Finite Group Databasebeta

← A4×#4018 #14513977

Subgroups — A4×#4018 #14513977

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
2C42×C5×A4C211yesmaximal, characteristic, complemented
3A4×#685C212yesmaximal
4A4×#683C212yesmaximal, complemented
5C4×A4×Dic5C211yesmaximal, characteristic, complemented
6C22×#4018C311yesmaximal, characteristic, complemented, Hall
7C22×D5×A4C2211yescharacteristic
8C2×C4×C5×A4C2212yes—
9C2×C4×C5×A4C2211yescharacteristic
10C2×A4×Dic5C2212yes—
11C2×A4×Dic5C2211yescharacteristic
12C4×D5×A4C414yescomplemented
13C3×#4018—41nomaximal
14A4×#117—51nomaximal, Hall
15C23×C4×D5C2×C311yescharacteristic
16C22×C42×C5C2×C311yescharacteristic, complemented
17C22×#685C2×C312yes—
18C22×#683C2×C312yescomplemented
19C22×C4×Dic5C2×C311yescharacteristic, complemented
20C2×#4018—31no—
21C2×#4018—31no—
22C2×#4018—31no—
23C2×#4018—32no—
24C2×#4018—32no—
25C2×#4018—31no—
26C22×C5×A4C2311yescharacteristic
27C2×D5×A4—22no—
28C2×D5×A4C2×C412yes—
29C2×C3×C4×D5—41no—
30C4×C5×A4—22no—
31C4×C5×A4C2×C412yes—
32A4×Dic5—22no—
33A4×Dic5C2×C412yes—
34C3×C42×C5—41no—
35C3×#685—42no—
36C3×#683—42no—
37C3×C4×Dic5—41no—
38C22×C4×A4—51no—
39A4×C4⋊C4—52no—
40A4×C22⋊C4—52no—
41C42×A4—51no—
42C42×A4D511yescharacteristic, complemented
43C24×D5C22×C311yescharacteristic
44C23×C4×C5C22×C312yes—
45C23×C4×C5C22×C311yescharacteristic
46C23×Dic5C22×C312yes—
47C23×Dic5C22×C311yescharacteristic
48C22×C4×D5—31no—
49C22×C4×D5—31no—
50C22×C4×D5—31no—
51C22×C4×D5—31no—
52C22×C4×D5—34no—
53C22×C4×D5C3×C414yescomplemented
54C2×C42×C5—31no—
55C2×C42×C5—31no—
56C2×C42×C5—32no—
57C2×#685—32no—
58C2×#685—32no—
59C2×#685—32no—
60C2×#685—32no—
61C2×#683—32no—
62C2×#683—32no—
63C2×#683—32no—
64C2×#683—32no—
65C2×C4×Dic5—31no—
66C2×C4×Dic5—31no—
67C2×C4×Dic5—32no—
68#4018—32no—
69#4018—34no—
70#4018—32no—
71#4018—32no—
72#4018—34no—
73#4018—31no—
74#4018—31no—
75#4018—32no—
76#4018—32no—
77#4018—31no—
78#4018A411yescharacteristic, direct product factor
79C22×#117—51noSylow
80C22×C3×D5—41no—
81C2×C5×A4C22×C411yescharacteristic
82C2×C5×A4#4112yes—
83D5×A4—22no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—42no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5—42no—
88C3×C4×D5—44no—
89C23×A4—51no—
90C2×C4×A4—51no—
91C2×C4×A4—54no—
92C2×C4×A4—52no—
93C2×C4×A4C2×D512yes—
94C2×C4×A4C2×D511yescharacteristic
95C3×#117—201no—
96C24×C5C23×C311yescharacteristic
97C23×D5—22no—
98C23×D5—31no—
99C23×D5—32no—
100C23×D5—31no—
101C23×D5—62no—
102C23×D5C2×C3×C412yes—
