Finite Group Databasebeta

← C5×A4×#117 #14511310

Subgroups — C5×A4×#117 #14511310

Order 1920.

880 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×A4C211yesmaximal, characteristic
2C5×A4×C4⋊C4C212yesmaximal, complemented
3C5×A4×C22⋊C4C212yesmaximal
4C42×C5×A4C212yesmaximal, complemented
5C22×C5×#117C311yesmaximal, characteristic, complemented, Hall
6C23×C5×A4C2211yescharacteristic
7C2×C4×C5×A4C414yescomplemented
8C2×C4×C5×A4C2214yes—
9C2×C4×C5×A4C2211yescharacteristic
10C2×C4×C5×A4C2211yescharacteristic
11C3×C5×#117—41nomaximal
12A4×#117C511yesmaximal, characteristic, direct product factor, Hall
13C24×C4×C5C2×C311yescharacteristic
14C2×C5×#117—31no—
15C2×C5×#117—32no—
16C2×C5×#117—32no—
17C2×C5×#117—32no—
18C2×C5×#117—31no—
19C22×C5×C4⋊C4C2×C312yescomplemented
20C22×C5×C22⋊C4C2×C312yes—
21C22×C42×C5C2×C312yescomplemented
22C22×C5×A4—22no—
23C22×C5×A4C2×C412yes—
24C22×C5×A4C2311yescharacteristic
25C22×C3×C4×C5—41no—
26C4×C5×A4—24no—
27C4×C5×A4C2×C412yes—
28C4×C5×A4C2×C412yes—
29C3×C5×C4⋊C4—42no—
30C3×C5×C22⋊C4—42no—
31C3×C42×C5—42no—
32C22×C4×A4C2×C511yescharacteristic
33A4×C4⋊C4C2×C512yescomplemented
34A4×C22⋊C4C2×C512yes—
35C42×A4C2×C512yescomplemented
36C25×C5C22×C311yescharacteristic
37C23×C4×C5—31no—
38C23×C4×C5—31no—
39C23×C4×C5—31no—
40C23×C4×C5—31no—
41C23×C4×C5—34no—
42C23×C4×C5C3×C414yescomplemented
43C23×C4×C5C22×C314yes—
44C23×C4×C5C22×C311yescharacteristic
45C23×C4×C5C22×C311yescharacteristic
46C5×#117—32no—
47C5×#117—32no—
48C5×#117—38no—
49C5×#117—32no—
50C5×#117—31no—
51C5×#117—32no—
52C5×#117—32no—
53C5×#117—32no—
54C5×#117A411yescharacteristic, direct product factor
55C2×C5×C4⋊C4—32no—
56C2×C5×C4⋊C4—32no—
57C2×C5×C4⋊C4—34no—
58C2×C5×C22⋊C4—32no—
59C2×C5×C22⋊C4—32no—
60C2×C5×C22⋊C4—34no—
61C2×C42×C5—32no—
62C2×C42×C5—34no—
63C2×C42×C5—32no—
64C22×#117C3×C511yescharacteristic, complemented, Sylow
65C23×C3×C5—41no—
66C2×C5×A4—22no—
67C2×C5×A4C22×C411yescharacteristic
68C2×C5×A4#4112yes—
69C2×C3×C4×C5—44no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—44no—
73C23×A4C22×C511yescharacteristic
74C2×C4×A4C4×C514yescomplemented
75C2×C4×A4C22×C514yes—
76C2×C4×A4C22×C511yescharacteristic
77C2×C4×A4C22×C511yescharacteristic
78C3×#117—41no—
79C24×C5—22no—
80C24×C5—31no—
81C24×C5—32no—
82C24×C5—31no—
83C24×C5—62no—
84C24×C5C2×C3×C412yes—
85C24×C5C23×C311yescharacteristic
86C22×C4×C5—24no—
87C22×C4×C5—32no—
88C22×C4×C5—34no—
89C22×C4×C5—34no—
90C22×C4×C5—34no—
91C22×C4×C5—31no—
92C22×C4×C5—34no—
93C22×C4×C5—34no—
94C22×C4×C5—31no—
95C22×C4×C5—31no—
96C22×C4×C5—31no—
97C22×C4×C5—31no—
98C22×C4×C5—31no—
99C22×C4×C5—31no—
100C22×C4×C5—34no—
101C22×C4×C5—34no—
102C22×C4×C5—34no—
103C22×C4×C5—32no—
104C22×C4×C5—32no—
105C22×C4×C5—34no—
106C22×C4×C5—34no—
107C22×C4×C5—64no—
108C22×C4×C5C2×C3×C412yes—
109C22×C4×C5C2×C3×C412yes—
110C22×C4×C5C2×A411yescharacteristic
111C5×C4⋊C4—34no—
112C5×C4⋊C4—34no—
113C5×C4⋊C4—32no—
114C5×C4⋊C4C2×A412yescomplemented
115C5×C22⋊C4—34no—
116C5×C22⋊C4—32no—
117C5×C22⋊C4—34no—
118C5×C22⋊C4C2×A412yes—
119C42×C5—34no—
120C42×C5—34no—
121C42×C5—32no—
122C42×C5C2×A412yescomplemented
123C24×C4C2×C3×C511yescharacteristic
124C2×#117—31no—
125C2×#117—32no—
126C2×#117—32no—
127C2×#117—32no—
128C2×#117—31no—
129C22×C4⋊C4C2×C3×C512yescomplemented
130C22×C22⋊C4C2×C3×C512yes—
131C22×C42C2×C3×C512yescomplemented
132C22×C3×C5—42no—
133C22×C3×C5—41no—
134C22×C3×C5—82no—
135C5×A4#11711yescharacteristic, direct product factor
136C3×C4×C5—42no—
137C3×C4×C5—42no—
138C3×C4×C5—84no—
139C22×A4—22no—
140C22×A4C2×C4×C512yes—
141C22×A4C23×C511yescharacteristic
142C22×C3×C4—41no—
143C4×A4—24no—
144C4×A4C2×C4×C512yes—
145C4×A4C2×C4×C512yes—
146C3×C4⋊C4—42no—
147C3×C22⋊C4—42no—
148C3×C42—42no—
149C23×C5—22no—
150C23×C5—31no—
151C23×C5—32no—
152C23×C5—31no—
153C23×C5—32no—
154C23×C5—32no—
155C23×C5—32no—
156C23×C5—32no—
157C23×C5—31no—
158C23×C5—62no—
159C23×C5—62no—
160C23×C5—62no—
161C23×C5—64no—
162C23×C5—62no—
163C23×C5—62no—
164C23×C5—64no—
165C23×C5C22×C3×C411yescharacteristic
166C23×C5C3×#4112yes—
167C23×C5C22×A411yescharacteristic
168C2×C4×C5—32no—
169C2×C4×C5—32no—
170C2×C4×C5—38no—
171C2×C4×C5—34no—
172C2×C4×C5—31no—
173C2×C4×C5—31no—
174C2×C4×C5—32no—
175C2×C4×C5—34no—
176C2×C4×C5—32no—
177C2×C4×C5—34no—
178C2×C4×C5—32no—
179C2×C4×C5—32no—
