Finite Group Databasebeta

← A4×(C2×AGL(1,𝔽5))⋊C4 #14512563

Subgroups — A4×(C2×AGL(1,𝔽5))⋊C4 #14512563

Order 1920.

880 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C22×A4×AGL(1,𝔽5)C212yesmaximal
2C2×C4×D5×A4C211yesmaximal, characteristic
3C22×(C2×AGL(1,𝔽5))⋊C4C311yesmaximal, characteristic, complemented, Hall
4C22×D5×A4C2211yescharacteristic
5C2×A4×AGL(1,𝔽5)—22no—
6C2×A4×AGL(1,𝔽5)—22no—
7C2×A4×AGL(1,𝔽5)C414yescomplemented
8C2×C4×C5×A4C411yescharacteristic, complemented
9C2×A4×Dic5C411yescharacteristic, complemented
10C4×D5×A4—22no—
11C3×(C2×AGL(1,𝔽5))⋊C4—41nomaximal
12A4×#95—51nomaximal, Hall
13C24×AGL(1,𝔽5)C2×C312yes—
14C23×C4×D5C2×C311yescharacteristic
15C2×(C2×AGL(1,𝔽5))⋊C4—31no—
16C2×(C2×AGL(1,𝔽5))⋊C4—32no—
17C2×(C2×AGL(1,𝔽5))⋊C4—31no—
18C22×C5×A4C2×C411yescharacteristic
19C22×C3×AGL(1,𝔽5)—42no—
20C2×D5×A4C2×C412yes—
21C2×D5×A4D411yescharacteristic
22C2×D5×A4D412yes—
23C2×D5×A4Q811yescharacteristic
24A4×AGL(1,𝔽5)—24no—
25C2×C3×C4×D5—41no—
26C4×C5×A4—21no—
27A4×Dic5—21no—
28C22×C4×A4—52no—
29C22×C4×A4—51no—
30C24×D5C22×C311yescharacteristic
31C23×AGL(1,𝔽5)—22no—
32C23×AGL(1,𝔽5)—22no—
33C23×AGL(1,𝔽5)—32no—
34C23×AGL(1,𝔽5)—32no—
35C23×AGL(1,𝔽5)—34no—
36C23×AGL(1,𝔽5)—62no—
37C23×AGL(1,𝔽5)—62no—
38C23×AGL(1,𝔽5)C3×C414yescomplemented
39C23×C4×C5C3×C411yescharacteristic, complemented
40C23×Dic5C3×C411yescharacteristic, complemented
41C22×C4×D5—22no—
42C22×C4×D5—31no—
43C22×C4×D5—31no—
44C22×C4×D5—31no—
45C22×C4×D5—31no—
46C22×C4×D5—62no—
47(C2×AGL(1,𝔽5))⋊C4—32no—
48(C2×AGL(1,𝔽5))⋊C4—32no—
49(C2×AGL(1,𝔽5))⋊C4—31no—
50(C2×AGL(1,𝔽5))⋊C4A411yescharacteristic, direct product factor
51C22×#95—51noSylow
52C22×C3×D5—41no—
53C2×C5×A4C4211yescharacteristic
54C2×C5×A4C22⋊C411yescharacteristic
55C2×C5×A4C4⋊C411yescharacteristic
56C2×C3×AGL(1,𝔽5)—44no—
57C2×C3×AGL(1,𝔽5)—82no—
58C2×C3×AGL(1,𝔽5)—82no—
59D5×A4C22⋊C412yes—
60D5×A4C4⋊C412yes—
61C2×C3×C4×C5—41no—
62C2×C3×Dic5—41no—
63C3×C4×D5—82no—
64C23×A4—51no—
65C2×C4×A4—54no—
66C2×C4×A4—51no—
67C2×C4×A4—102no—
68C2×C4×A4—102no—
69C2×C4×A4—102no—
70C2×C4×A4AGL(1,𝔽5)11yescharacteristic, complemented
71C3×#95—201no—
72C24×C5C2×C3×C411yescharacteristic
73C23×D5—31no—
74C23×D5—31no—
75C23×D5—32no—
76C23×D5—32no—
77C23×D5—31no—
78C23×D5—31no—
79C23×D5C2×C3×C412yes—
80C23×D5C3×D411yescharacteristic
81C23×D5C3×D412yes—
82C23×D5C3×Q811yescharacteristic
83C22×AGL(1,𝔽5)—24no—
84C22×AGL(1,𝔽5)—34no—
85C22×AGL(1,𝔽5)—32no—
86C22×AGL(1,𝔽5)—34no—
87C22×AGL(1,𝔽5)—34no—
88C22×AGL(1,𝔽5)—34no—
89C22×AGL(1,𝔽5)—62no—
90C22×AGL(1,𝔽5)—62no—
91C22×AGL(1,𝔽5)—62no—
92C22×AGL(1,𝔽5)—62no—
93C22×AGL(1,𝔽5)—68no—
94C22×AGL(1,𝔽5)—64no—
95C22×AGL(1,𝔽5)—64no—
96C22×AGL(1,𝔽5)—62no—
97C22×AGL(1,𝔽5)—62no—
98C22×AGL(1,𝔽5)—62no—
