Finite Group Databasebeta

← A4×#4021 #14513980

Subgroups — A4×#4021 #14513980

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×A4×D20C211yesmaximal, characteristic
2C2×A4×Dic10C211yesmaximal, characteristic, complemented
3C42×C5×A4C211yesmaximal, characteristic, complemented
4A4×#685C214yesmaximal, complemented
5C22×#4021C311yesmaximal, characteristic, complemented, Hall
6C22×D5×A4C2212yes—
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4×Dic5C2212yes—
10A4×D20—22no—
11A4×Dic10—22no—
12C3×#4021—41nomaximal
13A4×#124—51nomaximal, Hall
14C23×D20C2×C311yescharacteristic
15C23×Dic10C2×C311yescharacteristic, complemented
16C22×C42×C5C2×C311yescharacteristic, complemented
17C22×#685C2×C314yescomplemented
18C2×#4021—31no—
19C2×#4021—31no—
20C2×#4021—31no—
21C2×#4021—31no—
22C2×#4021—34no—
23C22×C5×A4C2311yescharacteristic
24C2×D5×A4—22no—
25C2×D5×A4—24no—
26C2×C3×D20—41no—
27C2×C3×Dic10—41no—
28C4×C5×A4—22no—
29C4×C5×A4D412yes—
30A4×Dic5—22no—
31C3×C42×C5—41no—
32C3×#685—44no—
33C2×Q8×A4—51no—
34C2×D4×A4—51no—
35A4×C22⋊C4—54no—
36C42×A4D511yescharacteristic, complemented
37C24×D5C22×C312yes—
38C23×C4×C5C22×C312yes—
39C23×C4×C5C22×C311yescharacteristic
40C23×Dic5C22×C312yes—
41C22×D20—22no—
42C22×D20—31no—
43C22×D20—32no—
44C22×D20—31no—
45C22×D20—62no—
46C22×Dic10—22no—
47C22×Dic10—31no—
48C22×Dic10—31no—
49C22×Dic10—32no—
50C22×Dic10—62no—
51C2×C42×C5—31no—
52C2×C42×C5—31no—
53C2×C42×C5—32no—
54C2×#685—34no—
55C2×#685—34no—
56C2×#685—34no—
57C2×#685—34no—
58#4021—32no—
59#4021—34no—
60#4021—34no—
61#4021—34no—
62#4021—31no—
63#4021—31no—
64#4021—31no—
65#4021—34no—
66#4021A411yescharacteristic, direct product factor
67C22×#124—51noSylow
68C22×C3×D5—42no—
69C2×C5×A4C2×D411yescharacteristic
70C2×C5×A4#4112yes—
71D5×A4—42no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—42no—
74C2×C3×Dic5—42no—
75C3×D20—82no—
76C3×Dic10—82no—
77C23×A4—52no—
78Q8×A4—102no—
79D4×A4—102no—
80C2×C4×A4—52no—
81C2×C4×A4C2×D512yes—
82C2×C4×A4C2×D511yescharacteristic
83C3×#124—201no—
84C24×C5C23×C311yescharacteristic
85C23×D5—22no—
86C23×D5—24no—
87C23×D5—32no—
88C23×D5—32no—
89C23×D5—62no—
90C23×D5—64no—
91C22×C4×C5—22no—
92C22×C4×C5—31no—
93C22×C4×C5—31no—
94C22×C4×C5—32no—
95C22×C4×C5—32no—
96C22×C4×C5—32no—
97C22×C4×C5—62no—
98C22×C4×C5C3×D412yes—
99C22×Dic5—22no—
100C22×Dic5—32no—
101C22×Dic5—32no—
102C22×Dic5—62no—
103C2×D20—32no—
104C2×D20—32no—
105C2×D20—31no—
106C2×D20—62no—
107C2×D20—62no—
108C2×D20—64no—
109C2×D20—64no—
110C2×D20—62no—
111C2×D20—62no—
112C2×D20C2×A411yescharacteristic
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
123C42×C5—32no—
124C42×C5—32no—
125C42×C5—31no—
126C42×C5C2×A411yescharacteristic, complemented
127#685—38no—
128#685—34no—
129#685—34no—
130#685—34no—
131#685C2×A414yescomplemented
132C23×Q8—51no—