103C22×C4×C5—22no—
104C22×C4×C5—31no—
105C22×C4×C5—31no—
106C22×C4×C5—32no—
107C22×C4×C5—32no—
108C22×C4×C5—32no—
109C22×C4×C5—62no—
110C22×C4×C5C2×C3×C412yes—
111C22×Dic5—22no—
112C22×Dic5—31no—
113C22×Dic5—32no—
114C22×Dic5—31no—
115C22×Dic5—32no—
116C22×Dic5—32no—
117C22×Dic5—62no—
118C22×Dic5C2×C3×C412yes—
119C2×C4×D5—34no—
120C2×C4×D5—34no—
121C2×C4×D5—34no—
122C2×C4×D5—32no—
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×C4×D5—31no—
126C2×C4×D5—34no—
127C2×C4×D5—34no—
128C2×C4×D5—34no—
129C2×C4×D5—34no—
130C2×C4×D5—34no—
131C2×C4×D5C2×A411yescharacteristic
132C42×C5—32no—
133C42×C5—32no—
134C42×C5—31no—
135C42×C5C2×A411yescharacteristic, complemented
136#685—34no—
137#685—32no—
138#685—32no—
139#685—32no—
140#685C2×A412yes—
141#683—34no—
142#683—32no—
143#683—32no—
144#683—32no—
145#683C2×A412yescomplemented
146C4×Dic5—32no—
147C4×Dic5—31no—
148C4×Dic5—32no—
149C4×Dic5C2×A411yescharacteristic, complemented
150C24×C4—51no—
151C2×#117—151no—
152C2×#117—151no—
153C2×#117—151no—
154C2×#117—152no—
155C2×#117—152no—
156C2×#117—151no—
157C22×C4⋊C4—52no—
158C22×C22⋊C4—52no—
159C22×C42—51no—
160C22×C42C3×D511yescharacteristic, complemented
161C22×C3×C5—41no—
162C2×C3×D5—42no—
163C2×C3×D5—82no—
164C5×A4#11711yescharacteristic, complemented
165C3×C4×C5—42no—
166C3×C4×C5—82no—
167C3×Dic5—42no—
168C3×Dic5—82no—
169C22×A4—52no—
170C22×A4—102no—
171C22×A4C22×D511yescharacteristic
172C22×C3×C4—201no—
173C4×A4—22no—
174C4×A4—52no—
175C4×A4—102no—
176C4×A4C4×D512yes—
177C3×C4⋊C4—202no—
178C3×C22⋊C4—202no—
179C3×C42—41no—
180C3×C42—201no—
181C23×C5—31no—
182C23×C5—32no—
183C23×C5—31no—
184C23×C5C22×C3×C411yescharacteristic
185C23×C5C3×#4112yes—
186C22×D5—22no—
187C22×D5—32no—
188C22×D5—31no—
189C22×D5—32no—
190C22×D5—32no—
191C22×D5—32no—
192C22×D5—62no—
193C22×D5—62no—
194C22×D5—64no—
195C22×D5—64no—
196C22×D5—62no—
197C22×D5—62no—
198C22×D5—62no—
199C22×D5C22×A411yescharacteristic
200C2×C4×C5—32no—
201C2×C4×C5—31no—
202C2×C4×C5—32no—
203C2×C4×C5—32no—
204C2×C4×C5—32no—
205C2×C4×C5—32no—
206C2×C4×C5—62no—
207C2×C4×C5—62no—
208C2×C4×C5—62no—
209C2×C4×C5—62no—
210C2×C4×C5C22×A412yes—
211C2×C4×C5C22×A411yescharacteristic
212C2×Dic5—32no—
213C2×Dic5—31no—
214C2×Dic5—32no—
215C2×Dic5—32no—
216C2×Dic5—32no—
217C2×Dic5—32no—
218C2×Dic5—62no—
219C2×Dic5—62no—
220C2×Dic5—62no—
221C2×Dic5—62no—
222C2×Dic5C22×A412yes—
223C2×Dic5C22×A411yescharacteristic
224C4×D5—38no—
225C4×D5—34no—
226C4×D5—34no—
227C4×D5—34no—
228C4×D5C4×A414yescomplemented