180C2×C4×C5—32no—
181C2×C4×C5—32no—
182C2×C4×C5—34no—
183C2×C4×C5—64no—
184C2×C4×C5—64no—
185C2×C4×C5—64no—
186C2×C4×C5—64no—
187C2×C4×C5C4×A414yescomplemented
188C2×C4×C5C22×A414yes—
189C2×C4×C5C22×A411yescharacteristic
190C2×C4×C5C22×A411yescharacteristic
191C25C22×C3×C511yescharacteristic
192C23×C4—31no—
193C23×C4—31no—
194C23×C4—31no—
195C23×C4—31no—
196C23×C4—34no—
197C23×C4C3×C4×C514yescomplemented
198C23×C4C22×C3×C514yes—
199C23×C4C22×C3×C511yescharacteristic
200C23×C4C22×C3×C511yescharacteristic
201#117—32no—
202#117—32no—
203#117—38no—
204#117—32no—
205#117—31no—
206#117—32no—
207#117—32no—
208#117—32no—
209#117C5×A411yescharacteristic, direct product factor
210C2×C4⋊C4—32no—
211C2×C4⋊C4—32no—
212C2×C4⋊C4—34no—
213C2×C22⋊C4—32no—
214C2×C22⋊C4—32no—
215C2×C22⋊C4—34no—
216C2×C42—32no—
217C2×C42—32no—
218C2×C42—34no—
219C2×C3×C5—41no—
220C2×C3×C5—42no—
221C2×C3×C5—82no—
222C23×C3—41no—
223C2×A4—22no—
224C2×A4C22×C4×C511yescharacteristic
225C2×A4C5×#4112yes—
226C2×C3×C4—44no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—44no—
230C22×C5—22no—
231C22×C5—31no—
232C22×C5—32no—
233C22×C5—32no—
234C22×C5—31no—
235C22×C5—31no—
236C22×C5—32no—
237C22×C5—32no—
238C22×C5—32no—
239C22×C5—62no—
240C22×C5—64no—
241C22×C5—62no—
242C22×C5—62no—
243C22×C5—62no—
244C22×C5—64no—
245C22×C5—62no—
246C22×C5C3×#11711yescharacteristic, complemented
247C22×C5C2×C4×A412yes—
248C22×C5C23×A411yescharacteristic
249C4×C5—24no—
250C4×C5—32no—
251C4×C5—32no—
252C4×C5—64no—
253C4×C5C2×C4×A412yes—
254C4×C5C2×C4×A412yes—
255C24—22no—
256C24—31no—
257C24—32no—
258C24—31no—
259C24—62no—
260C24C2×C3×C4×C512yes—
261C24C23×C3×C511yescharacteristic
262C22×C4—24no—
263C22×C4—32no—
264C22×C4—34no—
265C22×C4—34no—
266C22×C4—34no—
267C22×C4—31no—
268C22×C4—34no—
269C22×C4—34no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—34no—
277C22×C4—34no—
278C22×C4—34no—
279C22×C4—32no—
280C22×C4—32no—
281C22×C4—34no—
282C22×C4—34no—
283C22×C4—64no—
284C22×C4C2×C3×C4×C512yes—
285C22×C4C2×C3×C4×C512yes—
286C22×C4C2×C5×A411yescharacteristic
287C4⋊C4—34no—
288C4⋊C4—34no—
289C4⋊C4—32no—
290C4⋊C4C2×C5×A412yescomplemented
291C22⋊C4—34no—
292C22⋊C4—32no—
293C22⋊C4—34no—
294C22⋊C4C2×C5×A412yes—
295C42—34no—
296C42—34no—
297C42—32no—
298C42C2×C5×A412yescomplemented
299C3×C5—41noHall
300C22×C3—42no—
301C22×C3—41no—
302C22×C3—82no—
303A4C5×#11711yescharacteristic, direct product factor
304C3×C4—42no—
305C3×C4—42no—
306C3×C4—84no—
307C2×C5—22no—
308C2×C5—31no—
309C2×C5—32no—
310C2×C5—31no—
311C2×C5—62no—
312C2×C5C22×C4×A411yescharacteristic
313C2×C5A4×#4112yes—
314C23—22no—
315C23—31no—
316C23—32no—
317C23—31no—
318C23—32no—
319C23—32no—
320C23—32no—
321C23—32no—
322C23—31no—
323C23—62no—
324C23—62no—
325C23—62no—
326C23—64no—
327C23—62no—
328C23—62no—
329C23—64no—
330C23C22×C3×C4×C511yescharacteristic
331C23C3×C5×#4112yes—
332C23C22×C5×A411yescharacteristic
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—38no—
336C2×C4—34no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—32no—
340C2×C4—32no—
341C2×C4—32no—
342C2×C4—32no—
343C2×C4—34no—
344C2×C4—34no—
345C2×C4—32no—
346C2×C4—32no—
347C2×C4—34no—
348C2×C4—64no—
349C2×C4—64no—
350C2×C4—64no—
351C2×C4—64no—
352C2×C4C4×C5×A414yescomplemented
353C2×C4C22×C5×A414yes—
354C2×C4C22×C5×A411yescharacteristic
355C2×C4C22×C5×A411yescharacteristic
356C2×C3—41no—
357C2×C3—42no—
358C2×C3—82no—
359C5A4×#11711yescharacteristic, direct product factor, Sylow
360C22—22no—
361C22—31no—
362C22—32no—
363C22—32no—
364C22—31no—
365C22—31no—
366C22—32no—
367C22—32no—
368C22—32no—
369C22—62no—
370C22—62no—
371C22—64no—
372C22—62no—
373C22—62no—
374C22—64no—
375C22—62no—
376C22C3×C5×#11711yescharacteristic, complemented
377C22C2×C4×C5×A412yes—
378C22C23×C5×A411yescharacteristic
379C4—24no—
380C4—32no—
381C4—32no—
382C4—64no—
383C4C2×C4×C5×A412yes—
384C4C2×C4×C5×A412yes—
385C3—41noSylow
386C2—22no—
387C2—31no—
388C2—31no—
389C2—32no—
390C2—62no—
391C2C22×C4×C5×A411yescharacteristic
392C2C5×A4×#4112yes—
subgroupG/H
centerC2×C4×C5C22×A4
commutatorC23C22×C3×C4×C5
FrattiniC22C23×C5×A4
FittingC22×C5×#117C3
socleC24×C5C23×C3
prime radicalC23×C5×A4C22
cosocleC24C23×C3×C5
hypercenterC5×#117A4
hypocenterC22C3×C5×#117
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C4×C5 ◁ C5×#117

