Finite Group Databasebeta

← A4×#4041 #14514001

Subgroups — A4×#4041 #14514001

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×A4×D20C212yesmaximal, complemented
2C2×A4×D20C211yesmaximal, characteristic, complemented
3C2×C4×D5×A4C211yesmaximal, characteristic, complemented
4C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
5A4×#685C212yesmaximal, complemented
6C22×#4041C311yesmaximal, characteristic, complemented, Hall
7C22×D5×A4C2212yes—
8C22×D5×A4C2211yescharacteristic
9C2×C4×C5×A4C2212yes—
10C2×C4×C5×A4C2211yescharacteristic
11C2×A4×Dic5C2211yescharacteristic
12A4×D20—24no—
13A4×D20—22no—
14C4×D5×A4—22no—
15C3×#4041—41nomaximal
16A4×#121—51nomaximal, Hall
17C23×D20C2×C312yescomplemented
18C23×D20C2×C311yescharacteristic, complemented
19C23×C4×D5C2×C311yescharacteristic, complemented
20C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
21C22×#685C2×C312yescomplemented
22C2×#4041—31no—
23C2×#4041—31no—
24C2×#4041—31no—
25C2×#4041—31no—
26C2×#4041—32no—
27C2×#4041—32no—
28C22×C5×A4C2311yescharacteristic
29C2×D5×A4—21no—
30C2×D5×A4—21no—
31C2×D5×A4—22no—
32C2×D5×A4—22no—
33C2×D5×A4—22no—
34C2×D5×A4D412yescomplemented
35C2×C3×D20—41no—
36C2×C3×D20—42no—
37C2×C3×C4×D5—41no—
38C4×C5×A4—22no—
39C4×C5×A4D412yescomplemented
40A4×Dic5—21no—
41C3×C5×C4⋊C4—41no—
42C3×#685—42no—
43C2×D4×A4—52no—
44C2×D4×A4—51no—
45C22×C4×A4—51no—
46A4×C4⋊C4D511yescharacteristic, complemented
47A4×C22⋊C4—52no—
48C24×D5C22×C312yes—
49C24×D5C22×C311yescharacteristic
50C23×C4×C5C22×C312yes—
51C23×C4×C5C22×C311yescharacteristic
52C23×Dic5C22×C311yescharacteristic
53C22×D20—24no—
54C22×D20—22no—
55C22×D20—31no—
56C22×D20—32no—
57C22×D20—32no—
58C22×D20—32no—
59C22×D20—32no—
60C22×D20—32no—
61C22×D20—31no—
62C22×D20—62no—
63C22×D20—64no—
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×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4—31no—
72C2×C5×C4⋊C4—32no—
73C2×#685—32no—
74C2×#685—32no—
75C2×#685—32no—
76C2×#685—32no—
77#4041—32no—
78#4041—32no—
79#4041—34no—
80#4041—34no—
81#4041—32no—
82#4041—31no—
83#4041—32no—
84#4041—31no—
85#4041—31no—
86#4041—32no—
87#4041A411yescharacteristic, direct product factor
88C22×#121—51noSylow
89C22×C3×D5—41no—
90C22×C3×D5—42no—
91C2×C5×A4C2×D411yescharacteristic
92C2×C5×A4C2×D411yescharacteristic
93C2×C5×A4#4111yescharacteristic
94D5×A4—22no—
95D5×A4—42no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—42no—
98C2×C3×Dic5—41no—
99C3×D20—82no—
100C3×D20—84no—
101C3×C4×D5—82no—
102C23×A4—51no—
103C23×A4—52no—
104D4×A4—104no—
105D4×A4—102no—
106C2×C4×A4—51no—
107C2×C4×A4—102no—
108C2×C4×A4C2×D512yes—
109C2×C4×A4C2×D511yescharacteristic
110C3×#121—201no—
111C24×C5C23×C311yescharacteristic
112C23×D5—21no—
113C23×D5—21no—
114C23×D5—22no—
115C23×D5—22no—
116C23×D5—22no—
117C23×D5—31no—
118C23×D5—31no—
119C23×D5—32no—
120C23×D5—32no—
121C23×D5—32no—
122C23×D5—61no—
123C23×D5—61no—
124C23×D5—62no—
125C23×D5—62no—
126C23×D5—62no—
127C23×D5C3×D412yescomplemented
128C22×C4×C5—22no—
129C22×C4×C5—31no—
130C22×C4×C5—31no—
131C22×C4×C5—32no—
132C22×C4×C5—32no—
133C22×C4×C5—32no—
134C22×C4×C5—62no—
135C22×C4×C5C3×D412yescomplemented
136C22×Dic5—21no—
137C22×Dic5—31no—