99C22×AGL(1,𝔽5)—62no—
100C22×AGL(1,𝔽5)—64no—
101C22×AGL(1,𝔽5)C2×A412yes—
102C22×C4×C5—21no—
103C22×C4×C5—31no—
104C22×C4×C5—31no—
105C22×C4×C5—61no—
106C22×Dic5—21no—
107C22×Dic5—31no—
108C22×Dic5—31no—
109C22×Dic5—61no—
110C2×C4×D5—32no—
111C2×C4×D5—31no—
112C2×C4×D5—31no—
113C2×C4×D5—31no—
114C2×C4×D5—62no—
115C2×C4×D5—62no—
116C2×C4×D5—62no—
117C2×C4×D5—62no—
118C2×C4×D5—62no—
119C2×C4×D5—62no—
120C2×C4×D5—62no—
121C2×C4×D5—62no—
122C2×C4×D5C2×A411yescharacteristic
123C24×C4—52no—
124C24×C4—51no—
125C2×#95—151no—
126C2×#95—151no—
127C2×#95—152no—
128C22×C3×C5—41no—
129C2×C3×D5—42no—
130C2×C3×D5—42no—
131C2×C3×D5—41no—
132C2×C3×D5—41no—
133C5×A4#9511yescharacteristic, complemented
134C3×AGL(1,𝔽5)—84no—
135C3×C4×C5—81no—
136C3×Dic5—81no—
137C22×A4—52no—
138C22×A4—51no—
139C22×A4—51no—
140C22×A4—52no—
141C22×A4C2×AGL(1,𝔽5)11yescharacteristic
142C22×C3×C4—201no—
143C22×C3×C4—202no—
144C4×A4—21no—
145C4×A4—104no—
146C4×A4—101no—
147C23×C5—31no—
148C23×C5—31no—
149C23×C5—31no—
150C23×C5—31no—
151C23×C5C3×C4211yescharacteristic
152C23×C5C3×C22⋊C411yescharacteristic
153C23×C5C3×C4⋊C411yescharacteristic
154C22×D5—32no—
155C22×D5—34no—
156C22×D5—32no—
157C22×D5—32no—
158C22×D5—34no—
159C22×D5—31no—
160C22×D5—32no—
161C22×D5—32no—
162C22×D5—32no—
163C22×D5—32no—
164C22×D5—31no—
165C22×D5—31no—
166C22×D5—31no—
167C22×D5—31no—
168C22×D5—32no—
169C22×D5—32no—
170C22×D5—32no—
171C22×D5—32no—
172C22×D5—32no—
173C22×D5—32no—
174C22×D5—31no—
175C22×D5—32no—
176C22×D5—31no—
177C22×D5—32no—
178C22×D5C3×C22⋊C412yes—
179C22×D5C3×C4⋊C412yes—
180C22×D5C22×A411yescharacteristic
181C2×AGL(1,𝔽5)—22no—
182C2×AGL(1,𝔽5)—22no—
183C2×AGL(1,𝔽5)—34no—
184C2×AGL(1,𝔽5)—64no—
185C2×AGL(1,𝔽5)—64no—
186C2×AGL(1,𝔽5)—64no—
187C2×AGL(1,𝔽5)—64no—
188C2×AGL(1,𝔽5)—64no—
189C2×AGL(1,𝔽5)—64no—
190C2×AGL(1,𝔽5)—62no—
191C2×AGL(1,𝔽5)—62no—
192C2×AGL(1,𝔽5)—64no—
193C2×AGL(1,𝔽5)—64no—
194C2×AGL(1,𝔽5)C4×A414yescomplemented
195C2×C4×C5—31no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5—61no—
200C2×C4×C5C4×A411yescharacteristic, complemented
201C2×Dic5—31no—
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5C4×A411yescharacteristic, complemented
207C4×D5—22no—
208C4×D5—62no—
209C4×D5—62no—
210C4×D5—64no—
211C4×D5—62no—
212C25—51no—
213C23×C4—54no—
214C23×C4—51no—
215C23×C4—102no—
216C23×C4—102no—
217C23×C4—102no—
218C23×C4—151no—
219C23×C4—151no—
220C23×C4—151no—
221C23×C4—151no—
222C23×C4—152no—
223C23×C4—154no—
224C23×C4—152no—
225C23×C4—302no—
226C23×C4—302no—
227C23×C4—302no—
228C23×C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
229#95—51no—
230#95—152no—
231#95—151no—
232#95—152no—
233C2×C3×C5—41no—
234C2×C3×C5—41no—
235C2×C3×C5—41no—
236C3×D5—42no—
237C3×D5—42no—
