Finite Group Databasebeta

← A4×#4055 #14514140

Subgroups — A4×#4055 #14514140

Order 1920.

688 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 688 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
1A4×#709C211yesmaximal, characteristic
2C2×A4×Dic10C211yesmaximal, characteristic, complemented
3C5×A4×M16C211yesmaximal, characteristic, complemented
4A4×Dic20C212yesmaximal, complemented
5A4×#677C212yesmaximal, complemented
6C22×#4055C311yesmaximal, characteristic, complemented, Hall
7C2×C4×C5×A4C2211yescharacteristic
8A4×C22⋊D5—21no—
9C2×A4×Dic5—21no—
10A4×D20C2211yescharacteristic
11C4×D5×A4—21no—
12A4×Dic10—21no—
13A4×Dic10C2212yes—
14A4×Dic10C2211yescharacteristic
15C3×#4055—41nomaximal
16C5×C8×A4C2212yes—
17A4×#137—51nomaximal, Hall
18C22×#709C2×C311yescharacteristic
19C23×Dic10C2×C311yescharacteristic, complemented
20C22×C5×M16C2×C311yescharacteristic, complemented
21C2×#4055—31no—
22C2×#4055—31no—
23C2×#4055—31no—
24C2×#4055—32no—
25C2×#4055—32no—
26C2×#4055—31no—
27C22×Dic20C2×C312yescomplemented
28C22×#677C2×C312yescomplemented
29C22×C5×A4D411yescharacteristic
30C2×D5×A4—21no—
31C3×#709—41no—
32C2×C3×Dic10—41no—
33C4×C5×A4D411yescharacteristic
34C4×C5×A4C2311yescharacteristic
35A4×Dic5—22no—
36A4×Dic5—21no—
37C3×C5×M16—41no—
38C3×Dic20—42no—
39C3×#677—42no—
40A4×#41—51no—
41C2×Q8×A4—51no—
42A4×Q16—52no—
43A4×SD16—52no—
44A4×M16D511yescharacteristic, complemented
45C23×C4×C5C22×C311yescharacteristic
46C22×C22⋊D5—21no—
47C23×Dic5—21no—
48C2×#709—31no—
49C2×#709—31no—
50C2×#709—31no—
51C2×#709—31no—
52C2×#709—61no—
53C2×#709—61no—
54C22×D20C22×C311yescharacteristic
55C22×C4×D5—21no—
56C22×Dic10—21no—
57C22×Dic10—31no—
58C22×Dic10—31no—
59C22×Dic10—32no—
60C22×Dic10—61no—
61C22×Dic10—61no—
62C22×Dic10C22×C312yes—
63C22×Dic10C22×C311yescharacteristic
64C2×C5×M16—31no—
65C2×C5×M16—32no—
66C2×C5×M16—31no—
67C22×C5×C8C22×C312yes—
68#4055—32no—
69#4055—32no—
70#4055—34no—
71#4055—34no—
72#4055—32no—
73#4055—31no—
74#4055—31no—
75#4055—31no—
76#4055—32no—
77#4055—32no—
78#4055A411yescharacteristic, direct product factor
79C2×Dic20—32no—
80C2×Dic20—32no—
81C2×Dic20—32no—
82C2×Dic20—32no—
83C2×#677—32no—
84C2×#677—32no—
85C2×#677—32no—
86C2×#677—32no—
87C22×#137—51noSylow
88C2×C5×A4—21no—
89C2×C5×A4C2×D411yescharacteristic
90D5×A4—41no—
91C2×C3×C4×C5—41no—
92C3×C22⋊D5—81no—
93C2×C3×Dic5—81no—
94C3×D20—41no—
95C3×C4×D5—81no—
96C3×Dic10—42no—
97C3×Dic10—41no—
98C3×Dic10—81no—
99C3×C5×C8—42no—
100Q8×A4—52no—
101Q8×A4—51no—
102Q8×A4—101no—
103D4×A4—51no—
104D4×A4—101no—
105C2×C4×A4—101no—
106C2×C4×A4—101no—
107C2×C4×A4C2×D511yescharacteristic
108C3×#137—201no—
109C8×A4C2×D512yes—
110C24×C5C3×D411yescharacteristic
