Finite Group Databasebeta

← A4×#4044 #14514003

Subgroups — A4×#4044 #14514003

Order 1920.

640 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
2A4×#685C211yesmaximal, characteristic
3A4×#685C211yesmaximal, characteristic
4A4×#685C211yesmaximal, characteristic
5A4×C4⋊Dic5C211yesmaximal, characteristic, complemented
6A4×#683C211yesmaximal, characteristic, complemented
7C4×A4×Dic5C211yesmaximal, characteristic, complemented
8C22×#4044C311yesmaximal, characteristic, complemented, Hall
9C22×D5×A4C2211yescharacteristic
10C2×C4×C5×A4C2211yescharacteristic
11C2×C4×C5×A4C2211yescharacteristic
12C2×C4×C5×A4C2211yescharacteristic
13C2×A4×Dic5C2211yescharacteristic
14C2×A4×Dic5C2211yescharacteristic
15C2×A4×Dic5C2211yescharacteristic
16C3×#4044—41nomaximal
17A4×#126—51nomaximal, Hall
18C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
19C22×#685C2×C311yescharacteristic
20C22×#685C2×C311yescharacteristic
21C22×#685C2×C311yescharacteristic
22C22×C4⋊Dic5C2×C311yescharacteristic, complemented
23C22×#683C2×C311yescharacteristic, complemented
24C22×C4×Dic5C2×C311yescharacteristic, complemented
25C2×#4044—31no—
26C2×#4044—31no—
27C2×#4044—31no—
28C2×#4044—31no—
29C2×#4044—31no—
30C2×#4044—31no—
31C2×#4044—31no—
32C2×#4044—31no—
33C22×C5×A4C2311yescharacteristic
34C2×D5×A4—21no—
35C2×D5×A4—21no—
36C2×D5×A4—21no—
37C4×C5×A4—21no—
38C4×C5×A4—21no—
39C4×C5×A4—21no—
40A4×Dic5—21no—
41A4×Dic5—21no—
42A4×Dic5—21no—
43C3×C5×C4⋊C4—41no—
44C3×#685—41no—
45C3×#685—41no—
46C3×#685—41no—
47C3×C4⋊Dic5—41no—
48C3×#683—41no—
49C3×C4×Dic5—41no—
50A4×C4⋊C4—51no—
51A4×C4⋊C4—51no—
52A4×C4⋊C4D511yescharacteristic, complemented
53A4×C22⋊C4—51no—
54A4×C22⋊C4—51no—
55A4×C22⋊C4—51no—
56C42×A4—51no—
57C24×D5C22×C311yescharacteristic
58C23×C4×C5C22×C311yescharacteristic
59C23×C4×C5C22×C311yescharacteristic
60C23×C4×C5C22×C311yescharacteristic
61C23×Dic5C22×C311yescharacteristic
62C23×Dic5C22×C311yescharacteristic
63C23×Dic5C22×C311yescharacteristic
64C2×C5×C4⋊C4—31no—
65C2×C5×C4⋊C4—31no—
66C2×C5×C4⋊C4—31no—
67C2×C5×C4⋊C4—31no—
68C2×#685—31no—
69C2×#685—31no—
70C2×#685—31no—
71C2×#685—31no—
72C2×#685—31no—
73C2×#685—31no—
74C2×#685—31no—
75C2×#685—31no—
76C2×#685—31no—
77C2×#685—31no—
78C2×#685—31no—
79C2×#685—31no—
80C2×C4⋊Dic5—31no—
81C2×C4⋊Dic5—31no—
82C2×C4⋊Dic5—31no—
83C2×C4⋊Dic5—31no—
84C2×#683—31no—
85C2×#683—31no—
86C2×#683—31no—
87C2×#683—31no—
88C2×C4×Dic5—31no—
89C2×C4×Dic5—31no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—31no—
92#4044—32no—
93#4044—32no—
94#4044—32no—
95#4044—32no—
96#4044—32no—
97#4044—32no—
98#4044—32no—
99#4044—31no—
100#4044—31no—
101#4044—31no—
102#4044—31no—
103#4044—31no—
104#4044—31no—
105#4044—31no—
106#4044A411yescharacteristic, direct product factor
107C22×#126—51noSylow
108C22×C3×D5—41no—
109C2×C5×A4#4111yescharacteristic
110C2×C5×A4#4111yescharacteristic
111C2×C5×A4#4111yescharacteristic
112D5×A4—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C23×A4—51no—
120C2×C4×A4—51no—
121C2×C4×A4—51no—
122C2×C4×A4—51no—
123C2×C4×A4C2×D511yescharacteristic
124C2×C4×A4C2×D511yescharacteristic