238C23×C3—201no—
239C2×A4—52no—
240C2×A4—52no—
241C2×A4C4×AGL(1,𝔽5)11yescharacteristic
242C2×A4C4⋊AGL(1,𝔽5)11yescharacteristic
243C2×A4C22⋊AGL(1,𝔽5)11yescharacteristic
244C2×C3×C4—41no—
245C2×C3×C4—201no—
246C2×C3×C4—204no—
247C2×C3×C4—402no—
248C2×C3×C4—402no—
249C2×C3×C4—402no—
250C22×C5—31no—
251C22×C5—31no—
252C22×C5—31no—
253C22×C5—32no—
254C22×C5—31no—
255C22×C5—31no—
256C22×C5—31no—
257C22×C5—31no—
258C22×C5—31no—
259C22×C5—31no—
260C22×C5C3×#9511yescharacteristic, complemented
261C22×C5C2×C4×A411yescharacteristic
262C2×D5—32no—
263C2×D5—34no—
264C2×D5—32no—
265C2×D5—34no—
266C2×D5—32no—
267C2×D5—32no—
268C2×D5—31no—
269C2×D5—31no—
270C2×D5—32no—
271C2×D5—32no—
272C2×D5—32no—
273C2×D5—32no—
274C2×D5—32no—
275C2×D5—32no—
276C2×D5—32no—
277C2×D5—32no—
278C2×D5—32no—
279C2×D5—32no—
280C2×D5C2×C4×A412yes—
281C2×D5D4×A411yescharacteristic
282C2×D5D4×A412yes—
283C2×D5Q8×A411yescharacteristic
284AGL(1,𝔽5)—24no—
285AGL(1,𝔽5)—64no—
286C4×C5—21no—
287C4×C5—61no—
288Dic5—21no—
289Dic5—61no—
290C24—52no—
291C24—51no—
292C24—51no—
293C24—52no—
294C24—151no—
295C24—152no—
296C24—151no—
297C24—152no—
298C24—151no—
299C24—151no—
300C24C2×C3×AGL(1,𝔽5)11yescharacteristic
301C22×C4—21no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—52no—
305C22×C4—51no—
306C22×C4—61no—
307C22×C4—104no—
308C22×C4—101no—
309C22×C4—151no—
310C22×C4—151no—
311C22×C4—152no—
312C22×C4—151no—
313C22×C4—154no—
314C22×C4—154no—
315C22×C4—152no—
316C22×C4—154no—
317C22×C4—151no—
318C22×C4—151no—
319C22×C4—154no—
320C22×C4—302no—
321C22×C4—302no—
322C22×C4—302no—
323C22×C4—302no—
324C22×C4—302no—
325C22×C4—302no—
326C22×C4—302no—
327C22×C4—302no—
328C22×C4—302no—
329C22×C4—302no—
330C22×C4—302no—
331C22×C4—302no—
332C22×C4—308no—
333C22×C4—304no—
334C22×C4—304no—
335C22×C4—302no—
336C22×C4—302no—
337C22×C4—302no—
338C22×C4—302no—
339C22×C4—301no—
340C22×C4—304no—
341C3×C5—41noHall
342C22×C3—41no—
343C22×C3—202no—
344C22×C3—201no—
345C22×C3—202no—
346C22×C3—201no—
347A4(C2×AGL(1,𝔽5))⋊C411yescharacteristic, direct product factor
348C3×C4—81no—
349C3×C4—401no—
350C3×C4—404no—
351C2×C5—31no—
352C2×C5—31no—
353C2×C5—31no—
354C2×C5—31no—
355C2×C5C42×A411yescharacteristic
356C2×C5A4×C22⋊C411yescharacteristic
357C2×C5A4×C4⋊C411yescharacteristic
358D5—32no—
359D5—32no—
360D5A4×C22⋊C412yes—
361D5A4×C4⋊C412yes—
362C23—31no—
363C23—31no—
364C23—31no—
365C23—31no—
366C23—51no—
367C23—52no—
368C23—52no—
369C23—152no—
370C23—152no—
371C23—151no—
372C23—152no—
373C23—151no—
374C23—152no—
375C23—151no—
376C23—151no—
377C23—152no—
378C23—152no—
379C23—152no—
380C23—152no—
381C23—152no—
382C23—152no—
383C23—152no—
384C23—152no—
385C23—151no—
386C23—151no—
387C23—154no—
388C23—152no—