138C22×Dic5—31no—
139C22×Dic5—61no—
140C2×D20—32no—
141C2×D20—34no—
142C2×D20—32no—
143C2×D20—32no—
144C2×D20—32no—
145C2×D20—32no—
146C2×D20—31no—
147C2×D20—62no—
148C2×D20—62no—
149C2×D20—64no—
150C2×D20—64no—
151C2×D20—64no—
152C2×D20—64no—
153C2×D20—64no—
154C2×D20—64no—
155C2×D20—62no—
156C2×D20—62no—
157C2×D20—64no—
158C2×D20—64no—
159C2×D20—64no—
160C2×D20—64no—
161C2×D20C2×A412yescomplemented
162C2×D20C2×A411yescharacteristic, complemented
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
176C5×C4⋊C4—32no—
177C5×C4⋊C4—32no—
178C5×C4⋊C4—31no—
179C5×C4⋊C4C2×A411yescharacteristic, complemented
180#685—34no—
181#685—32no—
182#685—32no—
183#685—32no—
184#685C2×A412yescomplemented
185C23×D4—52no—
186C23×D4—51no—
187C24×C4—51no—
188C2×#121—151no—
189C2×#121—152no—
190C2×#121—151no—
191C2×#121—151no—
192C2×#121—151no—
193C2×#121—152no—
194C22×C4⋊C4C3×D511yescharacteristic, complemented
195C22×C22⋊C4—52no—
196C22×C3×C5—41no—
197C2×C3×D5—42no—
198C2×C3×D5—81no—
199C2×C3×D5—81no—
200C2×C3×D5—82no—
201C2×C3×D5—82no—
202C2×C3×D5—82no—
203C5×A4#12111yescharacteristic, complemented
204C3×C4×C5—42no—
205C3×C4×C5—82no—
206C3×Dic5—81no—
207C22×A4—52no—
208C22×A4—101no—
209C22×A4—101no—
210C22×A4—102no—
211C22×A4—102no—
212C22×A4—102no—
213C22×A4C22×D511yescharacteristic
214C2×C3×D4—201no—
215C2×C3×D4—202no—
216C22×C3×C4—201no—
217C4×A4—22no—
218C4×A4—101no—
219C4×A4D2012yescomplemented
220C3×C4⋊C4—41no—
221C3×C22⋊C4—202no—
222C23×C5—31no—
223C23×C5—31no—
224C23×C5—31no—
225C23×C5—31no—
226C23×C5C2×C3×D411yescharacteristic
227C23×C5C2×C3×D411yescharacteristic
228C23×C5C3×#4111yescharacteristic
229C22×D5—22no—
230C22×D5—32no—
231C22×D5—31no—
232C22×D5—32no—
233C22×D5—32no—
234C22×D5—32no—
235C22×D5—32no—
236C22×D5—42no—
237C22×D5—61no—
238C22×D5—61no—
239C22×D5—61no—
240C22×D5—61no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—62no—
244C22×D5—62no—
245C22×D5—62no—
246C22×D5—62no—
247C22×D5—64no—
248C22×D5—61no—
249C22×D5—61no—
250C22×D5—62no—
251C22×D5—62no—
252C22×D5—61no—
253C22×D5—61no—
254C22×D5—62no—
255C22×D5—62no—
256C22×D5—62no—
257C22×D5—62no—
258C22×D5—62no—
259C22×D5—62no—
260C22×D5—62no—
261C22×D5—124no—
262C22×D5—122no—
263C22×D5—122no—
264C22×D5—122no—
265C22×D5C22×A412yes—
266C22×D5C22×A411yescharacteristic
267C2×C4×C5—32no—
268C2×C4×C5—31no—
269C2×C4×C5—32no—
270C2×C4×C5—32no—
271C2×C4×C5—32no—
272C2×C4×C5—32no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5C22×A412yes—
278C2×C4×C5C22×A411yescharacteristic
279C2×Dic5—31no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5C22×A411yescharacteristic
285D20—24no—
286D20—22no—
287D20—64no—
288D20—64no—
289D20—64no—
290D20—64no—
291D20—68no—
292D20—64no—
293D20—62no—
294C4×D5—22no—
295C4×D5—62no—
296C4×D5—62no—
297C4×D5—64no—
298C4×D5—62no—
299C25—51no—
300C25—52no—
301C22×D4—104no—
302C22×D4—102no—
303C22×D4—151no—
304C22×D4—152no—
305C22×D4—151no—
306C22×D4—152no—
307C22×D4—152no—
308C22×D4—152no—
309C22×D4—152no—
310C22×D4—302no—
311C22×D4—304no—
312C23×C4—51no—
313C23×C4—102no—
314C23×C4—151no—
315C23×C4—151no—
316C23×C4—151no—
317C23×C4—151no—
318C23×C4—302no—
319C23×C4C2×C3×D512yes—