111C23×D5—21no—
112C22×C4×C5—31no—
113C22×C4×C5—31no—
114C22×C4×C5—31no—
115C22×C4×C5—31no—
116C22×C4×C5C3×D411yescharacteristic
117C22×C4×C5C23×C311yescharacteristic
118C2×C22⋊D5—61no—
119C2×C22⋊D5—61no—
120C2×C22⋊D5—61no—
121C2×C22⋊D5—61no—
122C22×Dic5—22no—
123C22×Dic5—21no—
124C22×Dic5—61no—
125C22×Dic5—62no—
126C22×Dic5—61no—
127#709—32no—
128#709—31no—
129#709—31no—
130#709—31no—
131#709—61no—
132#709—61no—
133#709—62no—
134#709—62no—
135#709—61no—
136#709—61no—
137#709C2×A411yescharacteristic
138C2×D20—31no—
139C2×D20—31no—
140C2×D20—61no—
141C2×C4×D5—61no—
142C2×C4×D5—61no—
143C2×C4×D5—61no—
144C2×C4×D5—61no—
145C2×Dic10—32no—
146C2×Dic10—31no—
147C2×Dic10—32no—
148C2×Dic10—32no—
149C2×Dic10—31no—
150C2×Dic10—32no—
151C2×Dic10—31no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10—64no—
156C2×Dic10—61no—
157C2×Dic10—62no—
158C2×Dic10—61no—
159C2×Dic10—61no—
160C2×Dic10—62no—
161C2×Dic10—61no—
162C2×Dic10C2×A411yescharacteristic, complemented
163C5×M16—32no—
164C5×M16—31no—
165C5×M16—32no—
166C5×M16C2×A411yescharacteristic, complemented
167C2×C5×C8—32no—
168C2×C5×C8—32no—
169Dic20—34no—
170Dic20—32no—
171Dic20—32no—
172Dic20—32no—
173Dic20C2×A412yescomplemented
174#677—34no—
175#677—32no—
176#677—32no—
177#677—32no—
178#677C2×A412yescomplemented
179C22×#41—51no—
180C23×Q8—51no—
181C2×#137—151no—
182C2×#137—151no—
183C2×#137—152no—
184C2×#137—152no—
185C2×#137—151no—
186C2×#137—151no—
187C22×Q16—52no—
188C22×SD16—52no—
189C22×M16C3×D511yescharacteristic, complemented
190C22×C3×C5—41no—
191C2×C3×D5—81no—
192C5×A4#13711yescharacteristic, complemented
193C3×C4×C5—41no—
194C3×C4×C5—41no—
195C3×Dic5—82no—
196C3×Dic5—81no—
197C22×A4—101no—
198C22×A4D2011yescharacteristic
199C3×#41—201no—
200C2×C3×Q8—201no—
201C4×A4—101no—
202C4×A4—102no—
203C4×A4D2011yescharacteristic
204C4×A4C22×D511yescharacteristic
205C3×Q16—202no—
206C3×SD16—202no—
207C3×M16—41no—
208C23×C5—21no—
209C23×C5—31no—
210C23×C5—31no—
211C23×C5—61no—
212C23×C5C2×C3×D411yescharacteristic
213C22×D5—41no—
214C22×D5—61no—
215C22×D5—61no—
216C22×D5—121no—
217C2×C4×C5—32no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—31no—
225C2×C4×C5C22×A411yescharacteristic
226C22⋊D5—21no—
227C22⋊D5—61no—
228C22⋊D5—61no—
229C22⋊D5—62no—
230C22⋊D5—61no—
231C2×Dic5—21no—
232C2×Dic5—62no—
233C2×Dic5—62no—
234C2×Dic5—61no—
235C2×Dic5—62no—
236C2×Dic5—61no—
237C2×Dic5—62no—
238C2×Dic5—61no—
239D20—31no—
240D20—61no—
241D20—61no—
242D20C22×A411yescharacteristic
243C4×D5—21no—
244C4×D5—61no—
245C4×D5—61no—
246C4×D5—62no—
247C4×D5—61no—
248Dic10—21no—
249Dic10—32no—
250Dic10—31no—
251Dic10—62no—
252Dic10—62no—
253Dic10—61no—
254Dic10—62no—
255Dic10—61no—
