Finite Group Databasebeta

← A4×#4086 #14514185

Subgroups — A4×#4086 #14514185

Order 1920.

1360 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 111 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×C5×D4×A4C211yesmaximal, characteristic, complemented
2C2×A4×C22⋊D5C214yesmaximal, complemented
3C2×A4×D20C211yesmaximal, characteristic, complemented
4C4×A4×Dic5C211yesmaximal, characteristic, complemented
5C22×#4086C311yesmaximal, characteristic, complemented, Hall
6C23×C5×A4C2212yes—
7C22×D5×A4C2212yes—
8C5×D4×A4—22no—
9C2×C4×C5×A4C2211yescharacteristic
10A4×C22⋊D5—28no—
11C2×A4×Dic5C2212yes—
12A4×D20—22no—
13C3×#4086—41nomaximal
14A4×#127—51nomaximal, Hall
15C23×C5×D4C2×C311yescharacteristic, complemented
16C23×C22⋊D5C2×C314yescomplemented
17C23×D20C2×C311yescharacteristic, complemented
18C2×#4086—31no—
19C2×#4086—34no—
20C2×#4086—31no—
21C2×#4086—31no—
22C2×#4086—31no—
23C22×C4×Dic5C2×C311yescharacteristic, complemented
24C22×C5×A4—24no—
25C22×C5×A4—22no—
26C22×C5×A4C2311yescharacteristic
27C2×D5×A4—22no—
28C2×D5×A4—24no—
29C2×C3×C5×D4—41no—
30C2×C3×C22⋊D5—44no—
31C2×C3×D20—41no—
32C4×C5×A4D412yescomplemented
33A4×Dic5D414yescomplemented
34C3×C4×Dic5—41no—
35C2×D4×A4—54no—
36C2×D4×A4—51no—
37C2×D4×A4D511yescharacteristic, complemented
38C42×A4—51no—
39C25×C5C22×C312yes—
40C24×D5C22×C312yes—
41C22×C5×D4—22no—
42C22×C5×D4—31no—
43C22×C5×D4—31no—
44C22×C5×D4—32no—
45C22×C5×D4—62no—
46C23×C4×C5C22×C311yescharacteristic
47C22×C22⋊D5—28no—
48C22×C22⋊D5—34no—
49C22×C22⋊D5—34no—
50C22×C22⋊D5—34no—
51C22×C22⋊D5—34no—
52C22×C22⋊D5—68no—
53C23×Dic5C22×C312yes—
54C22×D20—22no—
55C22×D20—31no—
56C22×D20—32no—
57C22×D20—31no—
58C22×D20—62no—
59#4086—34no—
60#4086—34no—
61#4086—32no—
62#4086—34no—
63#4086—31no—
64#4086—34no—
65#4086—31no—
66#4086—31no—
67#4086A411yescharacteristic, direct product factor
68C2×C4×Dic5—31no—
69C2×C4×Dic5—31no—
70C2×C4×Dic5—32no—
71C22×#127—51noSylow
72C23×C3×C5—42no—
73C22×C3×D5—42no—
74C2×C5×A4—42no—
75C2×C5×A4C2×D412yes—
76C2×C5×A4C2×D411yescharacteristic
77D5×A4—42no—
78C3×C5×D4—82no—
79C2×C3×C4×C5—41no—
80C3×C22⋊D5—88no—
81C2×C3×Dic5—42no—
82C3×D20—82no—
83C23×A4—52no—
84C23×A4C2×D512yes—
85D4×A4—22no—
86D4×A4—108no—
87D4×A4—102no—
88C2×C4×A4—52no—
89C2×C4×A4C2×D511yescharacteristic
90C3×#127—201no—
91C24×C5—24no—
92C24×C5—22no—
93C24×C5—32no—
94C24×C5—32no—
95C24×C5—64no—
96C24×C5—62no—
97C24×C5C23×C311yescharacteristic
98C23×D5—22no—
99C23×D5—24no—
100C23×D5—32no—
101C23×D5—32no—
102C23×D5—62no—
103C23×D5—64no—
104C2×C5×D4—32no—
105C2×C5×D4—32no—
106C2×C5×D4—31no—
107C2×C5×D4—62no—
108C2×C5×D4—62no—
109C2×C5×D4—64no—
110C2×C5×D4—62no—
