Finite Group Databasebeta

← A4×#4025 #14513985

Subgroups — A4×#4025 #14513985

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×C22⋊C4C211yesmaximal, characteristic
2A4×C22⋊Dic5C211yesmaximal, characteristic
3A4×C22⋊Dic5C211yesmaximal, characteristic
4A4×C4⋊Dic5C211yesmaximal, characteristic, complemented
5A4×#683C211yesmaximal, characteristic, complemented
6A4×#683C211yesmaximal, characteristic, complemented
7C4×A4×Dic5C211yesmaximal, characteristic, complemented
8C22×#4025C311yesmaximal, characteristic, complemented, Hall
9C23×C5×A4C2211yescharacteristic
10C2×C4×C5×A4C2211yescharacteristic
11C2×C4×C5×A4C2211yescharacteristic
12C2×A4×Dic5C2211yescharacteristic
13C2×A4×Dic5C2211yescharacteristic
14C2×A4×Dic5C2211yescharacteristic
15C2×A4×Dic5C2211yescharacteristic
16C3×#4025—41nomaximal
17A4×#126—51nomaximal, Hall
18C22×C5×C22⋊C4C2×C311yescharacteristic
19C22×C22⋊Dic5C2×C311yescharacteristic
20C22×C22⋊Dic5C2×C311yescharacteristic
21C22×C4⋊Dic5C2×C311yescharacteristic, complemented
22C22×#683C2×C311yescharacteristic, complemented
23C22×#683C2×C311yescharacteristic, complemented
24C22×C4×Dic5C2×C311yescharacteristic, complemented
25C2×#4025—31no—
26C2×#4025—31no—
27C2×#4025—31no—
28C2×#4025—31no—
29C2×#4025—31no—
30C2×#4025—31no—
31C2×#4025—31no—
32C2×#4025—31no—
33C22×C5×A4—21no—
34C22×C5×A4—21no—
35C22×C5×A4—21no—
36C22×C5×A4C2311yescharacteristic
37C4×C5×A4—21no—
38C4×C5×A4—21no—
39A4×Dic5—21no—
40A4×Dic5—21no—
41A4×Dic5—21no—
42A4×Dic5—21no—
43C3×C5×C22⋊C4—41no—
44C3×C22⋊Dic5—41no—
45C3×C22⋊Dic5—41no—
46C3×C4⋊Dic5—41no—
47C3×#683—41no—
48C3×#683—41no—
49C3×C4×Dic5—41no—
50A4×C4⋊C4—51no—
51A4×C4⋊C4—51no—
52A4×C4⋊C4—51no—
53A4×C22⋊C4—51no—
54A4×C22⋊C4—51no—
55A4×C22⋊C4D511yescharacteristic
56C42×A4—51no—
57C25×C5C22×C311yescharacteristic
58C23×C4×C5C22×C311yescharacteristic
59C23×C4×C5C22×C311yescharacteristic
60C23×Dic5C22×C311yescharacteristic
61C23×Dic5C22×C311yescharacteristic
62C23×Dic5C22×C311yescharacteristic
63C23×Dic5C22×C311yescharacteristic
64C2×C5×C22⋊C4—31no—
65C2×C5×C22⋊C4—31no—
66C2×C5×C22⋊C4—31no—
67C2×C5×C22⋊C4—31no—
68C2×C22⋊Dic5—31no—
69C2×C22⋊Dic5—31no—
70C2×C22⋊Dic5—31no—
71C2×C22⋊Dic5—31no—
72C2×C22⋊Dic5—31no—
73C2×C22⋊Dic5—31no—
74C2×C22⋊Dic5—31no—
75C2×C22⋊Dic5—31no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—31no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5—31no—
80C2×#683—31no—
81C2×#683—31no—
82C2×#683—31no—
83C2×#683—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#4025—32no—
93#4025—32no—
94#4025—32no—
95#4025—32no—
96#4025—32no—
97#4025—32no—
98#4025—32no—
99#4025—31no—
100#4025—31no—
101#4025—31no—
102#4025—31no—
103#4025—31no—
104#4025—31no—
105#4025—31no—
106#4025A411yescharacteristic, direct product factor
107C22×#126—51noSylow
108C23×C3×C5—41no—
109C2×C5×A4—41no—
110C2×C5×A4#4111yescharacteristic
