Finite Group Databasebeta

← #12021856

Subgroups — #12021856

Order 1280.

1766 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic10C211yesmaximal, characteristic
2C2×#64935C212yesmaximal
3C2×#64939C211yesmaximal, characteristic
4C2×#64938C211yesmaximal, characteristic
5C5×#1434C211yesmaximal, characteristic
6#10602327C211yesmaximal, characteristic
7#10600204C212yesmaximal
8#10600202C212yesmaximal
9#10600197C212yesmaximal
10#10600195C211yesmaximal, characteristic
11#10600195C211yesmaximal, characteristic
12C23×Dic10C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C22×#683C2212yes—
16C22×#683C2212yes—
17C22×#683C2211yescharacteristic
18C22×#683C2211yescharacteristic
19C22×C4×Dic5C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C2×C4×Dic10—24no—
23C2×C4×Dic10—24no—
24C2×C4×Dic10C418yescomplemented
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#64939—24no—
39#64938—24no—
40#64935—28no—
41#13942—51nomaximal, Sylow
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×Dic10—22no—
54C22×Dic10—22no—
55C22×Dic10—22no—
56C22×Dic10—22no—
57C22×Dic10C2×C414yes—
58C22×Dic10D414yes—
59C22×Dic10Q814yes—
60C2×C42×C5—22no—
61C2×C42×C5—22no—
62C2×C42×C5C2×C414yes—
63C2×C4⋊Dic5—22no—
64C2×C4⋊Dic5—22no—
65C2×C4⋊Dic5C2×C414yes—
66C2×#683—24no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683—22no—
70C2×#683—22no—
71C2×#683—24no—
72C2×#683—24no—
73C2×#683—24no—
74C2×#683—24no—
75C2×#683—24no—
76C2×#683C2×C414yes—
77C2×#683C2×C414yes—
78C2×C4×Dic5—22no—
79C2×C4×Dic5—22no—
80C2×C4×Dic5—24no—
81C2×C4×Dic5—24no—
82C2×C4×Dic5—24no—
83C2×C4×Dic5C2×C414yes—
84C2×C4×Dic5C2×C414yes—
85C2×C4×Dic5D414yes—
86C2×C4×Dic5D414yes—
87C4×Dic10—232no—
88C5×#95—24no—
89C5×#95—22no—
90C5×#95—22no—
91C5×#95—24no—
92#3963—24no—
93#3963—22no—
94#3963—22no—
95#3963—24no—
96#3963—24no—
97#3963—24no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101C22×C4×Q8—51no—
102C2×#391—52no—
103C2×#382—51no—
104C2×C4×C4⋊C4—51no—
105#1441—52no—
106#1441—52no—
107C4⋊#95—52no—
108#1434—51no—
109#1434—51no—
110#1434—51no—
111#1434D511yescharacteristic
112C24×C5C2411yescharacteristic
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5C22×C412yes—
137C22×C4×C5C22×C412yes—
138C22×C4×C5C22×C412yes—
139C22×C4×C5C2×D412yes—
140C22×C4×C5C2×D412yes—
141C22×C4×C5C2×D412yes—
142C22×C4×C5C2×Q812yes—
143C22×C4×C5#4114yes—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5C22×C412yes—
168C22×Dic5C22×C412yes—
169C22×Dic5C22×C412yes—
170C22×Dic5C22×C412yes—
171C22×Dic5C2×D412yes—
172C22×Dic5C2×D412yes—
173C22×Dic5C2×D412yes—
174C22×Dic5C2×D412yes—
175C22×Dic5C2×D412yes—
176C22×Dic5C2×D412yes—
177C22×Dic5C2×Q812yes—
178C22×Dic5C2×Q812yes—
179C22×Dic5#4114yes—
180C22×Dic5#4112yes—
181C22×Dic5#4112yes—
182C2×Dic10—28no—
183C2×Dic10—28no—
184C2×Dic10—28no—
185C2×Dic10—28no—
186C2×Dic10—28no—
187C2×Dic10—28no—
188C2×Dic10C4⋊C4116yescomplemented
189C42×C5—28no—
190C4⋊Dic5—28no—
191#683—216no—
192#683—28no—
193#683—28no—
194#683—48no—
195C4×Dic5—28no—
196C4×Dic5—48no—
197C4×Dic5C22⋊C4116yes—
198C23×Q8—51no—
199C2×C4×Q8—58no—
200C2×C4×Q8—104no—
201C2×C4×Q8—104no—
202C22×C4⋊C4—51no—
203C22×C4⋊C4—51no—
204C22×C4⋊C4—51no—
205C22×C4⋊C4—52no—
206C22×C4⋊C4—52no—
207C22×C42—51no—
208C22×C42—51no—
209C22×C42—52no—
210C22×C42C2×D511yescharacteristic
211#391—108no—
212#382—104no—
213C4×C4⋊C4—104no—
214C2×#95—51no—
215C2×#95—51no—
216C2×#95—52no—
