Finite Group Databasebeta

← #12065743

Subgroups — #12065743

Order 1280.

1214 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D5C211yesmaximal, characteristic
2#10611013C211yesmaximal, characteristic
3#10610769C211yesmaximal, characteristic
4C5×#1487C211yesmaximal, characteristic, complemented
5#10602415C211yesmaximal, characteristic, complemented
6#10601563C211yesmaximal, characteristic, complemented
7#10601293C211yesmaximal, characteristic, complemented
8#10599032C214yesmaximal, complemented
9#10599024C214yesmaximal, complemented
10C22×Q8×D5C411yescharacteristic
11C2×C4×C5×Q8C2211yescharacteristic
12C2×Q8×Dic5C411yescharacteristic
13C4×Q8×D5—21no—
14C4×Q8×D5—21no—
15C4×Q8×D5—21no—
16C4×Q8×D5—21no—
17C4×Q8×D5C412yes—
18C4×Q8×D5C412yes—
19C4×Q8×D5C2212yes—
20C4×Q8×D5C2212yes—
21C2×D5×C4⋊C4—21no—
22C2×D5×C4⋊C4C411yescharacteristic
23C2×#4033—21no—
24C2×#4033C411yescharacteristic
25C2×C42×D5—21no—
26C2×C42×D5C2211yescharacteristic
27C2×C4×Dic10—21no—
28C2×C4×Dic10C2211yescharacteristic
29C5×#431C2211yescharacteristic
30C5×#423C2211yescharacteristic
31#65415—21no—
32M16×Dic5—21no—
33#65214C2211yescharacteristic
34#65213C2211yescharacteristic
35#65126—21no—
36#65124—21no—
37#65124—21no—
38#65124C2212yes—
39#65122—21no—
40#65122C2212yes—
41#65015—21no—
42#65008—21no—
43C4×#676C2212yes—
44#64974C2212yes—
45C5×Q8⋊C8C2214yescomplemented
46Q8⋊#168C2214yescomplemented
47#64704C2214yescomplemented
48#64676C2214yescomplemented
49#17449—51nomaximal, Sylow
50C22×C5×Q8C2×C411yescharacteristic
51C2×Q8×D5—28no—
52C2×Q8×D5—21no—
53C2×Q8×D5—21no—
54C2×Q8×D5C2×C412yes—
55C2×Q8×D5C2×C412yes—
56C22×C4×D5—21no—
57C22×C4×D5—21no—
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5D411yescharacteristic
60C22×C4×D5D411yescharacteristic
61C22×Dic10—21no—
62C22×Dic10C2×C411yescharacteristic
63C2×C5×M16—21no—
64C4×C5×Q8—21no—
65C4×C5×Q8—21no—
66C4×C5×Q8C2×C412yes—
67C4×C5×Q8C2312yes—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4C2×C411yescharacteristic
70C2×C42×C5—21no—
71C2×C42×C5C2311yescharacteristic
72Q8×Dic5—21no—
73Q8×Dic5—21no—
74Q8×Dic5C2×C412yes—
75Q8×Dic5C2×C412yes—
76C2×C4⋊Dic5—21no—
77C2×C4⋊Dic5C2×C411yescharacteristic
78C2×#683—21no—
79C2×#683—21no—
80C2×#683—21no—
81C2×C4×Dic5—21no—
82C2×C4×Dic5—21no—
83C2×C4×Dic5—21no—
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5D411yescharacteristic
86C2×C4×Dic5D411yescharacteristic
87C2×#681—21no—
88C2×#676—22no—
89D5×C4⋊C4—22no—
90D5×C4⋊C4—22no—
91D5×C4⋊C4—21no—
92D5×C4⋊C4—21no—
93D5×C4⋊C4—22no—
94D5×C4⋊C4—22no—
95D5×C4⋊C4C2×C412yes—
96D5×C4⋊C4C2×C412yes—
97#4033—22no—
98#4033—22no—
99#4033—21no—
100#4033—21no—
101#4033—22no—
102#4033—22no—
103#4033C2×C412yes—
104#4033C2×C412yes—
105C42×D5—22no—
106C42×D5—22no—
107C42×D5—22no—
108C42×D5—22no—
109C42×D5C2×C411yescharacteristic
110C42×D5C2×C411yescharacteristic
