Finite Group Databasebeta

← C2×C4×A4×Dic5 #14514174

Subgroups — C2×C4×A4×Dic5 #14514174

Order 1920.

1360 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 243 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×C4×C5×A4C211yesmaximal, characteristic
2C22×A4×Dic5C212yesmaximal
3C4×A4×Dic5C214yesmaximal, direct product factor
4C23×C4×Dic5C311yesmaximal, characteristic, complemented, Hall
5C23×C5×A4C2211yescharacteristic
6C2×C4×C5×A4C414yescomplemented
7C2×C4×C5×A4C2212yes—
8C2×A4×Dic5C418yesdirect product factor
9C2×A4×Dic5C2214yes—
10C2×C3×C4×Dic5—41nomaximal
11C2×C42×A4—51nomaximal, Hall
12C24×C4×C5C2×C311yescharacteristic
13C24×Dic5C2×C312yes—
14C22×C4×Dic5—31no—
15C22×C4×Dic5—32no—
16C22×C4×Dic5—31no—
17C22×C4×Dic5—34no—
18C22×C4×Dic5C2×C314yescomplemented
19C22×C5×A4C2×C414yes—
20C22×C5×A4C2×C412yes—
21C22×C5×A4C2311yescharacteristic
22C22×C3×C4×C5—41no—
23C22×C3×Dic5—42no—
24C4×C5×A4C2×C414yescomplemented
25A4×Dic5C2×C418yesdirect product factor
26C3×C4×Dic5—44no—
27C22×C4×A4—52no—
28C22×C4×A4D511yescharacteristic
29C42×A4—54no—
30C25×C5C22×C311yescharacteristic
31C23×C4×C5—31no—
32C23×C4×C5—31no—
33C23×C4×C5—32no—
34C23×C4×C5—34no—
35C23×C4×C5C3×C414yescomplemented
36C23×C4×C5C22×C312yes—
37C23×Dic5—32no—
38C23×Dic5—32no—
39C23×Dic5—34no—
40C23×Dic5—38no—
41C23×Dic5C3×C418yescomplemented
42C23×Dic5C22×C314yes—
43C2×C4×Dic5—32no—
44C2×C4×Dic5—34no—
45C2×C4×Dic5—38no—
46C2×C4×Dic5—31no—
47C2×C4×Dic5—32no—
48C2×C4×Dic5—34no—
49C2×C4×Dic5—34no—
50C2×C4×Dic5—34no—
51C2×C4×Dic5—38no—
52C2×C4×Dic5A411yescharacteristic, direct product factor
53C23×C42—51noSylow
54C23×C3×C5—41no—
55C2×C5×A4C4214yescomplemented
56C2×C5×A4C22×C412yes—
57C2×C5×A4C22×C411yescharacteristic
58C2×C3×C4×C5—44no—
59C2×C3×C4×C5—42no—
60C2×C3×Dic5—48no—
61C2×C3×Dic5—44no—
62C23×A4C2×D511yescharacteristic
63C2×C4×A4—58no—
64C2×C4×A4—54no—
65C2×C4×A4Dic514yesdirect product factor
66C2×C4×A4C2×D512yes—
67C2×C3×C42—201no—
68C24×C5—31no—
69C24×C5—34no—
70C24×C5—32no—
71C24×C5—31no—
72C24×C5C2×C3×C414yes—
73C24×C5C2×C3×C412yes—
74C24×C5C23×C311yescharacteristic
75C22×C4×C5—34no—
76C22×C4×C5—38no—
77C22×C4×C5—32no—
78C22×C4×C5—31no—
79C22×C4×C5—34no—
80C22×C4×C5—34no—
81C22×C4×C5—32no—
82C22×C4×C5—32no—
83C22×C4×C5—34no—
84C22×C4×C5—38no—
85C22×C4×C5—34no—
86C22×C4×C5—32no—
87C22×C4×C5C2×C3×C414yescomplemented
88C22×C4×C5C2×A411yescharacteristic
89C22×Dic5—38no—
90C22×Dic5—316no—
91C22×Dic5—34no—
92C22×Dic5—32no—
93C22×Dic5—38no—
94C22×Dic5—38no—
95C22×Dic5—34no—
96C22×Dic5—34no—
97C22×Dic5—38no—
98C22×Dic5—316no—
99C22×Dic5—38no—
100C22×Dic5—34no—
101C22×Dic5C2×C3×C418yescomplemented
102C22×Dic5C2×A412yes—
103C4×Dic5—38no—
104C4×Dic5—34no—
105C4×Dic5—38no—
106C4×Dic5C2×A414yesdirect product factor
107C24×C4—52no—
108C24×C4C3×D511yescharacteristic
109C22×C42—54no—
110C22×C42—151no—
111C22×C42—154no—
112C22×C42—152no—
113C22×C42—151no—
114C22×C3×C5—44no—
115C22×C3×C5—42no—
116C22×C3×C5—41no—
117C5×A4C2×C4211yescharacteristic, complemented