133C23×D4—51no—
134C2×#124—151no—
135C2×#124—151no—
136C2×#124—154no—
137C2×#124—151no—
138C2×#124—151no—
139C22×C22⋊C4—54no—
140C22×C42C3×D511yescharacteristic, complemented
141C22×C3×C5—41no—
142C2×C3×D5—82no—
143C2×C3×D5—84no—
144C5×A4#12411yescharacteristic, complemented
145C3×C4×C5—42no—
146C3×C4×C5—82no—
147C3×Dic5—82no—
148C22×A4—102no—
149C22×A4—104no—
150C22×A4C22×D511yescharacteristic
151C2×C3×Q8—201no—
152C2×C3×D4—201no—
153C4×A4—22no—
154C4×A4—102no—
155C4×A4D2012yes—
156C3×C22⋊C4—204no—
157C3×C42—41no—
158C23×C5—31no—
159C23×C5—32no—
160C23×C5—31no—
161C23×C5C2×C3×D411yescharacteristic
162C23×C5C3×#4112yes—
163C22×D5—32no—
164C22×D5—42no—
165C22×D5—62no—
166C22×D5—62no—
167C22×D5—64no—
168C22×D5—64no—
169C22×D5—62no—
170C22×D5—62no—
171C22×D5—64no—
172C22×D5—64no—
173C22×D5—124no—
174C22×D5—122no—
175C22×D5—124no—
176C22×D5C22×A412yes—
177C2×C4×C5—32no—
178C2×C4×C5—31no—
179C2×C4×C5—32no—
180C2×C4×C5—32no—
181C2×C4×C5—32no—
182C2×C4×C5—32no—
183C2×C4×C5—62no—
184C2×C4×C5—62no—
185C2×C4×C5—62no—
186C2×C4×C5—62no—
187C2×C4×C5C22×A412yes—
188C2×C4×C5C22×A411yescharacteristic
189C2×Dic5—32no—
190C2×Dic5—62no—
191C2×Dic5—62no—
192C2×Dic5—62no—
193C2×Dic5—62no—
194C2×Dic5C22×A412yes—
195D20—22no—
196D20—64no—
197D20—64no—
198D20—62no—
199Dic10—22no—
200Dic10—64no—
201Dic10—64no—
202Dic10—62no—
203C25—52no—
204C22×Q8—102no—
205C22×Q8—151no—
206C22×Q8—151no—
207C22×Q8—152no—
208C22×Q8—302no—
209C22×D4—102no—
210C22×D4—151no—
211C22×D4—151no—
212C22×D4—152no—
213C22×D4—302no—
214C23×C4—52no—
215C23×C4C2×C3×D512yes—
216C23×C4C2×C3×D511yescharacteristic
217#124—51no—
218#124—154no—
219#124—151no—
220#124—151no—
221#124—154no—
222#124—154no—
223#124—152no—
224#124—154no—
225#124—151no—
226C2×C22⋊C4—154no—
227C2×C22⋊C4—154no—
228C2×C22⋊C4—154no—
229C2×C22⋊C4—154no—
230C2×C42—31no—
231C2×C42—31no—
232C2×C42—32no—
233C2×C3×C5—41no—
234C2×C3×C5—42no—
235C3×D5—162no—
236C23×C3—202no—
237C2×A4—202no—
238C2×A4C2×D2011yescharacteristic
239C2×A4#70912yes—
240C3×Q8—402no—
241C3×D4—402no—
242C2×C3×C4—41no—
243C2×C3×C4—42no—
244C2×C3×C4—202no—
245C22×C5—31no—
246C22×C5—32no—
247C22×C5—32no—
248C22×C5—31no—
249C22×C5—31no—
250C22×C5—32no—
251C22×C5—32no—
252C22×C5C3×#12411yescharacteristic, complemented
253C22×C5C23×A411yescharacteristic
254C2×D5—22no—
255C2×D5—24no—
256C2×D5—62no—
257C2×D5—64no—
258C2×D5—122no—
259C2×D5—122no—
260C2×D5—124no—
261C2×D5—122no—
262C2×D5—122no—
263C2×D5—124no—
264C4×C5—22no—
265C4×C5—32no—
266C4×C5—62no—
267C4×C5D4×A412yes—
268Dic5—22no—
269Dic5—62no—
270C24—102no—
271C24—104no—
272C24—152no—
273C24—152no—
274C24—302no—
275C24—304no—
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—51no—
288C2×D4—152no—
289C2×D4—152no—
290C2×D4—151no—
291C2×D4—302no—
292C2×D4—302no—
293C2×D4—304no—
294C2×D4—302no—
295C2×D4—304no—
