Finite Group Databasebeta

← C2×C5×A4×C4⋊C4 #14511309

Subgroups — C2×C5×A4×C4⋊C4 #14511309

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×A4C212yesmaximal
2C22×C4×C5×A4C211yesmaximal, characteristic
3C5×A4×C4⋊C4C214yesmaximal, direct product factor
4C23×C5×C4⋊C4C311yesmaximal, characteristic, complemented, Hall
5C23×C5×A4C2211yescharacteristic
6C2×C4×C5×A4—24no—
7C2×C4×C5×A4C414yescomplemented
8C2×C4×C5×A4C2214yes—
9C2×C4×C5×A4C2212yes—
10C2×C3×C5×C4⋊C4—41nomaximal
11C2×A4×C4⋊C4C511yesmaximal, characteristic, direct product factor, Hall
12C24×C4×C5C2×C312yes—
13C24×C4×C5C2×C311yescharacteristic
14C22×C5×C4⋊C4—31no—
15C22×C5×C4⋊C4—31no—
16C22×C5×C4⋊C4—32no—
17C22×C5×C4⋊C4—34no—
18C22×C5×C4⋊C4C2×C314yescomplemented
19C22×C5×A4C2×C412yes—
20C22×C5×A4D412yes—
21C22×C5×A4Q812yes—
22C22×C5×A4C2311yescharacteristic
23C22×C3×C4×C5—41no—
24C22×C3×C4×C5—42no—
25C4×C5×A4—24no—
26C4×C5×A4C2×C414yescomplemented
27C3×C5×C4⋊C4—44no—
28C22×C4×A4C2×C512yes—
29C22×C4×A4C2×C511yescharacteristic
30A4×C4⋊C4C2×C514yesdirect product factor
31C25×C5C22×C311yescharacteristic
32C23×C4×C5—24no—
33C23×C4×C5—31no—
34C23×C4×C5—31no—
35C23×C4×C5—32no—
36C23×C4×C5—34no—
37C23×C4×C5—32no—
38C23×C4×C5—32no—
39C23×C4×C5—34no—
40C23×C4×C5—64no—
41C23×C4×C5C3×C414yescomplemented
42C23×C4×C5C22×C314yes—
43C23×C4×C5C22×C312yes—
44C2×C5×C4⋊C4—32no—
45C2×C5×C4⋊C4—38no—
46C2×C5×C4⋊C4—34no—
47C2×C5×C4⋊C4—32no—
48C2×C5×C4⋊C4—31no—
49C2×C5×C4⋊C4—34no—
50C2×C5×C4⋊C4—34no—
51C2×C5×C4⋊C4—34no—
52C2×C5×C4⋊C4—38no—
53C2×C5×C4⋊C4A411yescharacteristic, direct product factor
54C23×C4⋊C4C3×C511yescharacteristic, complemented, Sylow
55C23×C3×C5—41no—
56C2×C5×A4C4⋊C414yesdirect product factor
57C2×C5×A4C22×C411yescharacteristic
58C2×C5×A4C2×D411yescharacteristic
59C2×C5×A4C2×Q811yescharacteristic
60C2×C3×C4×C5—44no—
61C2×C3×C4×C5—42no—
62C2×C3×C4×C5—44no—
63C2×C3×C4×C5—84no—
64C23×A4C22×C511yescharacteristic
65C2×C4×A4—24no—
66C2×C4×A4C4×C514yescomplemented
67C2×C4×A4C22×C514yes—
68C2×C4×A4C22×C512yes—
69C2×C3×C4⋊C4—41no—
70C24×C5—31no—
71C24×C5—32no—
72C24×C5—32no—
73C24×C5—32no—
74C24×C5—31no—
75C24×C5C2×C3×C412yes—
76C24×C5C3×D412yes—
77C24×C5C3×Q812yes—
78C24×C5C23×C311yescharacteristic
79C22×C4×C5—24no—
80C22×C4×C5—32no—
81C22×C4×C5—34no—
82C22×C4×C5—38no—
83C22×C4×C5—31no—
84C22×C4×C5—34no—
85C22×C4×C5—34no—
86C22×C4×C5—32no—
87C22×C4×C5—32no—
88C22×C4×C5—32no—
89C22×C4×C5—34no—
90C22×C4×C5—38no—
91C22×C4×C5—34no—
92C22×C4×C5—34no—
93C22×C4×C5—32no—
94C22×C4×C5—34no—
95C22×C4×C5—34no—