125C2×C4×A4C2×D511yescharacteristic
126C3×#126—201no—
127C24×C5C23×C311yescharacteristic
128C23×D5—21no—
129C23×D5—21no—
130C23×D5—21no—
131C23×D5—31no—
132C23×D5—31no—
133C23×D5—61no—
134C23×D5—61no—
135C23×D5—61no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—31no—
140C22×C4×C5—31no—
141C22×C4×C5—31no—
142C22×C4×C5—31no—
143C22×C4×C5—31no—
144C22×C4×C5—31no—
145C22×C4×C5—61no—
146C22×C4×C5—61no—
147C22×C4×C5—61no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—31no—
152C22×Dic5—31no—
153C22×Dic5—31no—
154C22×Dic5—31no—
155C22×Dic5—31no—
156C22×Dic5—31no—
157C22×Dic5—61no—
158C22×Dic5—61no—
159C22×Dic5—61no—
160C5×C4⋊C4—32no—
161C5×C4⋊C4—31no—
162C5×C4⋊C4—31no—
163C5×C4⋊C4—31no—
164C5×C4⋊C4C2×A411yescharacteristic, complemented
165#685—32no—
166#685—32no—
167#685—32no—
168#685—31no—
169#685—31no—
170#685—31no—
171#685—31no—
172#685—31no—
173#685—31no—
174#685—31no—
175#685—31no—
176#685—31no—
177#685C2×A411yescharacteristic
178#685C2×A411yescharacteristic
179#685C2×A411yescharacteristic
180C4⋊Dic5—32no—
181C4⋊Dic5—31no—
182C4⋊Dic5—31no—
183C4⋊Dic5—31no—
184C4⋊Dic5C2×A411yescharacteristic, complemented
185#683—32no—
186#683—31no—
187#683—31no—
188#683—31no—
189#683C2×A411yescharacteristic, complemented
190C4×Dic5—32no—
191C4×Dic5—31no—
192C4×Dic5—31no—
193C4×Dic5—31no—
194C4×Dic5C2×A411yescharacteristic, complemented
195C2×#126—151no—
196C2×#126—151no—
197C2×#126—151no—
198C2×#126—151no—
199C2×#126—151no—
200C2×#126—151no—
201C2×#126—151no—
202C2×#126—151no—
203C22×C4⋊C4—51no—
204C22×C4⋊C4—51no—
205C22×C4⋊C4C3×D511yescharacteristic, complemented
206C22×C22⋊C4—51no—
207C22×C22⋊C4—51no—
208C22×C22⋊C4—51no—
209C22×C42—51no—
210C22×C3×C5—41no—
211C2×C3×D5—81no—
212C2×C3×D5—81no—
213C2×C3×D5—81no—
214C5×A4#12611yescharacteristic, complemented
215C3×C4×C5—81no—
216C3×C4×C5—81no—
217C3×C4×C5—81no—
218C3×Dic5—81no—
219C3×Dic5—81no—
220C3×Dic5—81no—
221C22×A4—101no—
222C22×A4—101no—
223C22×A4—101no—
224C22×A4C22×D511yescharacteristic
225C4×A4—21no—
226C4×A4—21no—
227C4×A4—21no—
228C4×A4—101no—
229C4×A4—101no—
230C4×A4—101no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—201no—
233C3×C4⋊C4—201no—
234C3×C22⋊C4—201no—
235C3×C22⋊C4—201no—
236C3×C22⋊C4—201no—
237C3×C42—201no—
238C23×C5—31no—
239C23×C5—31no—
240C23×C5—31no—
241C23×C5—31no—
242C23×C5C3×#4111yescharacteristic
243C23×C5C3×#4111yescharacteristic
244C23×C5C3×#4111yescharacteristic
245C22×D5—31no—
246C22×D5—41no—
247C22×D5—61no—
248C22×D5—61no—
249C22×D5—61no—
250C22×D5—61no—
251C22×D5—61no—
252C22×D5—61no—
253C22×D5—61no—
254C22×D5—61no—
255C22×D5—61no—
256C22×D5—61no—
257C22×D5—61no—
258C22×D5—61no—
259C22×D5—122no—
260C22×D5—121no—
261C22×D5—121no—
262C22×D5—121no—
263C22×D5C22×A411yescharacteristic
264C2×C4×C5—31no—
265C2×C4×C5—31no—
266C2×C4×C5—31no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—61no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5C22×A411yescharacteristic
280C2×C4×C5C22×A411yescharacteristic
281C2×C4×C5C22×A411yescharacteristic
282C2×Dic5—31no—
283C2×Dic5—31no—
284C2×Dic5—31no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—61no—
