Finite Group Databasebeta

← #12108853

Subgroups — #12108853

Order 1280.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65853C211yesmaximal, characteristic
2C2×C5×#433C211yesmaximal, characteristic
3#10613962C211yesmaximal, characteristic
4#10601254C211yesmaximal, characteristic, complemented
5#10601254C211yesmaximal, characteristic, complemented
6#10601253C211yesmaximal, characteristic, complemented
7#10601252C211yesmaximal, characteristic, complemented
8#10600719C211yesmaximal, characteristic
9#10600719C211yesmaximal, characteristic
10#10600718C211yesmaximal, characteristic
11#10600717C211yesmaximal, characteristic
12#10600621C211yesmaximal, characteristic, complemented
13#10600620C211yesmaximal, characteristic, complemented
14#10600571C211yesmaximal, characteristic, complemented
15#10600570C211yesmaximal, characteristic, complemented
16C2×C5×#117C2211yescharacteristic
17C2×#4072C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19#65853—24no—
20#65853C418yescomplemented
21C2×#4036—21no—
22C2×#4034—21no—
23C2×#4024—21no—
24C2×#4024—21no—
25C2×#4016C2211yescharacteristic
26C2×#4016C2211yescharacteristic
27C2×#4015C2211yescharacteristic
28C2×#4015C2211yescharacteristic
29C5×#433—24no—
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C2×C5×#97C2211yescharacteristic
35C2×C4×C5×C8C2211yescharacteristic
36#65501C2211yescharacteristic
37#65501C2211yescharacteristic
38#65270—21no—
39#65270—21no—
40#65240—21no—
41#65240—21no—
42#65225C2211yescharacteristic
43#65224C2211yescharacteristic
44C4×C4⋊Dic5C2211yescharacteristic
45C4×C4⋊Dic5C2211yescharacteristic
46#64771C2211yescharacteristic
47#64771C2211yescharacteristic
48#64771C2211yescharacteristic
49#64771C2211yescharacteristic
50#64771C2211yescharacteristic
51#64771C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64771C2211yescharacteristic
59#64771C2211yescharacteristic
60#64771C2211yescharacteristic
61#64771C2211yescharacteristic
62#21843—51nomaximal, Sylow
63C23×C4×C5C2311yescharacteristic
64C23×Dic5—21no—
65C22×Dic10—21no—
66C22×Dic10—21no—
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C5×#117C2×C414yes—
72C5×#117D414yes—
73C2×C5×C4⋊C4D411yescharacteristic
74C2×C5×C4⋊C4D411yescharacteristic
75C2×C5×C22⋊C4D411yescharacteristic
76C2×C5×C22⋊C4D411yescharacteristic
77C2×C42×C5C2311yescharacteristic
78C2×C42×C5C2311yescharacteristic
79C2×C22⋊Dic5—21no—
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—21no—
82#4072—22no—
83#4072C2×C414yes—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5C2×C414yes—
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2311yescharacteristic
94C2×C4⋊Dic5C2311yescharacteristic
95C2×C4⋊Dic5C2311yescharacteristic
96C2×C4⋊Dic5C2311yescharacteristic
97C2×C4⋊Dic5C2311yescharacteristic
98C2×C4⋊Dic5C2311yescharacteristic
99C2×#683—21no—
100C2×#683—21no—
101C2×#683—21no—
102C2×#683—21no—
103C2×C4×Dic5—21no—
104C2×C4×Dic5—21no—
105C2×C4×Dic5—21no—
106#4036—28no—
107#4034—28no—
108#4024—28no—
109#4024—28no—
110#4016—22no—
111#4016—22no—
112#4016C2×C414yes—
113#4016C2×C414yes—
114#4015—22no—
115#4015—22no—
116#4015C2×C414yes—
117#4015C2×C414yes—
118C5×C4⋊C8—22no—
119C5×C4⋊C8—22no—
120C5×C22⋊C8—22no—
121C5×C22⋊C8—22no—
122C5×#97—22no—
123C4×C5×C8—22no—
124#3963—21no—
125#3963—21no—
126#3963—21no—
127#3963—21no—
128#3963—21no—
129#3963—21no—
130C2×#544—51no—
131C2×#433D511yescharacteristic
132#2314—51no—
133#1993—51no—
134#1992—51no—
135#1991—51no—
136#1990—51no—
137#1989—51no—
138#1989—51no—
139#1988—51no—
140#1987—51no—
141#1825—51no—
142#1825—51no—
143#1824—51no—
144#1823—51no—
145C24×C5C2×D411yescharacteristic
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2411yescharacteristic
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5—24no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—81no—
168C22×Dic5—81no—
169C2×Dic10—24no—
170C2×Dic10—24no—
171C2×Dic10—81no—
172C2×Dic10—81no—
173C2×Dic10—81no—
174C2×Dic10—81no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C5×C4⋊C4C22⋊C414yes—
188C5×C4⋊C4C22⋊C414yes—