111C2×C5×A4#4111yescharacteristic
112C2×C5×A4#4111yescharacteristic
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C23×A4C2×D511yescharacteristic
120C2×C4×A4—51no—
121C2×C4×A4—51no—
122C2×C4×A4—51no—
123C2×C4×A4—51no—
124C2×C4×A4C2×D511yescharacteristic
125C2×C4×A4C2×D511yescharacteristic
126C3×#126—201no—
127C24×C5—21no—
128C24×C5—21no—
129C24×C5—21no—
130C24×C5—31no—
131C24×C5—31no—
132C24×C5—61no—
133C24×C5—61no—
134C24×C5—61no—
135C24×C5C23×C311yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—31no—
139C22×C4×C5—31no—
140C22×C4×C5—31no—
141C22×C4×C5—31no—
142C22×C4×C5—61no—
143C22×C4×C5—61no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—31no—
149C22×Dic5—31no—
150C22×Dic5—31no—
151C22×Dic5—31no—
152C22×Dic5—31no—
153C22×Dic5—31no—
154C22×Dic5—31no—
155C22×Dic5—31no—
156C22×Dic5—61no—
157C22×Dic5—61no—
158C22×Dic5—61no—
159C22×Dic5—61no—
160C5×C22⋊C4—32no—
161C5×C22⋊C4—31no—
162C5×C22⋊C4—31no—
163C5×C22⋊C4—31no—
164C5×C22⋊C4C2×A411yescharacteristic
165C22⋊Dic5—32no—
166C22⋊Dic5—32no—
167C22⋊Dic5—31no—
168C22⋊Dic5—31no—
169C22⋊Dic5—31no—
170C22⋊Dic5—31no—
171C22⋊Dic5—31no—
172C22⋊Dic5—31no—
173C22⋊Dic5C2×A411yescharacteristic
174C22⋊Dic5C2×A411yescharacteristic
175C4⋊Dic5—32no—
176C4⋊Dic5—31no—
177C4⋊Dic5—31no—
178C4⋊Dic5—31no—
179C4⋊Dic5C2×A411yescharacteristic, complemented
180#683—32no—
181#683—32no—
182#683—31no—
183#683—31no—
184#683—31no—
185#683—31no—
186#683—31no—
187#683—31no—
188#683C2×A411yescharacteristic, complemented
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⋊C4—51no—
206C22×C22⋊C4—51no—
207C22×C22⋊C4—51no—
208C22×C22⋊C4C3×D511yescharacteristic
209C22×C42—51no—
210C22×C3×C5—41no—
211C22×C3×C5—81no—
212C22×C3×C5—81no—
213C22×C3×C5—81no—
214C5×A4#12611yescharacteristic, complemented
215C3×C4×C5—81no—
216C3×C4×C5—81no—
217C3×Dic5—81no—
218C3×Dic5—81no—
219C3×Dic5—81no—
220C3×Dic5—81no—
221C22×A4—21no—
222C22×A4—21no—
223C22×A4—21no—
224C22×A4C22×D511yescharacteristic
225C4×A4—21no—
226C4×A4—21no—
227C4×A4—101no—
228C4×A4—101no—
229C4×A4—101no—
230C4×A4—101no—
231C3×C4⋊C4—201no—
232C3×C4⋊C4—201no—
233C3×C4⋊C4—201no—
234C3×C22⋊C4—41no—
235C3×C22⋊C4—201no—
236C3×C22⋊C4—201no—
237C3×C42—201no—
238C23×C5—31no—
239C23×C5—31no—
240C23×C5—31no—
241C23×C5—31no—
242C23×C5—31no—
243C23×C5—41no—
244C23×C5—61no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—61no—
248C23×C5—61no—
249C23×C5—61no—
250C23×C5—61no—
251C23×C5—61no—
252C23×C5—61no—
253C23×C5—61no—
254C23×C5—61no—
255C23×C5—61no—
256C23×C5—121no—
257C23×C5—121no—
258C23×C5—121no—
259C23×C5—122no—
260C23×C5C3×#4111yescharacteristic
261C23×C5C3×#4111yescharacteristic
262C23×C5C3×#4111yescharacteristic
263C23×C5C22×A411yescharacteristic
264C2×C4×C5—31no—
265C2×C4×C5—31no—
266C2×C4×C5—61no—
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×C5C22×A411yescharacteristic
