Finite Group Databasebeta

← A4×#4015 #14513971

Subgroups — A4×#4015 #14513971

Order 1920.

768 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×A4×Dic10C212yesmaximal
2C42×C5×A4C211yesmaximal, characteristic
3A4×C4⋊Dic5C214yesmaximal
4C22×#4015C311yesmaximal, characteristic, complemented, Hall
5C2×C4×C5×A4C2211yescharacteristic
6C2×C4×C5×A4C2212yes—
7C2×A4×Dic5C2214yes—
8A4×Dic10—24no—
9C3×#4015—41nomaximal
10A4×C4⋊Q8—51nomaximal, Hall
11C23×Dic10C2×C312yes—
12C22×C42×C5C2×C311yescharacteristic
13C22×C4⋊Dic5C2×C314yes—
14C2×#4015—31no—
15C2×#4015—31no—
16C2×#4015—32no—
17C2×#4015—34no—
18C22×C5×A4C2311yescharacteristic
19C2×C3×Dic10—42no—
20C4×C5×A4D412yes—
21C4×C5×A4Q814yescomplemented
22A4×Dic5—24no—
23C3×C42×C5—41no—
24C3×C4⋊Dic5—44no—
25C2×Q8×A4—52no—
26A4×C4⋊C4—54no—
27C42×A4D511yescharacteristic
28C23×C4×C5C22×C311yescharacteristic
29C23×C4×C5C22×C312yes—
30C23×Dic5C22×C314yes—
31C22×Dic10—24no—
32C22×Dic10—32no—
33C22×Dic10—32no—
34C22×Dic10—34no—
35C22×Dic10—64no—
36C2×C42×C5—31no—
37C2×C42×C5—31no—
38C2×C42×C5—32no—
39C2×C4⋊Dic5—34no—
40C2×C4⋊Dic5—34no—
41C2×C4⋊Dic5—38no—
42#4015—32no—
43#4015—34no—
44#4015—38no—
45#4015—32no—
46#4015—31no—
47#4015—34no—
48#4015A411yescharacteristic, direct product factor
49C22×C4⋊Q8—51noSylow
50C2×C5×A4C2×D411yescharacteristic
51C2×C5×A4C2×Q812yes—
52C2×C3×C4×C5—42no—
53C2×C3×C4×C5—41no—
54C2×C3×Dic5—44no—
55C3×Dic10—84no—
56Q8×A4—104no—
57C2×C4×A4—54no—
58C2×C4×A4C2×D512yes—
59C2×C4×A4C2×D511yescharacteristic
60C3×C4⋊Q8—201no—
61C24×C5C23×C311yescharacteristic
62C22×C4×C5—31no—
63C22×C4×C5—32no—
64C22×C4×C5—31no—
65C22×C4×C5—32no—
66C22×C4×C5—32no—
67C22×C4×C5—34no—
68C22×C4×C5C3×D412yes—
69C22×C4×C5C3×Q814yescomplemented
70C22×Dic5—24no—
71C22×Dic5—34no—
72C22×Dic5—34no—
73C22×Dic5—64no—
74C2×Dic10—34no—
75C2×Dic10—32no—
76C2×Dic10—34no—
77C2×Dic10—64no—
78C2×Dic10—64no—
79C2×Dic10—68no—
80C2×Dic10—68no—
81C2×Dic10—64no—
82C2×Dic10—64no—
83C2×Dic10C2×A412yes—
84C42×C5—32no—
85C42×C5—31no—
86C42×C5—32no—
87C42×C5C2×A411yescharacteristic
88C4⋊Dic5—38no—
89C4⋊Dic5—34no—
90C4⋊Dic5—38no—
91C4⋊Dic5C2×A414yes—
92C23×Q8—52no—
93C2×C4⋊Q8—151no—
94C2×C4⋊Q8—151no—
95C2×C4⋊Q8—154no—
96C2×C4⋊Q8—152no—
97C22×C4⋊C4—54no—
98C22×C42C3×D511yescharacteristic
99C22×C3×C5—41no—
100C5×A4C4⋊Q811yescharacteristic, complemented
101C3×C4×C5—42no—
102C3×C4×C5—44no—
103C3×Dic5—84no—
104C22×A4C22×D511yescharacteristic
105C2×C3×Q8—202no—
106C4×A4—104no—
107C4×A4Dic1014yescomplemented
108C4×A4D2012yes—
109C3×C4⋊C4—204no—
110C3×C42—41no—
111C23×C5—31no—
112C23×C5—32no—
113C23×C5—31no—
114C23×C5C2×C3×D411yescharacteristic
115C23×C5C2×C3×Q812yes—
116C2×C4×C5—32no—
117C2×C4×C5—34no—
118C2×C4×C5—32no—
119C2×C4×C5—31no—
120C2×C4×C5—32no—
121C2×C4×C5—32no—
122C2×C4×C5—34no—
123C2×C4×C5—34no—
124C2×C4×C5—32no—
125C2×C4×C5—34no—
126C2×C4×C5C22×A411yescharacteristic
127C2×C4×C5C22×A412yes—
128C2×Dic5—34no—
129C2×Dic5—64no—
130C2×Dic5—64no—
131C2×Dic5—64no—
132C2×Dic5—64no—
133C2×Dic5C22×A414yes—
134Dic10—24no—
135Dic10—68no—
136Dic10—68no—
137Dic10—64no—
138C22×Q8—104no—
139C22×Q8—152no—
140C22×Q8—152no—
141C22×Q8—154no—
142C22×Q8—304no—
143C23×C4—54no—
