Finite Group Databasebeta

← C2×C5×A4×C22⋊C4 #14511308

Subgroups — C2×C5×A4×C22⋊C4 #14511308

Order 1920.

1984 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 228 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
1C24×C5×A4C211yesmaximal, characteristic
2C22×C4×C5×A4C212yesmaximal, complemented
3C5×A4×C22⋊C4C214yesmaximal, direct product factor
4C23×C5×C22⋊C4C311yesmaximal, characteristic, complemented, Hall
5C23×C5×A4—24no—
6C23×C5×A4C414yescomplemented
7C23×C5×A4C2212yes—
8C23×C5×A4C2211yescharacteristic
9C2×C4×C5×A4—24no—
10C2×C4×C5×A4C2214yescomplemented
11C2×C3×C5×C22⋊C4—41nomaximal
12C2×A4×C22⋊C4C511yesmaximal, characteristic, direct product factor, Hall
13C26×C5C2×C311yescharacteristic
14C24×C4×C5C2×C312yescomplemented
15C22×C5×C22⋊C4—31no—
16C22×C5×C22⋊C4—31no—
17C22×C5×C22⋊C4—32no—
18C22×C5×C22⋊C4—34no—
19C22×C5×C22⋊C4C2×C314yescomplemented
20C24×C3×C5—41no—
21C22×C5×A4—28no—
22C22×C5×A4—24no—
23C22×C5×A4C2×C412yes—
24C22×C5×A4C2×C414yescomplemented
25C22×C5×A4D414yes—
26C22×C5×A4C2311yescharacteristic
27C22×C3×C4×C5—42no—
28C4×C5×A4—24no—
29C3×C5×C22⋊C4—44no—
30C24×A4C2×C511yescharacteristic
31C22×C4×A4C2×C512yescomplemented
32A4×C22⋊C4C2×C514yesdirect product factor
33C25×C5—24no—
34C25×C5—32no—
35C25×C5—31no—
36C25×C5—34no—
37C25×C5—31no—
38C25×C5—64no—
39C25×C5C3×C414yescomplemented
40C25×C5C22×C312yes—
41C25×C5C22×C311yescharacteristic
42C23×C4×C5—24no—
43C23×C4×C5—32no—
44C23×C4×C5—32no—
45C23×C4×C5—34no—
46C23×C4×C5—64no—
47C23×C4×C5C22×C314yescomplemented
48C2×C5×C22⋊C4—32no—
49C2×C5×C22⋊C4—34no—
50C2×C5×C22⋊C4—38no—
51C2×C5×C22⋊C4—31no—
52C2×C5×C22⋊C4—32no—
53C2×C5×C22⋊C4—34no—
54C2×C5×C22⋊C4—34no—
55C2×C5×C22⋊C4—34no—
56C2×C5×C22⋊C4—38no—
57C2×C5×C22⋊C4A411yescharacteristic, direct product factor
58C23×C22⋊C4C3×C511yescharacteristic, complemented, Sylow
59C23×C3×C5—41no—
60C23×C3×C5—44no—
61C23×C3×C5—42no—
62C23×C3×C5—84no—
63C2×C5×A4—24no—
64C2×C5×A4C22⋊C414yesdirect product factor
65C2×C5×A4C22×C411yescharacteristic
66C2×C5×A4C2×D412yes—
67C2×C3×C4×C5—44no—
68C2×C3×C4×C5—84no—
69C23×A4—24no—
70C23×A4C4×C514yescomplemented
71C23×A4C22×C512yes—
72C23×A4C22×C511yescharacteristic
73C2×C4×A4—24no—
74C2×C4×A4C22×C514yescomplemented
75C2×C3×C22⋊C4—41no—
76C24×C5—28no—
77C24×C5—24no—
78C24×C5—31no—
79C24×C5—34no—
80C24×C5—32no—
81C24×C5—31no—
82C24×C5—32no—
83C24×C5—38no—
84C24×C5—34no—
85C24×C5—32no—
86C24×C5—38no—
87C24×C5—34no—
88C24×C5—34no—
89C24×C5—34no—
90C24×C5—34no—
91C24×C5—32no—
92C24×C5—32no—
93C24×C5—31no—
94C24×C5—64no—
95C24×C5—64no—
96C24×C5—68no—
97C24×C5—64no—
98C24×C5—68no—
99C24×C5—616no—
100C24×C5—64no—
101C24×C5—64no—
102C24×C5—68no—
103C24×C5—616no—
104C24×C5C2×C3×C412yes—
105C24×C5C2×C3×C414yescomplemented
106C24×C5C3×D414yes—
107C24×C5C2×A411yescharacteristic
108C24×C5C23×C311yescharacteristic
109C22×C4×C5—24no—
