Finite Group Databasebeta

← A4×#4084 #14514192

Subgroups — A4×#4084 #14514192

Order 1920.

1156 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D4×A4C211yesmaximal, characteristic, complemented
2C2×A4×C22⋊D5C212yesmaximal, complemented
3C2×C4×D5×A4C211yesmaximal, characteristic, complemented
4A4×C22⋊Dic5C212yesmaximal, complemented
5A4×C4⋊Dic5C211yesmaximal, characteristic, complemented
6C22×#4084C311yesmaximal, characteristic, complemented, Hall
7C23×C5×A4C2212yes—
8C22×D5×A4C2211yescharacteristic
9C5×D4×A4—22no—
10C2×C4×C5×A4C2211yescharacteristic
11A4×C22⋊D5—24no—
12C2×A4×Dic5C2211yescharacteristic
13C2×A4×Dic5C2212yes—
14C4×D5×A4—22no—
15C3×#4084—41nomaximal
16A4×#121—51nomaximal, Hall
17C23×C5×D4C2×C311yescharacteristic, complemented
18C23×C22⋊D5C2×C312yescomplemented
19C23×C4×D5C2×C311yescharacteristic, complemented
20C22×C22⋊Dic5C2×C312yescomplemented
21C2×#4084—32no—
22C2×#4084—31no—
23C2×#4084—32no—
24C2×#4084—31no—
25C2×#4084—31no—
26C2×#4084—31no—
27C22×C4⋊Dic5C2×C311yescharacteristic, complemented
28C22×C5×A4—22no—
29C22×C5×A4—22no—
30C22×C5×A4—22no—
31C22×C5×A4C2311yescharacteristic
32C2×D5×A4—21no—
33C2×D5×A4—21no—
34C2×D5×A4D412yescomplemented
35C2×C3×C5×D4—41no—
36C2×C3×C22⋊D5—42no—
37C2×C3×C4×D5—41no—
38C4×C5×A4D412yescomplemented
39A4×Dic5—21no—
40A4×Dic5—22no—
41C3×C22⋊Dic5—42no—
42C3×C4⋊Dic5—41no—
43C2×D4×A4—52no—
44C2×D4×A4D511yescharacteristic, complemented
45C22×C4×A4—51no—
46A4×C4⋊C4—51no—
47A4×C22⋊C4—52no—
48C25×C5C22×C312yes—
49C24×D5C22×C311yescharacteristic
50C22×C5×D4—22no—
51C22×C5×D4—31no—
52C22×C5×D4—31no—
53C22×C5×D4—32no—
54C22×C5×D4—62no—
55C23×C4×C5C22×C311yescharacteristic
56C22×C22⋊D5—24no—
57C22×C22⋊D5—32no—
58C22×C22⋊D5—32no—
59C22×C22⋊D5—32no—
60C22×C22⋊D5—32no—
61C22×C22⋊D5—64no—
62C23×Dic5C22×C312yes—
63C23×Dic5C22×C311yescharacteristic
64C22×C4×D5—22no—
65C22×C4×D5—31no—
66C22×C4×D5—31no—
67C22×C4×D5—31no—
68C22×C4×D5—31no—
69C22×C4×D5—62no—
70C2×C22⋊Dic5—32no—
71C2×C22⋊Dic5—32no—
72C2×C22⋊Dic5—32no—
73C2×C22⋊Dic5—32no—
74#4084—32no—
75#4084—34no—
76#4084—32no—
77#4084—32no—
78#4084—34no—
79#4084—31no—
80#4084—32no—
81#4084—31no—
82#4084—32no—
83#4084—31no—
84#4084A411yescharacteristic, direct product factor
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5—31no—
87C2×C4⋊Dic5—32no—
88C22×#121—51noSylow
89C23×C3×C5—42no—
90C22×C3×D5—41no—
91C2×C5×A4—42no—
92C2×C5×A4C2×D411yescharacteristic
93C2×C5×A4C2×D411yescharacteristic
94C2×C5×A4#4111yescharacteristic
95D5×A4—22no—
96C3×C5×D4—82no—
97C2×C3×C4×C5—41no—
98C3×C22⋊D5—84no—
99C2×C3×Dic5—42no—
100C2×C3×Dic5—41no—
101C3×C4×D5—82no—
102C23×A4—51no—
103C23×A4C2×D512yes—
104D4×A4—22no—
105D4×A4—104no—
106C2×C4×A4—51no—
107C2×C4×A4—52no—