96C22×C4×C5—34no—
97C22×C4×C5—64no—
98C22×C4×C5—64no—
99C22×C4×C5—68no—
100C22×C4×C5—68no—
101C22×C4×C5—64no—
102C22×C4×C5—64no—
103C22×C4×C5—64no—
104C22×C4×C5C2×C3×C414yescomplemented
105C22×C4×C5C2×A412yes—
106C22×C4×C5C2×A411yescharacteristic
107C5×C4⋊C4—38no—
108C5×C4⋊C4—38no—
109C5×C4⋊C4—34no—
110C5×C4⋊C4C2×A414yesdirect product factor
111C24×C4C2×C3×C512yes—
112C24×C4C2×C3×C511yescharacteristic
113C22×C4⋊C4—31no—
114C22×C4⋊C4—31no—
115C22×C4⋊C4—32no—
116C22×C4⋊C4—34no—
117C22×C4⋊C4C2×C3×C514yescomplemented
118C22×C3×C5—42no—
119C22×C3×C5—42no—
120C22×C3×C5—42no—
121C22×C3×C5—41no—
122C5×A4C2×C4⋊C411yescharacteristic, direct product factor
123C3×C4×C5—44no—
124C3×C4×C5—84no—
125C22×A4C2×C4×C512yes—
126C22×A4C5×D412yes—
127C22×A4C5×Q812yes—
128C22×A4C23×C511yescharacteristic
129C22×C3×C4—41no—
130C22×C3×C4—42no—
131C4×A4—24no—
132C4×A4C2×C4×C514yescomplemented
133C3×C4⋊C4—44no—
134C23×C5—32no—
135C23×C5—31no—
136C23×C5—32no—
137C23×C5—31no—
138C23×C5—34no—
139C23×C5—34no—
140C23×C5—32no—
141C23×C5—34no—
142C23×C5—31no—
143C23×C5—32no—
144C23×C5—32no—
145C23×C5—32no—
146C23×C5—38no—
147C23×C5—32no—
148C23×C5—32no—
149C23×C5—32no—
150C23×C5—32no—
151C23×C5—32no—
152C23×C5—32no—
153C23×C5—31no—
154C23×C5—31no—
155C23×C5C3×C4⋊C414yescomplemented
156C23×C5C22×C3×C411yescharacteristic
157C23×C5C2×C3×D411yescharacteristic
158C23×C5C2×C3×Q811yescharacteristic
159C23×C5C22×A411yescharacteristic
160C2×C4×C5—24no—
161C2×C4×C5—38no—
162C2×C4×C5—34no—
163C2×C4×C5—34no—
164C2×C4×C5—32no—
165C2×C4×C5—34no—
166C2×C4×C5—38no—
167C2×C4×C5—34no—
168C2×C4×C5—34no—
169C2×C4×C5—34no—
170C2×C4×C5—64no—
171C2×C4×C5—68no—
172C2×C4×C5—64no—
173C2×C4×C5—68no—
174C2×C4×C5—64no—
175C2×C4×C5—64no—
176C2×C4×C5—64no—
177C2×C4×C5C4×A414yescomplemented
178C2×C4×C5C22×A414yes—
179C2×C4×C5C22×A412yes—
180C25C22×C3×C511yescharacteristic
181C23×C4—24no—
182C23×C4—31no—
183C23×C4—31no—
184C23×C4—32no—
185C23×C4—34no—
186C23×C4—32no—
187C23×C4—32no—
188C23×C4—34no—
189C23×C4—64no—
190C23×C4C3×C4×C514yescomplemented
191C23×C4C22×C3×C514yes—
192C23×C4C22×C3×C512yes—
193C2×C4⋊C4—32no—
194C2×C4⋊C4—38no—
195C2×C4⋊C4—34no—
196C2×C4⋊C4—32no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—34no—
199C2×C4⋊C4—34no—
200C2×C4⋊C4—34no—
201C2×C4⋊C4—38no—
202C2×C4⋊C4C5×A411yescharacteristic, direct product factor
203C2×C3×C5—41no—
204C2×C3×C5—41no—
205C2×C3×C5—41no—
206C2×C3×C5—44no—
207C23×C3—41no—
208C2×A4C5×C4⋊C414yesdirect product factor
209C2×A4C22×C4×C511yescharacteristic
210C2×A4C2×C5×D411yescharacteristic