110C22×C4×C5—34no—
111C22×C4×C5—32no—
112C22×C4×C5—34no—
113C22×C4×C5—34no—
114C22×C4×C5—34no—
115C22×C4×C5—64no—
116C22×C4×C5—64no—
117C22×C4×C5—68no—
118C22×C4×C5—68no—
119C22×C4×C5—64no—
120C22×C4×C5—64no—
121C22×C4×C5—64no—
122C22×C4×C5C2×A412yescomplemented
123C5×C22⋊C4—38no—
124C5×C22⋊C4—34no—
125C5×C22⋊C4—38no—
126C5×C22⋊C4C2×A414yesdirect product factor
127C26C2×C3×C511yescharacteristic
128C24×C4C2×C3×C512yescomplemented
129C22×C22⋊C4—31no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—34no—
133C22×C22⋊C4C2×C3×C514yescomplemented
134C22×C3×C5—42no—
135C22×C3×C5—44no—
136C22×C3×C5—44no—
137C22×C3×C5—41no—
138C22×C3×C5—84no—
139C22×C3×C5—88no—
140C5×A4C2×C22⋊C411yescharacteristic, direct product factor
141C3×C4×C5—84no—
142C24×C3—41no—
143C22×A4—28no—
144C22×A4—24no—
145C22×A4C2×C4×C512yes—
146C22×A4C2×C4×C514yescomplemented
147C22×A4C5×D414yes—
148C22×A4C23×C511yescharacteristic
149C22×C3×C4—42no—
150C4×A4—24no—
151C3×C22⋊C4—44no—
152C23×C5—24no—
153C23×C5—24no—
154C23×C5—34no—
155C23×C5—32no—
156C23×C5—32no—
157C23×C5—31no—
158C23×C5—34no—
159C23×C5—38no—
160C23×C5—34no—
161C23×C5—32no—
162C23×C5—38no—
163C23×C5—32no—
164C23×C5—32no—
165C23×C5—34no—
166C23×C5—34no—
167C23×C5—31no—
168C23×C5—31no—
169C23×C5—38no—
170C23×C5—34no—
171C23×C5—34no—
172C23×C5—34no—
173C23×C5—38no—
174C23×C5—34no—
175C23×C5—34no—
176C23×C5—32no—
177C23×C5—64no—
178C23×C5—68no—
179C23×C5—68no—
180C23×C5—64no—
181C23×C5—616no—
182C23×C5—68no—
183C23×C5—64no—
184C23×C5—616no—
185C23×C5—68no—
186C23×C5—64no—
187C23×C5—68no—
188C23×C5—64no—
189C23×C5—68no—
190C23×C5—616no—
191C23×C5—68no—
192C23×C5—632no—
193C23×C5—68no—
194C23×C5—616no—
195C23×C5—64no—
196C23×C5C3×C22⋊C414yescomplemented
197C23×C5C4×A414yescomplemented
198C23×C5C22×C3×C411yescharacteristic
199C23×C5C2×C3×D412yes—
200C23×C5C22×A412yes—
201C23×C5C22×A411yescharacteristic
202C2×C4×C5—24no—
203C2×C4×C5—34no—
204C2×C4×C5—64no—
205C2×C4×C5—68no—
206C2×C4×C5—64no—
207C2×C4×C5—68no—
208C2×C4×C5—64no—
209C2×C4×C5—64no—
210C2×C4×C5—64no—
211C2×C4×C5C22×A414yescomplemented
212C25—24no—
213C25—32no—
214C25—31no—
215C25—34no—
216C25—31no—
217C25—64no—
218C25C3×C4×C514yescomplemented
219C25C22×C3×C512yes—
220C25C22×C3×C511yescharacteristic
221C23×C4—24no—
222C23×C4—32no—
223C23×C4—32no—
224C23×C4—34no—
225C23×C4—64no—
226C23×C4C22×C3×C514yescomplemented
227C2×C22⋊C4—32no—
228C2×C22⋊C4—34no—
229C2×C22⋊C4—38no—
230C2×C22⋊C4—31no—
231C2×C22⋊C4—32no—
232C2×C22⋊C4—34no—
233C2×C22⋊C4—34no—
234C2×C22⋊C4—34no—
235C2×C22⋊C4—38no—
236C2×C22⋊C4C5×A411yescharacteristic, direct product factor
237C2×C3×C5—41no—
238C2×C3×C5—42no—
239C2×C3×C5—44no—
240C2×C3×C5—84no—
241C23×C3—44no—
242C23×C3—41no—
243C23×C3—42no—
244C23×C3—84no—
245C2×A4—24no—
246C2×A4C5×C22⋊C414yesdirect product factor
247C2×A4C22×C4×C511yescharacteristic