189C5×C22⋊C4C22⋊C414yes—
190C5×C22⋊C4C22⋊C414yes—
191C42×C5C22×C412yes—
192C42×C5C22×C412yes—
193C42×C5C2×D412yes—
194C42×C5C2×D412yes—
195C22⋊Dic5—24no—
196C22⋊Dic5—81no—
197C22⋊Dic5—81no—
198C4⋊Dic5—24no—
199C4⋊Dic5—24no—
200C4⋊Dic5—24no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—21no—
205C4⋊Dic5—21no—
206C4⋊Dic5—21no—
207C4⋊Dic5—21no—
208C4⋊Dic5—21no—
209C4⋊Dic5—21no—
210C4⋊Dic5—21no—
211C4⋊Dic5—21no—
212C4⋊Dic5—21no—
213C4⋊Dic5—81no—
214C4⋊Dic5—81no—
215C4⋊Dic5C22×C412yes—
216C4⋊Dic5C22×C412yes—
217C4⋊Dic5C22×C412yes—
218C4⋊Dic5C22×C412yes—
219#683—24no—
220#683—24no—
221#683—24no—
222#683—24no—
223C4×Dic5—24no—
224C4×Dic5—81no—
225C4×Dic5—81no—
226#544—58no—
227#544—104no—
228C2×C4⋊Q8—51no—
229C2×C4⋊Q8—51no—
230C2×C4⋊Q8—101no—
231C2×#125—51no—
232C2×#125—51no—
233C2×#125—101no—
234C2×C22⋊Q8—101no—
235C2×C22⋊Q8—101no—
236C2×#117—51no—
237C2×#117C2×D511yescharacteristic
238C22×C4⋊C4—51no—
239#433—24no—
240C2×C4⋊C8C2×D511yescharacteristic
241C2×C4⋊C8C2×D511yescharacteristic
242C2×C22⋊C8C2×D511yescharacteristic
243C2×C22⋊C8C2×D511yescharacteristic
244C2×#97C2×D511yescharacteristic
245C2×C4×C8C2×D511yescharacteristic
246#388—101no—
247#388—101no—
248#387—101no—
249#387—101no—
250#384—51no—
251#382—51no—
252#380—51no—
253#380—51no—
254C4×C4⋊C4—51no—
255C4×C4⋊C4—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264#340—51no—
265#340—51no—
266#340—51no—
267#340—51no—
268#340—51no—
269#340—51no—
270#340—51no—
271#340—51no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5C2×C22⋊C412yes—
279C23×C5C22×D411yescharacteristic
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—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5C2×C22⋊C412yes—
295C2×C4×C5C2×C22⋊C412yes—
296C2×C4×C5C2×C22⋊C412yes—
297C2×C4×C5C2×C22⋊C412yes—
298C2×C4×C5C2×C22⋊C412yes—
299C2×C4×C5C23×C411yescharacteristic
300C2×C4×C5C22×D411yescharacteristic
301C2×C4×C52−1+411yescharacteristic
302C2×C4×C52−1+411yescharacteristic
303C2×C4×C52−1+411yescharacteristic
304C2×C4×C52−1+411yescharacteristic
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—22no—
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—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5—41no—
326C2×Dic5—41no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—84no—
330Dic10—84no—
331Dic10—84no—
332C5×C8—41no—
333C5×C8—41no—
334C5×C8—41no—
335C5×C8—41no—
336C22×Q8—101no—
337C22×Q8—101no—
338C23×C4—101no—
339C23×C4C22×D511yescharacteristic
340C22×C8C22×D511yescharacteristic
341C22×C8C22×D511yescharacteristic
342C22×C8C22×D511yescharacteristic
343C22×C8C22×D511yescharacteristic
344C4⋊Q8—54no—
345C4⋊Q8—54no—
346C4⋊Q8—108no—
347C4⋊Q8—102no—
348C4⋊Q8—102no—
349#125—54no—
350#125—54no—
351#125—108no—
352#125—102no—
353#125—102no—
354C22⋊Q8—108no—
355C22⋊Q8—108no—
356#117—54no—
357#117—102no—
358#117C4×D514yes—
359#117C22⋊D514yes—
360C2×C4⋊C4—54no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—51no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—101no—
370C2×C4⋊C4—101no—
371C2×C4⋊C4—101no—
372C2×C4⋊C4—101no—
373C2×C4⋊C4—101no—
374C2×C4⋊C4—101no—
375C2×C4⋊C4—101no—
376C2×C4⋊C4—102no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4D2011yescharacteristic
380C2×C4⋊C4D2011yescharacteristic
381C2×C22⋊C4—101no—
382C2×C22⋊C4—101no—
383C2×C22⋊C4—101no—
384C2×C22⋊C4D2011yescharacteristic
385C2×C22⋊C4D2011yescharacteristic
386C2×C42—101no—
387C2×C42—101no—
388C2×C42—101no—
389C2×C42C22×D511yescharacteristic
390C2×C42C22×D511yescharacteristic
391C4⋊C8—22no—
392C4⋊C8—22no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395#97—22no—
396C4×C8—22no—
397#95—101no—
398#95—101no—
399#95—101no—
400#95—101no—
401#95—101no—
402#95—101no—
403C22×C5—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—41no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5C22×C22⋊C411yescharacteristic
411C22×C5#53611yescharacteristic
412C22×C5#53611yescharacteristic
413C22×C5#57611yescharacteristic
414C22×C5#57711yescharacteristic
415C22×C5#57711yescharacteristic
416C22×C5#57811yescharacteristic
