Finite Group Databasebeta

← A4×#3994 #14512543

Subgroups — A4×#3994 #14512543

Order 1920.

320 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 54 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
1A4×C4⋊AGL(1,𝔽5)C212yesmaximal
2C8×D5×A4C211yesmaximal, characteristic
3C22×#3994C311yesmaximal, characteristic, complemented, Hall
4C2×A4×AGL(1,𝔽5)—22no—
5C4×D5×A4C2211yescharacteristic
6C5×C8×A4C411yescharacteristic, complemented
7C3×#3994—41nomaximal
8A4×#168C411yescharacteristic, complemented
9A4×#107—51nomaximal, Hall
10C22×C4⋊AGL(1,𝔽5)C2×C312yes—
11C22×C8×D5C2×C311yescharacteristic
12C2×#3994—31no—
13C2×#3994—32no—
14C2×#3994—31no—
15C2×D5×A4D411yescharacteristic
16A4×AGL(1,𝔽5)—42no—
17C4×C5×A4C2×C411yescharacteristic
18C3×C4⋊AGL(1,𝔽5)—42no—
19A4×Dic5Q811yescharacteristic
20C3×C8×D5—41no—
21C2×C8×A4—51no—
22A4×C4⋊C4—52no—
23C23×AGL(1,𝔽5)—22no—
24C22×C4×D5C22×C311yescharacteristic
25C2×C4⋊AGL(1,𝔽5)—32no—
26C2×C4⋊AGL(1,𝔽5)—32no—
27C2×C4⋊AGL(1,𝔽5)—62no—
28C22×C5×C8C3×C411yescharacteristic, complemented
29C22×#168C3×C411yescharacteristic, complemented
30C2×C8×D5—31no—
31C2×C8×D5—31no—
32C2×C8×D5—31no—
33C2×C8×D5—31no—
34#3994—32no—
35#3994—32no—
36#3994—31no—
37#3994A411yescharacteristic, direct product factor
38C22×#107—51noSylow
39C2×C5×A4C4⋊C411yescharacteristic
40C2×C3×AGL(1,𝔽5)—82no—
41D5×A4D811yescharacteristic
42D5×A4Q1611yescharacteristic
43C3×C4×D5—41no—
44C3×C5×C8—41no—
45C3×#168—41no—
46C2×C4×A4—51no—
47C2×C4×A4—102no—
48C8×A4—51no—
49C8×A4AGL(1,𝔽5)11yescharacteristic, complemented
50C3×#107—201no—
51C23×D5C3×D411yescharacteristic
52C22×AGL(1,𝔽5)—42no—
53C22×AGL(1,𝔽5)—62no—
54C22×AGL(1,𝔽5)—62no—
55C22×AGL(1,𝔽5)—122no—
56C22×C4×C5C2×C3×C411yescharacteristic
57C22×Dic5C3×Q811yescharacteristic
58C2×C4×D5—31no—
59C2×C4×D5—31no—
60C2×C4×D5—31no—
61C2×C4×D5—31no—
62C4⋊AGL(1,𝔽5)—32no—
63C4⋊AGL(1,𝔽5)—62no—
64C4⋊AGL(1,𝔽5)—62no—
65C4⋊AGL(1,𝔽5)C2×A412yes—
66C2×C5×C8—31no—
67C2×C5×C8—31no—
68C2×#168—31no—
69C2×#168—31no—
70C8×D5—32no—
71C8×D5—31no—
72C8×D5—31no—
73C8×D5—31no—
74C8×D5C2×A411yescharacteristic
75C23×C8—51no—
76C22×C4⋊C4—52no—
77C2×#107—151no—
78C2×#107—152no—
79C2×#107—151no—
80C2×C3×D5—41no—
81C5×A4#10711yescharacteristic, complemented
82C3×AGL(1,𝔽5)—162no—
83C3×C4×C5—41no—
84C3×Dic5—41no—
85C22×A4—51no—
86C4×A4—51no—
87C4×A4—202no—
88C4×A4C2×AGL(1,𝔽5)11yescharacteristic
89C2×C3×C8—201no—
90C3×C4⋊C4—202no—
91C23×C5C3×C4⋊C411yescharacteristic
92C22×D5—31no—
93C22×D5—31no—
94C22×D5—31no—
95C22×D5—31no—
96C22×D5C3×D811yescharacteristic
97C22×D5C3×Q1611yescharacteristic
98C2×AGL(1,𝔽5)—22no—
99C2×AGL(1,𝔽5)—62no—
100C2×AGL(1,𝔽5)—122no—
101C2×AGL(1,𝔽5)—122no—
102C2×AGL(1,𝔽5)—122no—
103C2×AGL(1,𝔽5)—122no—
104C2×C4×C5—31no—
105C2×C4×C5—31no—
106C2×Dic5—31no—
107C2×Dic5—31no—
108C4×D5—32no—
109C4×D5—31no—
110C4×D5—31no—
111C4×D5—31no—
112C4×D5C22×A411yescharacteristic
113C5×C8—31no—
114C5×C8C4×A411yescharacteristic, complemented
115#168—31no—
116#168C4×A411yescharacteristic, complemented
117C23×C4—51no—
118C23×C4—102no—
119C22×C8—51no—
120C22×C8—151no—
121C22×C8—151no—
122C22×C8—151no—
123C22×C8—151no—
124C22×C8C3×AGL(1,𝔽5)11yescharacteristic, complemented
125C2×C4⋊C4—152no—
126C2×C4⋊C4—152no—