111C42×D5D411yescharacteristic
112C42×D5D411yescharacteristic
113C42×D5D411yescharacteristic
114C42×D5D411yescharacteristic
115C42×D5C2311yescharacteristic
116C42×D5C2311yescharacteristic
117C4×Dic10—21no—
118C4×Dic10—21no—
119C4×Dic10—22no—
120C4×Dic10—22no—
121C4×Dic10—22no—
122C4×Dic10—22no—
123C4×Dic10C2×C412yes—
124C4×Dic10C2312yes—
125C5×C4⋊C8—21no—
126C5×C4⋊C8—21no—
127C5×C4⋊C8C2312yes—
128C5×C22⋊C8—21no—
129C4×C5×C8C2312yes—
130C22⋊#168—21no—
131#3952—22no—
132#3952—22no—
133#3952—22no—
134#3947—22no—
135#3947—22no—
136#3946—22no—
137C8×Dic5—22no—
138C4⋊#168—21no—
139C4⋊#168—21no—
140C4⋊#168C2312yes—
141C4×#168C2312yes—
142C22×C4×Q8—51no—
143#2920—51no—
144#2920—51no—
145#1491—54no—
146#1487—51no—
147#1487—51no—
148#1487—51no—
149#1487D511yescharacteristic, complemented
150#1479—54no—
151C23×D5C22⋊C411yescharacteristic
152C2×C5×Q8—24no—
153C2×C5×Q8—21no—
154C2×C5×Q8C22×C412yes—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5C22×C411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5C22⋊C411yescharacteristic
163C22×Dic5C22⋊C411yescharacteristic
164C22×Dic5C22⋊C411yescharacteristic
165Q8×D5—28no—
166Q8×D5—28no—
167Q8×D5—24no—
168Q8×D5—24no—
169Q8×D5—24no—
170Q8×D5M1618yescomplemented
171C2×C4×D5—28no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—22no—
175C2×C4×D5—22no—
176C2×C4×D5—24no—
177C2×C4×D5—22no—
178C2×C4×D5—22no—
179C2×C4×D5—42no—
180C2×C4×D5—44no—
181C2×C4×D5C22⋊C411yescharacteristic
182C2×C4×D5C22⋊C411yescharacteristic
183C2×C4×D5C22⋊C411yescharacteristic
184C2×C4×D5C22⋊C411yescharacteristic
185C2×C4×D5C22⋊C411yescharacteristic
186C2×C4×D5C22⋊C411yescharacteristic
187C2×C4×D5C22×C411yescharacteristic
188C2×C4×D5C22×C411yescharacteristic
189C2×C4×D5C2×D411yescharacteristic
190C2×C4×D5C2×D411yescharacteristic
191C2×C4×D5C2×D411yescharacteristic
192C2×C4×D5C2×D411yescharacteristic
193C2×Dic10—28no—
194C2×Dic10—21no—
195C2×Dic10—22no—
196C2×Dic10—22no—
197C2×Dic10—24no—
198C2×Dic10C22×C412yes—
199C5×M16—42no—
200C2×C5×C8—22no—
201C2×C5×C8—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4C22×C412yes—
206C42×C5—22no—
207C42×C5—22no—
208C42×C5C22×C411yescharacteristic
209C42×C5C2×D411yescharacteristic
210C42×C5C2×D411yescharacteristic
211C42×C5C2411yescharacteristic
212C4⋊Dic5—21no—
213C4⋊Dic5—22no—
214C4⋊Dic5—22no—
215C4⋊Dic5C22×C412yes—
216#683—22no—
217#683—22no—
218#683—22no—
219#683—22no—
220#683—22no—
221#683—22no—
222C4×Dic5—22no—
223C4×Dic5—22no—
224C4×Dic5—22no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C4×Dic5—22no—
228C4×Dic5C22⋊C411yescharacteristic
229C4×Dic5C22⋊C411yescharacteristic
230C4×Dic5C22⋊C411yescharacteristic
231C4×Dic5C22⋊C411yescharacteristic
232C4×Dic5C22⋊C411yescharacteristic
233C4×Dic5C22⋊C411yescharacteristic
234C4×Dic5C22×C411yescharacteristic
235C4×Dic5C22×C411yescharacteristic
236C4×Dic5C2×D411yescharacteristic