111C2×C5×D4—64no—
112C2×C5×D4—62no—
113C2×C5×D4C2×A411yescharacteristic, complemented
114C22×C4×C5—31no—
115C22×C4×C5—31no—
116C22×C4×C5—32no—
117C22×C4×C5C3×D412yescomplemented
118C2×C22⋊D5—38no—
119C2×C22⋊D5—34no—
120C2×C22⋊D5—34no—
121C2×C22⋊D5—34no—
122C2×C22⋊D5—68no—
123C2×C22⋊D5—68no—
124C2×C22⋊D5—68no—
125C2×C22⋊D5—68no—
126C2×C22⋊D5—68no—
127C2×C22⋊D5—68no—
128C2×C22⋊D5—68no—
129C2×C22⋊D5—68no—
130C2×C22⋊D5C2×A414yescomplemented
131C22×Dic5—32no—
132C22×Dic5—32no—
133C22×Dic5—34no—
134C22×Dic5C3×D414yescomplemented
135C2×D20—32no—
136C2×D20—32no—
137C2×D20—31no—
138C2×D20—62no—
139C2×D20—62no—
140C2×D20—64no—
141C2×D20—64no—
142C2×D20—62no—
143C2×D20—62no—
144C2×D20C2×A411yescharacteristic, complemented
145C4×Dic5—32no—
146C4×Dic5—31no—
147C4×Dic5—32no—
148C4×Dic5C2×A411yescharacteristic, complemented
149C23×D4—54no—
150C23×D4—51no—
151C23×D4C3×D511yescharacteristic, complemented
152C2×#127—151no—
153C2×#127—151no—
154C2×#127—151no—
155C2×#127—154no—
156C2×#127—151no—
157C22×C42—51no—
158C22×C3×C5—41no—
159C22×C3×C5—84no—
160C22×C3×C5—82no—
161C2×C3×D5—82no—
162C2×C3×D5—84no—
163C5×A4#12711yescharacteristic, complemented
164C3×C4×C5—42no—
165C3×Dic5—44no—
166C22×A4—24no—
167C22×A4—22no—
168C22×A4—104no—
169C22×A4—102no—
170C22×A4C22×D511yescharacteristic
171C2×C3×D4—41no—
172C2×C3×D4—201no—
173C2×C3×D4—204no—
174C4×A4—54no—
175C4×A4C22⋊D512yescomplemented
176C3×C42—201no—
177C23×C5—32no—
178C23×C5—31no—
179C23×C5—31no—
180C23×C5—32no—
181C23×C5—42no—
182C23×C5—64no—
183C23×C5—64no—
184C23×C5—62no—
185C23×C5—62no—
186C23×C5—64no—
187C23×C5—64no—
188C23×C5—62no—
189C23×C5—62no—
190C23×C5—124no—
191C23×C5—122no—
192C23×C5—124no—
193C23×C5C2×C3×D412yes—
194C23×C5C2×C3×D411yescharacteristic
195C23×C5C22×A412yes—
196C22×D5—32no—
197C22×D5—42no—
198C22×D5—62no—
199C22×D5—62no—
200C22×D5—64no—
201C22×D5—64no—
202C22×D5—62no—
203C22×D5—62no—
204C22×D5—64no—
205C22×D5—64no—
206C22×D5—124no—
207C22×D5—122no—
208C22×D5—124no—
209C22×D5C22×A412yes—
210C5×D4—22no—
211C5×D4—64no—
212C5×D4—64no—
213C5×D4—62no—
214C2×C4×C5—32no—
215C2×C4×C5—31no—
216C2×C4×C5—32no—
217C2×C4×C5—32no—
218C2×C4×C5—32no—
219C2×C4×C5C22×A411yescharacteristic
220C22⋊D5—28no—
221C22⋊D5—68no—
222C22⋊D5—68no—
223C22⋊D5—616no—
224C22⋊D5—68no—
225C2×Dic5—34no—
226C2×Dic5—32no—
227C2×Dic5—34no—
228C2×Dic5—34no—
229C2×Dic5—34no—
230C2×Dic5C22×A412yes—
231D20—22no—
232D20—64no—
233D20—64no—
234D20—62no—
235C25—52no—
236C25C2×C3×D512yes—
237C22×D4—22no—
238C22×D4—31no—
239C22×D4—31no—
240C22×D4—32no—
241C22×D4—62no—
242C22×D4—108no—
243C22×D4—102no—
244C22×D4—151no—
245C22×D4—151no—
246C22×D4—152no—
247C22×D4—154no—
