Finite Group Databasebeta

← #14512463

Subgroups — #14512463

Order 1920.

310 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C4⋊(A4⋊AGL(1,𝔽5))C212yesmaximal
2C8×D5×A4C211yesmaximal, characteristic
3#10604722—31nomaximal, Hall
4C2×A4⋊AGL(1,𝔽5)—22no—
5C4×D5×A4C2211yescharacteristic
6C5×C8×A4C411yescharacteristic, complemented
7#91222—41nomaximal
8A4×#168C411yescharacteristic, complemented
9#73110—51nomaximal, Hall
10C22×C8×D5D311yescharacteristic
11#65765—32no—
12C2×#3993—31no—
13C2×#3993—31no—
14#64893—32no—
15C2×D5×A4D411yescharacteristic
16A4⋊AGL(1,𝔽5)—42no—
17C4×C5×A4C2×C411yescharacteristic
18C4⋊ΓL(1,𝔽16)—42no—
19A4×Dic5Q811yescharacteristic
20C3×C8×D5—41no—
21C2×C8×A4—51no—
22C4⋊SL(2,ℤ/4)—52no—
23C22×C4×D5C2×D311yescharacteristic
24C2×C22⋊AGL(1,𝔽5)—62no—
25C2×C4⋊AGL(1,𝔽5)—32no—
26C2×C4⋊AGL(1,𝔽5)—32no—
27C22×C5×C8Dic311yescharacteristic, complemented
28C22×#168Dic311yescharacteristic, complemented
29C2×C8×D5—31no—
30C2×C8×D5—31no—
31C2×C8×D5—31no—
32C2×C8×D5—31no—
33(C2×AGL(1,𝔽5))⋊C4—62no—
34#3993—61no—
35#3993—61no—
36#3993—61no—
37#3993—61no—
38#1807—151noSylow
39C2×C5×A4C4⋊C411yescharacteristic
40C2×ΓL(1,𝔽16)—82no—
41D5×A4SD1612yes—
42C3×C4×D5—41no—
43C3×C5×C8—41no—
44C3×#168—41no—
45C2×C4×A4—51no—
46C2×SL(2,ℤ/4)—102no—
47C8×A4—51no—
48C8×A4AGL(1,𝔽5)11yescharacteristic, complemented
49#817—201no—
50C23×D5D1211yescharacteristic
51C22×AGL(1,𝔽5)—62no—
52C22×AGL(1,𝔽5)—62no—
53C22×C4×C5C2×Dic311yescharacteristic
54C22×Dic5Dic611yescharacteristic
55C2×C4×D5—31no—
56C2×C4×D5—31no—
57C2×C4×D5—31no—
58C2×C4×D5—31no—
59C22⋊AGL(1,𝔽5)—122no—
60C22⋊AGL(1,𝔽5)—122no—
61C4⋊AGL(1,𝔽5)—62no—
62C4⋊AGL(1,𝔽5)—62no—
63C4⋊AGL(1,𝔽5)—62no—
64C4⋊AGL(1,𝔽5)—62no—
65C2×C5×C8—31no—
66C2×C5×C8—31no—
67C2×#168—31no—
68C2×#168—31no—
69C8×D5—31no—
70C8×D5—31no—
71C8×D5—31no—
72C8×D5—61no—
73C8×D5S411yescharacteristic
74C23×C8—51no—
75C2×#106—151no—
76C2×#106—151no—
77#380—152no—
78#340—152no—
79C2×C3×D5—41no—
80C5×A4#10611yescharacteristic, complemented
81ΓL(1,𝔽16)—162no—
82C3×C4×C5—41no—
83C3×Dic5—41no—
84C22×A4—51no—
85C4×A4—51no—
86C4×A4C2×AGL(1,𝔽5)11yescharacteristic
87SL(2,ℤ/4)—202no—
88C2×C3×C8—201no—
89C4⋊Dic3—202no—
90C23×C5C4⋊Dic311yescharacteristic
91C22×D5—31no—
92C22×D5—32no—
93C22×D5—31no—
94C22×D5#20412yes—
95C2×AGL(1,𝔽5)—122no—
96C2×AGL(1,𝔽5)—122no—
97C2×AGL(1,𝔽5)—122no—
98C2×AGL(1,𝔽5)—122no—
99C2×AGL(1,𝔽5)—122no—
100C2×AGL(1,𝔽5)—122no—
101C2×C4×C5—31no—
102C2×C4×C5—31no—
103C2×Dic5—31no—
104C2×Dic5—31no—
105C4×D5—31no—
106C4×D5—31no—
107C4×D5—31no—
108C4×D5—61no—
109C4×D5C2×S411yescharacteristic
110C5×C8—31no—
111C5×C8SL(2,ℤ/4)11yescharacteristic, complemented
112#168—31no—
113#168SL(2,ℤ/4)11yescharacteristic, complemented
114C23×C4—51no—
115C22×C8—51no—
116C22×C8—151no—
117C22×C8—151no—
118C22×C8—151no—
119C22×C8—151no—
120C22×C8ΓL(1,𝔽16)11yescharacteristic, complemented
121C2×C4⋊C4—152no—
122C2×C4⋊C4—152no—
123C2×C22⋊C4—302no—