217C2×#95—52no—
218C2×#95—52no—
219C2×#95—52no—
220C2×#95—52no—
221C2×#95—52no—
222C2×#95—52no—
223C2×#95C2×D511yescharacteristic
224C2×#95C2×D511yescharacteristic
225C2×#95C2×D512yes—
226C2×#95C2×D512yes—
227C23×C5C23×C411yescharacteristic
228C23×C5C22×D411yescharacteristic
229C23×C5C22×D411yescharacteristic
230C23×C5C22×D411yescharacteristic
231C23×C5C22×Q811yescharacteristic
232C23×C5C2×#4112yes—
233C23×C5C2×#4111yescharacteristic
234C23×C5C2×#4111yescharacteristic
235C23×C5C2×#4112yes—
236C23×C52−1+412yes—
237C23×C52−1+412yes—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5—24no—
247C2×C4×C5—24no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—24no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5C2×C22⋊C414yes—
268C2×C4×C5C2×C4⋊C414yes—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—24no—
278C2×Dic5—24no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—24no—
283C2×Dic5—24no—
284C2×Dic5—24no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5C2×C22⋊C414yes—
299C2×Dic5C2×C22⋊C414yes—
300C2×Dic5C2×C4⋊C414yes—
301C2×Dic5C2×C4⋊C414yes—
302C2×Dic5#11714yes—
303C2×Dic5#12114yes—
304C2×Dic5#12114yes—
305C2×Dic5C22⋊Q814yes—
306C2×Dic5C22⋊Q814yes—
307Dic10—232no—
308C22×Q8—54no—
309C22×Q8—54no—
310C22×Q8—54no—
311C22×Q8—102no—
312C22×Q8—102no—
313C22×Q8—102no—
314C22×Q8—102no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—51no—
318C23×C4—51no—
319C23×C4—52no—
320C23×C4—52no—
321C23×C4C22×D512yes—
322C23×C4C22×D511yescharacteristic
323C23×C4C22×D512yes—
324C23×C4C22×D511yescharacteristic
325C23×C4C22×D511yescharacteristic
326C4×Q8—1032no—
327C2×C4⋊C4—54no—
328C2×C4⋊C4—54no—
329C2×C4⋊C4—54no—
330C2×C4⋊C4—102no—
331C2×C4⋊C4—102no—
332C2×C4⋊C4—102no—
333C2×C4⋊C4—102no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—102no—
336C2×C4⋊C4—104no—
337C2×C4⋊C4—104no—
338C2×C4⋊C4—104no—
339C2×C4⋊C4—104no—
340C2×C4⋊C4—104no—
341C2×C4⋊C4—104no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—54no—
345C2×C42—54no—
346C2×C42—54no—
347C2×C42—54no—
348C2×C42—102no—
349C2×C42—102no—
350C2×C42—104no—
351C2×C42—104no—
352C2×C42—104no—
353C2×C42C4×D514yes—
354#95—24no—
355#95—22no—
356#95—22no—
357#95—24no—
358#95—104no—
359#95—104no—
360#95—104no—
361#95—104no—
362#95—104no—
363#95—104no—
364#95—102no—
365#95—102no—
366#95—104no—
367C22×C5C22×C22⋊C411yescharacteristic
368C22×C5C22×C4⋊C411yescharacteristic
369C22×C5C2×#11711yescharacteristic
370C22×C5C4×#4111yescharacteristic
371C22×C5C4×#4111yescharacteristic
372C22×C5#51911yescharacteristic
373C22×C5#51911yescharacteristic
374C22×C5C2×#12111yescharacteristic
375C22×C5C2×#12111yescharacteristic
376C22×C5C2×C22⋊Q811yescharacteristic
377C22×C5C2×C22⋊Q811yescharacteristic
378C22×C5#52512yes—
379C22×C5#53212yes—
380C22×C5#53612yes—
381C22×C5#53612yes—
382C22×C5#54812yes—
383C22×C5#54812yes—
384C22×C5#55212yes—
385C22×C5#55212yes—
386C22×C5#55612yes—
387C22×C5#55612yes—
388C22×C5#55712yes—
389C22×C5#55712yes—
390C4×C5—24no—
391C4×C5—24no—
392C4×C5—44no—
393C4×C5—42no—
394C4×C5—82no—
395Dic5—24no—
396Dic5—24no—
397Dic5—44no—
398Dic5—42no—
399Dic5—82no—
400Dic5#38018yes—
401C24C23×D511yescharacteristic
402C2×Q8—516no—
403C2×Q8—108no—
404C2×Q8—108no—
405C2×Q8—108no—
406C2×Q8—108no—
407C2×Q8—108no—
408C2×Q8—108no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—52no—
433C22×C4—52no—
