Finite Group Databasebeta

← #12158102

Subgroups — #12158102

Order 1280.

826 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2439C211yesmaximal, characteristic
2C2×#65367C211yesmaximal, characteristic, complemented
3C2×#65284C211yesmaximal, characteristic
4#10605224C211yesmaximal, characteristic
5#10602575C211yesmaximal, characteristic, complemented
6#10602369C211yesmaximal, characteristic
7#10600413C211yesmaximal, characteristic, complemented
8#10600411C211yesmaximal, characteristic, complemented
9#10600400C211yesmaximal, characteristic, complemented
10#10600398C211yesmaximal, characteristic, complemented
11#10600343C211yesmaximal, characteristic, complemented
12#10600334C211yesmaximal, characteristic, complemented
13#10600306C211yesmaximal, characteristic
14#10600297C211yesmaximal, characteristic
15#10600241C211yesmaximal, characteristic
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C5×#117C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×#681C2211yescharacteristic
20C2×#4024—21no—
21C2×#4015C2211yescharacteristic
22C5×#396—21no—
23C5×#393—21no—
24C5×#391—21no—
25C5×#389C2211yescharacteristic
26C5×#389C2211yescharacteristic
27C5×#387—21no—
28C5×#382C2211yescharacteristic
29C5×#380C2211yescharacteristic
30C4×C5×C22⋊C4C2211yescharacteristic
31#65501C2211yescharacteristic
32C2×C22⋊#168C2211yescharacteristic
33#65367—24no—
34#65284—24no—
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
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#26074—51nomaximal, Sylow
62C22×C5×Q8—21no—
63C23×C4×C5C2311yescharacteristic
64C23×Dic5—21no—
65C22×Dic10—21no—
66C5×C4⋊Q8—22no—
67C5×C4⋊Q8—41no—
68C5×#117—22no—
69C5×#117—41no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4D411yescharacteristic
80C2×C5×C22⋊C4D411yescharacteristic
81C2×C42×C5—21no—
82C2×C42×C5C2311yescharacteristic
83C2×C42×C5C2311yescharacteristic
84C2×C22⋊Dic5—21no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5—41no—
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2311yescharacteristic
94C2×C4⋊Dic5C2311yescharacteristic
95C2×#683—21no—
96C2×#683—21no—
97C2×#681—22no—
98C2×#681—22no—
99C2×#681Q814yescomplemented
100C22×#168C2311yescharacteristic
101C22×#168C2311yescharacteristic
102C22×#168C2311yescharacteristic
103C22×#168C2311yescharacteristic
104#4024—44no—
105#4015—22no—
106#4015—41no—
107C5×#95—21no—
108C5×#95—21no—
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—41no—
122#3939—22no—
123#3939—22no—
124#3939—22no—
125#3939—22no—
126#3939—41no—
127#3939D414yes—
128#3935—22no—
129C4×#168—22no—
130C2×#500—51no—
131C2×#428—51no—
132#2440—51no—
133#2439D511yescharacteristic
134#2085—51no—
135#2083—51no—
136#2058—51no—
137#2057—51no—
138#1943—51no—
139#1941—51no—
140#1854—51no—
141#1852—51no—
142#1847—51no—
143#1809—51no—
144#1753—51no—
145C24×C5C2×D411yescharacteristic
146C2×C5×Q8—42no—
147C2×C5×Q8—42no—
148C2×C5×Q8—81no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×Q812yes—
163C22×C4×C5C2×Q812yes—
164C22×C4×C5C2411yescharacteristic
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—42no—
170C22×Dic5—42no—
171C22×Dic5—81no—
172C2×Dic10—42no—
173C2×Dic10—42no—
174C2×Dic10—81no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—42no—
183C5×C4⋊C4—42no—
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×C4⋊Q8C2×D511yescharacteristic
226C2×C22⋊Q8—101no—
227C2×#117C2×D511yescharacteristic
228C22×C4⋊C4—51no—
229#500—104no—
230#428—104no—
231C2×#107—51no—
232C2×#107—51no—
233C2×#107—51no—
234C2×#107—51no—
235C2×#107—51no—
236C2×#107—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#398—101no—
245#396—21no—
246#395—101no—
247#393—21no—
248#391—21no—
249#389—51no—
250#389—51no—
251#389C2×D511yescharacteristic
252#389C2×D511yescharacteristic
253#387—21no—
254#385—101no—
255#384—51no—
256#382C2×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
276C5×Q8—84no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
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×C5—41no—
305C2×C4×C5C4⋊Q812yes—
306C2×C4×C5AGL(1,ℤ/8)12yes—
307C2×C4×C5#13712yes—
308C2×C4×C5C22×D411yescharacteristic
309C2×C4×C5C22×Q811yescharacteristic
310C2×C4×C5C22×Q811yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5H(5,𝔽2)11yescharacteristic
313C2×C4×C52−1+411yescharacteristic
314C2×Dic5—22no—
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—41no—
326C2×Dic5—84no—
327Dic10—84no—
328#168—22no—
329#168—22no—
330#168—22no—
331#168C22⋊Q814yescomplemented
332C22×Q8—21no—
333C22×Q8—101no—
334C23×C4—101no—
335C23×C4C22×D511yescharacteristic
336C2×M16—54no—
337C2×M16—102no—
338C2×M16—102no—
339C22×C8—51no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—51no—
343C4⋊Q8—22no—
344C4⋊Q8—41no—
345C4⋊Q8—102no—
346C4⋊Q8—201no—
347C22⋊Q8—204no—
348#117—22no—
349#117—41no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—102no—
358C2×C4⋊C4—101no—
359C2×C4⋊C4—101no—
360C2×C4⋊C4—101no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4—201no—
