Finite Group Databasebeta

← A4×#4016 #14513972

Subgroups — A4×#4016 #14513972

Order 1920.

584 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C42×C5×A4C211yesmaximal, characteristic
2A4×C4⋊Dic5C212yesmaximal
3A4×#683C214yesmaximal
4C22×#4016C311yesmaximal, characteristic, complemented, Hall
5C2×C4×C5×A4C2212yes—
6C2×C4×C5×A4C2211yescharacteristic
7C2×A4×Dic5C2214yes—
8C3×#4016—41nomaximal
9A4×#125—51nomaximal, Hall
10C22×C42×C5C2×C311yescharacteristic
11C22×C4⋊Dic5C2×C312yes—
12C22×#683C2×C314yes—
13C2×#4016—31no—
14C2×#4016—31no—
15C2×#4016—32no—
16C2×#4016—34no—
17C22×C5×A4C2311yescharacteristic
18C4×C5×A4—22no—
19C4×C5×A4Q812yes—
20A4×Dic5—24no—
21C3×C42×C5—41no—
22C3×C4⋊Dic5—42no—
23C3×#683—44no—
24A4×C4⋊C4—54no—
25A4×C4⋊C4—52no—
26C42×A4D511yescharacteristic
27C23×C4×C5C22×C312yes—
28C23×C4×C5C22×C311yescharacteristic
29C23×Dic5C22×C314yes—
30C2×C42×C5—31no—
31C2×C42×C5—31no—
32C2×C42×C5—32no—
33C2×C4⋊Dic5—32no—
34C2×C4⋊Dic5—32no—
35C2×C4⋊Dic5—34no—
36C2×#683—34no—
37C2×#683—34no—
38C2×#683—38no—
39#4016—32no—
40#4016—34no—
41#4016—38no—
42#4016—31no—
43#4016—32no—
44#4016—34no—
45#4016A411yescharacteristic, direct product factor
46C22×#125—51noSylow
47C2×C5×A4C2×Q811yescharacteristic
48C2×C5×A4#4112yes—
49C2×C3×C4×C5—41no—
50C2×C3×C4×C5—42no—
51C2×C3×Dic5—44no—
52C2×C4×A4—54no—
53C2×C4×A4C2×D512yes—
54C2×C4×A4C2×D511yescharacteristic
55C3×#125—201no—
56C24×C5C23×C311yescharacteristic
57C22×C4×C5—22no—
58C22×C4×C5—31no—
59C22×C4×C5—31no—
60C22×C4×C5—32no—
61C22×C4×C5—32no—
62C22×C4×C5—32no—
63C22×C4×C5—62no—
64C22×C4×C5C3×Q812yes—
65C22×Dic5—24no—
66C22×Dic5—34no—
67C22×Dic5—34no—
68C22×Dic5—64no—
69C42×C5—32no—
70C42×C5—32no—
71C42×C5—31no—
72C42×C5C2×A411yescharacteristic
73C4⋊Dic5—34no—
74C4⋊Dic5—32no—
75C4⋊Dic5—34no—
76C4⋊Dic5C2×A412yes—
77#683—38no—
78#683—34no—
79#683—38no—
80#683C2×A414yes—
81C2×#125—151no—
82C2×#125—151no—
83C2×#125—154no—
84C2×#125—152no—
85C22×C4⋊C4—54no—
86C22×C4⋊C4—52no—
87C22×C42C3×D511yescharacteristic
88C22×C3×C5—41no—
89C5×A4#12511yescharacteristic, complemented
90C3×C4×C5—42no—
91C3×C4×C5—82no—
92C3×Dic5—84no—
93C22×A4C22×D511yescharacteristic
94C4×A4—22no—
95C4×A4—104no—
96C4×A4Dic1012yes—
97C3×C4⋊C4—204no—
98C3×C4⋊C4—202no—
99C3×C42—41no—
100C23×C5—32no—
101C23×C5—31no—
102C23×C5—31no—
103C23×C5C2×C3×Q811yescharacteristic
104C23×C5C3×#4112yes—
105C2×C4×C5—32no—
106C2×C4×C5—31no—
107C2×C4×C5—32no—
108C2×C4×C5—32no—
109C2×C4×C5—32no—
110C2×C4×C5—32no—
111C2×C4×C5—62no—
112C2×C4×C5—62no—
113C2×C4×C5—62no—
114C2×C4×C5—62no—
115C2×C4×C5C22×A412yes—
116C2×C4×C5C22×A411yescharacteristic
117C2×Dic5—34no—
118C2×Dic5—64no—
119C2×Dic5—64no—
120C2×Dic5—64no—
121C2×Dic5—64no—
122C2×Dic5C22×A414yes—
123C23×C4—54no—
124C23×C4C2×C3×D512yes—
125C23×C4C2×C3×D511yescharacteristic