108C2×C4×A4—102no—
109C2×C4×A4C2×D511yescharacteristic
110C3×#121—201no—
111C24×C5—22no—
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—32no—
115C24×C5—32no—
116C24×C5—62no—
117C24×C5—62no—
118C24×C5—62no—
119C24×C5C23×C311yescharacteristic
120C23×D5—21no—
121C23×D5—21no—
122C23×D5—31no—
123C23×D5—31no—
124C23×D5—32no—
125C23×D5—61no—
126C23×D5—61no—
127C23×D5C3×D412yescomplemented
128C2×C5×D4—32no—
129C2×C5×D4—32no—
130C2×C5×D4—31no—
131C2×C5×D4—62no—
132C2×C5×D4—62no—
133C2×C5×D4—64no—
134C2×C5×D4—62no—
135C2×C5×D4—64no—
136C2×C5×D4—62no—
137C2×C5×D4C2×A411yescharacteristic, complemented
138C22×C4×C5—31no—
139C22×C4×C5—31no—
140C22×C4×C5—32no—
141C22×C4×C5C3×D412yescomplemented
142C2×C22⋊D5—34no—
143C2×C22⋊D5—32no—
144C2×C22⋊D5—32no—
145C2×C22⋊D5—32no—
146C2×C22⋊D5—64no—
147C2×C22⋊D5—64no—
148C2×C22⋊D5—64no—
149C2×C22⋊D5—64no—
150C2×C22⋊D5—64no—
151C2×C22⋊D5—64no—
152C2×C22⋊D5—64no—
153C2×C22⋊D5—64no—
154C2×C22⋊D5C2×A412yescomplemented
155C22×Dic5—21no—
156C22×Dic5—22no—
157C22×Dic5—31no—
158C22×Dic5—32no—
159C22×Dic5—31no—
160C22×Dic5—32no—
161C22×Dic5—61no—
162C22×Dic5—62no—
163C2×C4×D5—32no—
164C2×C4×D5—31no—
165C2×C4×D5—31no—
166C2×C4×D5—31no—
167C2×C4×D5—62no—
168C2×C4×D5—62no—
169C2×C4×D5—62no—
170C2×C4×D5—62no—
171C2×C4×D5—62no—
172C2×C4×D5—62no—
173C2×C4×D5—62no—
174C2×C4×D5—62no—
175C2×C4×D5C2×A411yescharacteristic, complemented
176C22⋊Dic5—34no—
177C22⋊Dic5—32no—
178C22⋊Dic5—32no—
179C22⋊Dic5—32no—
180C22⋊Dic5C2×A412yescomplemented
181C4⋊Dic5—32no—
182C4⋊Dic5—31no—
183C4⋊Dic5—32no—
184C4⋊Dic5C2×A411yescharacteristic, complemented
185C23×D4—52no—
186C23×D4C3×D511yescharacteristic, complemented
187C24×C4—51no—
188C2×#121—151no—
189C2×#121—152no—
190C2×#121—151no—
191C2×#121—151no—
192C2×#121—152no—
193C2×#121—151no—
194C22×C4⋊C4—51no—
195C22×C22⋊C4—52no—
196C22×C3×C5—41no—
197C22×C3×C5—82no—
198C22×C3×C5—82no—
199C22×C3×C5—82no—
200C2×C3×D5—42no—
201C2×C3×D5—81no—
202C2×C3×D5—81no—
203C5×A4#12111yescharacteristic, complemented
204C3×C4×C5—42no—
205C3×Dic5—81no—
206C3×Dic5—82no—
207C22×A4—22no—
208C22×A4—22no—
209C22×A4—22no—
210C22×A4—52no—
211C22×A4—101no—
212C22×A4—101no—
213C22×A4C22×D511yescharacteristic
214C2×C3×D4—41no—
215C2×C3×D4—202no—
216C22×C3×C4—201no—
217C4×A4—102no—
218C4×A4—101no—
219C4×A4C22⋊D512yescomplemented
220C3×C4⋊C4—201no—
221C3×C22⋊C4—202no—
222C23×C5—31no—
223C23×C5—31no—
224C23×C5—31no—
225C23×C5—31no—
226C23×C5—32no—
227C23×C5—42no—
228C23×C5—62no—
229C23×C5—62no—
230C23×C5—62no—
231C23×C5—62no—
232C23×C5—62no—
233C23×C5—62no—
234C23×C5—62no—
235C23×C5—62no—
236C23×C5—62no—
237C23×C5—62no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—122no—
241C23×C5—122no—
242C23×C5—122no—
243C23×C5—124no—