275C2×C4×C5C22×A411yescharacteristic
276C2×Dic5—31no—
277C2×Dic5—31no—
278C2×Dic5—31no—
279C2×Dic5—31no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—61no—
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×Dic5C22×A411yescharacteristic
297C2×Dic5C22×A411yescharacteristic
298C2×Dic5C22×A411yescharacteristic
299C2×Dic5C22×A411yescharacteristic
300C25C2×C3×D511yescharacteristic
301C23×C4—51no—
302C23×C4—51no—
303C23×C4—51no—
304C23×C4—51no—
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—151no—
323C2×C4⋊C4—151no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4—151no—
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—31no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—31no—
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—
353C2×C3×C5—161no—
354C23×C3—41no—
355C2×A4—41no—
356C2×A4#70911yescharacteristic
357C2×A4#71111yescharacteristic
358C2×A4#71111yescharacteristic
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—201no—
362C2×C3×C4—201no—
363C2×C3×C4—201no—
364C2×C3×C4—201no—
365C22×C5—21no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—31no—
369C22×C5—31no—
370C22×C5—31no—
371C22×C5—32no—
372C22×C5—31no—
373C22×C5—31no—
374C22×C5—31no—
375C22×C5—31no—
376C22×C5—31no—
377C22×C5—31no—
378C22×C5—61no—
379C22×C5—61no—
380C22×C5—61no—
381C22×C5—121no—
382C22×C5—121no—
383C22×C5—121no—
384C22×C5—121no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5—121no—
388C22×C5—121no—
389C22×C5C3×#12611yescharacteristic, complemented
390C22×C5C23×A411yescharacteristic
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—61no—
394C4×C5—61no—
395Dic5—21no—
396Dic5—21no—
397Dic5—21no—
398Dic5—21no—
399Dic5—61no—
400Dic5—61no—
401Dic5—61no—
402Dic5—61no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—31no—
407C24—31no—
408C24—61no—
409C24—61no—
410C24—61no—
411C24C22×C3×D511yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—101no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—151no—
428C22×C4—151no—
429C22×C4—151no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—301no—
433C22×C4—301no—
434C22×C4—301no—
435C22×C4—301no—
436C4⋊C4—51no—
437C4⋊C4—51no—
438C4⋊C4—51no—
439C4⋊C4—151no—
440C4⋊C4—151no—
441C4⋊C4—151no—
442C4⋊C4—151no—
443C4⋊C4—151no—
444C4⋊C4—151no—
445C4⋊C4—152no—
446C4⋊C4—152no—
447C4⋊C4—152no—
448C4⋊C4—151no—
449C4⋊C4—151no—
450C4⋊C4—151no—
451C22⋊C4—32no—
452C22⋊C4—31no—
453C22⋊C4—31no—
454C22⋊C4—31no—
455C22⋊C4—51no—
456C22⋊C4—51no—
457C22⋊C4—151no—
458C22⋊C4—151no—
459C22⋊C4—151no—
460C22⋊C4—151no—
461C22⋊C4—152no—
462C22⋊C4—152no—
463C22⋊C4—151no—
464C22⋊C4—151no—
465C22⋊C4D5×A411yescharacteristic
466C42—51no—
467C42—151no—
468C42—151no—
469C42—152no—
470C42—151no—
471C3×C5—41noHall
472C22×C3—41no—
473C22×C3—81no—
474C22×C3—81no—
475C22×C3—81no—
476A4#402511yescharacteristic, direct product factor
