Finite Group Databasebeta

← C2×A4×C4⋊Dic5 #14514177

Subgroups — C2×A4×C4⋊Dic5 #14514177

Order 1920.

1136 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 195 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
3A4×C4⋊Dic5C214yesmaximal, direct product factor
4C23×C4⋊Dic5C311yesmaximal, characteristic, complemented, Hall
5C23×C5×A4C2211yescharacteristic
6C2×C4×C5×A4C414yescomplemented
7C2×C4×C5×A4C2212yes—
8C2×A4×Dic5—24no—
9C2×A4×Dic5C2214yes—
10C2×C3×C4⋊Dic5—41nomaximal
11C2×A4×C4⋊C4—51nomaximal, Hall
12C24×C4×C5C2×C311yescharacteristic
13C24×Dic5C2×C312yes—
14C22×C4⋊Dic5—32no—
15C22×C4⋊Dic5—31no—
16C22×C4⋊Dic5—34no—
17C22×C4⋊Dic5—31no—
18C22×C4⋊Dic5C2×C314yescomplemented
19C22×C5×A4C2×C412yes—
20C22×C5×A4D412yes—
21C22×C5×A4Q812yes—
22C22×C5×A4C2311yescharacteristic
23C22×C3×C4×C5—41no—
24C22×C3×Dic5—42no—
25C4×C5×A4C2×C414yescomplemented
26A4×Dic5—24no—
27C3×C4⋊Dic5—44no—
28C22×C4×A4—52no—
29C22×C4×A4D511yescharacteristic
30A4×C4⋊C4—54no—
31C25×C5C22×C311yescharacteristic
32C23×C4×C5—31no—
33C23×C4×C5—31no—
34C23×C4×C5—32no—
35C23×C4×C5—34no—
36C23×C4×C5C3×C414yescomplemented
37C23×C4×C5C22×C312yes—
38C23×Dic5—24no—
39C23×Dic5—32no—
40C23×Dic5—32no—
41C23×Dic5—34no—
42C23×Dic5—64no—
43C23×Dic5C22×C314yes—
44C2×C4⋊Dic5—32no—
45C2×C4⋊Dic5—34no—
46C2×C4⋊Dic5—38no—
47C2×C4⋊Dic5—31no—
48C2×C4⋊Dic5—32no—
49C2×C4⋊Dic5—34no—
50C2×C4⋊Dic5—34no—
51C2×C4⋊Dic5—34no—
52C2×C4⋊Dic5—38no—
53C2×C4⋊Dic5A411yescharacteristic, direct product factor
54C23×C4⋊C4—51noSylow
55C23×C3×C5—41no—
56C2×C5×A4C4⋊C414yescomplemented
57C2×C5×A4C22×C411yescharacteristic
58C2×C5×A4C2×D411yescharacteristic
59C2×C5×A4C2×Q811yescharacteristic
60C2×C3×C4×C5—44no—
61C2×C3×C4×C5—42no—
62C2×C3×Dic5—44no—
63C2×C3×Dic5—84no—
64C23×A4C2×D511yescharacteristic
65C2×C4×A4—54no—
66C2×C4×A4—104no—
67C2×C4×A4Dic514yescomplemented
68C2×C4×A4C2×D512yes—
69C2×C3×C4⋊C4—201no—
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—34no—
80C22×C4×C5—38no—
81C22×C4×C5—32no—
82C22×C4×C5—31no—
83C22×C4×C5—34no—
84C22×C4×C5—34no—
85C22×C4×C5—32no—
86C22×C4×C5—32no—
87C22×C4×C5—34no—
88C22×C4×C5—38no—
89C22×C4×C5—34no—
90C22×C4×C5—32no—
91C22×C4×C5C2×C3×C414yescomplemented
92C22×C4×C5C2×A411yescharacteristic
93C22×Dic5—24no—
94C22×Dic5—34no—
95C22×Dic5—32no—
96C22×Dic5—34no—
97C22×Dic5—34no—
98C22×Dic5—34no—
99C22×Dic5—64no—
100C22×Dic5—64no—
101C22×Dic5—68no—
102C22×Dic5—68no—
103C22×Dic5—64no—
104C22×Dic5—64no—
105C22×Dic5—64no—
106C22×Dic5C2×A412yes—
107C4⋊Dic5—38no—
108C4⋊Dic5—34no—
109C4⋊Dic5—38no—
110C4⋊Dic5C2×A414yesdirect product factor
111C24×C4—52no—
112C24×C4C3×D511yescharacteristic
113C22×C4⋊C4—54no—
114C22×C4⋊C4—151no—
115C22×C4⋊C4—154no—
