Finite Group Databasebeta

← A4×#4035 #14513995

Subgroups — A4×#4035 #14513995

Order 1920.

584 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 93 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
2A4×C4⋊Dic5C211yesmaximal, characteristic
3A4×#683C211yesmaximal, characteristic
4A4×#683C211yesmaximal, characteristic
5A4×#683C211yesmaximal, characteristic
6A4×#683C211yesmaximal, characteristic
7C4×A4×Dic5C211yesmaximal, characteristic
8C22×#4035C311yesmaximal, characteristic, complemented, Hall
9C2×C4×C5×A4C2211yescharacteristic
10C2×C4×C5×A4C2211yescharacteristic
11C2×C4×C5×A4C2211yescharacteristic
12C2×A4×Dic5C2211yescharacteristic
13C2×A4×Dic5C2211yescharacteristic
14C2×A4×Dic5C2211yescharacteristic
15C2×A4×Dic5C2211yescharacteristic
16C3×#4035—41nomaximal
17A4×#125—51nomaximal, Hall
18C22×C5×C4⋊C4C2×C311yescharacteristic
19C22×C4⋊Dic5C2×C311yescharacteristic
20C22×#683C2×C311yescharacteristic
21C22×#683C2×C311yescharacteristic
22C22×#683C2×C311yescharacteristic
23C22×#683C2×C311yescharacteristic
24C22×C4×Dic5C2×C311yescharacteristic
25C2×#4035—31no—
26C2×#4035—31no—
27C2×#4035—31no—
28C2×#4035—31no—
29C2×#4035—31no—
30C2×#4035—31no—
31C2×#4035—31no—
32C2×#4035—31no—
33C22×C5×A4C2311yescharacteristic
34C4×C5×A4—21no—
35C4×C5×A4—21no—
36C4×C5×A4—21no—
37A4×Dic5—21no—
38A4×Dic5—21no—
39A4×Dic5—21no—
40A4×Dic5Q812yes—
41C3×C5×C4⋊C4—41no—
42C3×C4⋊Dic5—41no—
43C3×#683—41no—
44C3×#683—41no—
45C3×#683—41no—
46C3×#683—41no—
47C3×C4×Dic5—41no—
48A4×C4⋊C4—51no—
49A4×C4⋊C4—51no—
50A4×C4⋊C4—51no—
51A4×C4⋊C4—51no—
52A4×C4⋊C4—51no—
53A4×C4⋊C4D511yescharacteristic
54C42×A4—51no—
55C23×C4×C5C22×C311yescharacteristic
56C23×C4×C5C22×C311yescharacteristic
57C23×C4×C5C22×C311yescharacteristic
58C23×Dic5C22×C311yescharacteristic
59C23×Dic5C22×C311yescharacteristic
60C23×Dic5C22×C311yescharacteristic
61C23×Dic5C22×C311yescharacteristic
62C2×C5×C4⋊C4—31no—
63C2×C5×C4⋊C4—31no—
64C2×C5×C4⋊C4—31no—
65C2×C5×C4⋊C4—31no—
66C2×C4⋊Dic5—31no—
67C2×C4⋊Dic5—31no—
68C2×C4⋊Dic5—31no—
69C2×C4⋊Dic5—31no—
70C2×#683—31no—
71C2×#683—31no—
72C2×#683—31no—
73C2×#683—31no—
74C2×#683—31no—
75C2×#683—31no—
76C2×#683—31no—
77C2×#683—31no—
78C2×#683—31no—
79C2×#683—31no—
80C2×#683—31no—
81C2×#683—31no—
82C2×#683—31no—
83C2×#683—31no—
84C2×#683—31no—
85C2×#683—31no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5—31no—
88C2×C4×Dic5—31no—
89C2×C4×Dic5—31no—
90#4035—32no—
91#4035—32no—
92#4035—32no—
93#4035—32no—
94#4035—32no—
95#4035—32no—
96#4035—32no—
97#4035—31no—
98#4035—31no—
99#4035—31no—
100#4035—31no—
101#4035—31no—
102#4035—31no—
103#4035—31no—
104#4035A411yescharacteristic, direct product factor
105C22×#125—51noSylow
106C2×C5×A4C2×Q811yescharacteristic
107C2×C5×A4#4111yescharacteristic