237C4×Dic5C2×D411yescharacteristic
238C4×Dic5C2×D411yescharacteristic
239C4×Dic5C2×D411yescharacteristic
240#681—42no—
241C2×#168—22no—
242C2×#168—22no—
243#676—44no—
244C23×Q8—51no—
245C2×C4×Q8—51no—
246C2×C4×Q8—52no—
247C2×C4×Q8—52no—
248C2×C4×Q8—52no—
249C2×C4×Q8—52no—
250C2×C4×Q8—51no—
251C2×C4×Q8—51no—
252C2×C4×Q8—101no—
253C2×C4×Q8—101no—
254C2×C4×Q8—101no—
255C2×C4×Q8—101no—
256C2×C4×Q8—101no—
257C2×C4×Q8—101no—
258C2×C4×Q8C2×D511yescharacteristic
259C22×C4⋊C4—51no—
260C22×C4⋊C4—101no—
261C22×C42—51no—
262C22×C42—101no—
263#432—52no—
264#432—101no—
265#432—101no—
266#432—101no—
267#431—51no—
268#431—52no—
269#431—52no—
270#431—101no—
271#431C2×D511yescharacteristic
272#423—51no—
273#423—101no—
274#423C2×D511yescharacteristic
275#407—101no—
276#407—101no—
277C4×M16—52no—
278C4×M16—101no—
279Q8⋊C8—54no—
280Q8⋊C8—54no—
281Q8⋊C8—54no—
282Q8⋊C8C2×D514yescomplemented
283C23×C5C2×C22⋊C411yescharacteristic
284C22×D5—22no—
285C22×D5—22no—
286C22×D5—22no—
287C22×D5C2×C22⋊C411yescharacteristic
288C22×D5C2×C22⋊C411yescharacteristic
289C5×Q8—24no—
290C5×Q8—22no—
291C5×Q8C2×M1614yes—
292C2×C4×C5—24no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—41no—
297C2×C4×C5—42no—
298C2×C4×C5C2×C22⋊C411yescharacteristic
299C2×C4×C5C2×C22⋊C411yescharacteristic
300C2×C4×C5C2×C22⋊C411yescharacteristic
301C2×C4×C5#13712yes—
302C2×C4×C5#13712yes—
303C2×C4×C5C23×C411yescharacteristic
304C2×C4×C5C22×D411yescharacteristic
305C2×C4×C5C22×D411yescharacteristic
306C2×Dic5—24no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—41no—
312C2×Dic5—42no—
313C2×Dic5C2×C22⋊C411yescharacteristic
314C2×Dic5C2×C22⋊C411yescharacteristic
315C2×Dic5C2×C22⋊C411yescharacteristic
316C2×Dic5C2×C22⋊C411yescharacteristic
317C2×Dic5C2×C22⋊C411yescharacteristic
318C2×Dic5C2×C22⋊C411yescharacteristic
319C4×D5—28no—
320C4×D5—28no—
321C4×D5—22no—
322C4×D5—22no—
323C4×D5—22no—
324C4×D5—22no—
325C4×D5—21no—
326C4×D5—21no—
327C4×D5—21no—
328C4×D5—21no—
329C4×D5—22no—
330C4×D5—22no—
331C4×D5—22no—
332C4×D5—41no—
333C4×D5—41no—
334C4×D5—44no—
335C4×D5—44no—
336C4×D5C2×M1614yes—
337Dic10—28no—
338Dic10—24no—
339Dic10—22no—
340Dic10—28no—
341Dic10C2×M1614yes—
342C5×C8—42no—
343C5×C8—42no—
344#168—42no—
345#168—42no—
346C22×Q8—52no—
347C22×Q8—52no—
348C22×Q8—51no—
349C22×Q8—101no—
350C22×Q8—101no—
351C22×Q8—101no—
352C22×Q8—108no—
353C22×Q8C4×D511yescharacteristic
354C23×C4—51no—
355C23×C4—51no—
356C23×C4—51no—
357C23×C4—101no—
358C23×C4—101no—
359C2×M16—21no—
360C2×M16—102no—
361C2×M16—101no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—52no—
365C4×Q8—52no—
366C4×Q8—52no—
367C4×Q8—52no—
368C4×Q8—52no—
369C4×Q8—52no—
370C4×Q8—102no—
371C4×Q8—102no—
372C4×Q8—102no—
373C4×Q8—102no—
374C4×Q8—102no—
375C4×Q8—102no—
376C4×Q8—102no—
377C4×Q8—102no—
378C4×Q8—101no—
379C4×Q8—101no—
380C4×Q8—101no—
381C4×Q8—101no—
382C4×Q8—101no—