144C23×C4C2×C3×D512yes—
145C23×C4C2×C3×D511yescharacteristic
146C4⋊Q8—51no—
147C4⋊Q8—154no—
148C4⋊Q8—152no—
149C4⋊Q8—158no—
150C4⋊Q8—152no—
151C4⋊Q8—154no—
152C4⋊Q8—151no—
153C2×C4⋊C4—154no—
154C2×C4⋊C4—158no—
155C2×C4⋊C4—154no—
156C2×C42—31no—
157C2×C42—32no—
158C2×C42—31no—
159C2×C3×C5—41no—
160C2×C3×C5—42no—
161C2×A4C2×Dic1012yes—
162C2×A4C2×D2011yescharacteristic
163C3×Q8—404no—
164C2×C3×C4—42no—
165C2×C3×C4—41no—
166C2×C3×C4—204no—
167C22×C5—31no—
168C22×C5—32no—
169C22×C5—32no—
170C22×C5—31no—
171C22×C5—31no—
172C22×C5—32no—
173C22×C5—32no—
174C22×C5C3×C4⋊Q811yescharacteristic, complemented
175C22×C5C23×A411yescharacteristic
176C4×C5—32no—
177C4×C5—34no—
178C4×C5D4×A412yes—
179C4×C5Q8×A414yescomplemented
180Dic5—24no—
181Dic5—64no—
182C24C22×C3×D511yescharacteristic
183C2×Q8—52no—
184C2×Q8—154no—
185C2×Q8—154no—
186C2×Q8—152no—
187C2×Q8—304no—
188C2×Q8—304no—
189C2×Q8—304no—
190C2×Q8—308no—
191C2×Q8—304no—
192C2×Q8—308no—
193C22×C4—32no—
194C22×C4—31no—
195C22×C4—32no—
196C22×C4—31no—
197C22×C4—32no—
198C22×C4—34no—
199C22×C4—104no—
200C22×C4—154no—
201C22×C4—154no—
202C22×C4—304no—
203C22×C4C3×Dic1014yescomplemented
204C22×C4C3×D2012yes—
205C4⋊C4—54no—
206C4⋊C4—158no—
207C4⋊C4—158no—
208C4⋊C4—154no—
209C42—32no—
210C42—31no—
211C42—32no—
212C42D5×A411yescharacteristic
213C3×C5—41noHall
214C22×C3—41no—
215A4#401511yescharacteristic, direct product factor
216C3×C4—44no—
217C3×C4—42no—
218C3×C4—404no—
219C2×C5—31no—
220C2×C5—32no—
221C2×C5—31no—
222C2×C5C2×D4×A411yescharacteristic
223C2×C5C2×Q8×A412yes—
224C23—31no—
225C23—32no—
226C23—31no—
227C23C2×C3×Dic1012yes—
228C23C2×C3×D2011yescharacteristic
229Q8—104no—
230Q8—308no—
231Q8—308no—
232Q8—304no—
233C2×C4—32no—
234C2×C4—34no—
235C2×C4—32no—
236C2×C4—31no—
237C2×C4—34no—
238C2×C4—34no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—34no—
242C2×C4—32no—
243C2×C4—54no—
244C2×C4—154no—
245C2×C4—304no—
246C2×C4—304no—
247C2×C4—304no—
248C2×C4—304no—
249C2×C4C2×D5×A412yes—
250C2×C4C2×D5×A411yescharacteristic
251C2×C3—42no—
252C2×C3—41no—
253C5A4×C4⋊Q811yescharacteristic, complemented, Sylow
254C22—32no—
255C22—31no—
256C22—32no—
257C22—32no—
258C22—32no—
259C22—31no—
260C22—31no—
261C22C3×#401511yescharacteristic, complemented
262C22C22×D5×A411yescharacteristic
263C4—34no—
264C4—32no—
265C4—104no—
266C4—304no—
267C4A4×Dic1014yescomplemented
268C4A4×D2012yes—
269C3—41noSylow
270C2—31no—
271C2—32no—
272C2—31no—
273C2C2×A4×Dic1012yes—
274C2C2×A4×D2011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C42×C5C2×C3
prime radicalC22×C5×A4C23
hypercenterC42D5×A4
hypocenterC22×C5C3×C4⋊Q8
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. C22×#4015C3semidirect
21. C4×C5×A4Q8semidirect
48. #4015A4direct (N × H)
69. C22×C4×C5C3×Q8semidirect
100. C5×A4C4⋊Q8semidirect
107. C4×A4Dic10semidirect
174. C22×C5C3×C4⋊Q8semidirect
179. C4×C5Q8×A4semidirect
203. C22×C4C3×Dic10semidirect
215. A4#4015direct (N × H)
253. C5A4×C4⋊Q8semidirect
261. C22C3×#4015semidirect
267. C4A4×Dic10semidirect

Maximal subgroups

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

subgroupindex
C2×A4×Dic102
C42×C5×A42
A4×C4⋊Dic52
C22×#40153
C3×#40154
A4×C4⋊Q85