Finite Group Databasebeta

← #12158162

Subgroups — #12158162

Order 1280.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2441C211yesmaximal, characteristic
2C2×#65354C211yesmaximal, characteristic, complemented
3C2×#65284C211yesmaximal, characteristic
4#10605224C211yesmaximal, characteristic
5#10602532C211yesmaximal, characteristic, complemented
6#10602369C211yesmaximal, characteristic
7#10600413C211yesmaximal, characteristic, complemented
8#10600412C211yesmaximal, characteristic, complemented
9#10600400C211yesmaximal, characteristic, complemented
10#10600398C211yesmaximal, characteristic, complemented
11#10600369C211yesmaximal, 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×#4024—21no—
21C2×#4015C2211yescharacteristic
22C5×#399—21no—
23C5×#396—21no—
24C5×#389—21no—
25C5×#389C2211yescharacteristic
26C5×#389C2211yescharacteristic
27C5×#387—21no—
28C5×#384C2211yescharacteristic
29C5×#380C2211yescharacteristic
30C4×C5×C22⋊C4C2211yescharacteristic
31#65501C2211yescharacteristic
32C2×C22⋊#168C2211yescharacteristic
33#65354—24no—
34#65284—24no—
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40C2×#3940C2211yescharacteristic
41C2×#3939C2211yescharacteristic
42C2×#3939C2211yescharacteristic
43C2×#3939C2211yescharacteristic
44C2×#3939C2211yescharacteristic
45#65239—21no—
46#65224C2211yescharacteristic
47#65217C2211yescharacteristic
48#65217C2211yescharacteristic
49C2×#3935C2211yescharacteristic
50C2×C4×#168C2211yescharacteristic
51#64950—21no—
52#64945—21no—
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64744C2211yescharacteristic
60#64744C2211yescharacteristic
61#26078—51nomaximal, Sylow
62C23×C4×C5C2311yescharacteristic
63C23×Dic5—21no—
64C22×Dic10—21no—
65C5×#125—22no—
66C5×#125—41no—
67C5×#117—22no—
68C5×#117—41no—
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⋊C4—21no—
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4D411yescharacteristic
82C2×C5×C22⋊C4D411yescharacteristic
83C2×C42×C5—21no—
84C2×C42×C5C2311yescharacteristic
85C2×C42×C5C2311yescharacteristic
86C2×C22⋊Dic5—21no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5—21no—
91C2×C4⋊Dic5—21no—
92C2×C4⋊Dic5—41no—
93C2×C4⋊Dic5C2311yescharacteristic
94C2×C4⋊Dic5C2311yescharacteristic
95C2×C4⋊Dic5C2311yescharacteristic
96C2×C4⋊Dic5C2311yescharacteristic
97C2×#683—21no—
98C2×#683—21no—
99C2×#681—22no—
100C2×#681—22no—
101C2×#681Q814yescomplemented
102C22×#168C2311yescharacteristic
103C22×#168C2311yescharacteristic
104C22×#168C2311yescharacteristic
105C22×#168C2311yescharacteristic
106#4024—44no—
107#4015—22no—
108#4015—41no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95—21no—
112C5×#95D411yescharacteristic
113C5×#95D411yescharacteristic
114#3963—21no—
115#3963—21no—
116#3963—21no—
117C22⋊#168Q814yescomplemented
118#3940—22no—
119#3940—22no—
120#3940—22no—
121#3940—22no—
122#3940—41no—
123#3940—41no—
124#3939—22no—
125#3939—22no—
126#3939—22no—
127#3939D414yes—
128#3935—22no—
129C4×#168—22no—
130C2×#501—51no—
131C2×#428—51no—
132#2441D511yescharacteristic
133#2440—51no—
134#2084—51no—
135#2083—51no—
136#2059—51no—
137#2058—51no—
138#1943—51no—
139#1942—51no—
140#1854—51no—
141#1853—51no—
142#1844—51no—
143#1809—51no—
144#1753—51no—
145C24×C5C2×D411yescharacteristic
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×C5—21no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×Q812yes—
160C22×C4×C5C2×Q812yes—
161C22×C4×C5C2411yescharacteristic
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—42no—
167C22×Dic5—42no—
168C22×Dic5—81no—
169C2×Dic10—42no—
170C2×Dic10—42no—
171C2×Dic10—81no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—42no—
180C5×C4⋊C4—42no—
181C5×C4⋊C4—42no—
182C5×C4⋊C4—42no—
183C5×C4⋊C4—81no—
184C5×C4⋊C4—81no—