244C23×C5C2×C3×D411yescharacteristic
245C23×C5C2×C3×D411yescharacteristic
246C23×C5C3×#4111yescharacteristic
247C23×C5C22×A412yes—
248C22×D5—22no—
249C22×D5—32no—
250C22×D5—31no—
251C22×D5—32no—
252C22×D5—32no—
253C22×D5—32no—
254C22×D5—61no—
255C22×D5—61no—
256C22×D5—61no—
257C22×D5—61no—
258C22×D5—64no—
259C22×D5—61no—
260C22×D5—61no—
261C22×D5—62no—
262C22×D5—62no—
263C22×D5—61no—
264C22×D5—61no—
265C22×D5—62no—
266C22×D5C22×A411yescharacteristic
267C5×D4—22no—
268C5×D4—64no—
269C5×D4—64no—
270C5×D4—62no—
271C2×C4×C5—32no—
272C2×C4×C5—31no—
273C2×C4×C5—32no—
274C2×C4×C5—32no—
275C2×C4×C5—32no—
276C2×C4×C5C22×A411yescharacteristic
277C22⋊D5—24no—
278C22⋊D5—64no—
279C22⋊D5—64no—
280C22⋊D5—68no—
281C22⋊D5—64no—
282C2×Dic5—32no—
283C2×Dic5—31no—
284C2×Dic5—61no—
285C2×Dic5—61no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5—61no—
289C2×Dic5—61no—
290C2×Dic5—62no—
291C2×Dic5—62no—
292C2×Dic5C22×A412yes—
293C2×Dic5C22×A411yescharacteristic
294C4×D5—22no—
295C4×D5—62no—
296C4×D5—62no—
297C4×D5—64no—
298C4×D5—62no—
299C25—51no—
300C25C2×C3×D512yes—
301C22×D4—22no—
302C22×D4—31no—
303C22×D4—31no—
304C22×D4—32no—
305C22×D4—62no—
306C22×D4—104no—
307C22×D4—152no—
308C22×D4—152no—
309C22×D4—152no—
310C22×D4—152no—
311C22×D4—304no—
312C23×C4—51no—
313C23×C4—52no—
314C23×C4—102no—
315C23×C4—151no—
316C23×C4—151no—
317C23×C4—151no—
318C23×C4—151no—
319C23×C4—302no—
320C23×C4C2×C3×D511yescharacteristic
321#121—51no—
322#121—152no—
323#121—151no—
324#121—151no—
325#121—152no—
326#121—152no—
327#121—154no—
328#121—152no—
329#121—152no—
330#121—154no—
331#121—151no—
332C2×C4⋊C4—151no—
333C2×C4⋊C4—152no—
334C2×C4⋊C4—151no—
335C2×C22⋊C4—152no—
336C2×C22⋊C4—152no—
337C2×C22⋊C4—152no—
338C2×C22⋊C4—152no—
339C2×C3×C5—41no—
340C2×C3×C5—41no—
341C2×C3×C5—41no—
342C2×C3×C5—162no—
343C3×D5—82no—
344C23×C3—42no—
345C23×C3—201no—
346C2×A4—42no—
347C2×A4—102no—
348C2×A4D4×D511yescharacteristic
349C2×A4#71111yescharacteristic
350C2×A4C2×C22⋊D511yescharacteristic
351C3×D4—82no—
352C3×D4—404no—
353C2×C3×C4—41no—
354C2×C3×C4—201no—
355C2×C3×C4—202no—
356C2×C3×C4—402no—
357C22×C5—22no—
358C22×C5—22no—
359C22×C5—22no—
360C22×C5—31no—
361C22×C5—31no—
362C22×C5—31no—
363C22×C5—32no—
364C22×C5—31no—
365C22×C5—31no—
366C22×C5—31no—
367C22×C5—31no—
368C22×C5—31no—
369C22×C5—31no—
370C22×C5—62no—
371C22×C5—62no—
372C22×C5—62no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5—122no—
376C22×C5—122no—
377C22×C5—122no—
378C22×C5—122no—
379C22×C5—122no—
380C22×C5—122no—
381C22×C5C3×#12111yescharacteristic, complemented
382C22×C5C23×A411yescharacteristic
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—32no—
386C2×D5—62no—
387C2×D5—62no—
388C2×D5—62no—