211C2×A4C2×C5×Q811yescharacteristic
212C2×C3×C4—44no—
213C2×C3×C4—42no—
214C2×C3×C4—44no—
215C2×C3×C4—84no—
216C22×C5—34no—
217C22×C5—31no—
218C22×C5—31no—
219C22×C5—31no—
220C22×C5—34no—
221C22×C5—32no—
222C22×C5—34no—
223C22×C5—34no—
224C22×C5—32no—
225C22×C5—31no—
226C22×C5—31no—
227C22×C5—32no—
228C22×C5—31no—
229C22×C5—31no—
230C22×C5—32no—
231C22×C5—31no—
232C22×C5—31no—
233C22×C5—34no—
234C22×C5—34no—
235C22×C5—34no—
236C22×C5—34no—
237C22×C5C2×C3×C4⋊C411yescharacteristic, complemented
238C22×C5C2×C4×A412yes—
239C22×C5D4×A412yes—
240C22×C5Q8×A412yes—
241C22×C5C23×A411yescharacteristic
242C4×C5—24no—
243C4×C5—34no—
244C4×C5—64no—
245C4×C5C2×C4×A414yescomplemented
246C24—31no—
247C24—32no—
248C24—32no—
249C24—32no—
250C24—31no—
251C24C2×C3×C4×C512yes—
252C24C3×C5×D412yes—
253C24C3×C5×Q812yes—
254C24C23×C3×C511yescharacteristic
255C22×C4—24no—
256C22×C4—32no—
257C22×C4—34no—
258C22×C4—38no—
259C22×C4—31no—
260C22×C4—34no—
261C22×C4—34no—
262C22×C4—32no—
263C22×C4—32no—
264C22×C4—32no—
265C22×C4—34no—
266C22×C4—38no—
267C22×C4—34no—
268C22×C4—34no—
269C22×C4—32no—
270C22×C4—34no—
271C22×C4—34no—
272C22×C4—34no—
273C22×C4—64no—
274C22×C4—64no—
275C22×C4—68no—
276C22×C4—68no—
277C22×C4—64no—
278C22×C4—64no—
279C22×C4—64no—
280C22×C4C2×C3×C4×C514yescomplemented
281C22×C4C2×C5×A412yes—
282C22×C4C2×C5×A411yescharacteristic
283C4⋊C4—38no—
284C4⋊C4—38no—
285C4⋊C4—34no—
286C4⋊C4C2×C5×A414yesdirect product factor
287C3×C5—41noHall
288C22×C3—42no—
289C22×C3—42no—
290C22×C3—42no—
291C22×C3—41no—
292A4C2×C5×C4⋊C411yescharacteristic, direct product factor
293C3×C4—44no—
294C3×C4—84no—
295C2×C5—34no—
296C2×C5—31no—
297C2×C5—31no—
298C2×C5—31no—
299C2×C5—31no—
300C2×C5A4×C4⋊C414yesdirect product factor
301C2×C5C22×C4×A411yescharacteristic
302C2×C5C2×D4×A411yescharacteristic
303C2×C5C2×Q8×A411yescharacteristic
304C23—32no—
305C23—31no—
306C23—32no—
307C23—31no—
308C23—34no—
309C23—34no—
310C23—32no—
311C23—34no—
312C23—31no—
313C23—32no—
314C23—32no—
315C23—32no—
316C23—38no—
317C23—32no—
318C23—32no—
319C23—32no—
320C23—32no—
321C23—32no—
322C23—32no—
323C23—31no—
324C23—31no—
325C23C3×C5×C4⋊C414yescomplemented
326C23C22×C3×C4×C511yescharacteristic
327C23C2×C3×C5×D411yescharacteristic
328C23C2×C3×C5×Q811yescharacteristic
329C23C22×C5×A411yescharacteristic
330C2×C4—24no—
331C2×C4—38no—
332C2×C4—34no—
333C2×C4—34no—
334C2×C4—32no—
335C2×C4—34no—
336C2×C4—38no—
337C2×C4—34no—
338C2×C4—34no—
339C2×C4—34no—
340C2×C4—64no—
341C2×C4—64no—
342C2×C4—68no—
343C2×C4—68no—