185C5×C4⋊C4C2×D412yes—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—42no—
189C5×C22⋊C4—81no—
190C42×C5—21no—
191C42×C5—21no—
192C42×C5—21no—
193C42×C5—21no—
194C42×C5—42no—
195C22⋊Dic5—42no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—42no—
204C4⋊Dic5—42no—
205C4⋊Dic5—42no—
206C4⋊Dic5—81no—
207C4⋊Dic5C2×D412yes—
208#683—42no—
209#683—42no—
210#681—28no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168C2×D412yes—
218C2×#168C2×Q812yes—
219C2×#168C2×Q812yes—
220C2×#168C2×Q812yes—
221C2×#168C2×Q812yes—
222C2×#168#4112yes—
223C22×M16—51no—
224C2×C4⋊Q8—51no—
225C2×#125C2×D511yescharacteristic
226C2×C22⋊Q8—101no—
227C2×#117C2×D511yescharacteristic
228C22×C4⋊C4—51no—
229#501—104no—
230#428—104no—
231C2×#107—51no—
232C2×#107—51no—
233C2×#107—51no—
234C2×#107—51no—
235C2×#106—51no—
236C2×#106—51no—
237C2×#106—51no—
238C2×#106—51no—
239C2×#106—51no—
240C2×#106—51no—
241C2×C22⋊C8—51no—
242C2×#97—51no—
243C2×C4×C8—51no—
244#399—21no—
245#398—101no—
246#396—21no—
247#395—101no—
248#389—21no—
249#389—51no—
250#389—51no—
251#389C2×D511yescharacteristic
252#389C2×D511yescharacteristic
253#387—21no—
254#385—101no—
255#384—51no—
256#384C2×D511yescharacteristic
257#380—51no—
258#380C2×D511yescharacteristic
259C4×C22⋊C4C2×D511yescharacteristic
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264#340—51no—
265#340—51no—
266#336—51no—
267#336—51no—
268C23×C5—21no—
269C23×C5—21no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5C4⋊Q812yes—
275C23×C5C22×D411yescharacteristic
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—22no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
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×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5C4⋊Q812yes—
305C2×C4×C5AGL(1,ℤ/8)12yes—
306C2×C4×C5#13712yes—
307C2×C4×C5C22×D411yescharacteristic
308C2×C4×C5C22×Q811yescharacteristic
309C2×C4×C5C22×Q811yescharacteristic
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5H(5,𝔽2)11yescharacteristic
312C2×C4×C52−1+411yescharacteristic
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5—84no—
326Dic10—84no—
327#168—22no—
328#168—22no—
329#168—22no—
330#168C22⋊Q814yescomplemented
331C22×Q8—101no—
332C23×C4—101no—
333C23×C4C22×D511yescharacteristic
334C2×M16—54no—
335C2×M16—102no—
336C2×M16—102no—
337C22×C8—51no—
338C22×C8—51no—
339C22×C8—51no—
340C22×C8—51no—
341C4⋊Q8—102no—
342C4⋊Q8—201no—
343#125—22no—
344#125—41no—
345C22⋊Q8—204no—
346#117—22no—
347#117—41no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—51no—
358C2×C4⋊C4—102no—
359C2×C4⋊C4—101no—
360C2×C4⋊C4—101no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4—101no—
365C2×C4⋊C4—201no—
366C2×C4⋊C4C22×D511yescharacteristic
367C2×C4⋊C4C22×D511yescharacteristic
368C2×C4⋊C4C22×D511yescharacteristic
369C2×C4⋊C4C22×D511yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—101no—
373C2×C22⋊C4C22⋊D511yescharacteristic
374C2×C22⋊C4C22⋊D511yescharacteristic
375C2×C42—21no—
376C2×C42C22×D511yescharacteristic
377C2×C42C22×D511yescharacteristic
378#107—54no—
379#107—102no—
380#107—102no—
381#107—102no—
382#106—102no—
383#106—102no—
384#106—102no—
385#106—102no—
386#106—201no—
387#106—201no—
388C22⋊C8—54no—
389#97—102no—
390C4×C8—102no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—101no—
395#95—101no—
396#95—101no—
397#95C22⋊D511yescharacteristic
398#95C22⋊D511yescharacteristic
399C22×C5—22no—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5C2×C4⋊Q811yescharacteristic
407C22×C5D4211yescharacteristic
408C22×C5#54711yescharacteristic
409C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C5C2×#13711yescharacteristic
411C22×C5#57711yescharacteristic
412C22×C5#57711yescharacteristic
413C4×C5—22no—
414C4×C5—22no—
415C4×C5—22no—
416C4×C5—41no—