290C2×Dic5—61no—
291C2×Dic5—61no—
292C2×Dic5—61no—
293C2×Dic5—61no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—61no—
297C2×Dic5C22×A411yescharacteristic
298C2×Dic5C22×A411yescharacteristic
299C2×Dic5C22×A411yescharacteristic
300C25—51no—
301C23×C4—51no—
302C23×C4—51no—
303C23×C4—51no—
304C23×C4C2×C3×D511yescharacteristic
305C23×C4C2×C3×D511yescharacteristic
306C23×C4C2×C3×D511yescharacteristic
307#126—51no—
308#126—151no—
309#126—151no—
310#126—151no—
311#126—151no—
312#126—151no—
313#126—151no—
314#126—152no—
315#126—152no—
316#126—152no—
317#126—152no—
318#126—152no—
319#126—152no—
320#126—152no—
321#126—151no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—151no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4—151no—
329C2×C4⋊C4—151no—
330C2×C4⋊C4—151no—
331C2×C4⋊C4—151no—
332C2×C4⋊C4—151no—
333C2×C4⋊C4—151no—
334C2×C22⋊C4—151no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—151no—
337C2×C22⋊C4—151no—
338C2×C22⋊C4—151no—
339C2×C22⋊C4—151no—
340C2×C22⋊C4—151no—
341C2×C22⋊C4—151no—
342C2×C22⋊C4—151no—
343C2×C22⋊C4—151no—
344C2×C22⋊C4—151no—
345C2×C22⋊C4—151no—
346C2×C42—151no—
347C2×C42—151no—
348C2×C42—151no—
349C2×C42—151no—
350C2×C3×C5—41no—
351C2×C3×C5—41no—
352C2×C3×C5—41no—
353C3×D5—161no—
354C23×C3—201no—
355C2×A4—201no—
356C2×A4#70911yescharacteristic
357C2×A4#71111yescharacteristic
358C2×A4#71311yescharacteristic
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—201no—
363C2×C3×C4—201no—
364C2×C3×C4—201no—
365C22×C5—31no—
366C22×C5—31no—
367C22×C5—31no—
368C22×C5—32no—
369C22×C5—31no—
370C22×C5—31no—
371C22×C5—31no—
372C22×C5—31no—
373C22×C5—31no—
374C22×C5—31no—
375C22×C5C3×#12611yescharacteristic, complemented
376C22×C5C23×A411yescharacteristic
377C2×D5—21no—
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—61no—
381C2×D5—61no—
382C2×D5—61no—
383C2×D5—121no—
384C2×D5—121no—
385C2×D5—121no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—21no—
394C4×C5—61no—
395C4×C5—61no—
396C4×C5—61no—
397Dic5—21no—
398Dic5—21no—
399Dic5—21no—
400Dic5—61no—
401Dic5—61no—
402Dic5—61no—
403C24—101no—
404C24—101no—
405C24—101no—
406C24—151no—
407C24—151no—
408C24—301no—
409C24—301no—
410C24—301no—
411C24C22×C3×D511yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—151no—
428C22×C4—151no—
429C22×C4—151no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—301no—
434C22×C4—301no—
435C22×C4—301no—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—31no—
439C4⋊C4—31no—
440C4⋊C4—51no—
441C4⋊C4—51no—
442C4⋊C4—151no—
443C4⋊C4—151no—
444C4⋊C4—151no—
445C4⋊C4—151no—
446C4⋊C4—152no—
447C4⋊C4—152no—
448C4⋊C4—151no—
449C4⋊C4—151no—
450C4⋊C4D5×A411yescharacteristic, complemented
451C22⋊C4—51no—
452C22⋊C4—51no—
453C22⋊C4—51no—
454C22⋊C4—151no—
455C22⋊C4—151no—
456C22⋊C4—151no—
457C22⋊C4—151no—
458C22⋊C4—151no—
459C22⋊C4—151no—
460C22⋊C4—152no—
461C22⋊C4—152no—
462C22⋊C4—152no—
463C22⋊C4—151no—
464C22⋊C4—151no—
465C22⋊C4—151no—
466C42—51no—
467C42—151no—
468C42—151no—
469C42—152no—
470C42—151no—
471C3×C5—41noHall
472C22×C3—41no—
473C22×C3—401no—
474C22×C3—401no—