108C2×C5×A4#4111yescharacteristic
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C4×A4—51no—
117C2×C4×A4—51no—
118C2×C4×A4—51no—
119C2×C4×A4—51no—
120C2×C4×A4C2×D511yescharacteristic
121C2×C4×A4C2×D511yescharacteristic
122C2×C4×A4C2×D511yescharacteristic
123C3×#125—201no—
124C24×C5C23×C311yescharacteristic
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—31no—
129C22×C4×C5—31no—
130C22×C4×C5—31no—
131C22×C4×C5—31no—
132C22×C4×C5—31no—
133C22×C4×C5—31no—
134C22×C4×C5—61no—
135C22×C4×C5—61no—
136C22×C4×C5—61no—
137C22×Dic5—21no—
138C22×Dic5—21no—
139C22×Dic5—21no—
140C22×Dic5—31no—
141C22×Dic5—32no—
142C22×Dic5—31no—
143C22×Dic5—31no—
144C22×Dic5—31no—
145C22×Dic5—31no—
146C22×Dic5—31no—
147C22×Dic5—31no—
148C22×Dic5—31no—
149C22×Dic5—61no—
150C22×Dic5—61no—
151C22×Dic5—61no—
152C22×Dic5C3×Q812yes—
153C5×C4⋊C4—32no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—31no—
156C5×C4⋊C4—31no—
157C5×C4⋊C4C2×A411yescharacteristic
158C4⋊Dic5—32no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—31no—
162C4⋊Dic5C2×A411yescharacteristic
163#683—32no—
164#683—32no—
165#683—32no—
166#683—32no—
167#683—31no—
168#683—31no—
169#683—31no—
170#683—31no—
171#683—31no—
172#683—31no—
173#683—31no—
174#683—31no—
175#683—31no—
176#683—31no—
177#683—31no—
178#683—31no—
179#683C2×A411yescharacteristic
180#683C2×A411yescharacteristic
181#683C2×A411yescharacteristic
182#683C2×A411yescharacteristic
183C4×Dic5—32no—
184C4×Dic5—31no—
185C4×Dic5—31no—
186C4×Dic5—31no—
187C4×Dic5C2×A411yescharacteristic
188C2×#125—151no—
189C2×#125—151no—
190C2×#125—151no—
191C2×#125—151no—
192C2×#125—151no—
193C2×#125—151no—
194C2×#125—151no—
195C2×#125—151no—
196C22×C4⋊C4—51no—
197C22×C4⋊C4—51no—
198C22×C4⋊C4—51no—
199C22×C4⋊C4—51no—
200C22×C4⋊C4—51no—
201C22×C4⋊C4C3×D511yescharacteristic
202C22×C42—51no—
203C22×C3×C5—41no—
204C5×A4#12511yescharacteristic, complemented
205C3×C4×C5—81no—
206C3×C4×C5—81no—
207C3×C4×C5—81no—
208C3×Dic5—42no—
209C3×Dic5—81no—
210C3×Dic5—81no—
211C3×Dic5—81no—
212C22×A4C22×D511yescharacteristic
213C4×A4—21no—
214C4×A4—21no—
215C4×A4—21no—
216C4×A4—52no—
217C4×A4—101no—
218C4×A4—101no—
219C4×A4—101no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—201no—
222C3×C4⋊C4—201no—
223C3×C4⋊C4—201no—
224C3×C4⋊C4—201no—
225C3×C4⋊C4—201no—
226C3×C42—201no—
227C23×C5—31no—
228C23×C5—31no—
229C23×C5—31no—
230C23×C5—31no—
231C23×C5C2×C3×Q811yescharacteristic
232C23×C5C3×#4111yescharacteristic
233C23×C5C3×#4111yescharacteristic
234C2×C4×C5—31no—
235C2×C4×C5—31no—
236C2×C4×C5—31no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5—61no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—61no—
245C2×C4×C5—61no—
246C2×C4×C5—61no—
247C2×C4×C5—61no—
248C2×C4×C5—61no—
249C2×C4×C5C22×A411yescharacteristic