417C4×C5—42no—
418C4×C5—41no—
419C4×C5—81no—
420C4×C5—81no—
421C4×C5—81no—
422C4×C5C2×C22⋊Q811yescharacteristic
423C4×C5#54411yescharacteristic
424C4×C5D4×Q811yescharacteristic
425C4×C5#55411yescharacteristic
426Dic5—42no—
427Dic5—81no—
428Dic5—81no—
429Dic5—81no—
430C24C2×C22⋊D511yescharacteristic
431C2×Q8—202no—
432C2×Q8—202no—
433C2×Q8—401no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—202no—
447C22×C4—202no—
448C22×C4—401no—
449C22×C4Q8×D512yes—
450C22×C4Q8×D512yes—
451C22×C4C2×C22⋊D511yescharacteristic
452C22×C4C2×C22⋊D511yescharacteristic
453C22×C4C2×C22⋊D511yescharacteristic
454C22×C4C2×C22⋊D511yescharacteristic
455C22×C4C2×C22⋊D511yescharacteristic
456C22×C4C23×D511yescharacteristic
457M16—108no—
458C2×C8—52no—
459C2×C8—52no—
460C2×C8—52no—
461C2×C8—52no—
462C2×C8—52no—
463C2×C8—52no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—52no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—101no—
485C4⋊C4—101no—
486C4⋊C4—101no—
487C4⋊C4—101no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—202no—
492C4⋊C4—202no—
493C4⋊C4—202no—
494C4⋊C4—202no—
495C4⋊C4—202no—
496C4⋊C4—401no—
497C4⋊C4D4×D512yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—42no—
501C22⋊C4—81no—
502C22⋊C4—202no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C2×C5—42no—
509C2×C5#244011yescharacteristic
510C2×C5#316311yescharacteristic
511C2×C5#316511yescharacteristic
512C2×C5#327211yescharacteristic
513C2×C5#327811yescharacteristic
514C2×C5#334411yescharacteristic
515C2×C5#334511yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23#409012yes—
523C23C22×C22⋊D511yescharacteristic
524Q8—404no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—102no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—201no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—201no—
562C2×C4—201no—
563C2×C4—201no—
564C2×C4—201no—
565C2×C4—404no—
566C2×C4#409012yes—
567C2×C4#409512yes—
568C2×C4#409712yes—
569C2×C4C2×D4×D511yescharacteristic
570C2×C4#414411yescharacteristic
571C2×C4C2×Q8×D511yescharacteristic
572C2×C4C2×Q8×D511yescharacteristic
573C2×C4D5×#4111yescharacteristic
574C2×C4#415011yescharacteristic
575C8—54no—
576C8—102no—
577C8—102no—
578C8—102no—
579C5#2607811yescharacteristic, complemented, Sylow
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22D4×C22⋊D511yescharacteristic
588C22C2×#409011yescharacteristic
589C22C2×#409511yescharacteristic
590C22C2×#409711yescharacteristic
591C22#6615811yescharacteristic
592C22#6617011yescharacteristic
593C22#6617111yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—202no—
604C4—401no—
605C4—401no—
606C4—401no—
607C4#6595711yescharacteristic
608C4D5×C22⋊Q811yescharacteristic
609C4#6596611yescharacteristic
610C4#6597011yescharacteristic
611C2—42no—
612C2#1061449411yescharacteristic
613C2#1061507211yescharacteristic
614C2#1061520311yescharacteristic
615C2#1061525411yescharacteristic
616C2#1061531511yescharacteristic
617C2#1061532411yescharacteristic
618C2#1061533911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2441C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenter#2441D5
hypocenterC5#26078
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×#65354C2semidirect
5. #10602532C2semidirect
7. #10600413C2semidirect
8. #10600412C2semidirect
9. #10600400C2semidirect
10. #10600398C2semidirect
11. #10600369C2semidirect
12. #10600363C2semidirect
101. C2×#681Q8semidirect
117. C22⋊#168Q8semidirect
330. #168C22⋊Q8semidirect
579. C5#26078semidirect

Maximal subgroups

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

subgroupindex
C5×#24412
C2×#653542
C2×#652842
#106052242
#106025322
#106023692
#106004132
#106004122
#106004002
#106003982
#106003692
#106003632
#106003062
#106002982
#106002412
#260785