Finite Group Databasebeta

← A4×#4082 #14514187

Subgroups — A4×#4082 #14514187

Order 1920.

880 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 99 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
2C2×A4×Dic10C211yesmaximal, characteristic, complemented
3A4×C22⋊Dic5C214yesmaximal, complemented
4C4×A4×Dic5C211yesmaximal, characteristic, complemented
5C22×#4082C311yesmaximal, characteristic, complemented, Hall
6C23×C5×A4C2212yes—
7C5×D4×A4—22no—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4×Dic5C2212yes—
10C2×A4×Dic5C2212yes—
11A4×Dic10—22no—
12C3×#4082—41nomaximal
13A4×#124—51nomaximal, Hall
14C23×C5×D4C2×C311yescharacteristic
15C23×Dic10C2×C311yescharacteristic, complemented
16C22×C22⋊Dic5C2×C314yescomplemented
17C2×#4082—34no—
18C2×#4082—31no—
19C2×#4082—31no—
20C2×#4082—31no—
21C2×#4082—31no—
22C22×C4×Dic5C2×C311yescharacteristic, complemented
23C22×C5×A4—22no—
24C22×C5×A4—24no—
25C22×C5×A4C2311yescharacteristic
26C2×C3×C5×D4—41no—
27C2×C3×Dic10—41no—
28C4×C5×A4D412yes—
29A4×Dic5—22no—
30A4×Dic5—22no—
31C3×C22⋊Dic5—44no—
32C3×C4×Dic5—41no—
33C2×Q8×A4—51no—
34C2×D4×A4D511yescharacteristic
35A4×C22⋊C4—54no—
36C42×A4—51no—
37C25×C5C22×C312yes—
38C22×C5×D4—22no—
39C22×C5×D4—31no—
40C22×C5×D4—31no—
41C22×C5×D4—32no—
42C22×C5×D4—62no—
43C23×C4×C5C22×C311yescharacteristic
44C23×Dic5C22×C312yes—
45C23×Dic5C22×C312yes—
46C22×Dic10—22no—
47C22×Dic10—31no—
48C22×Dic10—31no—
49C22×Dic10—32no—
50C22×Dic10—62no—
51C2×C22⋊Dic5—34no—
52C2×C22⋊Dic5—34no—
53C2×C22⋊Dic5—34no—
54C2×C22⋊Dic5—34no—
55#4082—34no—
56#4082—34no—
57#4082—32no—
58#4082—34no—
59#4082—31no—
60#4082—31no—
61#4082—34no—
62#4082—31no—
63#4082A411yescharacteristic, direct product factor
64C2×C4×Dic5—31no—
65C2×C4×Dic5—31no—
66C2×C4×Dic5—32no—
67C22×#124—51noSylow
68C23×C3×C5—42no—
69C2×C5×A4—42no—
70C2×C5×A4C2×D411yescharacteristic
71C2×C5×A4#4112yes—
72C3×C5×D4—82no—
73C2×C3×C4×C5—41no—
74C2×C3×Dic5—42no—
75C2×C3×Dic5—42no—
76C3×Dic10—82no—
77C23×A4C2×D512yes—
78Q8×A4—102no—
79D4×A4—22no—
80C2×C4×A4—52no—
81C2×C4×A4—52no—
82C2×C4×A4C2×D511yescharacteristic
83C3×#124—201no—
84C24×C5—22no—
85C24×C5—24no—
86C24×C5—32no—
87C24×C5—32no—
88C24×C5—62no—
89C24×C5—64no—
90C24×C5C23×C311yescharacteristic
91C2×C5×D4—32no—
92C2×C5×D4—32no—
93C2×C5×D4—31no—
94C2×C5×D4—62no—
95C2×C5×D4—62no—
96C2×C5×D4—64no—
97C2×C5×D4—62no—
98C2×C5×D4—64no—
99C2×C5×D4—62no—
100C2×C5×D4C2×A411yescharacteristic
101C22×C4×C5—31no—
102C22×C4×C5—31no—
103C22×C4×C5—32no—
104C22×C4×C5C3×D412yes—
105C22×Dic5—22no—
106C22×Dic5—22no—
107C22×Dic5—32no—
108C22×Dic5—32no—
109C22×Dic5—32no—
110C22×Dic5—32no—
111C22×Dic5—62no—
112C22×Dic5—62no—
113C2×Dic10—32no—
114C2×Dic10—31no—
115C2×Dic10—32no—
116C2×Dic10—62no—
117C2×Dic10—62no—
118C2×Dic10—64no—
119C2×Dic10—64no—
120C2×Dic10—62no—
121C2×Dic10—62no—
122C2×Dic10C2×A411yescharacteristic, complemented
123C22⋊Dic5—38no—
124C22⋊Dic5—34no—
125C22⋊Dic5—34no—
126C22⋊Dic5—34no—