124#106—301no—
125#106—301no—
126#106—301no—
127#106—301no—
128#95—302no—
129C2×C3×C5—41no—
130C3×D5—42no—
131C2×A4—52no—
132C2×A4C4⋊AGL(1,𝔽5)11yescharacteristic
133C2×C3×C4—201no—
134C2×Dic3—402no—
135C3×C8—41no—
136C3×C8—201no—
137C22×C5—31no—
138C22×C5—31no—
139C22×C5#81711yescharacteristic, complemented
140C2×D5—31no—
141C2×D5—32no—
142C2×D5—32no—
143C2×D5—32no—
144C2×D5—61no—
145C2×D5C4⋊S411yescharacteristic
146AGL(1,𝔽5)—242no—
147AGL(1,𝔽5)—242no—
148C4×C5—31no—
149C4×C5C2×SL(2,ℤ/4)11yescharacteristic
150Dic5—31no—
151Dic5A4⋊Q811yescharacteristic
152C24—51no—
153C22×C4—51no—
154C22×C4—151no—
155C22×C4—151no—
156C22×C4—151no—
157C22×C4—151no—
158C22×C4—302no—
159C22×C4—302no—
160C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
161C2×C8—31no—
162C2×C8—31no—
163C2×C8—51no—
164C2×C8—151no—
165C2×C8—151no—
166C2×C8—151no—
167C2×C8—151no—
168C2×C8—151no—
169C2×C8—301no—
170C4⋊C4—302no—
171C4⋊C4—302no—
172C4⋊C4—302no—
173C4⋊C4—302no—
174C22⋊C4—602no—
175C22⋊C4—602no—
176C3×C5—41noHall
177C22×C3—201no—
178A4#399311yescharacteristic, complemented
179C3×C4—41no—
180C3×C4—201no—
181Dic3—802no—
182C2×C5—31no—
183C2×C5—31no—
184C2×C5C4⋊SL(2,ℤ/4)11yescharacteristic
185D5—32no—
186D5#540112yes—
187C23—52no—
188C23—151no—
189C23—152no—
190C23—151no—
191C23C4⋊ΓL(1,𝔽16)11yescharacteristic
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—51no—
195C2×C4—151no—
196C2×C4—151no—
197C2×C4—151no—
198C2×C4—151no—
199C2×C4—151no—
200C2×C4—301no—
201C2×C4—602no—
202C2×C4—602no—
203C2×C4—602no—
204C2×C4—602no—
205C2×C4—602no—
206C2×C4—602no—
207C8—31no—
208C8—51no—
209C8—151no—
210C8A4⋊AGL(1,𝔽5)11yescharacteristic, complemented
211C2×C3—41no—
212C2×C3—202no—
213C5#7311011yescharacteristic, complemented, Sylow
214C22—31no—
215C22—31no—
216C22—51no—
217C22—152no—
218C22—152no—
219C22—152no—
220C22—151no—
221C22—301no—
222C22#9122211yescharacteristic, complemented
223C4—31no—
224C4—51no—
225C4—151no—
226C4—1202no—
227C4—1202no—
228C4C2×A4⋊AGL(1,𝔽5)11yescharacteristic
229C3—41noSylow
230C2—31no—
231C2—31no—
232C2—52no—
233C2—152no—
234C2C4⋊(A4⋊AGL(1,𝔽5))11yescharacteristic
subgroupG/H
centerC2C4⋊(A4⋊AGL(1,𝔽5))
commutatorC4×C5×A4C2×C4
FrattiniC4C2×A4⋊AGL(1,𝔽5)
FittingC22×C5×C8Dic3
socleC23×C5C4⋊Dic3
prime radicalC2×D5×A4D4
cosocleC4×D5×A4C22
hypercenterC8A4⋊AGL(1,𝔽5)
hypocenterC5×A4#106
LCSG ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
6. C5×C8×A4C4semidirect
8. A4×#168C4semidirect
27. C22×C5×C8Dic3semidirect
28. C22×#168Dic3semidirect
48. C8×A4AGL(1,𝔽5)semidirect
80. C5×A4#106semidirect
111. C5×C8SL(2,ℤ/4)semidirect
113. #168SL(2,ℤ/4)semidirect
120. C22×C8ΓL(1,𝔽16)semidirect
139. C22×C5#817semidirect
178. A4#3993semidirect
210. C8A4⋊AGL(1,𝔽5)semidirect
213. C5#73110semidirect
222. C22#91222semidirect

Maximal subgroups

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

subgroupindex
C4⋊(A4⋊AGL(1,𝔽5))2
C8×D5×A42
#106047223
#912224
#731105