Complements

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

NH ≅ G/Ntype
2. C5×A4×C4⋊C4C2semidirect
4. C42×C5×A4C2semidirect
5. C22×C5×#117C3semidirect
7. C2×C4×C5×A4C4semidirect
12. A4×#117C5direct (N × H)
19. C22×C5×C4⋊C4C2×C3semidirect
21. C22×C42×C5C2×C3semidirect
33. A4×C4⋊C4C2×C5semidirect
35. C42×A4C2×C5semidirect
42. C23×C4×C5C3×C4semidirect
54. C5×#117A4direct (N × H)
64. C22×#117C3×C5semidirect
74. C2×C4×A4C4×C5semidirect
114. C5×C4⋊C4C2×A4semidirect
122. C42×C5C2×A4semidirect
129. C22×C4⋊C4C2×C3×C5semidirect
131. C22×C42C2×C3×C5semidirect
135. C5×A4#117direct (N × H)
187. C2×C4×C5C4×A4semidirect
197. C23×C4C3×C4×C5semidirect
209. #117C5×A4direct (N × H)
246. C22×C5C3×#117semidirect
290. C4⋊C4C2×C5×A4semidirect
298. C42C2×C5×A4semidirect
303. A4C5×#117direct (N × H)
352. C2×C4C4×C5×A4semidirect
359. C5A4×#117direct (N × H)
376. C22C3×C5×#117semidirect

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
C5×A4×C22⋊C42
C42×C5×A42
C22×C5×#1173
C3×C5×#1174
A4×#1175