365C2×C4⋊C4C22×D511yescharacteristic
366C2×C4⋊C4C22×D511yescharacteristic
367C2×C4⋊C4C22×D511yescharacteristic
368C2×C4⋊C4C22×D511yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—101no—
372C2×C22⋊C4C22⋊D511yescharacteristic
373C2×C22⋊C4C22⋊D511yescharacteristic
374C2×C42—21no—
375C2×C42C22×D511yescharacteristic
376C2×C42C22×D511yescharacteristic
377#107—54no—
378#107—102no—
379#107—102no—
380#107—102no—
381#107—102no—
382#107—201no—
383#106—102no—
384#106—102no—
385#106—102no—
386#106—201no—
387C22⋊C8—54no—
388#97—102no—
389C4×C8—102no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—101no—
396#95—101no—
397#95—101no—
398#95C22⋊D511yescharacteristic
399#95C22⋊D511yescharacteristic
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5C2×C4⋊Q811yescharacteristic
408C22×C5D4211yescharacteristic
409C22×C5#54711yescharacteristic
410C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C5C2×#13711yescharacteristic
412C22×C5#57611yescharacteristic
413C22×C5#57811yescharacteristic
414C4×C5—22no—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5—42no—
420C4×C5—81no—
421C4×C5—81no—
422C4×C5—81no—
423C4×C5C2×C22⋊Q811yescharacteristic
424C4×C5#54411yescharacteristic
425C4×C5D4×Q811yescharacteristic
426C4×C5#55411yescharacteristic
427Dic5—42no—
428Dic5—81no—
429Dic5—81no—
430Dic5—81no—
431C24C2×C22⋊D511yescharacteristic
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8—202no—
436C2×Q8—202no—
437C2×Q8—401no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—202no—
451C22×C4—202no—
452C22×C4—401no—
453C22×C4Q8×D512yes—
454C22×C4Q8×D512yes—
455C22×C4C2×C22⋊D511yescharacteristic
456C22×C4C2×C22⋊D511yescharacteristic
457C22×C4C2×C22⋊D511yescharacteristic
458C22×C4C2×C22⋊D511yescharacteristic
459C22×C4C2×C22⋊D511yescharacteristic
460C22×C4C23×D511yescharacteristic
461M16—108no—
462C2×C8—52no—
463C2×C8—52no—
464C2×C8—52no—
465C2×C8—52no—
466C2×C8—52no—
467C2×C8—52no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—52no—
484C4⋊C4—81no—
485C4⋊C4—101no—
486C4⋊C4—101no—
487C4⋊C4—101no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—202no—
493C4⋊C4—202no—
494C4⋊C4—202no—
495C4⋊C4—202no—
496C4⋊C4—202no—
497C4⋊C4—401no—
498C4⋊C4D4×D512yes—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—42no—
502C22⋊C4—81no—
503C22⋊C4—202no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—42no—
509C2×C5—42no—
510C2×C5#244011yescharacteristic
511C2×C5#316411yescharacteristic
512C2×C5#316511yescharacteristic
513C2×C5#326411yescharacteristic
514C2×C5#327011yescharacteristic
515C2×C5#335311yescharacteristic
516C2×C5#335711yescharacteristic
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#409012yes—
524C23C22×C22⋊D511yescharacteristic
525Q8—84no—
526Q8—404no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
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—41no—
554C2×C4—41no—
555C2×C4—102no—
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—201no—
566C2×C4—201no—
567C2×C4—404no—
568C2×C4#409012yes—
569C2×C4#409512yes—
570C2×C4#409712yes—
571C2×C4C2×D4×D511yescharacteristic
572C2×C4#414411yescharacteristic
573C2×C4C2×Q8×D511yescharacteristic
574C2×C4C2×Q8×D511yescharacteristic
575C2×C4D5×#4111yescharacteristic
576C2×C4#415011yescharacteristic
577C8—54no—
578C8—102no—
579C8—102no—
580C8—102no—
581C5#2607411yescharacteristic, complemented, Sylow
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22D4×C22⋊D511yescharacteristic
590C22C2×#409011yescharacteristic
591C22C2×#409511yescharacteristic
592C22C2×#409711yescharacteristic
593C22#6615811yescharacteristic
594C22#6616911yescharacteristic
595C22#6617211yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—202no—
606C4—401no—
607C4—401no—
608C4—401no—
609C4#6595711yescharacteristic
610C4D5×C22⋊Q811yescharacteristic
611C4#6596611yescharacteristic
612C4#6597011yescharacteristic
613C2—42no—
614C2#1061449411yescharacteristic
615C2#1061507211yescharacteristic
616C2#1061520411yescharacteristic
617C2#1061523311yescharacteristic
618C2#1061527711yescharacteristic
619C2#1061538211yescharacteristic
620C2#1061539311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2439C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenter#2439D5
hypocenterC5#26074
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2439

Complements

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

NH ≅ G/Ntype
2. C2×#65367C2semidirect
5. #10602575C2semidirect
7. #10600413C2semidirect
8. #10600411C2semidirect
9. #10600400C2semidirect
10. #10600398C2semidirect
11. #10600343C2semidirect
12. #10600334C2semidirect
99. C2×#681Q8semidirect
117. C22⋊#168Q8semidirect
331. #168C22⋊Q8semidirect
581. C5#26074semidirect

Maximal subgroups

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

subgroupindex
C5×#24392
C2×#653672
C2×#652842
#106052242
#106025752
#106023692
#106004132
#106004112
#106004002
#106003982
#106003432
#106003342
#106003062
#106002972
#106002412
#260745