Finite Group Databasebeta

← A4×#4038 #14513998

Subgroups — A4×#4038 #14513998

Order 1920.

880 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 123 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×C4×D5×A4C211yesmaximal, characteristic
2C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
3A4×#685C212yesmaximal
4A4×C4⋊Dic5C211yesmaximal, characteristic, complemented
5C4×A4×Dic5C212yesmaximal, complemented
6C22×#4038C311yesmaximal, characteristic, complemented, Hall
7C22×D5×A4C2211yescharacteristic
8C2×C4×C5×A4C2212yes—
9C2×C4×C5×A4C2211yescharacteristic
10C2×A4×Dic5C2212yes—
11C2×A4×Dic5C2211yescharacteristic
12C4×D5×A4C414yescomplemented
13C3×#4038—41nomaximal
14A4×#117—51nomaximal, Hall
15C23×C4×D5C2×C311yescharacteristic
16C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
17C22×#685C2×C312yes—
18C22×C4⋊Dic5C2×C311yescharacteristic, complemented
19C22×C4×Dic5C2×C312yescomplemented
20C2×#4038—31no—
21C2×#4038—31no—
22C2×#4038—31no—
23C2×#4038—32no—
24C2×#4038—31no—
25C2×#4038—32no—
26C22×C5×A4C2311yescharacteristic
27C2×D5×A4—21no—
28C2×D5×A4—21no—
29C2×D5×A4C2×C412yes—
30C2×C3×C4×D5—41no—
31C4×C5×A4—22no—
32C4×C5×A4C2×C412yes—
33A4×Dic5—22no—
34A4×Dic5C2×C412yes—
35C3×C5×C4⋊C4—41no—
36C3×#685—42no—
37C3×C4⋊Dic5—41no—
38C3×C4×Dic5—42no—
39C22×C4×A4—51no—
40A4×C4⋊C4—51no—
41A4×C4⋊C4D511yescharacteristic, complemented
42A4×C22⋊C4—52no—
43C42×A4—52no—
44C24×D5C22×C311yescharacteristic
45C23×C4×C5C22×C312yes—
46C23×C4×C5C22×C311yescharacteristic
47C23×Dic5C22×C312yes—
48C23×Dic5C22×C311yescharacteristic
49C22×C4×D5—31no—
50C22×C4×D5—31no—
51C22×C4×D5—31no—
52C22×C4×D5—31no—
53C22×C4×D5—34no—
54C22×C4×D5C3×C414yescomplemented
55C2×C5×C4⋊C4—31no—
56C2×C5×C4⋊C4—31no—
57C2×C5×C4⋊C4—32no—
58C2×#685—32no—
59C2×#685—32no—
60C2×#685—32no—
61C2×#685—32no—
62C2×C4⋊Dic5—31no—
63C2×C4⋊Dic5—31no—
64C2×C4⋊Dic5—32no—
65C2×C4×Dic5—32no—
66C2×C4×Dic5—32no—
67C2×C4×Dic5—32no—
68C2×C4×Dic5—32no—
69#4038—32no—
70#4038—32no—
71#4038—34no—
72#4038—34no—
73#4038—32no—
74#4038—31no—
75#4038—31no—
76#4038—32no—
77#4038—31no—
78#4038—32no—
79#4038A411yescharacteristic, direct product factor
80C22×#117—51noSylow
81C22×C3×D5—41no—
82C2×C5×A4C22×C411yescharacteristic
83C2×C5×A4#4111yescharacteristic
84C2×C5×A4#4111yescharacteristic
85D5×A4—22no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—42no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5—42no—
90C3×C4×D5—44no—
91C23×A4—51no—
92C2×C4×A4—51no—
93C2×C4×A4—54no—
94C2×C4×A4—52no—
95C2×C4×A4C2×D512yes—
96C2×C4×A4C2×D511yescharacteristic
97C3×#117—201no—
98C24×C5C23×C311yescharacteristic
99C23×D5—21no—
100C23×D5—21no—
101C23×D5—31no—
102C23×D5—32no—
103C23×D5—31no—
104C23×D5—61no—
105C23×D5—61no—
106C23×D5C2×C3×C412yes—
107C22×C4×C5—22no—