417C4×C5—22no—
418C4×C5—22no—
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—22no—
422C4×C5#51911yescharacteristic
423C4×C5#51911yescharacteristic
424C4×C5#53611yescharacteristic
425C4×C5#53611yescharacteristic
426Dic5—42no—
427Dic5—42no—
428Dic5—42no—
429Dic5—42no—
430Dic5—81no—
431Dic5—81no—
432Dic5—81no—
433Dic5—81no—
434C24C2×D2011yescharacteristic
435C2×Q8—104no—
436C2×Q8—104no—
437C2×Q8—401no—
438C2×Q8—401no—
439C2×Q8—401no—
440C2×Q8—401no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—104no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4—401no—
455C22×C4—401no—
456C22×C4C2×C4×D512yes—
457C22×C4C2×D2011yescharacteristic
458C22×C4C2×D2011yescharacteristic
459C22×C4C2×D2011yescharacteristic
460C22×C4C2×D2011yescharacteristic
461C22×C4C2×D2011yescharacteristic
462C22×C4C2×C22⋊D512yes—
463C22×C4C23×D511yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C4⋊C4—52no—
477C4⋊C4—52no—
478C4⋊C4—52no—
479C4⋊C4—52no—
480C4⋊C4—101no—
481C4⋊C4—101no—
482C4⋊C4—101no—
483C4⋊C4—101no—
484C4⋊C4—104no—
485C4⋊C4—104no—
486C4⋊C4—104no—
487C4⋊C4—104no—
488C4⋊C4—104no—
489C4⋊C4—104no—
490C4⋊C4—104no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—101no—
495C4⋊C4—101no—
496C4⋊C4—101no—
497C4⋊C4—101no—
498C4⋊C4—101no—
499C4⋊C4—401no—
500C4⋊C4—401no—
501C4⋊C4#68514yes—
502C4⋊C4#68514yes—
503C22⋊C4—104no—
504C22⋊C4—401no—
505C22⋊C4—401no—
506C22⋊C4#68514yes—
507C22⋊C4#68514yes—
508C42—104no—
509C42—401no—
510C42—401no—
511C42C2×C4×D512yes—
512C42C2×C4×D512yes—
513C42C2×C22⋊D512yes—
514C42C2×C22⋊D512yes—
515C2×C5—42no—
516C2×C5#231011yescharacteristic
517C2×C5#289711yescharacteristic
518C2×C5#289811yescharacteristic
519C2×C5#324111yescharacteristic
520C2×C5#324211yescharacteristic
521C2×C5#324311yescharacteristic
522C2×C5#324411yescharacteristic
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23C2×#68512yes—
530C23C22×D2011yescharacteristic
531Q8—404no—
532Q8—404no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
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—201no—
566C2×C4—201no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—201no—
570C2×C4—201no—
571C2×C4—404no—
572C2×C4C2×#68512yes—
573C2×C4C2×#68512yes—
574C2×C4C2×#68512yes—
575C2×C4C2×#68512yes—
576C2×C4C2×#68512yes—
577C2×C4C22×C4×D511yescharacteristic
578C2×C4#415011yescharacteristic
579C2×C4#415011yescharacteristic
580C2×C4#415011yescharacteristic
581C2×C4#415011yescharacteristic
582C2×C4C22×C22⋊D511yescharacteristic
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C5#2184311yescharacteristic, complemented, Sylow
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22#6586011yescharacteristic
596C22#6586011yescharacteristic
597C22#6608511yescharacteristic
598C22#6608511yescharacteristic
599C22#6608611yescharacteristic
600C22#6608711yescharacteristic
601C22C22×#68511yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—202no—
608C4—202no—
609C4—202no—
610C4—202no—
611C4—401no—
612C4—401no—
613C4—401no—
614C4—401no—
615C4#6585011yescharacteristic
616C4#6585011yescharacteristic
617C4#6615911yescharacteristic
618C4#6615911yescharacteristic
619C2—42no—
620C2#1061109311yescharacteristic
621C2#1061109411yescharacteristic
622C2#1061109511yescharacteristic
623C2#1061109611yescharacteristic
624C2#1061396111yescharacteristic
625C2#1061552811yescharacteristic
626C2#1061553711yescharacteristic
subgroupG/H
centerC23C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#433C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenterC2×#433D5
hypocenterC5#21843
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
4. #10601254C2semidirect
5. #10601254C2semidirect
6. #10601253C2semidirect
7. #10601252C2semidirect
12. #10600621C2semidirect
13. #10600620C2semidirect
14. #10600571C2semidirect
15. #10600570C2semidirect
20. #65853C4semidirect
587. C5#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#658532
C2×C5×#4332
#106139622
#106012542
#106012532
#106012522
#106007192
#106007182
#106007172
#106006212
#106006202
#106005712
#106005702
#218435