477C3×C4—81no—
478C3×C4—81no—
479C3×C4—401no—
480C3×C4—401no—
481C3×C4—401no—
482C3×C4—401no—
483C2×C5—31no—
484C2×C5—31no—
485C2×C5—31no—
486C2×C5—31no—
487C2×C5—41no—
488C2×C5—121no—
489C2×C5A4×#4111yescharacteristic
490C2×C5A4×#4111yescharacteristic
491C2×C5A4×#4111yescharacteristic
492C23—31no—
493C23—31no—
494C23—31no—
495C23—31no—
496C23—31no—
497C23—41no—
498C23—61no—
499C23—61no—
500C23—61no—
501C23—61no—
502C23—61no—
503C23—61no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23—61no—
508C23—61no—
509C23—61no—
510C23—121no—
511C23—121no—
512C23—121no—
513C23—122no—
514C23C3×#70911yescharacteristic
515C23C3×#71111yescharacteristic
516C23C3×#71111yescharacteristic
517C23C2×D5×A411yescharacteristic
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—51no—
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—151no—
533C2×C4—151no—
534C2×C4—151no—
535C2×C4—151no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—301no—
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×C4—301no—
552C2×C4C2×D5×A411yescharacteristic
553C2×C4C2×D5×A411yescharacteristic
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—41no—
557C2×C3—161no—
558C5A4×#12611yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—21no—
562C22—31no—
563C22—31no—
564C22—31no—
565C22—32no—
566C22—31no—
567C22—31no—
568C22—31no—
569C22—31no—
570C22—31no—
571C22—31no—
572C22—61no—
573C22—61no—
574C22—61no—
575C22—121no—
576C22—121no—
577C22—121no—
578C22—121no—
579C22—121no—
580C22—121no—
581C22—121no—
582C22—121no—
583C22C3×#402511yescharacteristic, complemented
584C22C22×D5×A411yescharacteristic
585C4—21no—
586C4—21no—
587C4—61no—
588C4—61no—
589C4—101no—
590C4—101no—
591C4—101no—
592C4—101no—
593C4—301no—
594C4—301no—
595C4—301no—
596C4—301no—
597C3—41noSylow
598C2—31no—
599C2—31no—
600C2—31no—
601C2—31no—
602C2—41no—
603C2—121no—
604C2A4×#70911yescharacteristic
605C2A4×#71111yescharacteristic
606C2A4×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C5×C22⋊C4C2×C3
prime radicalC23×C5×A4C22
hypercenterC22⋊C4D5×A4
hypocenterC22×C5C3×#126
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
4. A4×C4⋊Dic5C2semidirect
5. A4×#683C2semidirect
6. A4×#683C2semidirect
7. C4×A4×Dic5C2semidirect
8. C22×#4025C3semidirect
21. C22×C4⋊Dic5C2×C3semidirect
22. C22×#683C2×C3semidirect
23. C22×#683C2×C3semidirect
24. C22×C4×Dic5C2×C3semidirect
106. #4025A4direct (N × H)
179. C4⋊Dic5C2×A4semidirect
188. #683C2×A4semidirect
189. #683C2×A4semidirect
194. C4×Dic5C2×A4semidirect
214. C5×A4#126semidirect
389. C22×C5C3×#126semidirect
476. A4#4025direct (N × H)
558. C5A4×#126semidirect
583. C22C3×#4025semidirect

Maximal subgroups

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

subgroupindex
C5×A4×C22⋊C42
A4×C22⋊Dic52
A4×C4⋊Dic52
A4×#6832
C4×A4×Dic52
C22×#40253
C3×#40254
A4×#1265