389C23—154no—
390C23—152no—
391C23—152no—
392C23—151no—
393C23C3×C4×AGL(1,𝔽5)11yescharacteristic
394C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
395C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
396C2×C4—31no—
397C2×C4—54no—
398C2×C4—51no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—102no—
404C2×C4—102no—
405C2×C4—102no—
406C2×C4—154no—
407C2×C4—151no—
408C2×C4—302no—
409C2×C4—302no—
410C2×C4—302no—
411C2×C4—304no—
412C2×C4—301no—
413C2×C4—301no—
414C2×C4—304no—
415C2×C4—304no—
416C2×C4—304no—
417C2×C4—304no—
418C2×C4—302no—
419C2×C4—302no—
420C2×C4—304no—
421C2×C4—304no—
422C2×C4—301no—
423C2×C4—301no—
424C2×C4—304no—
425C2×C4—304no—
426C2×C4A4×AGL(1,𝔽5)11yescharacteristic, complemented
427C2×C3—41no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3—202no—
431C2×C3—202no—
432C5A4×#9511yescharacteristic, complemented, Sylow
433C22—31no—
434C22—31no—
435C22—31no—
436C22—32no—
437C22—31no—
438C22—31no—
439C22—31no—
440C22—31no—
441C22—31no—
442C22—31no—
443C22—52no—
444C22—51no—
445C22—51no—
446C22—52no—
447C22—152no—
448C22—152no—
449C22—152no—
450C22—152no—
451C22—152no—
452C22—152no—
453C22—152no—
454C22—152no—
455C22—152no—
456C22—152no—
457C22—152no—
458C22—154no—
459C22—154no—
460C22—152no—
461C22—152no—
462C22—151no—
463C22—151no—
464C22—152no—
465C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic, complemented
466C22C2×A4×AGL(1,𝔽5)11yescharacteristic
467C4—21no—
468C4—61no—
469C4—104no—
470C4—101no—
471C4—304no—
472C4—301no—
473C3—41noSylow
474C2—31no—
475C2—31no—
476C2—31no—
477C2—31no—
478C2—52no—
479C2—52no—
480C2—152no—
481C2—152no—
482C2C4×A4×AGL(1,𝔽5)11yescharacteristic
483C2A4×C4⋊AGL(1,𝔽5)11yescharacteristic
484C2A4×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4×AGL(1,𝔽5)
commutatorC23×C5C3×C42
FittingC23×C4×C5C3×C4
socleC24×C5C2×C3×C4
prime radicalC22×D5×A4C22
cosocleC24×D5C22×C3
hypercenterC2×C4A4×AGL(1,𝔽5)
hypocenterC22×C5C3×#95
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C22×(C2×AGL(1,𝔽5))⋊C4C3semidirect
7. C2×A4×AGL(1,𝔽5)C4semidirect
8. C2×C4×C5×A4C4semidirect
9. C2×A4×Dic5C4semidirect
38. C23×AGL(1,𝔽5)C3×C4semidirect
39. C23×C4×C5C3×C4semidirect
40. C23×Dic5C3×C4semidirect
50. (C2×AGL(1,𝔽5))⋊C4A4direct (N × H)
70. C2×C4×A4AGL(1,𝔽5)semidirect
133. C5×A4#95semidirect
194. C2×AGL(1,𝔽5)C4×A4semidirect
200. C2×C4×C5C4×A4semidirect
206. C2×Dic5C4×A4semidirect
228. C23×C4C3×AGL(1,𝔽5)semidirect
260. C22×C5C3×#95semidirect
347. A4(C2×AGL(1,𝔽5))⋊C4direct (N × H)
426. C2×C4A4×AGL(1,𝔽5)semidirect
432. C5A4×#95semidirect
465. C22C3×(C2×AGL(1,𝔽5))⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×A4×AGL(1,𝔽5)2
C2×C4×D5×A42
C22×(C2×AGL(1,𝔽5))⋊C43
C3×(C2×AGL(1,𝔽5))⋊C44
A4×#955