108C22×C4×C5—31no—
109C22×C4×C5—31no—
110C22×C4×C5—32no—
111C22×C4×C5—32no—
112C22×C4×C5—32no—
113C22×C4×C5—62no—
114C22×C4×C5C2×C3×C412yes—
115C22×Dic5—22no—
116C22×Dic5—31no—
117C22×Dic5—32no—
118C22×Dic5—31no—
119C22×Dic5—32no—
120C22×Dic5—32no—
121C22×Dic5—62no—
122C22×Dic5C2×C3×C412yes—
123C2×C4×D5—34no—
124C2×C4×D5—34no—
125C2×C4×D5—34no—
126C2×C4×D5—32no—
127C2×C4×D5—31no—
128C2×C4×D5—31no—
129C2×C4×D5—31no—
130C2×C4×D5—34no—
131C2×C4×D5—34no—
132C2×C4×D5—34no—
133C2×C4×D5—34no—
134C2×C4×D5—34no—
135C2×C4×D5C2×A411yescharacteristic
136C5×C4⋊C4—32no—
137C5×C4⋊C4—32no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4C2×A411yescharacteristic, complemented
140#685—34no—
141#685—32no—
142#685—32no—
143#685—32no—
144#685C2×A412yes—
145C4⋊Dic5—32no—
146C4⋊Dic5—31no—
147C4⋊Dic5—32no—
148C4⋊Dic5C2×A411yescharacteristic, complemented
149C4×Dic5—34no—
150C4×Dic5—32no—
151C4×Dic5—32no—
152C4×Dic5—32no—
153C4×Dic5C2×A412yescomplemented
154C24×C4—51no—
155C2×#117—151no—
156C2×#117—152no—
157C2×#117—152no—
158C2×#117—151no—
159C2×#117—151no—
160C2×#117—151no—
161C22×C4⋊C4—51no—
162C22×C4⋊C4C3×D511yescharacteristic, complemented
163C22×C22⋊C4—52no—
164C22×C42—52no—
165C22×C3×C5—41no—
166C2×C3×D5—42no—
167C2×C3×D5—81no—
168C2×C3×D5—81no—
169C5×A4#11711yescharacteristic, complemented
170C3×C4×C5—42no—
171C3×C4×C5—82no—
172C3×Dic5—42no—
173C3×Dic5—82no—
174C22×A4—52no—
175C22×A4—101no—
176C22×A4—101no—
177C22×A4C22×D511yescharacteristic
178C22×C3×C4—201no—
179C4×A4—22no—
180C4×A4—52no—
181C4×A4—102no—
182C4×A4C4×D512yes—
183C3×C4⋊C4—41no—
184C3×C4⋊C4—201no—
185C3×C22⋊C4—202no—
186C3×C42—202no—
187C23×C5—31no—
188C23×C5—31no—
189C23×C5—31no—
190C23×C5—31no—
191C23×C5C22×C3×C411yescharacteristic
192C23×C5C3×#4111yescharacteristic
193C23×C5C3×#4111yescharacteristic
194C22×D5—22no—
195C22×D5—32no—
196C22×D5—31no—
197C22×D5—32no—
198C22×D5—32no—
199C22×D5—32no—
200C22×D5—61no—
201C22×D5—61no—
202C22×D5—61no—
203C22×D5—61no—
204C22×D5—64no—
205C22×D5—62no—
206C22×D5—62no—
207C22×D5—61no—
208C22×D5—61no—
209C22×D5—61no—
210C22×D5—61no—
211C22×D5—62no—
212C22×D5C22×A411yescharacteristic
213C2×C4×C5—32no—
214C2×C4×C5—31no—
215C2×C4×C5—32no—
216C2×C4×C5—32no—
217C2×C4×C5—32no—
218C2×C4×C5—32no—
219C2×C4×C5—62no—
220C2×C4×C5—62no—
221C2×C4×C5—62no—
222C2×C4×C5—62no—
223C2×C4×C5C22×A412yes—
224C2×C4×C5C22×A411yescharacteristic
225C2×Dic5—32no—
226C2×Dic5—31no—
227C2×Dic5—32no—
228C2×Dic5—32no—
229C2×Dic5—32no—
230C2×Dic5—32no—
231C2×Dic5—62no—
232C2×Dic5—62no—
233C2×Dic5—62no—
234C2×Dic5—62no—
235C2×Dic5C22×A412yes—
236C2×Dic5C22×A411yescharacteristic
237C4×D5—38no—
238C4×D5—34no—
239C4×D5—34no—
240C4×D5—34no—
241C4×D5C4×A414yescomplemented
242C25—51no—
243C23×C4—51no—
244C23×C4—54no—
245C23×C4—52no—