256Dic10—62no—
257Dic10—61no—
258Dic10C22×A412yes—
259Dic10C22×A411yescharacteristic
260C5×C8—32no—
261C5×C8C22×A412yes—
262C2×#41—151no—
263C2×#41—151no—
264C2×#41—151no—
265C2×#41—151no—
266C2×#41—301no—
267C2×#41—301no—
268C22×Q8—52no—
269C22×Q8—51no—
270C22×Q8—101no—
271C22×Q8—151no—
272C22×Q8—151no—
273C22×Q8—152no—
274C22×Q8—301no—
275C22×Q8—301no—
276C22×D4—51no—
277C22×D4—101no—
278C23×C4—101no—
279C23×C4—101no—
280C23×C4C2×C3×D511yescharacteristic
281#137—51no—
282#137—152no—
283#137—152no—
284#137—151no—
285#137—151no—
286#137—152no—
287#137—154no—
288#137—152no—
289#137—152no—
290#137—154no—
291#137—151no—
292C2×Q16—152no—
293C2×Q16—152no—
294C2×Q16—152no—
295C2×Q16—152no—
296C2×SD16—152no—
297C2×SD16—152no—
298C2×SD16—152no—
299C2×SD16—152no—
300C2×M16—31no—
301C2×M16—32no—
302C2×M16—31no—
303C22×C8C2×C3×D512yes—
304C2×C3×C5—41no—
305C2×C3×C5—81no—
306C3×D5—161no—
307C2×A4—21no—
308C2×A4—201no—
309C2×A4C2×D2011yescharacteristic
310C3×Q8—202no—
311C3×Q8—201no—
312C3×Q8—401no—
313C3×D4—201no—
314C3×D4—401no—
315C2×C3×C4—41no—
316C2×C3×C4—401no—
317C2×C3×C4—401no—
318C3×C8—42no—
319C22×C5—31no—
320C22×C5—31no—
321C22×C5—31no—
322C22×C5—61no—
323C22×C5—61no—
324C22×C5—61no—
325C22×C5—61no—
326C22×C5C3×#13711yescharacteristic, complemented
327C22×C5D4×A411yescharacteristic
328C2×D5—21no—
329C2×D5—61no—
330C2×D5—121no—
331C2×D5—121no—
332C2×D5—121no—
333C2×D5—121no—
334C4×C5—31no—
335C4×C5—31no—
336C4×C5D4×A411yescharacteristic
337C4×C5C23×A411yescharacteristic
338Dic5—22no—
339Dic5—21no—
340Dic5—62no—
341Dic5—61no—
342C24—101no—
343C24C3×D2011yescharacteristic
344#41—51no—
345#41—151no—
346#41—151no—
347#41—152no—
348#41—151no—
349#41—301no—
350#41—301no—
351#41—302no—
352#41—302no—
353#41—301no—
354#41—301no—
355C2×Q8—51no—
356C2×Q8—152no—
357C2×Q8—151no—
358C2×Q8—152no—
359C2×Q8—152no—
360C2×Q8—152no—
361C2×Q8—151no—
362C2×Q8—151no—
363C2×Q8—301no—
364C2×Q8—301no—
365C2×Q8—301no—
366C2×Q8—302no—
367C2×Q8—301no—
368C2×Q8—301no—
369C2×Q8—302no—
370C2×Q8—301no—
371C2×Q8—304no—
372C2×Q8—301no—
373C2×D4—151no—
374C2×D4—151no—
375C2×D4—301no—
376C2×D4—301no—
377C2×D4—301no—
378C2×D4—301no—
379C2×D4—301no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—101no—
385C22×C4—102no—
386C22×C4—301no—
387C22×C4—301no—
388C22×C4—301no—
389C22×C4—301no—
390C22×C4—301no—
391C22×C4—302no—
392C22×C4—301no—
393C22×C4C3×D2011yescharacteristic
394C22×C4C22×C3×D511yescharacteristic
395Q16—52no—
396Q16—152no—
397Q16—152no—
398Q16—154no—
399Q16—152no—
400SD16—52no—
401SD16—152no—
402SD16—152no—
403SD16—154no—
404SD16—152no—
405M16—32no—
406M16—31no—
407M16—32no—
408M16D5×A411yescharacteristic, complemented
409C2×C8—32no—