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—31no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—32no—
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—
342C3×D5—82no—
343C3×D5—162no—
344C23×C3—201no—
345C23×C3—202no—
346C2×A4—102no—
347C2×A4—202no—
348C2×A4C2×D2011yescharacteristic
349C2×A4D4×D511yescharacteristic
350C2×A4#71311yescharacteristic
351C3×D4—402no—
352C3×D4—404no—
353C2×C3×C4—41no—
354C2×C3×C4—42no—
355C2×C3×C4—201no—
356C2×C3×C4—402no—
357C22×C5—31no—
358C22×C5—31no—
359C22×C5—31no—
360C22×C5—32no—
361C22×C5—31no—
362C22×C5—31no—
363C22×C5—31no—
364C22×C5—31no—
365C22×C5—31no—
366C22×C5—31no—
367C22×C5C3×#12111yescharacteristic, complemented
368C22×C5C23×A411yescharacteristic
369C2×D5—21no—
370C2×D5—21no—
371C2×D5—22no—
372C2×D5—22no—
373C2×D5—22no—
374C2×D5—32no—
375C2×D5—62no—
376C2×D5—62no—
377C2×D5—62no—
378C2×D5—62no—
379C2×D5—62no—
380C2×D5—62no—
381C2×D5—61no—
382C2×D5—61no—
383C2×D5—62no—
384C2×D5—62no—
385C2×D5—62no—
386C2×D5—62no—
387C2×D5—62no—
388C2×D5—122no—
389C2×D5—122no—
390C2×D5—122no—
391C2×D5—122no—
392C2×D5—122no—
393C2×D5—122no—
394C2×D5—122no—
395C2×D5—122no—
396C2×D5D4×A412yescomplemented
397C4×C5—22no—
398C4×C5—32no—
399C4×C5—62no—
400C4×C5D4×A412yescomplemented
401Dic5—21no—
402Dic5—61no—
403C24—52no—
404C24—101no—
405C24—101no—
406C24—102no—
407C24—102no—
408C24—102no—
409C24—151no—
410C24—152no—
411C24—151no—
412C24—152no—
413C24—152no—
414C24—301no—
415C24—301no—
416C24—302no—
417C24—302no—
418C24—302no—
419C24C22×C3×D511yescharacteristic
420C2×D4—52no—
421C2×D4—51no—
422C2×D4—152no—
423C2×D4—152no—
424C2×D4—152no—
425C2×D4—152no—
426C2×D4—154no—
427C2×D4—152no—
428C2×D4—151no—
429C2×D4—302no—
430C2×D4—302no—
431C2×D4—304no—
432C2×D4—302no—
433C2×D4—304no—
434C2×D4—302no—
435C2×D4—304no—
436C2×D4—304no—
437C2×D4—304no—
438C2×D4—304no—
439C2×D4—304no—
440C2×D4—304no—
441C2×D4—304no—
442C2×D4—304no—
443C22×C4—22no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—51no—
450C22×C4—62no—
451C22×C4—101no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—152no—
455C22×C4—151no—
456C22×C4—151no—
457C22×C4—151no—
458C22×C4—302no—
459C22×C4—302no—
460C22×C4—302no—
461C22×C4—302no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—302no—
465C22×C4—302no—
466C22×C4—301no—
467C22×C4C3×D2012yescomplemented
468C4⋊C4—32no—
469C4⋊C4—32no—
470C4⋊C4—31no—
471C4⋊C4D5×A411yescharacteristic, complemented
472C22⋊C4—52no—
473C22⋊C4—152no—
474C22⋊C4—152no—
475C22⋊C4—154no—
476C22⋊C4—152no—
477C3×C5—41noHall
478C22×C3—41no—
479C22×C3—202no—
480C22×C3—401no—
481C22×C3—401no—
482C22×C3—402no—
483C22×C3—402no—
484C22×C3—402no—
485A4#404111yescharacteristic, direct product factor
486C3×C4—42no—
487C3×C4—82no—
488C3×C4—401no—
489C2×C5—31no—
490C2×C5—31no—
491C2×C5—31no—
492C2×C5—31no—
493C2×C5C2×D4×A411yescharacteristic
494C2×C5C2×D4×A411yescharacteristic
495C2×C5A4×#4111yescharacteristic
496D5—22no—
497D5—42no—
498D5—62no—
499D5—122no—
500C23—31no—
501C23—31no—
502C23—31no—
503C23—31no—
504C23—51no—
505C23—52no—
506C23—102no—
507C23—152no—
508C23—152no—
509C23—152no—
510C23—152no—
511C23—151no—
512C23—152no—
513C23—202no—
514C23—301no—
515C23—301no—
516C23—301no—