475C22×C3—401no—
476A4#404411yescharacteristic, direct product factor
477C3×C4—81no—
478C3×C4—81no—
479C3×C4—81no—
480C3×C4—401no—
481C3×C4—401no—
482C3×C4—401no—
483C2×C5—31no—
484C2×C5—31no—
485C2×C5—31no—
486C2×C5—31no—
487C2×C5A4×#4111yescharacteristic
488C2×C5A4×#4111yescharacteristic
489C2×C5A4×#4111yescharacteristic
490D5—41no—
491D5—121no—
492C23—31no—
493C23—31no—
494C23—31no—
495C23—31no—
496C23—51no—
497C23—151no—
498C23—201no—
499C23—301no—
500C23—301no—
501C23—301no—
502C23—301no—
503C23—301no—
504C23—301no—
505C23—301no—
506C23—301no—
507C23—301no—
508C23—301no—
509C23—301no—
510C23—301no—
511C23—601no—
512C23—601no—
513C23—601no—
514C23—602no—
515C23C3×#70911yescharacteristic
516C23C3×#71111yescharacteristic
517C23C3×#71311yescharacteristic
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—51no—
522C2×C4—51no—
523C2×C4—51no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—151no—
537C2×C4—151no—
538C2×C4—151no—
539C2×C4—301no—
540C2×C4—301no—
541C2×C4—301no—
542C2×C4—301no—
543C2×C4—301no—
544C2×C4—301no—
545C2×C4—301no—
546C2×C4—301no—
547C2×C4—301no—
548C2×C4—301no—
549C2×C4—301no—
550C2×C4—301no—
551C2×C4C2×D5×A411yescharacteristic
552C2×C4C2×D5×A411yescharacteristic
553C2×C4C2×D5×A411yescharacteristic
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—41no—
557C2×C3—801no—
558C5A4×#12611yescharacteristic, complemented, Sylow
559C22—31no—
560C22—31no—
561C22—31no—
562C22—32no—
563C22—31no—
564C22—31no—
565C22—31no—
566C22—31no—
567C22—31no—
568C22—31no—
569C22—101no—
570C22—101no—
571C22—101no—
572C22—301no—
573C22—301no—
574C22—301no—
575C22—601no—
576C22—601no—
577C22—601no—
578C22—601no—
579C22—601no—
580C22—601no—
581C22—601no—
582C22—601no—
583C22C3×#404411yescharacteristic, complemented
584C22C22×D5×A411yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—61no—
589C4—61no—
590C4—61no—
591C4—101no—
592C4—101no—
593C4—101no—
594C4—301no—
595C4—301no—
596C4—301no—
597C3—41noSylow
598C2—31no—
599C2—31no—
600C2—31no—
601C2—31no—
602C2—201no—
603C2—601no—
604C2A4×#70911yescharacteristic
605C2A4×#71111yescharacteristic
606C2A4×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C5×C4⋊C4C2×C3
prime radicalC22×D5×A4C22
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C3×#126
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×A4×C4⋊C4C2semidirect
5. A4×C4⋊Dic5C2semidirect
6. A4×#683C2semidirect
7. C4×A4×Dic5C2semidirect
8. C22×#4044C3semidirect
18. C22×C5×C4⋊C4C2×C3semidirect
22. C22×C4⋊Dic5C2×C3semidirect
23. C22×#683C2×C3semidirect
24. C22×C4×Dic5C2×C3semidirect
52. A4×C4⋊C4D5semidirect
106. #4044A4direct (N × H)
164. C5×C4⋊C4C2×A4semidirect
184. C4⋊Dic5C2×A4semidirect
189. #683C2×A4semidirect
194. C4×Dic5C2×A4semidirect
205. C22×C4⋊C4C3×D5semidirect
214. C5×A4#126semidirect
375. C22×C5C3×#126semidirect
450. C4⋊C4D5×A4semidirect
476. A4#4044direct (N × H)
558. C5A4×#126semidirect
583. C22C3×#4044semidirect

Maximal subgroups

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

subgroupindex
C5×A4×C4⋊C42
A4×#6852
A4×C4⋊Dic52
A4×#6832
C4×A4×Dic52
C22×#40443
C3×#40444
A4×#1265