296C2×D4—302no—
297C22×C4—22no—
298C22×C4—31no—
299C22×C4—31no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—62no—
304C22×C4—102no—
305C22×C4—152no—
306C22×C4—152no—
307C22×C4—302no—
308C22×C4C3×D2012yes—
309C22⋊C4—54no—
310C22⋊C4—154no—
311C22⋊C4—154no—
312C22⋊C4—158no—
313C22⋊C4—154no—
314C42—32no—
315C42—32no—
316C42—31no—
317C42D5×A411yescharacteristic, complemented
318C3×C5—41noHall
319C22×C3—41no—
320C22×C3—402no—
321C22×C3—404no—
322A4#402111yescharacteristic, direct product factor
323C3×C4—42no—
324C3×C4—82no—
325C3×C4—402no—
326C2×C5—31no—
327C2×C5—32no—
328C2×C5—31no—
329C2×C5C2×D4×A411yescharacteristic
330C2×C5A4×#4112yes—
331D5—42no—
332D5—122no—
333C23—31no—
334C23—32no—
335C23—31no—
336C23—52no—
337C23—152no—
338C23—202no—
339C23—302no—
340C23—302no—
341C23—304no—
342C23—304no—
343C23—302no—
344C23—302no—
345C23—304no—
346C23—304no—
347C23—602no—
348C23—604no—
349C23—604no—
350C23C2×C3×D2011yescharacteristic
351C23C3×#70912yes—
352Q8—102no—
353Q8—304no—
354Q8—304no—
355Q8—302no—
356D4—102no—
357D4—304no—
358D4—304no—
359D4—302no—
360C2×C4—32no—
361C2×C4—31no—
362C2×C4—32no—
363C2×C4—32no—
364C2×C4—32no—
365C2×C4—32no—
366C2×C4—52no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4—62no—
371C2×C4—152no—
372C2×C4—302no—
373C2×C4—302no—
374C2×C4—302no—
375C2×C4—302no—
376C2×C4C2×D5×A412yes—
377C2×C4C2×D5×A411yescharacteristic
378C2×C3—41no—
379C2×C3—42no—
380C2×C3—802no—
381C5A4×#12411yescharacteristic, complemented, Sylow
382C22—31no—
383C22—32no—
384C22—32no—
385C22—31no—
386C22—31no—
387C22—32no—
388C22—32no—
389C22—102no—
390C22—104no—
391C22—302no—
392C22—304no—
393C22—602no—
394C22—602no—
395C22—604no—
396C22—602no—
397C22—602no—
398C22—604no—
399C22C3×#402111yescharacteristic, complemented
400C22C22×D5×A411yescharacteristic
401C4—22no—
402C4—32no—
403C4—62no—
404C4—102no—
405C4—302no—
406C4A4×D2012yes—
407C3—41noSylow
408C2—31no—
409C2—31no—
410C2—32no—
411C2—202no—
412C2—602no—
413C2C2×A4×D2011yescharacteristic
414C2A4×#70912yes—
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C42×C5C2×C3
prime radicalC2×A4×D20C2
hypercenterC42D5×A4
hypocenterC22×C5C3×#124
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic10C2semidirect
3. C42×C5×A4C2semidirect
4. A4×#685C2semidirect
5. C22×#4021C3semidirect
15. C23×Dic10C2×C3semidirect
16. C22×C42×C5C2×C3semidirect
17. C22×#685C2×C3semidirect
36. C42×A4D5semidirect
66. #4021A4direct (N × H)
122. C2×Dic10C2×A4semidirect
126. C42×C5C2×A4semidirect
131. #685C2×A4semidirect
140. C22×C42C3×D5semidirect
144. C5×A4#124semidirect
252. C22×C5C3×#124semidirect
317. C42D5×A4semidirect
322. A4#4021direct (N × H)
381. C5A4×#124semidirect
399. C22C3×#4021semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D202
C2×A4×Dic102
C42×C5×A42
A4×#6852
C22×#40213
C3×#40214
A4×#1245