517C23—301no—
518C23—302no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23—302no—
523C23—302no—
524C23—302no—
525C23—301no—
526C23—301no—
527C23—302no—
528C23—302no—
529C23—301no—
530C23—301no—
531C23—304no—
532C23—302no—
533C23—302no—
534C23—302no—
535C23—302no—
536C23—302no—
537C23—302no—
538C23—602no—
539C23—602no—
540C23—602no—
541C23—604no—
542C23C2×C3×D2011yescharacteristic
543C23C3×D4×D511yescharacteristic
544C23C3×#71311yescharacteristic
545D4—104no—
546D4—102no—
547D4—304no—
548D4—304no—
549D4—304no—
550D4—304no—
551D4—304no—
552D4—308no—
553D4—302no—
554C2×C4—32no—
555C2×C4—31no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—51no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—102no—
566C2×C4—151no—
567C2×C4—302no—
568C2×C4—302no—
569C2×C4—304no—
570C2×C4—301no—
571C2×C4—301no—
572C2×C4—302no—
573C2×C4—301no—
574C2×C4—301no—
575C2×C4C2×D5×A412yes—
576C2×C4C2×D5×A411yescharacteristic
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3—402no—
581C2×C3—802no—
582C5A4×#12111yescharacteristic, complemented, Sylow
583C22—31no—
584C22—31no—
585C22—31no—
586C22—32no—
587C22—31no—
588C22—31no—
589C22—31no—
590C22—31no—
591C22—31no—
592C22—31no—
593C22—52no—
594C22—101no—
595C22—101no—
596C22—102no—
597C22—102no—
598C22—102no—
599C22—152no—
600C22—302no—
601C22—302no—
602C22—302no—
603C22—302no—
604C22—302no—
605C22—302no—
606C22—302no—
607C22—302no—
608C22—301no—
609C22—301no—
610C22—302no—
611C22—302no—
612C22—302no—
613C22—602no—
614C22—602no—
615C22—602no—
616C22—602no—
617C22—602no—
618C22—602no—
619C22—602no—
620C22—602no—
621C22C3×#404111yescharacteristic, complemented
622C22C22×D5×A411yescharacteristic
623C4—22no—
624C4—32no—
625C4—62no—
626C4—101no—
627C4—301no—
628C4A4×D2012yescomplemented
629C3—41noSylow
630C2—31no—
631C2—31no—
632C2—31no—
633C2—31no—
634C2—102no—
635C2—202no—
636C2—302no—
637C2—602no—
638C2C2×A4×D2011yescharacteristic
639C2D4×D5×A411yescharacteristic
640C2A4×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C5×C4⋊C4C2×C3
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C3×#121
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×A4×D20C2semidirect
2. C2×A4×D20C2semidirect
3. C2×C4×D5×A4C2semidirect
4. C5×A4×C4⋊C4C2semidirect
5. A4×#685C2semidirect
6. C22×#4041C3semidirect
17. C23×D20C2×C3semidirect
18. C23×D20C2×C3semidirect
19. C23×C4×D5C2×C3semidirect
20. C22×C5×C4⋊C4C2×C3semidirect
21. C22×#685C2×C3semidirect
34. C2×D5×A4D4semidirect
39. C4×C5×A4D4semidirect
46. A4×C4⋊C4D5semidirect
87. #4041A4direct (N × H)
127. C23×D5C3×D4semidirect
135. C22×C4×C5C3×D4semidirect
161. C2×D20C2×A4semidirect
162. C2×D20C2×A4semidirect
175. C2×C4×D5C2×A4semidirect
179. C5×C4⋊C4C2×A4semidirect
184. #685C2×A4semidirect
194. C22×C4⋊C4C3×D5semidirect
203. C5×A4#121semidirect
219. C4×A4D20semidirect
367. C22×C5C3×#121semidirect
396. C2×D5D4×A4semidirect
400. C4×C5D4×A4semidirect
467. C22×C4C3×D20semidirect
471. C4⋊C4D5×A4semidirect
485. A4#4041direct (N × H)
582. C5A4×#121semidirect
621. C22C3×#4041semidirect
628. C4A4×D20semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D202
C2×C4×D5×A42
C5×A4×C4⋊C42
A4×#6852
C22×#40413
C3×#40414
A4×#1215