383C4×Q8—101no—
384C4×Q8C4×D512yes—
385C4×Q8C22×D512yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—51no—
388C2×C4⋊C4—52no—
389C2×C4⋊C4—52no—
390C2×C4⋊C4—101no—
391C2×C4⋊C4—101no—
392C2×C4⋊C4—102no—
393C2×C4⋊C4—102no—
394C2×C4⋊C4—102no—
395C2×C4⋊C4—102no—
396C2×C4⋊C4—101no—
397C2×C4⋊C4—101no—
398C2×C4⋊C4—101no—
399C2×C4⋊C4—101no—
400C2×C4⋊C4C4×D511yescharacteristic
401C2×C42—21no—
402C2×C42—51no—
403C2×C42—51no—
404C2×C42—51no—
405C2×C42—51no—
406C2×C42—51no—
407C2×C42—51no—
408C2×C42—51no—
409C2×C42—51no—
410C2×C42—51no—
411C2×C42—51no—
412C2×C42—51no—
413C2×C42—102no—
414C2×C42—102no—
415C2×C42—102no—
416C2×C42—102no—
417C2×C42—101no—
418C2×C42—101no—
419C2×C42—101no—
420C2×C42C22×D511yescharacteristic
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—52no—
424C4⋊C8—102no—
425C4⋊C8—101no—
426C4⋊C8—101no—
427C4⋊C8C22×D512yes—
428C22⋊C8—21no—
429C22⋊C8—102no—
430C22⋊C8—102no—
431C22⋊C8—102no—
432C22⋊C8—101no—
433#97—102no—
434#97—102no—
435C4×C8—52no—
436C4×C8—102no—
437C4×C8C22×D512yes—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5#41912yes—
441C22×C5C22×C22⋊C411yescharacteristic
442C2×D5—28no—
443C2×D5—21no—
444C2×D5—21no—
445C2×D5—21no—
446C2×D5—21no—
447C2×D5#40712yes—
448C2×D5#42112yes—
449C4×C5—24no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—21no—
453C4×C5—42no—
454C4×C5#41912yes—
455C4×C5C22×M1612yes—
456C4×C5C2×#13711yescharacteristic
457C4×C5C2×#13711yescharacteristic
458Dic5—21no—
459Dic5—24no—
460Dic5—21no—
461Dic5—21no—
462Dic5—21no—
463Dic5—21no—
464Dic5—42no—
465Dic5#40712yes—
466C24—51no—
467C2×Q8—24no—
468C2×Q8—21no—
469C2×Q8—58no—
470C2×Q8—52no—
471C2×Q8—102no—
472C2×Q8—102no—
473C2×Q8—104no—
474C2×Q8—108no—
475C2×Q8—104no—
476C2×Q8—104no—
477C2×Q8—108no—
478C2×Q8—108no—
479C2×Q8—104no—
480C2×Q8—101no—
481C2×Q8C2×C4×D512yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—51no—
485C22×C4—51no—
486C22×C4—51no—
487C22×C4—51no—
488C22×C4—51no—
489C22×C4—51no—
490C22×C4—51no—
491C22×C4—51no—
492C22×C4—51no—
493C22×C4—51no—
494C22×C4—51no—
495C22×C4—51no—
496C22×C4—51no—
497C22×C4—51no—
498C22×C4—51no—
499C22×C4—104no—
500C22×C4—102no—
501C22×C4—102no—
502C22×C4—108no—
503C22×C4—102no—
504C22×C4—102no—
505C22×C4—101no—
506C22×C4—102no—
507C22×C4—102no—
508C22×C4—101no—
509C22×C4—202no—
510C22×C4—204no—
511C22×C4C2×C4×D511yescharacteristic
512C22×C4D4×D511yescharacteristic
513C22×C4D4×D511yescharacteristic
514M16—42no—
515M16—204no—
516M16—202no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—102no—
520C2×C8—102no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—52no—
525C4⋊C4—102no—
526C4⋊C4—102no—
527C4⋊C4—102no—
528C4⋊C4—102no—
529C4⋊C4—102no—
530C4⋊C4—102no—
531C4⋊C4—102no—
532C4⋊C4—101no—
533C4⋊C4—102no—
534C4⋊C4C2×C4×D512yes—
535C42—22no—
536C42—22no—
537C42—51no—
538C42—51no—
539C42—51no—
540C42—51no—
541C42—51no—