248C22×D4—154no—
249C22×D4—154no—
250C22×D4—154no—
251C22×D4—302no—
252C22×D4—308no—
253C23×C4—52no—
254C23×C4C2×C3×D511yescharacteristic
255#127—51no—
256#127—151no—
257#127—154no—
258#127—151no—
259#127—154no—
260#127—154no—
261#127—154no—
262#127—152no—
263#127—151no—
264C2×C42—151no—
265C2×C42—152no—
266C2×C42—151no—
267C2×C3×C5—42no—
268C2×C3×C5—41no—
269C2×C3×C5—162no—
270C3×D5—162no—
271C23×C3—42no—
272C23×C3—202no—
273C2×A4—42no—
274C2×A4—202no—
275C2×A4D4×D512yes—
276C2×A4C2×C22⋊D511yescharacteristic
277C3×D4—82no—
278C3×D4—402no—
279C3×D4—408no—
280C2×C3×C4—41no—
281C2×C3×C4—202no—
282C22×C5—24no—
283C22×C5—22no—
284C22×C5—32no—
285C22×C5—31no—
286C22×C5—32no—
287C22×C5—32no—
288C22×C5—32no—
289C22×C5—31no—
290C22×C5—31no—
291C22×C5—64no—
292C22×C5—62no—
293C22×C5—122no—
294C22×C5—124no—
295C22×C5—122no—
296C22×C5—122no—
297C22×C5—124no—
298C22×C5—122no—
299C22×C5C3×#12711yescharacteristic, complemented
300C22×C5C23×A411yescharacteristic
301C2×D5—22no—
302C2×D5—24no—
303C2×D5—62no—
304C2×D5—64no—
305C2×D5—122no—
306C2×D5—122no—
307C2×D5—124no—
308C2×D5—122no—
309C2×D5—122no—
310C2×D5—124no—
311C4×C5—32no—
312C4×C5D4×A412yescomplemented
313Dic5—34no—
314Dic5D4×A414yescomplemented
315C24—24no—
316C24—22no—
317C24—32no—
318C24—32no—
319C24—62no—
320C24—64no—
321C24—104no—
322C24—102no—
323C24—152no—
324C24—152no—
325C24—302no—
326C24—304no—
327C24C22×C3×D511yescharacteristic
328C2×D4—32no—
329C2×D4—32no—
330C2×D4—31no—
331C2×D4—54no—
332C2×D4—51no—
333C2×D4—62no—
334C2×D4—62no—
335C2×D4—64no—
336C2×D4—62no—
337C2×D4—64no—
338C2×D4—62no—
339C2×D4—152no—
340C2×D4—152no—
341C2×D4—154no—
342C2×D4—154no—
343C2×D4—158no—
344C2×D4—154no—
345C2×D4—151no—
346C2×D4—302no—
347C2×D4—302no—
348C2×D4—304no—
349C2×D4—302no—
350C2×D4—304no—
351C2×D4—302no—
352C2×D4—308no—
353C2×D4—308no—
354C2×D4—308no—
355C2×D4—308no—
356C2×D4—308no—
357C2×D4—308no—
358C2×D4—308no—
359C2×D4—308no—
360C2×D4D5×A411yescharacteristic, complemented
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—32no—
364C22×C4—54no—
365C22×C4—152no—
366C22×C4—152no—
367C22×C4—154no—
368C22×C4C3×C22⋊D512yescomplemented
369C42—51no—
370C42—152no—
371C42—152no—
372C42—151no—
373C3×C5—41noHall
374C22×C3—41no—
375C22×C3—82no—
376C22×C3—84no—
377C22×C3—404no—
378C22×C3—402no—
379A4#408611yescharacteristic, direct product factor
380C3×C4—42no—
381C3×C4—204no—
382C2×C5—31no—
383C2×C5—32no—
384C2×C5—31no—
385C2×C5—42no—
386C2×C5—122no—
387C2×C5C2×D4×A412yes—
388C2×C5C2×D4×A411yescharacteristic
389D5—42no—
390D5—122no—
391C23—31no—
392C23—32no—
393C23—31no—
394C23—32no—
395C23—42no—
396C23—52no—
397C23—62no—
398C23—62no—
399C23—64no—