127C2×C4⋊C4—302no—
128#107—51no—
129#107—152no—
130#107—151no—
131#107—152no—
132C2×C3×C5—41no—
133C3×D5—41no—
134C3×D5—41no—
135C2×A4—51no—
136C2×A4—51no—
137C2×A4C4⋊AGL(1,𝔽5)11yescharacteristic
138C2×C3×C4—201no—
139C2×C3×C4—402no—
140C3×C8—41no—
141C3×C8—201no—
142C22×C5—31no—
143C22×C5—31no—
144C22×C5C3×#10711yescharacteristic, complemented
145C2×D5—32no—
146C2×D5—31no—
147C2×D5—31no—
148C2×D5—31no—
149C2×D5—31no—
150C2×D5—31no—
151C2×D5—31no—
152C2×D5—31no—
153C2×D5D4×A411yescharacteristic
154AGL(1,𝔽5)—42no—
155AGL(1,𝔽5)—122no—
156C4×C5—31no—
157C4×C5C2×C4×A411yescharacteristic
158Dic5—31no—
159Dic5Q8×A411yescharacteristic
160C24—51no—
161C22×C4—51no—
162C22×C4—151no—
163C22×C4—151no—
164C22×C4—151no—
165C22×C4—151no—
166C22×C4—202no—
167C22×C4—302no—
168C22×C4—302no—
169C22×C4—602no—
170C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
171C2×C8—31no—
172C2×C8—31no—
173C2×C8—51no—
174C2×C8—151no—
175C2×C8—151no—
176C2×C8—152no—
177C2×C8—151no—
178C2×C8—151no—
179C2×C8—151no—
180C4⋊C4—52no—
181C4⋊C4—152no—
182C4⋊C4—302no—
183C4⋊C4—302no—
184C3×C5—41noHall
185C22×C3—201no—
186A4#399411yescharacteristic, direct product factor
187C3×C4—41no—
188C3×C4—201no—
189C3×C4—802no—
190C2×C5—31no—
191C2×C5—31no—
192C2×C5A4×C4⋊C411yescharacteristic
193D5—31no—
194D5—31no—
195D5A4×D811yescharacteristic
196D5A4×Q1611yescharacteristic
197C23—51no—
198C23—51no—
199C23—151no—
200C23—151no—
201C23—151no—
202C23—151no—
203C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—51no—
207C2×C4—102no—
208C2×C4—151no—
209C2×C4—151no—
210C2×C4—152no—
211C2×C4—151no—
212C2×C4—151no—
213C2×C4—151no—
214C2×C4—302no—
215C2×C4—602no—
216C2×C4—602no—
217C2×C4—602no—
218C2×C4—602no—
219C8—31no—
220C8—51no—
221C8—151no—
222C8A4×AGL(1,𝔽5)11yescharacteristic, complemented
223C2×C3—41no—
224C2×C3—201no—
225C2×C3—201no—
226C5A4×#10711yescharacteristic, complemented, Sylow
227C22—31no—
228C22—31no—
229C22—51no—
230C22—151no—
231C22—151no—
232C22—151no—
233C22—151no—
234C22—151no—
235C22—151no—
236C22—152no—
237C22—151no—
238C22C3×#399411yescharacteristic, complemented
239C4—31no—
240C4—51no—
241C4—151no—
242C4—202no—
243C4—602no—
244C4C2×A4×AGL(1,𝔽5)11yescharacteristic
245C3—41noSylow
246C2—31no—
247C2—31no—
248C2—51no—
249C2—51no—
250C2—151no—
251C2—151no—
252C2A4×C4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2A4×C4⋊AGL(1,𝔽5)
commutatorC22×C4×C5C2×C3×C4
FrattiniC4C2×A4×AGL(1,𝔽5)
FittingC22×C5×C8C3×C4
socleC23×C5C3×C4⋊C4
prime radicalC2×D5×A4D4
cosocleC22×C4×D5C22×C3
hypercenterC8A4×AGL(1,𝔽5)
hypocenterC22×C5C3×#107
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
3. C22×#3994C3semidirect
6. C5×C8×A4C4semidirect
8. A4×#168C4semidirect
28. C22×C5×C8C3×C4semidirect
29. C22×#168C3×C4semidirect
37. #3994A4direct (N × H)
49. C8×A4AGL(1,𝔽5)semidirect
81. C5×A4#107semidirect
114. C5×C8C4×A4semidirect
116. #168C4×A4semidirect
124. C22×C8C3×AGL(1,𝔽5)semidirect
144. C22×C5C3×#107semidirect
186. A4#3994direct (N × H)
222. C8A4×AGL(1,𝔽5)semidirect
226. C5A4×#107semidirect
238. C22C3×#3994semidirect

Maximal subgroups

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

subgroupindex
A4×C4⋊AGL(1,𝔽5)2
C8×D5×A42
C22×#39943
C3×#39944
A4×#1075