542C42—51no—
543C42—51no—
544C42—51no—
545C42—51no—
546C42—51no—
547C42—51no—
548C42—51no—
549C42—102no—
550C42—102no—
551C42—102no—
552C42—102no—
553C42—102no—
554C42—102no—
555C42C2×C4×D511yescharacteristic
556C42D4×D511yescharacteristic
557C42D4×D511yescharacteristic
558C42C23×D511yescharacteristic
559C2×C5—22no—
560C2×C5C2×#40711yescharacteristic
561C2×C5C2×#41911yescharacteristic
562C2×C5C2×#42111yescharacteristic
563D5—22no—
564D5—22no—
565C23—51no—
566C23—51no—
567C23—102no—
568C23—102no—
569C23—102no—
570C23D5×C22⋊C411yescharacteristic
571Q8—24no—
572Q8—22no—
573Q8—54no—
574Q8—108no—
575Q8—108no—
576Q8—104no—
577Q8—102no—
578Q8D5×M1614yes—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—51no—
586C2×C4—54no—
587C2×C4—51no—
588C2×C4—51no—
589C2×C4—51no—
590C2×C4—51no—
591C2×C4—51no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—102no—
596C2×C4—108no—
597C2×C4—108no—
598C2×C4—102no—
599C2×C4—104no—
600C2×C4—102no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—101no—
604C2×C4—101no—
605C2×C4—101no—
606C2×C4—101no—
607C2×C4—102no—
608C2×C4—102no—
609C2×C4—102no—
610C2×C4—201no—
611C2×C4—201no—
612C2×C4—204no—
613C2×C4—204no—
614C2×C4—201no—
615C2×C4—202no—
616C2×C4D5×C22⋊C411yescharacteristic
617C2×C4D5×C22⋊C411yescharacteristic
618C2×C4D5×C22⋊C411yescharacteristic
619C2×C4#406112yes—
620C2×C4#406412yes—
621C2×C4C22×C4×D511yescharacteristic
622C2×C4C2×D4×D511yescharacteristic
623C2×C4C2×D4×D511yescharacteristic
624C8—42no—
625C8—42no—
626C8—202no—
627C8—202no—
628C5#1744911yescharacteristic, complemented, Sylow
629C22—21no—
630C22—21no—
631C22—52no—
632C22—52no—
633C22—108no—
634C22—101no—
635C22—101no—
636C22—101no—
637C22—101no—
638C22#6509112yes—
639C22C2×D5×C22⋊C411yescharacteristic
640C4—21no—
641C4—21no—
642C4—24no—
643C4—21no—
644C4—42no—
645C4—52no—
646C4—101no—
647C4—101no—
648C4—101no—
649C4—101no—
650C4—101no—
651C4—104no—
652C4—202no—
653C4#6509112yes—
654C4C2×D5×M1612yes—
655C4C2×#406111yescharacteristic
656C4C2×#406411yescharacteristic
657C2—22no—
658C2—102no—
659C2—102no—
660C2D5×#40711yescharacteristic
661C2C2×#6509111yescharacteristic
662C2D5×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1487C2
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC42×C5C24
hypercenter#1487D5
hypocenterC5#17449
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. C5×#1487C2semidirect
5. #10602415C2semidirect
6. #10601563C2semidirect
7. #10601293C2semidirect
8. #10599032C2semidirect
9. #10599024C2semidirect
45. C5×Q8⋊C8C22semidirect
46. Q8⋊#168C22semidirect
47. #64704C22semidirect
48. #64676C22semidirect
149. #1487D5semidirect
170. Q8×D5M16semidirect
282. Q8⋊C8C2×D5semidirect
628. C5#17449semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D52
#106110132
#106107692
C5×#14872
#106024152
#106015632
#106012932
#105990322
#105990242
#174495