434C22×C4—52no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—52no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—52no—
442C22×C4—52no—
443C22×C4—52no—
444C22×C4—52no—
445C22×C4—52no—
446C22×C4—54no—
447C22×C4—102no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—102no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4C2×C4×D512yes—
471C22×C4C2×C4×D512yes—
472C22×C4C2×C4×D512yes—
473C22×C4#70914yes—
474C22×C4D4×D512yes—
475C22×C4D4×D512yes—
476C22×C4D4×D512yes—
477C22×C4Q8×D512yes—
478C4⋊C4—108no—
479C4⋊C4—108no—
480C4⋊C4—108no—
481C4⋊C4—1016no—
482C4⋊C4—208no—
483C42—28no—
484C42—516no—
485C42—108no—
486C42—208no—
487C2×C5C2×#38011yescharacteristic
488C2×C5#229711yescharacteristic
489C2×C5#231011yescharacteristic
490C2×C5#235111yescharacteristic
491C2×C5#235111yescharacteristic
492C2×C5#235611yescharacteristic
493C2×C5#235611yescharacteristic
494C2×C5#253612yes—
495C2×C5#254512yes—
496C2×C5#256512yes—
497C2×C5#258112yes—
498C23C22×C4×D511yescharacteristic
499C23C2×#70912yes—
500C23C2×D4×D511yescharacteristic
501C23C2×D4×D511yescharacteristic
502C23C2×D4×D511yescharacteristic
503C23C2×Q8×D511yescharacteristic
504C23D5×#4111yescharacteristic
505C23D5×#4111yescharacteristic
506C23D5×#4112yes—
507C23#415012yes—
508C23#415012yes—
509Q8—1032no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—54no—
540C2×C4—54no—
541C2×C4—54no—
542C2×C4—54no—
543C2×C4—54no—
544C2×C4—54no—
545C2×C4—54no—
546C2×C4—54no—
547C2×C4—54no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—104no—
553C2×C4—104no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—104no—
562C2×C4—104no—
563C2×C4—104no—
564C2×C4—202no—
565C2×C4—202no—
566C2×C4—202no—
567C2×C4—202no—
568C2×C4—202no—
569C2×C4—202no—
570C2×C4—202no—
571C2×C4—202no—
572C2×C4—202no—
573C2×C4—202no—
574C2×C4—202no—
575C2×C4—202no—
576C2×C4—202no—
577C2×C4D5×C22⋊C414yes—
578C2×C4D5×C4⋊C414yes—
579C5#1394211yescharacteristic, complemented, Sylow
580C22C4×#70911yescharacteristic
581C22C2×D5×C22⋊C411yescharacteristic
582C22C2×D5×C4⋊C411yescharacteristic
583C22#6585011yescharacteristic
584C22#6585011yescharacteristic
585C22D5×#11711yescharacteristic
586C22#6585611yescharacteristic
587C22#6586512yes—
588C22#6586712yes—
589C22#6588112yes—
590C22#6588212yes—
591C22#6588612yes—
592C22#6590112yes—
593C22D5×#12111yescharacteristic
594C22D5×#12111yescharacteristic
595C22D5×C22⋊Q811yescharacteristic
596C22D5×C22⋊Q811yescharacteristic
597C22#6598212yes—
598C22#6598212yes—
599C22#6601112yes—
600C22#6601912yes—
601C22#6603612yes—
602C22#6604212yes—
603C4—24no—
604C4—24no—
605C4—44no—
606C4—42no—
607C4—58no—
608C4—82no—
609C4—104no—
610C4—104no—
611C4—204no—
612C4—202no—
613C4—402no—
614C2#1060512411yescharacteristic
615C2#1060529411yescharacteristic
616C2#1060536811yescharacteristic
617C2D5×#38011yescharacteristic
618C2#1060578411yescharacteristic
619C2#1060588811yescharacteristic
620C2#1060599511yescharacteristic
621C2#1060680712yes—
622C2#1060682112yes—
623C2#1060732312yes—
624C2#1060732412yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1434C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1434D5
hypocenterC5#13942
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
24. C2×C4×Dic10C4semidirect
188. C2×Dic10C4⋊C4semidirect
579. C5#13942semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic102
C2×#649352
C2×#649392
C2×#649382
C5×#14342
#106023272
#106002042
#106002022
#106001972
#106001952
#139425