118C3×C4×C5—44no—
119C3×Dic5—48no—
120C22×A4C4×D514yes—
121C22×A4C2×Dic512yes—
122C22×A4C22×D511yescharacteristic
123C22×C3×C4—41no—
124C22×C3×C4—202no—
125C4×A4—58no—
126C4×A4C2×Dic514yesdirect product factor
127C3×C42—204no—
128C23×C5—34no—
129C23×C5—32no—
130C23×C5—32no—
131C23×C5—31no—
132C23×C5—38no—
133C23×C5—34no—
134C23×C5—34no—
135C23×C5—32no—
136C23×C5—38no—
137C23×C5—34no—
138C23×C5—34no—
139C23×C5—32no—
140C23×C5—32no—
141C23×C5—31no—
142C23×C5—31no—
143C23×C5C3×C4214yescomplemented
144C23×C5C22×C3×C412yes—
145C23×C5C22×C3×C411yescharacteristic
146C23×C5C22×A411yescharacteristic
147C2×C4×C5—34no—
148C2×C4×C5—38no—
149C2×C4×C5—34no—
150C2×C4×C5—32no—
151C2×C4×C5—34no—
152C2×C4×C5—38no—
153C2×C4×C5—34no—
154C2×C4×C5—34no—
155C2×C4×C5C4×A414yescomplemented
156C2×C4×C5C22×A412yes—
157C2×Dic5—38no—
158C2×Dic5—316no—
159C2×Dic5—38no—
160C2×Dic5—34no—
161C2×Dic5—38no—
162C2×Dic5—316no—
163C2×Dic5—38no—
164C2×Dic5—38no—
165C2×Dic5C4×A418yesdirect product factor
166C2×Dic5C22×A414yes—
167C25C2×C3×D511yescharacteristic
168C23×C4—31no—
169C23×C4—34no—
170C23×C4—31no—
171C23×C4—32no—
172C23×C4—58no—
173C23×C4—54no—
174C23×C4—152no—
175C23×C4—158no—
176C23×C4—154no—
177C23×C4—152no—
178C23×C4C3×Dic514yescomplemented
179C23×C4C2×C3×D512yes—
180C2×C42—51no—
181C2×C42—154no—
182C2×C42—154no—
183C2×C42—152no—
184C2×C42—158no—
185C2×C42—152no—
186C2×C42—154no—
187C2×C42—151no—
188C2×C42—158no—
189C2×C42—154no—
190C2×C3×C5—42no—
191C2×C3×C5—41no—
192C2×C3×C5—44no—
193C23×C3—41no—
194C2×A4C4×Dic514yesdirect product factor
195C2×A4C2×C4×D512yes—
196C2×A4C22×Dic511yescharacteristic
197C2×C3×C4—44no—
198C2×C3×C4—42no—
199C2×C3×C4—204no—
200C2×C3×C4—208no—
201C22×C5—34no—
202C22×C5—32no—
203C22×C5—31no—
204C22×C5—38no—
205C22×C5—32no—
206C22×C5—34no—
207C22×C5—34no—
208C22×C5—32no—
209C22×C5—32no—
210C22×C5—32no—
211C22×C5—31no—
212C22×C5—31no—
213C22×C5—34no—
214C22×C5—38no—
215C22×C5—34no—
216C22×C5C2×C3×C4211yescharacteristic, complemented
217C22×C5C2×C4×A414yes—
218C22×C5C2×C4×A412yes—
219C22×C5C23×A411yescharacteristic
220C4×C5—34no—
221C4×C5C2×C4×A414yescomplemented
222Dic5—38no—
223Dic5C2×C4×A418yesdirect product factor
224C24—31no—
225C24—32no—
226C24—34no—
227C24—31no—
228C24C3×C4×D514yes—
229C24C2×C3×Dic512yes—
230C24C22×C3×D511yescharacteristic
231C22×C4—32no—
232C22×C4—34no—
233C22×C4—38no—
234C22×C4—31no—
235C22×C4—34no—
236C22×C4—34no—
237C22×C4—32no—
238C22×C4—32no—
239C22×C4—32no—
240C22×C4—34no—
241C22×C4—38no—
242C22×C4—34no—
243C22×C4—52no—
244C22×C4—58no—
245C22×C4—154no—
246C22×C4—154no—
247C22×C4—158no—
248C22×C4—158no—
249C22×C4—154no—
250C22×C4—1516no—
251C22×C4—158no—
252C22×C4—152no—
253C22×C4—154no—
254C22×C4—1516no—
255C22×C4—158no—
256C22×C4—158no—
257C22×C4C2×C3×Dic514yescomplemented
258C22×C4D5×A411yescharacteristic
259C42—54no—
260C42—158no—
261C42—158no—
262C42—154no—
263C3×C5—41noHall
264C22×C3—44no—
265C22×C3—42no—
266C22×C3—41no—