250C2×C4×C5C22×A411yescharacteristic
251C2×C4×C5C22×A411yescharacteristic
252C2×Dic5—32no—
253C2×Dic5—31no—
254C2×Dic5—32no—
255C2×Dic5—32no—
256C2×Dic5—32no—
257C2×Dic5—31no—
258C2×Dic5—31no—
259C2×Dic5—31no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5—61no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5—61no—
266C2×Dic5—61no—
267C2×Dic5—61no—
268C2×Dic5—61no—
269C2×Dic5—61no—
270C2×Dic5—61no—
271C2×Dic5—61no—
272C2×Dic5C22×A411yescharacteristic
273C2×Dic5C22×A411yescharacteristic
274C2×Dic5C22×A411yescharacteristic
275C2×Dic5C22×A411yescharacteristic
276C23×C4—51no—
277C23×C4—51no—
278C23×C4—51no—
279C23×C4—51no—
280C23×C4C2×C3×D511yescharacteristic
281C23×C4C2×C3×D511yescharacteristic
282C23×C4C2×C3×D511yescharacteristic
283#125—51no—
284#125—151no—
285#125—151no—
286#125—151no—
287#125—151no—
288#125—151no—
289#125—151no—
290#125—152no—
291#125—152no—
292#125—152no—
293#125—152no—
294#125—152no—
295#125—152no—
296#125—152no—
297#125—151no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—151no—
303C2×C4⋊C4—151no—
304C2×C4⋊C4—151no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—151no—
307C2×C4⋊C4—151no—
308C2×C4⋊C4—151no—
309C2×C4⋊C4—151no—
310C2×C4⋊C4—151no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C4⋊C4—151no—
314C2×C4⋊C4—151no—
315C2×C4⋊C4—151no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—151no—
318C2×C4⋊C4—151no—
319C2×C4⋊C4—151no—
320C2×C4⋊C4—151no—
321C2×C4⋊C4—151no—
322C2×C42—151no—
323C2×C42—151no—
324C2×C42—151no—
325C2×C42—151no—
326C2×C3×C5—41no—
327C2×C3×C5—41no—
328C2×C3×C5—41no—
329C2×A4#70911yescharacteristic
330C2×A4#71111yescharacteristic
331C2×A4Q8×D511yescharacteristic
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—201no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4—201no—
339C22×C5—31no—
340C22×C5—31no—
341C22×C5—31no—
342C22×C5—32no—
343C22×C5—31no—
344C22×C5—31no—
345C22×C5—31no—
346C22×C5—31no—
347C22×C5—31no—
348C22×C5—31no—
349C22×C5C3×#12511yescharacteristic, complemented
350C22×C5C23×A411yescharacteristic
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—21no—
354C4×C5—61no—
355C4×C5—61no—
356C4×C5—61no—
357Dic5—21no—
358Dic5—21no—
359Dic5—21no—
360Dic5—32no—
361Dic5—61no—
362Dic5—61no—
363Dic5—61no—
364Dic5Q8×A412yes—
365C24C22×C3×D511yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—52no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—101no—
380C22×C4—101no—
381C22×C4—101no—
382C22×C4—151no—
383C22×C4—151no—
384C22×C4—151no—
385C22×C4—151no—
386C22×C4—151no—
387C22×C4—152no—
388C22×C4—151no—
389C22×C4—151no—
390C22×C4—151no—
391C22×C4—301no—
392C22×C4—301no—
393C22×C4—301no—
394C4⋊C4—32no—
395C4⋊C4—31no—
396C4⋊C4—31no—
397C4⋊C4—31no—
398C4⋊C4—51no—
399C4⋊C4—51no—