400C23—64no—
401C23—62no—
402C23—62no—
403C23—64no—
404C23—64no—
405C23—124no—
406C23—122no—
407C23—124no—
408C23—152no—
409C23—202no—
410C23—304no—
411C23—302no—
412C23—304no—
413C23—302no—
414C23—304no—
415C23—302no—
416C23—304no—
417C23—302no—
418C23—604no—
419C23—602no—
420C23—604no—
421C23C3×D4×D512yes—
422C23C2×C3×C22⋊D511yescharacteristic
423C23C2×D5×A412yes—
424D4—22no—
425D4—64no—
426D4—64no—
427D4—62no—
428D4—108no—
429D4—102no—
430D4—304no—
431D4—304no—
432D4—308no—
433D4—308no—
434D4—308no—
435D4—3016no—
436D4—302no—
437C2×C4—32no—
438C2×C4—31no—
439C2×C4—32no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—52no—
443C2×C4—154no—
444C2×C4—154no—
445C2×C4—154no—
446C2×C4—152no—
447C2×C4—154no—
448C2×C4C2×D5×A411yescharacteristic
449C2×C3—42no—
450C2×C3—41no—
451C2×C3—162no—
452C2×C3—802no—
453C5A4×#12711yescharacteristic, complemented, Sylow
454C22—24no—
455C22—22no—
456C22—32no—
457C22—31no—
458C22—32no—
459C22—32no—
460C22—32no—
461C22—31no—
462C22—31no—
463C22—64no—
464C22—62no—
465C22—104no—
466C22—102no—
467C22—122no—
468C22—122no—
469C22—124no—
470C22—122no—
471C22—122no—
472C22—124no—
473C22—304no—
474C22—302no—
475C22—602no—
476C22—604no—
477C22—602no—
478C22—602no—
479C22—604no—
480C22—602no—
481C22C3×#408611yescharacteristic, complemented
482C22C22×D5×A411yescharacteristic
483C4—32no—
484C4—54no—
485C4—154no—
486C4A4×C22⋊D512yescomplemented
487C3—41noSylow
488C2—31no—
489C2—32no—
490C2—31no—
491C2—42no—
492C2—122no—
493C2—202no—
494C2—602no—
495C2D4×D5×A412yes—
496C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC23×C5×D4C2×C3
hypercenterC2×D4D5×A4
hypocenterC22×C5C3×#127
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×A4C2semidirect
2. C2×A4×C22⋊D5C2semidirect
3. C2×A4×D20C2semidirect
4. C4×A4×Dic5C2semidirect
5. C22×#4086C3semidirect
15. C23×C5×D4C2×C3semidirect
16. C23×C22⋊D5C2×C3semidirect
17. C23×D20C2×C3semidirect
23. C22×C4×Dic5C2×C3semidirect
32. C4×C5×A4D4semidirect
33. A4×Dic5D4semidirect
37. C2×D4×A4D5semidirect
67. #4086A4direct (N × H)
113. C2×C5×D4C2×A4semidirect
117. C22×C4×C5C3×D4semidirect
130. C2×C22⋊D5C2×A4semidirect
134. C22×Dic5C3×D4semidirect
144. C2×D20C2×A4semidirect
148. C4×Dic5C2×A4semidirect
151. C23×D4C3×D5semidirect
163. C5×A4#127semidirect
175. C4×A4C22⋊D5semidirect
299. C22×C5C3×#127semidirect
312. C4×C5D4×A4semidirect
314. Dic5D4×A4semidirect
360. C2×D4D5×A4semidirect
368. C22×C4C3×C22⋊D5semidirect
379. A4#4086direct (N × H)
453. C5A4×#127semidirect
481. C22C3×#4086semidirect
486. C4A4×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×A42
C2×A4×C22⋊D52
C2×A4×D202
C4×A4×Dic52
C22×#40863
C3×#40864
A4×#1275