410C2×C8—32no—
411C3×C5—41noHall
412C22×C3—41no—
413C22×C3—401no—
414A4#405511yescharacteristic, direct product factor
415C3×C4—41no—
416C3×C4—41no—
417C3×C4—401no—
418C3×C4—402no—
419C2×C5—21no—
420C2×C5—31no—
421C2×C5—31no—
422C2×C5—61no—
423C2×C5C2×D4×A411yescharacteristic
424D5—41no—
425D5—121no—
426C23—21no—
427C23—31no—
428C23—31no—
429C23—61no—
430C23—201no—
431C23—301no—
432C23—301no—
433C23—601no—
434C23C2×C3×D2011yescharacteristic
435Q8—52no—
436Q8—51no—
437Q8—101no—
438Q8—152no—
439Q8—151no—
440Q8—302no—
441Q8—302no—
442Q8—301no—
443Q8—302no—
444Q8—301no—
445Q8—302no—
446Q8—301no—
447D4—51no—
448D4—101no—
449D4—151no—
450D4—301no—
451D4—301no—
452D4—301no—
453D4—301no—
454D4—302no—
455D4—301no—
456C2×C4—32no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—101no—
465C2×C4—101no—
466C2×C4—301no—
467C2×C4—301no—
468C2×C4—302no—
469C2×C4—301no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—301no—
474C2×C4—301no—
475C2×C4—301no—
476C2×C4—302no—
477C2×C4C2×D5×A411yescharacteristic
478C8—32no—
479C8C2×D5×A412yes—
480C2×C3—41no—
481C2×C3—81no—
482C2×C3—801no—
483C5A4×#13711yescharacteristic, complemented, Sylow
484C22—31no—
485C22—31no—
486C22—31no—
487C22—61no—
488C22—61no—
489C22—61no—
490C22—61no—
491C22—101no—
492C22—301no—
493C22—601no—
494C22—601no—
495C22—601no—
496C22—601no—
497C22C3×#405511yescharacteristic, complemented
498C22A4×D2011yescharacteristic
499C4—31no—
500C4—31no—
501C4—101no—
502C4—102no—
503C4—301no—
504C4—302no—
505C4A4×D2011yescharacteristic
506C4C22×D5×A411yescharacteristic
507C3—41noSylow
508C2—21no—
509C2—31no—
510C2—31no—
511C2—61no—
512C2—201no—
513C2—601no—
514C2C2×A4×D2011yescharacteristic
subgroupG/H
centerC2C2×A4×D20
commutator, cosocleC22×C4×C5C23×C3
FrattiniC4C22×D5×A4
FittingC22×C5×M16C2×C3
socleC23×C5C2×C3×D4
prime radicalA4×#709C2
hypercenterM16D5×A4
hypocenterC22×C5C3×#137
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic10C2semidirect
3. C5×A4×M16C2semidirect
4. A4×Dic20C2semidirect
5. A4×#677C2semidirect
6. C22×#4055C3semidirect
19. C23×Dic10C2×C3semidirect
20. C22×C5×M16C2×C3semidirect
27. C22×Dic20C2×C3semidirect
28. C22×#677C2×C3semidirect
44. A4×M16D5semidirect
78. #4055A4direct (N × H)
162. C2×Dic10C2×A4semidirect
166. C5×M16C2×A4semidirect
173. Dic20C2×A4semidirect
178. #677C2×A4semidirect
189. C22×M16C3×D5semidirect
192. C5×A4#137semidirect
326. C22×C5C3×#137semidirect
408. M16D5×A4semidirect
414. A4#4055direct (N × H)
483. C5A4×#137semidirect
497. C22C3×#4055semidirect

Maximal subgroups

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

subgroupindex
A4×#7092
C2×A4×Dic102
C5×A4×M162
A4×Dic202
A4×#6772
C22×#40553
C3×#40554
A4×#1375