116C22×C4⋊C4—152no—
117C22×C4⋊C4—151no—
118C22×C3×C5—42no—
119C22×C3×C5—42no—
120C22×C3×C5—42no—
121C22×C3×C5—41no—
122C5×A4C2×C4⋊C411yescharacteristic, complemented
123C3×C4×C5—44no—
124C3×Dic5—84no—
125C22×A4Dic1012yes—
126C22×A4D2012yes—
127C22×A4C2×Dic512yes—
128C22×A4C22×D511yescharacteristic
129C22×C3×C4—41no—
130C22×C3×C4—202no—
131C4×A4—104no—
132C4×A4C2×Dic514yescomplemented
133C3×C4⋊C4—204no—
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—34no—
161C2×C4×C5—38no—
162C2×C4×C5—34no—
163C2×C4×C5—32no—
164C2×C4×C5—34no—
165C2×C4×C5—38no—
166C2×C4×C5—34no—
167C2×C4×C5—34no—
168C2×C4×C5C4×A414yescomplemented
169C2×C4×C5C22×A412yes—
170C2×Dic5—24no—
171C2×Dic5—34no—
172C2×Dic5—64no—
173C2×Dic5—64no—
174C2×Dic5—68no—
175C2×Dic5—68no—
176C2×Dic5—64no—
177C2×Dic5—64no—
178C2×Dic5—64no—
179C2×Dic5C22×A414yes—
180C25C2×C3×D511yescharacteristic
181C23×C4—31no—
182C23×C4—31no—
183C23×C4—32no—
184C23×C4—34no—
185C23×C4—54no—
186C23×C4—104no—
187C23×C4—152no—
188C23×C4—154no—
189C23×C4—152no—
190C23×C4—304no—
191C23×C4C3×Dic514yescomplemented
192C23×C4C2×C3×D512yes—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—154no—
195C2×C4⋊C4—154no—
196C2×C4⋊C4—152no—
197C2×C4⋊C4—158no—
198C2×C4⋊C4—152no—
199C2×C4⋊C4—154no—
200C2×C4⋊C4—151no—
201C2×C4⋊C4—158no—
202C2×C4⋊C4—154no—
203C2×C3×C5—41no—
204C2×C3×C5—41no—
205C2×C3×C5—41no—
206C2×C3×C5—44no—
207C23×C3—41no—
208C2×A4C4⋊Dic514yesdirect product factor
209C2×A4C2×Dic1011yescharacteristic
210C2×A4C2×D2011yescharacteristic
211C2×A4C22×Dic511yescharacteristic
212C2×C3×C4—44no—
213C2×C3×C4—42no—
214C2×C3×C4—204no—
215C2×C3×C4—404no—
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—34no—
243C4×C5C2×C4×A414yescomplemented
244Dic5—24no—
245Dic5—64no—
246C24—31no—
247C24—32no—
248C24—32no—
249C24—32no—
250C24—31no—
251C24C3×Dic1012yes—
252C24C3×D2012yes—
253C24C2×C3×Dic512yes—
254C24C22×C3×D511yescharacteristic
255C22×C4—32no—
256C22×C4—34no—
257C22×C4—38no—
258C22×C4—31no—
259C22×C4—34no—
260C22×C4—34no—
261C22×C4—32no—
262C22×C4—32no—
263C22×C4—32no—
264C22×C4—34no—
265C22×C4—38no—
266C22×C4—34no—
267C22×C4—52no—
268C22×C4—104no—
269C22×C4—154no—
270C22×C4—154no—
271C22×C4—154no—
272C22×C4—152no—
273C22×C4—154no—
274C22×C4—304no—
275C22×C4—304no—
276C22×C4—308no—
277C22×C4—308no—
278C22×C4—304no—
279C22×C4—304no—
280C22×C4—304no—
281C22×C4C2×C3×Dic514yescomplemented
282C22×C4D5×A411yescharacteristic
283C4⋊C4—54no—
284C4⋊C4—158no—
285C4⋊C4—158no—
286C4⋊C4—154no—
287C3×C5—41noHall
288C22×C3—42no—
289C22×C3—42no—
290C22×C3—42no—
291C22×C3—41no—
292A4C2×C4⋊Dic511yescharacteristic, direct product factor
293C3×C4—44no—
294C3×C4—404no—