400C4⋊C4—51no—
401C4⋊C4—51no—
402C4⋊C4—51no—
403C4⋊C4—151no—
404C4⋊C4—151no—
405C4⋊C4—151no—
406C4⋊C4—151no—
407C4⋊C4—151no—
408C4⋊C4—151no—
409C4⋊C4—151no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—151no—
413C4⋊C4—152no—
414C4⋊C4—152no—
415C4⋊C4—152no—
416C4⋊C4—152no—
417C4⋊C4—152no—
418C4⋊C4—151no—
419C4⋊C4—151no—
420C4⋊C4—151no—
421C4⋊C4—151no—
422C4⋊C4—151no—
423C4⋊C4D5×A411yescharacteristic
424C42—51no—
425C42—151no—
426C42—151no—
427C42—152no—
428C42—151no—
429C3×C5—41noHall
430C22×C3—41no—
431A4#403511yescharacteristic, direct product factor
432C3×C4—81no—
433C3×C4—81no—
434C3×C4—81no—
435C3×C4—202no—
436C3×C4—401no—
437C3×C4—401no—
438C3×C4—401no—
439C2×C5—31no—
440C2×C5—31no—
441C2×C5—31no—
442C2×C5—31no—
443C2×C5C2×Q8×A411yescharacteristic
444C2×C5A4×#4111yescharacteristic
445C2×C5A4×#4111yescharacteristic
446C23—31no—
447C23—31no—
448C23—31no—
449C23—31no—
450C23C3×#70911yescharacteristic
451C23C3×#71111yescharacteristic
452C23C3×Q8×D511yescharacteristic
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—51no—
457C2×C4—51no—
458C2×C4—51no—
459C2×C4—51no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—152no—
473C2×C4—152no—
474C2×C4—152no—
475C2×C4—151no—
476C2×C4—152no—
477C2×C4—151no—
478C2×C4—151no—
479C2×C4—151no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4—301no—
483C2×C4—301no—
484C2×C4—301no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—301no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—301no—
491C2×C4—301no—
492C2×C4C2×D5×A411yescharacteristic
493C2×C4C2×D5×A411yescharacteristic
494C2×C4C2×D5×A411yescharacteristic
495C2×C3—41no—
496C2×C3—41no—
497C2×C3—41no—
498C5A4×#12511yescharacteristic, complemented, Sylow
499C22—31no—
500C22—31no—
501C22—31no—
502C22—32no—
503C22—31no—
504C22—31no—
505C22—31no—
506C22—31no—
507C22—31no—
508C22—31no—
509C22C3×#403511yescharacteristic, complemented
510C22C22×D5×A411yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—52no—
515C4—61no—
516C4—61no—
517C4—61no—
518C4—101no—
519C4—101no—
520C4—101no—
521C4—152no—
522C4—301no—
523C4—301no—
524C4—301no—
525C3—41noSylow
526C2—31no—
527C2—31no—
528C2—31no—
529C2—31no—
530C2A4×#70911yescharacteristic
531C2A4×#71111yescharacteristic
532C2Q8×D5×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C5×C4⋊C4C2×C3
prime radicalC22×C5×A4C23
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C3×#125
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C22×#4035C3semidirect
104. #4035A4direct (N × H)
204. C5×A4#125semidirect
349. C22×C5C3×#125semidirect
431. A4#4035direct (N × H)
498. C5A4×#125semidirect
509. C22C3×#4035semidirect

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×C4⋊Dic52
A4×#6832
C4×A4×Dic52
C22×#40353
C3×#40354
A4×#1255