248C2×A4C2×C5×D412yes—
249C2×C3×C4—44no—
250C2×C3×C4—84no—
251C22×C5—24no—
252C22×C5—28no—
253C22×C5—34no—
254C22×C5—31no—
255C22×C5—32no—
256C22×C5—38no—
257C22×C5—32no—
258C22×C5—34no—
259C22×C5—32no—
260C22×C5—31no—
261C22×C5—31no—
262C22×C5—34no—
263C22×C5—32no—
264C22×C5—32no—
265C22×C5—34no—
266C22×C5—38no—
267C22×C5—34no—
268C22×C5—34no—
269C22×C5—64no—
270C22×C5—616no—
271C22×C5—68no—
272C22×C5—64no—
273C22×C5—64no—
274C22×C5—64no—
275C22×C5—616no—
276C22×C5—68no—
277C22×C5—64no—
278C22×C5—68no—
279C22×C5C2×C3×C22⋊C411yescharacteristic, complemented
280C22×C5C2×C4×A412yes—
281C22×C5C2×C4×A414yescomplemented
282C22×C5D4×A414yes—
283C22×C5C23×A411yescharacteristic
284C4×C5—24no—
285C4×C5—64no—
286C24—28no—
287C24—24no—
288C24—31no—
289C24—34no—
290C24—32no—
291C24—31no—
292C24—32no—
293C24—38no—
294C24—34no—
295C24—32no—
296C24—38no—
297C24—34no—
298C24—34no—
299C24—34no—
300C24—34no—
301C24—32no—
302C24—32no—
303C24—31no—
304C24—64no—
305C24—64no—
306C24—68no—
307C24—64no—
308C24—68no—
309C24—616no—
310C24—64no—
311C24—64no—
312C24—68no—
313C24—616no—
314C24C2×C3×C4×C512yes—
315C24C2×C3×C4×C514yescomplemented
316C24C3×C5×D414yes—
317C24C2×C5×A411yescharacteristic
318C24C23×C3×C511yescharacteristic
319C22×C4—24no—
320C22×C4—34no—
321C22×C4—32no—
322C22×C4—34no—
323C22×C4—34no—
324C22×C4—34no—
325C22×C4—64no—
326C22×C4—64no—
327C22×C4—68no—
328C22×C4—68no—
329C22×C4—64no—
330C22×C4—64no—
331C22×C4—64no—
332C22×C4C2×C5×A412yescomplemented
333C22⋊C4—38no—
334C22⋊C4—34no—
335C22⋊C4—38no—
336C22⋊C4C2×C5×A414yesdirect product factor
337C3×C5—41noHall
338C22×C3—42no—
339C22×C3—44no—
340C22×C3—44no—
341C22×C3—41no—
342C22×C3—84no—
343C22×C3—88no—
344A4C2×C5×C22⋊C411yescharacteristic, direct product factor
345C3×C4—84no—
346C2×C5—24no—
347C2×C5—34no—
348C2×C5—31no—
349C2×C5—32no—
350C2×C5—31no—
351C2×C5—64no—
352C2×C5A4×C22⋊C414yesdirect product factor
353C2×C5C22×C4×A411yescharacteristic
354C2×C5C2×D4×A412yes—
355C23—24no—
356C23—24no—
357C23—34no—
358C23—32no—
359C23—32no—
360C23—31no—
361C23—34no—
362C23—38no—
363C23—34no—
364C23—32no—
365C23—38no—
366C23—32no—
367C23—32no—
368C23—34no—
369C23—34no—
370C23—31no—
371C23—31no—
372C23—38no—
373C23—34no—
374C23—34no—
375C23—34no—
376C23—34no—
377C23—38no—
378C23—34no—
379C23—32no—
380C23—64no—
381C23—68no—
382C23—64no—
383C23—68no—
384C23—68no—
385C23—616no—
386C23—64no—
387C23—616no—
388C23—68no—
389C23—64no—
390C23—68no—
391C23—64no—
392C23—68no—
393C23—616no—
394C23—68no—
395C23—632no—
396C23—68no—
397C23—616no—
398C23—64no—
399C23C3×C5×C22⋊C414yescomplemented
400C23C4×C5×A414yescomplemented
401C23C22×C3×C4×C511yescharacteristic
402C23C2×C3×C5×D412yes—
403C23C22×C5×A412yes—
404C23C22×C5×A411yescharacteristic
405C2×C4—24no—
406C2×C4—34no—
407C2×C4—64no—
408C2×C4—64no—
409C2×C4—68no—
410C2×C4—68no—
411C2×C4—64no—