344C2×C4—64no—
345C2×C4—64no—
346C2×C4—64no—
347C2×C4C4×C5×A414yescomplemented
348C2×C4C22×C5×A414yes—
349C2×C4C22×C5×A412yes—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—44no—
354C5C2×A4×C4⋊C411yescharacteristic, direct product factor, Sylow
355C22—34no—
356C22—31no—
357C22—31no—
358C22—31no—
359C22—34no—
360C22—32no—
361C22—34no—
362C22—34no—
363C22—31no—
364C22—32no—
365C22—31no—
366C22—31no—
367C22—32no—
368C22—31no—
369C22—31no—
370C22—32no—
371C22—31no—
372C22—34no—
373C22—34no—
374C22—34no—
375C22—34no—
376C22C2×C3×C5×C4⋊C411yescharacteristic, complemented
377C22C2×C4×C5×A412yes—
378C22C5×D4×A412yes—
379C22C5×Q8×A412yes—
380C22C23×C5×A411yescharacteristic
381C4—24no—
382C4—34no—
383C4—64no—
384C4C2×C4×C5×A414yescomplemented
385C3—41noSylow
386C2—31no—
387C2—34no—
388C2—31no—
389C2—31no—
390C2—31no—
391C2C5×A4×C4⋊C414yesdirect product factor
392C2C22×C4×C5×A411yescharacteristic
393C2C2×C5×D4×A411yescharacteristic
394C2C2×C5×Q8×A411yescharacteristic
subgroupG/H
centerC23×C5C22×A4
commutatorC23C22×C3×C4×C5
FrattiniC22C23×C5×A4
FittingC23×C5×C4⋊C4C3
socleC25×C5C22×C3
prime radicalC23×C5×A4C22
cosocleC24C23×C3×C5
hypercenterC2×C5×C4⋊C4A4
hypocenterC22C2×C3×C5×C4⋊C4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C23×C5 ◁ C2×C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×A4×C4⋊C4C2direct (N × H)
4. C23×C5×C4⋊C4C3semidirect
7. C2×C4×C5×A4C4semidirect
11. C2×A4×C4⋊C4C5direct (N × H)
18. C22×C5×C4⋊C4C2×C3semidirect
26. C4×C5×A4C2×C4semidirect
30. A4×C4⋊C4C2×C5direct (N × H)
41. C23×C4×C5C3×C4semidirect
53. C2×C5×C4⋊C4A4direct (N × H)
54. C23×C4⋊C4C3×C5semidirect
56. C2×C5×A4C4⋊C4direct (N × H)
66. C2×C4×A4C4×C5semidirect
104. C22×C4×C5C2×C3×C4semidirect
110. C5×C4⋊C4C2×A4direct (N × H)
117. C22×C4⋊C4C2×C3×C5semidirect
122. C5×A4C2×C4⋊C4direct (N × H)
132. C4×A4C2×C4×C5semidirect
155. C23×C5C3×C4⋊C4semidirect
177. C2×C4×C5C4×A4semidirect
190. C23×C4C3×C4×C5semidirect
202. C2×C4⋊C4C5×A4direct (N × H)
208. C2×A4C5×C4⋊C4direct (N × H)
237. C22×C5C2×C3×C4⋊C4semidirect
245. C4×C5C2×C4×A4semidirect
280. C22×C4C2×C3×C4×C5semidirect
286. C4⋊C4C2×C5×A4direct (N × H)
292. A4C2×C5×C4⋊C4direct (N × H)
300. C2×C5A4×C4⋊C4direct (N × H)
325. C23C3×C5×C4⋊C4semidirect
347. C2×C4C4×C5×A4semidirect
354. C5C2×A4×C4⋊C4direct (N × H)
376. C22C2×C3×C5×C4⋊C4semidirect
384. C4C2×C4×C5×A4semidirect
391. C2C5×A4×C4⋊C4direct (N × H)

Maximal subgroups

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

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