229C25—51no—
230C23×C4—51no—
231C23×C4—54no—
232C23×C4—52no—
233C23×C4—151no—
234C23×C4—151no—
235C23×C4—151no—
236C23×C4—151no—
237C23×C4—154no—
238C23×C4C2×C3×D512yes—
239C23×C4C2×C3×D511yescharacteristic
240#117—51no—
241#117—151no—
242#117—152no—
243#117—152no—
244#117—151no—
245#117—154no—
246#117—152no—
247#117—152no—
248#117—154no—
249#117—152no—
250#117—151no—
251C2×C4⋊C4—152no—
252C2×C4⋊C4—152no—
253C2×C4⋊C4—152no—
254C2×C4⋊C4—152no—
255C2×C22⋊C4—152no—
256C2×C22⋊C4—152no—
257C2×C22⋊C4—152no—
258C2×C22⋊C4—152no—
259C2×C42—31no—
260C2×C42—32no—
261C2×C42—31no—
262C2×C42—151no—
263C2×C42—152no—
264C2×C42—151no—
265C2×C3×C5—41no—
266C2×C3×C5—42no—
267C3×D5—82no—
268C23×C3—201no—
269C2×A4—102no—
270C2×A4C2×C4×D511yescharacteristic
271C2×A4#70912yes—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—204no—
275C2×C3×C4—201no—
276C2×C3×C4—202no—
277C22×C5—31no—
278C22×C5—32no—
279C22×C5—32no—
280C22×C5—31no—
281C22×C5—31no—
282C22×C5—32no—
283C22×C5—32no—
284C22×C5C3×#11711yescharacteristic, complemented
285C22×C5C23×A411yescharacteristic
286C2×D5—22no—
287C2×D5—32no—
288C2×D5—62no—
289C2×D5—64no—
290C2×D5—62no—
291C2×D5—64no—
292C2×D5—62no—
293C2×D5—62no—
294C2×D5—62no—
295C2×D5C2×C4×A412yes—
296C4×C5—22no—
297C4×C5—32no—
298C4×C5—62no—
299C4×C5C2×C4×A412yes—
300Dic5—22no—
301Dic5—32no—
302Dic5—62no—
303Dic5C2×C4×A412yes—
304C24—52no—
305C24—102no—
306C24—151no—
307C24—151no—
308C24—152no—
309C24—302no—
310C24C22×C3×D511yescharacteristic
311C22×C4—22no—
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—32no—
317C22×C4—51no—
318C22×C4—52no—
319C22×C4—62no—
320C22×C4—102no—
321C22×C4—151no—
322C22×C4—154no—
323C22×C4—154no—
324C22×C4—151no—
325C22×C4—152no—
326C22×C4—154no—
327C22×C4—154no—
328C22×C4—154no—
329C22×C4—154no—
330C22×C4—154no—
331C22×C4—154no—
332C22×C4—151no—
333C22×C4—152no—
334C22×C4—151no—
335C22×C4—151no—
336C22×C4—152no—
337C22×C4—152no—
338C22×C4—302no—
339C22×C4C3×C4×D512yes—
340C4⋊C4—52no—
341C4⋊C4—152no—
342C4⋊C4—152no—
343C4⋊C4—154no—
344C4⋊C4—152no—
345C22⋊C4—52no—
346C22⋊C4—152no—
347C22⋊C4—152no—
348C22⋊C4—154no—
349C22⋊C4—152no—
350C42—32no—
351C42—32no—
352C42—31no—
353C42—51no—
354C42—152no—
355C42—152no—
356C42—151no—
357C42D5×A411yescharacteristic, complemented
358C3×C5—41noHall
359C22×C3—41no—
360C22×C3—202no—
361C22×C3—402no—
362A4#401811yescharacteristic, direct product factor
363C3×C4—42no—
364C3×C4—82no—
365C3×C4—202no—
366C3×C4—402no—
367C2×C5—32no—
368C2×C5—31no—