389C2×D5—62no—
390C2×D5—62no—
391C2×D5—62no—
392C2×D5—61no—
393C2×D5—61no—
394C2×D5—62no—
395C2×D5—62no—
396C2×D5D4×A412yescomplemented
397C4×C5—32no—
398C4×C5D4×A412yescomplemented
399Dic5—21no—
400Dic5—22no—
401Dic5—61no—
402Dic5—62no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—32no—
407C24—32no—
408C24—52no—
409C24—62no—
410C24—62no—
411C24—62no—
412C24—101no—
413C24—101no—
414C24—151no—
415C24—151no—
416C24—152no—
417C24—301no—
418C24—301no—
419C24C22×C3×D511yescharacteristic
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—31no—
423C2×D4—52no—
424C2×D4—62no—
425C2×D4—62no—
426C2×D4—64no—
427C2×D4—62no—
428C2×D4—64no—
429C2×D4—62no—
430C2×D4—152no—
431C2×D4—152no—
432C2×D4—154no—
433C2×D4—152no—
434C2×D4—304no—
435C2×D4—304no—
436C2×D4—304no—
437C2×D4—304no—
438C2×D4—304no—
439C2×D4—304no—
440C2×D4—304no—
441C2×D4—304no—
442C2×D4D5×A411yescharacteristic, complemented
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—32no—
446C22×C4—51no—
447C22×C4—102no—
448C22×C4—101no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—152no—
452C22×C4—151no—
453C22×C4—152no—
454C22×C4—151no—
455C22×C4—151no—
456C22×C4—152no—
457C22×C4—302no—
458C22×C4—302no—
459C22×C4—302no—
460C22×C4—302no—
461C22×C4—302no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—302no—
465C22×C4—301no—
466C22×C4—302no—
467C22×C4C3×C22⋊D512yescomplemented
468C4⋊C4—51no—
469C4⋊C4—152no—
470C4⋊C4—152no—
471C4⋊C4—151no—
472C22⋊C4—52no—
473C22⋊C4—152no—
474C22⋊C4—152no—
475C22⋊C4—154no—
476C22⋊C4—152no—
477C3×C5—41noHall
478C22×C3—41no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—82no—
482C22×C3—202no—
483C22×C3—401no—
484C22×C3—401no—
485A4#408411yescharacteristic, direct product factor
486C3×C4—42no—
487C3×C4—401no—
488C3×C4—402no—
489C2×C5—31no—
490C2×C5—31no—
491C2×C5—31no—
492C2×C5—31no—
493C2×C5—42no—
494C2×C5—122no—
495C2×C5C2×D4×A411yescharacteristic
496C2×C5C2×D4×A411yescharacteristic
497C2×C5A4×#4111yescharacteristic
498D5—22no—
499D5—62no—
500C23—31no—
501C23—31no—
502C23—31no—
503C23—31no—
504C23—32no—
505C23—42no—
506C23—51no—
507C23—62no—
508C23—62no—
509C23—62no—
510C23—62no—
511C23—62no—
512C23—62no—
513C23—62no—
514C23—62no—
515C23—62no—
516C23—62no—
517C23—62no—
518C23—62no—
519C23—102no—
520C23—122no—
521C23—122no—
522C23—122no—
523C23—124no—
524C23—152no—
525C23—152no—
526C23—152no—
527C23—152no—
528C23—151no—
529C23—301no—
530C23—301no—
531C23—301no—
532C23—301no—
533C23—302no—
534C23—301no—
535C23—301no—
536C23—302no—
537C23—302no—
538C23—301no—
539C23—301no—
540C23—304no—
541C23C3×D4×D511yescharacteristic
542C23C3×#71111yescharacteristic
543C23C2×C3×C22⋊D511yescharacteristic
544C23C2×D5×A412yes—
545D4—22no—
546D4—64no—
547D4—64no—