126#125—51no—
127#125—154no—
128#125—152no—
129#125—158no—
130#125—152no—
131#125—154no—
132#125—151no—
133C2×C4⋊C4—154no—
134C2×C4⋊C4—152no—
135C2×C4⋊C4—158no—
136C2×C4⋊C4—154no—
137C2×C4⋊C4—154no—
138C2×C4⋊C4—152no—
139C2×C42—31no—
140C2×C42—31no—
141C2×C42—32no—
142C2×C3×C5—41no—
143C2×C3×C5—42no—
144C2×A4C2×Dic1011yescharacteristic
145C2×A4#70912yes—
146C2×C3×C4—41no—
147C2×C3×C4—42no—
148C2×C3×C4—204no—
149C22×C5—31no—
150C22×C5—32no—
151C22×C5—32no—
152C22×C5—31no—
153C22×C5—31no—
154C22×C5—32no—
155C22×C5—32no—
156C22×C5C3×#12511yescharacteristic, complemented
157C22×C5C23×A411yescharacteristic
158C4×C5—22no—
159C4×C5—32no—
160C4×C5—62no—
161C4×C5Q8×A412yes—
162Dic5—24no—
163Dic5—64no—
164C24C22×C3×D511yescharacteristic
165C22×C4—22no—
166C22×C4—31no—
167C22×C4—31no—
168C22×C4—32no—
169C22×C4—32no—
170C22×C4—32no—
171C22×C4—62no—
172C22×C4—104no—
173C22×C4—154no—
174C22×C4—154no—
175C22×C4—304no—
176C22×C4C3×Dic1012yes—
177C4⋊C4—54no—
178C4⋊C4—52no—
179C4⋊C4—158no—
180C4⋊C4—154no—
181C4⋊C4—158no—
182C4⋊C4—154no—
183C4⋊C4—154no—
184C4⋊C4—152no—
185C42—32no—
186C42—32no—
187C42—31no—
188C42D5×A411yescharacteristic
189C3×C5—41noHall
190C22×C3—41no—
191A4#401611yescharacteristic, direct product factor
192C3×C4—42no—
193C3×C4—82no—
194C3×C4—404no—
195C2×C5—31no—
196C2×C5—32no—
197C2×C5—31no—
198C2×C5C2×Q8×A411yescharacteristic
199C2×C5A4×#4112yes—
200C23—31no—
201C23—32no—
202C23—31no—
203C23C2×C3×Dic1011yescharacteristic
204C23C3×#70912yes—
205C2×C4—32no—
206C2×C4—31no—
207C2×C4—32no—
208C2×C4—32no—
209C2×C4—32no—
210C2×C4—32no—
211C2×C4—54no—
212C2×C4—62no—
213C2×C4—62no—
214C2×C4—62no—
215C2×C4—62no—
216C2×C4—154no—
217C2×C4—304no—
218C2×C4—304no—
219C2×C4—304no—
220C2×C4—304no—
221C2×C4C2×D5×A412yes—
222C2×C4C2×D5×A411yescharacteristic
223C2×C3—41no—
224C2×C3—42no—
225C5A4×#12511yescharacteristic, complemented, Sylow
226C22—31no—
227C22—32no—
228C22—32no—
229C22—31no—
230C22—31no—
231C22—32no—
232C22—32no—
233C22C3×#401611yescharacteristic, complemented
234C22C22×D5×A411yescharacteristic
235C4—22no—
236C4—32no—
237C4—62no—
238C4—104no—
239C4—304no—
240C4A4×Dic1012yes—
241C3—41noSylow
242C2—31no—
243C2—31no—
244C2—32no—
245C2C2×A4×Dic1011yescharacteristic
246C2A4×#70912yes—
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C42×C5C2×C3
prime radicalC22×C5×A4C23
hypercenterC42D5×A4
hypocenterC22×C5C3×#125
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. C22×#4016C3semidirect
45. #4016A4direct (N × H)
89. C5×A4#125semidirect
156. C22×C5C3×#125semidirect
191. A4#4016direct (N × H)
225. C5A4×#125semidirect
233. C22C3×#4016semidirect

Maximal subgroups

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

subgroupindex
C42×C5×A42
A4×C4⋊Dic52
A4×#6832
C22×#40163
C3×#40164
A4×#1255