412C2×C4—64no—
413C2×C4—64no—
414C2×C4C22×C5×A414yescomplemented
415C2×C3—41no—
416C2×C3—42no—
417C2×C3—44no—
418C2×C3—84no—
419C5C2×A4×C22⋊C411yescharacteristic, direct product factor, Sylow
420C22—24no—
421C22—28no—
422C22—34no—
423C22—31no—
424C22—32no—
425C22—38no—
426C22—32no—
427C22—34no—
428C22—31no—
429C22—32no—
430C22—31no—
431C22—32no—
432C22—34no—
433C22—32no—
434C22—34no—
435C22—34no—
436C22—38no—
437C22—34no—
438C22—64no—
439C22—64no—
440C22—616no—
441C22—68no—
442C22—64no—
443C22—64no—
444C22—616no—
445C22—68no—
446C22—64no—
447C22—68no—
448C22C2×C3×C5×C22⋊C411yescharacteristic, complemented
449C22C2×C4×C5×A412yes—
450C22C2×C4×C5×A414yescomplemented
451C22C5×D4×A414yes—
452C22C23×C5×A411yescharacteristic
453C4—24no—
454C4—64no—
455C3—41noSylow
456C2—24no—
457C2—31no—
458C2—34no—
459C2—31no—
460C2—32no—
461C2—64no—
462C2C5×A4×C22⋊C414yesdirect product factor
463C2C22×C4×C5×A411yescharacteristic
464C2C2×C5×D4×A412yes—
subgroupG/H
centerC23×C5C22×A4
commutatorC23C22×C3×C4×C5
FrattiniC22C23×C5×A4
FittingC23×C5×C22⋊C4C3
socleC25×C5C22×C3
prime radicalC24×C5×A4C2
cosocleC24C23×C3×C5
hypercenterC2×C5×C22⋊C4A4
hypocenterC22C2×C3×C5×C22⋊C4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C23×C5 ◁ C2×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C5×A4C2semidirect
3. C5×A4×C22⋊C4C2direct (N × H)
4. C23×C5×C22⋊C4C3semidirect
6. C23×C5×A4C4semidirect
10. C2×C4×C5×A4C22semidirect
12. C2×A4×C22⋊C4C5direct (N × H)
14. C24×C4×C5C2×C3semidirect
19. C22×C5×C22⋊C4C2×C3semidirect
24. C22×C5×A4C2×C4semidirect
31. C22×C4×A4C2×C5semidirect
32. A4×C22⋊C4C2×C5direct (N × H)
39. C25×C5C3×C4semidirect
47. C23×C4×C5C22×C3semidirect
57. C2×C5×C22⋊C4A4direct (N × H)
58. C23×C22⋊C4C3×C5semidirect
64. C2×C5×A4C22⋊C4direct (N × H)
70. C23×A4C4×C5semidirect
74. C2×C4×A4C22×C5semidirect
105. C24×C5C2×C3×C4semidirect
122. C22×C4×C5C2×A4semidirect
126. C5×C22⋊C4C2×A4direct (N × H)
128. C24×C4C2×C3×C5semidirect
133. C22×C22⋊C4C2×C3×C5semidirect
140. C5×A4C2×C22⋊C4direct (N × H)
146. C22×A4C2×C4×C5semidirect
196. C23×C5C3×C22⋊C4semidirect
197. C23×C5C4×A4semidirect
211. C2×C4×C5C22×A4semidirect
218. C25C3×C4×C5semidirect
226. C23×C4C22×C3×C5semidirect
236. C2×C22⋊C4C5×A4direct (N × H)
246. C2×A4C5×C22⋊C4direct (N × H)
279. C22×C5C2×C3×C22⋊C4semidirect
281. C22×C5C2×C4×A4semidirect
315. C24C2×C3×C4×C5semidirect
332. C22×C4C2×C5×A4semidirect
336. C22⋊C4C2×C5×A4direct (N × H)
344. A4C2×C5×C22⋊C4direct (N × H)
352. C2×C5A4×C22⋊C4direct (N × H)
399. C23C3×C5×C22⋊C4semidirect
400. C23C4×C5×A4semidirect
414. C2×C4C22×C5×A4semidirect
419. C5C2×A4×C22⋊C4direct (N × H)
448. C22C2×C3×C5×C22⋊C4semidirect
450. C22C2×C4×C5×A4semidirect
462. C2C5×A4×C22⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C5×A42
C22×C4×C5×A42
C5×A4×C22⋊C42
C23×C5×C22⋊C43
C2×C3×C5×C22⋊C44
C2×A4×C22⋊C45