
242#389—21no—
243#389—51no—
244#389—51no—
245#389C2×D511yescharacteristic
246#389C2×D511yescharacteristic
247#387—21no—
248#385—101no—
249#384C2×D511yescharacteristic
250#382—51no—
251#380—51no—
252#380—101no—
253#380C2×D511yescharacteristic
254C4×C22⋊C4C2×D511yescharacteristic
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#340—51no—
261#336—51no—
262#336—51no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5C4⋊Q812yes—
270C23×C5C22×D411yescharacteristic
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
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—21no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5C4⋊Q812yes—
302C2×C4×C5C22×D411yescharacteristic
303C2×C4×C5C22×Q811yescharacteristic
304C2×C4×C5C22×Q811yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×C4×C5H(5,𝔽2)11yescharacteristic
307C2×C4×C52−1+411yescharacteristic
308C2×Dic5—22no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—84no—
321#168—22no—
322#168—22no—
323#168—22no—
324#168C22⋊Q814yes—
325C23×C4—101no—
326C23×C4C22×D511yescharacteristic
327C2×M16—54no—
328C2×M16—102no—
329C2×M16—102no—
330C22×C8—51no—
331C22×C8—51no—
332C22×C8—51no—
333C22×C8—51no—
334#125—22no—
335#125—41no—
336#125—102no—
337#125—201no—
338#117—22no—
339#117—41no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—102no—
351C2×C4⋊C4—101no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4—101no—
356C2×C4⋊C4—201no—
357C2×C4⋊C4C22×D511yescharacteristic
358C2×C4⋊C4C22×D511yescharacteristic
359C2×C4⋊C4C22×D511yescharacteristic
360C2×C4⋊C4C22×D511yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—101no—
364C2×C22⋊C4C22⋊D511yescharacteristic
365C2×C22⋊C4C22⋊D511yescharacteristic
366C2×C42—21no—
367C2×C42C22×D511yescharacteristic
368C2×C42C22×D511yescharacteristic
369#107—54no—
370#107—102no—
371#107—102no—
372#107—201no—
373#106—102no—
374#106—102no—
375#106—102no—
376#106—102no—
377#106—102no—
378#106—201no—
379C22⋊C8—54no—
380#97—102no—
381C4×C8—102no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—101no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390#95C22⋊D511yescharacteristic
391#95C22⋊D511yescharacteristic
392C22×C5—22no—
393C22×C5—22no—
394C22×C5—22no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5C2×C4⋊Q811yescharacteristic
400C22×C5D4211yescharacteristic
401C22×C5#54711yescharacteristic
402C22×C5#57511yescharacteristic
403C22×C5#57511yescharacteristic
404C22×C5#57711yescharacteristic
405C22×C5#57711yescharacteristic
406C4×C5—22no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5—42no—
411C4×C5—41no—
412C4×C5—81no—
413C4×C5—81no—
414C4×C5—81no—
415C4×C5C2×C22⋊Q811yescharacteristic
416C4×C5#54411yescharacteristic
417C4×C5D4×Q811yescharacteristic
418C4×C5#55411yescharacteristic
419Dic5—42no—
420Dic5—81no—
421Dic5—81no—
422Dic5—81no—
423C24C2×C22⋊D511yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—202no—
437C22×C4—202no—
438C22×C4—401no—
439C22×C4Q8×D512yes—
440C22×C4Q8×D512yes—
441C22×C4C2×C22⋊D511yescharacteristic
442C22×C4C2×C22⋊D511yescharacteristic
443C22×C4C2×C22⋊D511yescharacteristic
444C22×C4C2×C22⋊D511yescharacteristic
445C22×C4C2×C22⋊D511yescharacteristic
446C22×C4C23×D511yescharacteristic
447M16—108no—
448C2×C8—52no—
449C2×C8—52no—
450C2×C8—52no—
451C2×C8—52no—
452C2×C8—52no—
453C2×C8—52no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—52no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—101no—
480C4⋊C4—101no—
481C4⋊C4—202no—
482C4⋊C4—202no—
483C4⋊C4—202no—
484C4⋊C4—401no—
485C4⋊C4—401no—
486C4⋊C4D4×D512yes—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—42no—
490C22⋊C4—81no—
491C22⋊C4—202no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C2×C5—42no—
498C2×C5#244011yescharacteristic
499C2×C5#316311yescharacteristic
500C2×C5#316611yescharacteristic
501C2×C5#326711yescharacteristic
502C2×C5#327111yescharacteristic
503C2×C5#335111yescharacteristic
504C2×C5#335111yescharacteristic
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23#409012yes—
512C23C22×C22⋊D511yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—102no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—404no—
556C2×C4#409012yes—
557C2×C4C2×D4×D511yescharacteristic
558C2×C4#414411yescharacteristic
559C2×C4C2×Q8×D511yescharacteristic
560C2×C4C2×Q8×D511yescharacteristic
561C2×C4D5×#4111yescharacteristic
562C2×C4#415011yescharacteristic
563C8—54no—
564C8—102no—
565C8—102no—
566C8—102no—
567C5#2607511yescharacteristic, complemented, Sylow
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22D4×C22⋊D511yescharacteristic
576C22C2×#409011yescharacteristic
577C22#6615611yescharacteristic
578C22#6615611yescharacteristic
579C22#6615811yescharacteristic
580C22#6617011yescharacteristic
581C22#6617111yescharacteristic
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—202no—
592C4—401no—
593C4—401no—
594C4—401no—
595C4#6595711yescharacteristic
596C4D5×C22⋊Q811yescharacteristic
597C4#6596611yescharacteristic
598C4#6597011yescharacteristic
599C2—42no—
600C2#1061449411yescharacteristic
601C2#1061507311yescharacteristic
602C2#1061520311yescharacteristic
603C2#1061525311yescharacteristic
604C2#1061531411yescharacteristic
605C2#1061532711yescharacteristic
606C2#1061534311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2441C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenter#2441D5
hypocenterC5#26075
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
2. C2×#65353C2semidirect
5. #10602532C2semidirect
7. #10600413C2semidirect
8. #10600411C2semidirect
9. #10600402C2semidirect
10. #10600399C2semidirect
11. #10600371C2semidirect
12. #10600363C2semidirect
567. C5#26075semidirect

Maximal subgroups

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

subgroupindex
C5×#24412
C2×#653532
C2×#652842
#106052262
#106025322
#106023692
#106004132
#106004112
#106004022
#106003992
#106003712
#106003632
#106003062
#106002982
#106002412
#260755