127C22⋊Dic5C2×A414yescomplemented
128C4×Dic5—32no—
129C4×Dic5—31no—
130C4×Dic5—32no—
131C4×Dic5C2×A411yescharacteristic, complemented
132C23×Q8—51no—
133C23×D4C3×D511yescharacteristic
134C2×#124—151no—
135C2×#124—151no—
136C2×#124—154no—
137C2×#124—151no—
138C2×#124—151no—
139C22×C22⋊C4—54no—
140C22×C42—51no—
141C22×C3×C5—41no—
142C22×C3×C5—82no—
143C22×C3×C5—84no—
144C5×A4#12411yescharacteristic, complemented
145C3×C4×C5—42no—
146C3×Dic5—82no—
147C3×Dic5—82no—
148C22×A4—24no—
149C22×A4—22no—
150C22×A4C22×D511yescharacteristic
151C2×C3×Q8—201no—
152C2×C3×D4—41no—
153C4×A4—102no—
154C4×A4—102no—
155C4×A4C22⋊D512yes—
156C3×C22⋊C4—204no—
157C3×C42—201no—
158C23×C5—31no—
159C23×C5—32no—
160C23×C5—31no—
161C23×C5—32no—
162C23×C5—42no—
163C23×C5—62no—
164C23×C5—62no—
165C23×C5—64no—
166C23×C5—64no—
167C23×C5—62no—
168C23×C5—62no—
169C23×C5—64no—
170C23×C5—64no—
171C23×C5—122no—
172C23×C5—124no—
173C23×C5—124no—
174C23×C5C2×C3×D411yescharacteristic
175C23×C5C3×#4112yes—
176C23×C5C22×A412yes—
177C5×D4—22no—
178C5×D4—64no—
179C5×D4—64no—
180C5×D4—62no—
181C2×C4×C5—32no—
182C2×C4×C5—31no—
183C2×C4×C5—32no—
184C2×C4×C5—32no—
185C2×C4×C5—32no—
186C2×C4×C5C22×A411yescharacteristic
187C2×Dic5—32no—
188C2×Dic5—32no—
189C2×Dic5—62no—
190C2×Dic5—62no—
191C2×Dic5—62no—
192C2×Dic5—62no—
193C2×Dic5—62no—
194C2×Dic5—62no—
195C2×Dic5—62no—
196C2×Dic5—62no—
197C2×Dic5C22×A412yes—
198C2×Dic5C22×A412yes—
199Dic10—22no—
200Dic10—64no—
201Dic10—64no—
202Dic10—62no—
203C25C2×C3×D512yes—
204C22×Q8—102no—
205C22×Q8—151no—
206C22×Q8—151no—
207C22×Q8—152no—
208C22×Q8—302no—
209C22×D4—22no—
210C22×D4—31no—
211C22×D4—31no—
212C22×D4—32no—
213C22×D4—62no—
214C23×C4—52no—
215C23×C4—52no—
216C23×C4C2×C3×D511yescharacteristic
217#124—51no—
218#124—151no—
219#124—154no—
220#124—151no—
221#124—154no—
222#124—154no—
223#124—154no—
224#124—152no—
225#124—151no—
226C2×C22⋊C4—154no—
227C2×C22⋊C4—154no—
228C2×C22⋊C4—154no—
229C2×C22⋊C4—154no—
230C2×C42—151no—
231C2×C42—152no—
232C2×C42—151no—
233C2×C3×C5—41no—
234C2×C3×C5—42no—
235C2×C3×C5—162no—
236C23×C3—42no—
237C2×A4—42no—
238C2×A4#71112yes—
239C2×A4C2×C22⋊D511yescharacteristic
240C3×Q8—402no—
241C3×D4—82no—
242C2×C3×C4—41no—
243C2×C3×C4—202no—
244C2×C3×C4—202no—
245C22×C5—22no—
246C22×C5—24no—
247C22×C5—31no—
248C22×C5—32no—
249C22×C5—32no—
250C22×C5—31no—
251C22×C5—31no—
252C22×C5—32no—
253C22×C5—32no—
254C22×C5—62no—
255C22×C5—64no—
256C22×C5—122no—
257C22×C5—122no—
258C22×C5—124no—
259C22×C5—122no—
260C22×C5—122no—
261C22×C5—124no—
262C22×C5C3×#12411yescharacteristic, complemented
263C22×C5C23×A411yescharacteristic
264C4×C5—32no—
265C4×C5D4×A412yes—
266Dic5—22no—
267Dic5—22no—
268Dic5—62no—
269Dic5—62no—
270C24—24no—
271C24—22no—
272C24—32no—
273C24—32no—
274C24—62no—
275C24—64no—
276C24C22×C3×D511yescharacteristic
277C2×Q8—51no—
278C2×Q8—152no—
279C2×Q8—152no—
280C2×Q8—151no—
281C2×Q8—302no—
282C2×Q8—302no—
283C2×Q8—302no—