246C23×C4—151no—
247C23×C4—151no—
248C23×C4—151no—
249C23×C4—151no—
250C23×C4—154no—
251C23×C4C2×C3×D512yes—
252C23×C4C2×C3×D511yescharacteristic
253#117—51no—
254#117—152no—
255#117—152no—
256#117—151no—
257#117—151no—
258#117—152no—
259#117—154no—
260#117—152no—
261#117—152no—
262#117—154no—
263#117—151no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—32no—
267C2×C4⋊C4—151no—
268C2×C4⋊C4—152no—
269C2×C4⋊C4—151no—
270C2×C22⋊C4—152no—
271C2×C22⋊C4—152no—
272C2×C22⋊C4—152no—
273C2×C22⋊C4—152no—
274C2×C42—152no—
275C2×C42—152no—
276C2×C42—152no—
277C2×C42—152no—
278C2×C3×C5—41no—
279C2×C3×C5—41no—
280C2×C3×C5—41no—
281C3×D5—82no—
282C23×C3—201no—
283C2×A4—102no—
284C2×A4C2×C4×D511yescharacteristic
285C2×A4#71111yescharacteristic
286C2×A4#71311yescharacteristic
287C2×C3×C4—41no—
288C2×C3×C4—42no—
289C2×C3×C4—204no—
290C2×C3×C4—201no—
291C2×C3×C4—202no—
292C22×C5—31no—
293C22×C5—31no—
294C22×C5—31no—
295C22×C5—32no—
296C22×C5—31no—
297C22×C5—31no—
298C22×C5—31no—
299C22×C5—31no—
300C22×C5—31no—
301C22×C5—31no—
302C22×C5C3×#11711yescharacteristic, complemented
303C22×C5C23×A411yescharacteristic
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—32no—
307C2×D5—62no—
308C2×D5—62no—
309C2×D5—62no—
310C2×D5—62no—
311C2×D5—62no—
312C2×D5—62no—
313C2×D5—61no—
314C2×D5—61no—
315C2×D5—62no—
316C2×D5—62no—
317C2×D5C2×C4×A412yes—
318C4×C5—22no—
319C4×C5—32no—
320C4×C5—62no—
321C4×C5C2×C4×A412yes—
322Dic5—22no—
323Dic5—32no—
324Dic5—62no—
325Dic5C2×C4×A412yes—
326C24—52no—
327C24—101no—
328C24—101no—
329C24—151no—
330C24—151no—
331C24—152no—
332C24—301no—
333C24—301no—
334C24C22×C3×D511yescharacteristic
335C22×C4—22no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4—32no—
341C22×C4—51no—
342C22×C4—52no—
343C22×C4—62no—
344C22×C4—102no—
345C22×C4—151no—
346C22×C4—154no—
347C22×C4—154no—
348C22×C4—151no—
349C22×C4—152no—
350C22×C4—154no—
351C22×C4—154no—
352C22×C4—154no—
353C22×C4—154no—
354C22×C4—154no—
355C22×C4—154no—
356C22×C4—151no—
357C22×C4—152no—
358C22×C4—151no—
359C22×C4—151no—
360C22×C4—152no—
361C22×C4—152no—
362C22×C4—302no—
363C22×C4C3×C4×D512yes—
364C4⋊C4—32no—
365C4⋊C4—32no—
366C4⋊C4—31no—
367C4⋊C4—51no—
368C4⋊C4—152no—
369C4⋊C4—152no—
370C4⋊C4—151no—
371C4⋊C4D5×A411yescharacteristic, complemented
372C22⋊C4—52no—
373C22⋊C4—152no—
374C22⋊C4—152no—
375C22⋊C4—154no—
376C22⋊C4—152no—
377C42—52no—
378C42—152no—
379C42—152no—
380C42—154no—
381C42—152no—
382C3×C5—41noHall
383C22×C3—41no—
384C22×C3—202no—
385C22×C3—401no—
386C22×C3—401no—
387A4#403811yescharacteristic, direct product factor
388C3×C4—42no—
389C3×C4—82no—
390C3×C4—202no—
391C3×C4—402no—
392C2×C5—31no—
393C2×C5—31no—
394C2×C5—31no—
395C2×C5—31no—
396C2×C5C22×C4×A411yescharacteristic
397C2×C5A4×#4111yescharacteristic