267A4C2×C4×Dic511yescharacteristic, direct product factor
268C3×C4—44no—
269C3×C4—208no—
270C2×C5—34no—
271C2×C5—31no—
272C2×C5—32no—
273C2×C5—31no—
274C2×C5C42×A414yescomplemented
275C2×C5C22×C4×A412yes—
276C2×C5C22×C4×A411yescharacteristic
277C23—32no—
278C23—31no—
279C23—34no—
280C23—32no—
281C23—38no—
282C23—34no—
283C23—32no—
284C23—34no—
285C23—38no—
286C23—34no—
287C23—34no—
288C23—32no—
289C23—32no—
290C23—31no—
291C23—31no—
292C23C3×C4×Dic514yescomplemented
293C23C2×C3×C4×D512yes—
294C23C22×C3×Dic511yescharacteristic
295C23C2×D5×A411yescharacteristic
296C2×C4—38no—
297C2×C4—34no—
298C2×C4—34no—
299C2×C4—32no—
300C2×C4—34no—
301C2×C4—38no—
302C2×C4—34no—
303C2×C4—34no—
304C2×C4—58no—
305C2×C4—54no—
306C2×C4—158no—
307C2×C4—158no—
308C2×C4—1516no—
309C2×C4—1516no—
310C2×C4—158no—
311C2×C4—158no—
312C2×C4—154no—
313C2×C4—158no—
314C2×C4A4×Dic514yesdirect product factor
315C2×C4C2×D5×A412yes—
316C2×C3—42no—
317C2×C3—41no—
318C2×C3—44no—
319C5C2×C42×A411yescharacteristic, complemented, Sylow
320C22—34no—
321C22—32no—
322C22—31no—
323C22—34no—
324C22—32no—
325C22—38no—
326C22—32no—
327C22—34no—
328C22—32no—
329C22—31no—
330C22—32no—
331C22—31no—
332C22—34no—
333C22—38no—
334C22—34no—
335C22C2×C3×C4×Dic511yescharacteristic, complemented
336C22C4×D5×A414yes—
337C22C2×A4×Dic512yes—
338C22C22×D5×A411yescharacteristic
339C4—34no—
340C4—58no—
341C4—158no—
342C4C2×A4×Dic514yesdirect product factor
343C3—41noSylow
344C2—31no—
345C2—34no—
346C2—32no—
347C2—31no—
348C2C4×A4×Dic514yesdirect product factor
349C2C2×C4×D5×A412yes—
350C2C22×A4×Dic511yescharacteristic
subgroupG/H
center, hypercenterC22×C4D5×A4
commutator, hypocenterC22×C5C2×C3×C42
FrattiniC22C22×D5×A4
FittingC24×C4×C5C2×C3
socleC25×C5C22×C3
prime radicalC23×C5×A4C22
cosocleC24×C5C23×C3
LCSG ▷ C22×C5
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C4×A4×Dic5C2direct (N × H)
4. C23×C4×Dic5C3semidirect
6. C2×C4×C5×A4C4semidirect
8. C2×A4×Dic5C4direct (N × H)
18. C22×C4×Dic5C2×C3semidirect
24. C4×C5×A4C2×C4semidirect
25. A4×Dic5C2×C4direct (N × H)
35. C23×C4×C5C3×C4semidirect
41. C23×Dic5C3×C4semidirect
52. C2×C4×Dic5A4direct (N × H)
55. C2×C5×A4C42semidirect
65. C2×C4×A4Dic5direct (N × H)
87. C22×C4×C5C2×C3×C4semidirect
101. C22×Dic5C2×C3×C4semidirect
106. C4×Dic5C2×A4direct (N × H)
117. C5×A4C2×C42semidirect
126. C4×A4C2×Dic5direct (N × H)
143. C23×C5C3×C42semidirect
155. C2×C4×C5C4×A4semidirect
165. C2×Dic5C4×A4direct (N × H)
178. C23×C4C3×Dic5semidirect
194. C2×A4C4×Dic5direct (N × H)
216. C22×C5C2×C3×C42semidirect
221. C4×C5C2×C4×A4semidirect
223. Dic5C2×C4×A4direct (N × H)
257. C22×C4C2×C3×Dic5semidirect
267. A4C2×C4×Dic5direct (N × H)
274. C2×C5C42×A4semidirect
292. C23C3×C4×Dic5semidirect
314. C2×C4A4×Dic5direct (N × H)
319. C5C2×C42×A4semidirect
335. C22C2×C3×C4×Dic5semidirect
342. C4C2×A4×Dic5direct (N × H)
348. C2C4×A4×Dic5direct (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
C22×A4×Dic52
C4×A4×Dic52
C23×C4×Dic53
C2×C3×C4×Dic54
C2×C42×A45