548D4—62no—
549D4—104no—
550D4—304no—
551D4—304no—
552D4—304no—
553D4—308no—
554C2×C4—32no—
555C2×C4—31no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—51no—
560C2×C4—52no—
561C2×C4—102no—
562C2×C4—151no—
563C2×C4—152no—
564C2×C4—302no—
565C2×C4—302no—
566C2×C4—304no—
567C2×C4—301no—
568C2×C4—302no—
569C2×C4—301no—
570C2×C4—302no—
571C2×C4—302no—
572C2×C4—301no—
573C2×C4—302no—
574C2×C4—301no—
575C2×C4—302no—
576C2×C4C2×D5×A411yescharacteristic
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3—162no—
581C2×C3—402no—
582C5A4×#12111yescharacteristic, complemented, Sylow
583C22—22no—
584C22—22no—
585C22—22no—
586C22—31no—
587C22—31no—
588C22—31no—
589C22—32no—
590C22—31no—
591C22—31no—
592C22—31no—
593C22—31no—
594C22—31no—
595C22—31no—
596C22—52no—
597C22—62no—
598C22—62no—
599C22—62no—
600C22—101no—
601C22—101no—
602C22—122no—
603C22—122no—
604C22—122no—
605C22—122no—
606C22—122no—
607C22—122no—
608C22—122no—
609C22—122no—
610C22—152no—
611C22—302no—
612C22—302no—
613C22—302no—
614C22—302no—
615C22—302no—
616C22—302no—
617C22—302no—
618C22—302no—
619C22—301no—
620C22—301no—
621C22C3×#408411yescharacteristic, complemented
622C22C22×D5×A411yescharacteristic
623C4—32no—
624C4—102no—
625C4—101no—
626C4—302no—
627C4—301no—
628C4A4×C22⋊D512yescomplemented
629C3—41noSylow
630C2—31no—
631C2—31no—
632C2—31no—
633C2—31no—
634C2—42no—
635C2—102no—
636C2—122no—
637C2—302no—
638C2D4×D5×A411yescharacteristic
639C2A4×#71111yescharacteristic
640C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC23×C5×D4C2×C3
hypercenterC2×D4D5×A4
hypocenterC22×C5C3×#121
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×A4C2semidirect
2. C2×A4×C22⋊D5C2semidirect
3. C2×C4×D5×A4C2semidirect
4. A4×C22⋊Dic5C2semidirect
5. A4×C4⋊Dic5C2semidirect
6. C22×#4084C3semidirect
17. C23×C5×D4C2×C3semidirect
18. C23×C22⋊D5C2×C3semidirect
19. C23×C4×D5C2×C3semidirect
20. C22×C22⋊Dic5C2×C3semidirect
27. C22×C4⋊Dic5C2×C3semidirect
34. C2×D5×A4D4semidirect
38. C4×C5×A4D4semidirect
44. C2×D4×A4D5semidirect
84. #4084A4direct (N × H)
127. C23×D5C3×D4semidirect
137. C2×C5×D4C2×A4semidirect
141. C22×C4×C5C3×D4semidirect
154. C2×C22⋊D5C2×A4semidirect
175. C2×C4×D5C2×A4semidirect
180. C22⋊Dic5C2×A4semidirect
184. C4⋊Dic5C2×A4semidirect
186. C23×D4C3×D5semidirect
203. C5×A4#121semidirect
219. C4×A4C22⋊D5semidirect
381. C22×C5C3×#121semidirect
396. C2×D5D4×A4semidirect
398. C4×C5D4×A4semidirect
442. C2×D4D5×A4semidirect
467. C22×C4C3×C22⋊D5semidirect
485. A4#4084direct (N × H)
582. C5A4×#121semidirect
621. C22C3×#4084semidirect
628. C4A4×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×A42
C2×A4×C22⋊D52
C2×C4×D5×A42
A4×C22⋊Dic52
A4×C4⋊Dic52
C22×#40843
C3×#40844
A4×#1215