284C2×Q8—304no—
285C2×Q8—302no—
286C2×Q8—304no—
287C2×D4—32no—
288C2×D4—32no—
289C2×D4—31no—
290C2×D4—62no—
291C2×D4—62no—
292C2×D4—64no—
293C2×D4—62no—
294C2×D4—64no—
295C2×D4—62no—
296C2×D4D5×A411yescharacteristic
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—32no—
300C22×C4—102no—
301C22×C4—102no—
302C22×C4—152no—
303C22×C4—152no—
304C22×C4—152no—
305C22×C4—152no—
306C22×C4—302no—
307C22×C4—302no—
308C22×C4C3×C22⋊D512yes—
309C22⋊C4—54no—
310C22⋊C4—154no—
311C22⋊C4—154no—
312C22⋊C4—158no—
313C22⋊C4—154no—
314C42—51no—
315C42—152no—
316C42—152no—
317C42—151no—
318C3×C5—41noHall
319C22×C3—41no—
320C22×C3—82no—
321C22×C3—84no—
322A4#408211yescharacteristic, direct product factor
323C3×C4—42no—
324C3×C4—402no—
325C3×C4—402no—
326C2×C5—31no—
327C2×C5—32no—
328C2×C5—31no—
329C2×C5—42no—
330C2×C5—122no—
331C2×C5C2×D4×A411yescharacteristic
332C2×C5A4×#4112yes—
333C23—31no—
334C23—32no—
335C23—31no—
336C23—32no—
337C23—42no—
338C23—62no—
339C23—62no—
340C23—64no—
341C23—64no—
342C23—62no—
343C23—62no—
344C23—64no—
345C23—64no—
346C23—124no—
347C23—122no—
348C23—124no—
349C23C3×#71112yes—
350C23C2×C3×C22⋊D511yescharacteristic
351C23C2×D5×A412yes—
352Q8—102no—
353Q8—304no—
354Q8—304no—
355Q8—302no—
356D4—22no—
357D4—64no—
358D4—64no—
359D4—62no—
360C2×C4—32no—
361C2×C4—31no—
362C2×C4—32no—
363C2×C4—32no—
364C2×C4—32no—
365C2×C4—52no—
366C2×C4—52no—
367C2×C4—152no—
368C2×C4—152no—
369C2×C4—302no—
370C2×C4—302no—
371C2×C4—302no—
372C2×C4—302no—
373C2×C4—302no—
374C2×C4—302no—
375C2×C4—302no—
376C2×C4—302no—
377C2×C4C2×D5×A411yescharacteristic
378C2×C3—42no—
379C2×C3—41no—
380C2×C3—162no—
381C5A4×#12411yescharacteristic, complemented, Sylow
382C22—24no—
383C22—22no—
384C22—32no—
385C22—31no—
386C22—32no—
387C22—32no—
388C22—32no—
389C22—31no—
390C22—31no—
391C22—64no—
392C22—62no—
393C22—122no—
394C22—122no—
395C22—124no—
396C22—122no—
397C22—122no—
398C22—124no—
399C22C3×#408211yescharacteristic, complemented
400C22C22×D5×A411yescharacteristic
401C4—32no—
402C4—102no—
403C4—102no—
404C4—302no—
405C4—302no—
406C4A4×C22⋊D512yes—
407C3—41noSylow
408C2—31no—
409C2—32no—
410C2—31no—
411C2—42no—
412C2—122no—
413C2A4×#71112yes—
414C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC23×C5×D4C2×C3
prime radicalC2×C5×D4×A4C2
hypercenterC2×D4D5×A4
hypocenterC22×C5C3×#124
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic10C2semidirect
3. A4×C22⋊Dic5C2semidirect
4. C4×A4×Dic5C2semidirect
5. C22×#4082C3semidirect
15. C23×Dic10C2×C3semidirect
16. C22×C22⋊Dic5C2×C3semidirect
22. C22×C4×Dic5C2×C3semidirect
63. #4082A4direct (N × H)
122. C2×Dic10C2×A4semidirect
127. C22⋊Dic5C2×A4semidirect
131. C4×Dic5C2×A4semidirect
144. C5×A4#124semidirect
262. C22×C5C3×#124semidirect
322. A4#4082direct (N × H)
381. C5A4×#124semidirect
399. C22C3×#4082semidirect

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×Dic102
A4×C22⋊Dic52
C4×A4×Dic52
C22×#40823
C3×#40824
A4×#1245