398C2×C5A4×#4111yescharacteristic
399D5—22no—
400D5—62no—
401C23—31no—
402C23—31no—
403C23—31no—
404C23—31no—
405C23—51no—
406C23—102no—
407C23—152no—
408C23—152no—
409C23—152no—
410C23—152no—
411C23—151no—
412C23—301no—
413C23—301no—
414C23—301no—
415C23—301no—
416C23—302no—
417C23—302no—
418C23—302no—
419C23—301no—
420C23—301no—
421C23—301no—
422C23—301no—
423C23—304no—
424C23C2×C3×C4×D511yescharacteristic
425C23C3×#71111yescharacteristic
426C23C3×#71311yescharacteristic
427C2×C4—32no—
428C2×C4—31no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—32no—
433C2×C4—51no—
434C2×C4—54no—
435C2×C4—52no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—154no—
441C2×C4—154no—
442C2×C4—158no—
443C2×C4—152no—
444C2×C4—152no—
445C2×C4—152no—
446C2×C4—151no—
447C2×C4—154no—
448C2×C4—152no—
449C2×C4—152no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4C2×D5×A412yes—
455C2×C4C2×D5×A411yescharacteristic
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—41no—
459C2×C3—402no—
460C5A4×#11711yescharacteristic, complemented, Sylow
461C22—31no—
462C22—31no—
463C22—31no—
464C22—32no—
465C22—31no—
466C22—31no—
467C22—31no—
468C22—31no—
469C22—31no—
470C22—31no—
471C22—52no—
472C22—101no—
473C22—101no—
474C22—152no—
475C22—302no—
476C22—302no—
477C22—302no—
478C22—302no—
479C22—302no—
480C22—302no—
481C22—302no—
482C22—302no—
483C22—301no—
484C22—301no—
485C22C3×#403811yescharacteristic, complemented
486C22C22×D5×A411yescharacteristic
487C4—22no—
488C4—32no—
489C4—52no—
490C4—62no—
491C4—102no—
492C4—152no—
493C4—302no—
494C4C4×D5×A412yes—
495C3—41noSylow
496C2—31no—
497C2—31no—
498C2—31no—
499C2—31no—
500C2—102no—
501C2—302no—
502C2C2×C4×D5×A411yescharacteristic
503C2A4×#71111yescharacteristic
504C2A4×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutatorC23×C5C22×C3×C4
FittingC22×C5×C4⋊C4C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC22×D5×A4C22
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C3×#117
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×A4×C4⋊C4C2semidirect
4. A4×C4⋊Dic5C2semidirect
5. C4×A4×Dic5C2semidirect
6. C22×#4038C3semidirect
12. C4×D5×A4C4semidirect
16. C22×C5×C4⋊C4C2×C3semidirect
18. C22×C4⋊Dic5C2×C3semidirect
19. C22×C4×Dic5C2×C3semidirect
41. A4×C4⋊C4D5semidirect
54. C22×C4×D5C3×C4semidirect
79. #4038A4direct (N × H)
139. C5×C4⋊C4C2×A4semidirect
148. C4⋊Dic5C2×A4semidirect
153. C4×Dic5C2×A4semidirect
162. C22×C4⋊C4C3×D5semidirect
169. C5×A4#117semidirect
241. C4×D5C4×A4semidirect
302. C22×C5C3×#117semidirect
371. C4⋊C4D5×A4semidirect
387. A4#4038direct (N × H)
460. C5A4×#117semidirect
485. C22C3×#4038semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C5×A4×C4⋊C42
A4×#6852
A4×C4⋊Dic52
C4×A4×Dic52
C22×#40383
C3×#40384
A4×#1175