295C2×C5—34no—
296C2×C5—31no—
297C2×C5—31no—
298C2×C5—31no—
299C2×C5—31no—
300C2×C5A4×C4⋊C414yescomplemented
301C2×C5C22×C4×A411yescharacteristic
302C2×C5C2×D4×A411yescharacteristic
303C2×C5C2×Q8×A411yescharacteristic
304C23—32no—
305C23—31no—
306C23—32no—
307C23—31no—
308C23—32no—
309C23—34no—
310C23—34no—
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×C4⋊Dic514yescomplemented
326C23C2×C3×Dic1011yescharacteristic
327C23C2×C3×D2011yescharacteristic
328C23C22×C3×Dic511yescharacteristic
329C23C2×D5×A411yescharacteristic
330C2×C4—38no—
331C2×C4—34no—
332C2×C4—34no—
333C2×C4—32no—
334C2×C4—34no—
335C2×C4—38no—
336C2×C4—34no—
337C2×C4—34no—
338C2×C4—54no—
339C2×C4—104no—
340C2×C4—154no—
341C2×C4—304no—
342C2×C4—304no—
343C2×C4—308no—
344C2×C4—308no—
345C2×C4—304no—
346C2×C4—304no—
347C2×C4—304no—
348C2×C4A4×Dic514yescomplemented
349C2×C4C2×D5×A412yes—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—44no—
354C5C2×A4×C4⋊C411yescharacteristic, complemented, 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×C4⋊Dic511yescharacteristic, complemented
377C22A4×Dic1012yes—
378C22A4×D2012yes—
379C22C2×A4×Dic512yes—
380C22C22×D5×A411yescharacteristic
381C4—34no—
382C4—104no—
383C4—304no—
384C4C2×A4×Dic514yescomplemented
385C3—41noSylow
386C2—31no—
387C2—34no—
388C2—31no—
389C2—31no—
390C2—31no—
391C2A4×C4⋊Dic514yesdirect product factor
392C2C2×A4×Dic1011yescharacteristic
393C2C2×A4×D2011yescharacteristic
394C2C22×A4×Dic511yescharacteristic
subgroupG/H
centerC23C2×D5×A4
commutatorC23×C5C22×C3×C4
FrattiniC22C22×D5×A4
FittingC24×C4×C5C2×C3
socleC25×C5C22×C3
prime radicalC23×C5×A4C22
cosocleC24×C5C23×C3
hypercenterC22×C4D5×A4
hypocenterC22×C5C2×C3×C4⋊C4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. A4×C4⋊Dic5C2direct (N × H)
4. C23×C4⋊Dic5C3semidirect
6. C2×C4×C5×A4C4semidirect
18. C22×C4⋊Dic5C2×C3semidirect
25. C4×C5×A4C2×C4semidirect
36. C23×C4×C5C3×C4semidirect
53. C2×C4⋊Dic5A4direct (N × H)
56. C2×C5×A4C4⋊C4semidirect
67. C2×C4×A4Dic5semidirect
91. C22×C4×C5C2×C3×C4semidirect
110. C4⋊Dic5C2×A4direct (N × H)
122. C5×A4C2×C4⋊C4semidirect
132. C4×A4C2×Dic5semidirect
155. C23×C5C3×C4⋊C4semidirect
168. C2×C4×C5C4×A4semidirect
191. C23×C4C3×Dic5semidirect
208. C2×A4C4⋊Dic5direct (N × H)
237. C22×C5C2×C3×C4⋊C4semidirect
243. C4×C5C2×C4×A4semidirect
281. C22×C4C2×C3×Dic5semidirect
292. A4C2×C4⋊Dic5direct (N × H)
300. C2×C5A4×C4⋊C4semidirect
325. C23C3×C4⋊Dic5semidirect
348. C2×C4A4×Dic5semidirect
354. C5C2×A4×C4⋊C4semidirect
376. C22C2×C3×C4⋊Dic5semidirect
384. C4C2×A4×Dic5semidirect
391. C2A4×C4⋊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
A4×C4⋊Dic52
C23×C4⋊Dic53
C2×C3×C4⋊Dic54
C2×A4×C4⋊C45