369C2×C5—31no—
370C2×C5C22×C4×A411yescharacteristic
371C2×C5A4×#4112yes—
372D5—22no—
373D5—62no—
374C23—31no—
375C23—32no—
376C23—31no—
377C23—51no—
378C23—102no—
379C23—152no—
380C23—152no—
381C23—152no—
382C23—152no—
383C23—151no—
384C23—302no—
385C23—302no—
386C23—302no—
387C23—304no—
388C23—302no—
389C23—302no—
390C23—304no—
391C23C2×C3×C4×D511yescharacteristic
392C23C3×#70912yes—
393C2×C4—32no—
394C2×C4—31no—
395C2×C4—32no—
396C2×C4—32no—
397C2×C4—32no—
398C2×C4—32no—
399C2×C4—51no—
400C2×C4—54no—
401C2×C4—52no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—154no—
407C2×C4—154no—
408C2×C4—158no—
409C2×C4—152no—
410C2×C4—152no—
411C2×C4—152no—
412C2×C4—151no—
413C2×C4—154no—
414C2×C4—152no—
415C2×C4—152no—
416C2×C4—302no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4—302no—
420C2×C4C2×D5×A412yes—
421C2×C4C2×D5×A411yescharacteristic
422C2×C3—41no—
423C2×C3—42no—
424C2×C3—402no—
425C5A4×#11711yescharacteristic, complemented, Sylow
426C22—31no—
427C22—32no—
428C22—32no—
429C22—31no—
430C22—31no—
431C22—32no—
432C22—32no—
433C22—52no—
434C22—102no—
435C22—152no—
436C22—302no—
437C22—302no—
438C22—304no—
439C22—302no—
440C22—302no—
441C22—304no—
442C22—302no—
443C22C3×#401811yescharacteristic, complemented
444C22C22×D5×A411yescharacteristic
445C4—22no—
446C4—32no—
447C4—52no—
448C4—62no—
449C4—102no—
450C4—152no—
451C4—302no—
452C4C4×D5×A412yes—
453C3—41noSylow
454C2—31no—
455C2—31no—
456C2—32no—
457C2—102no—
458C2—302no—
459C2C2×C4×D5×A411yescharacteristic
460C2A4×#70912yes—
subgroupG/H
centerC2×C4C2×D5×A4
commutatorC23×C5C22×C3×C4
FrattiniC22C22×D5×A4
FittingC22×C42×C5C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC22×D5×A4C22
hypercenterC42D5×A4
hypocenterC22×C5C3×#117
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C42×C5×A4C2semidirect
4. A4×#683C2semidirect
5. C4×A4×Dic5C2semidirect
6. C22×#4018C3semidirect
12. C4×D5×A4C4semidirect
16. C22×C42×C5C2×C3semidirect
18. C22×#683C2×C3semidirect
19. C22×C4×Dic5C2×C3semidirect
42. C42×A4D5semidirect
53. C22×C4×D5C3×C4semidirect
78. #4018A4direct (N × H)
135. C42×C5C2×A4semidirect
145. #683C2×A4semidirect
149. C4×Dic5C2×A4semidirect
160. C22×C42C3×D5semidirect
164. C5×A4#117semidirect
228. C4×D5C4×A4semidirect
284. C22×C5C3×#117semidirect
357. C42D5×A4semidirect
362. A4#4018direct (N × H)
425. C5A4×#117semidirect
443. C22C3×#4018semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C42×C5×A42
A4×#6852
A4×#6832
C4×A4×Dic52
C22×#40183
C3×#40184
A4×#1175