Finite Group Databasebeta

← C4×A4⋊#170 #14512475

Subgroups — C4×A4⋊#170 #14512475

Order 1920.

378 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 76 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⋊#170C212yesmaximal
2C4×A4×Dic5C211yesmaximal, characteristic
3C4×C22⋊#170—31nomaximal, Hall
4C2×C4×C5×A4C411yescharacteristic
5C2×A4×Dic5C411yescharacteristic
6C2×A4×Dic5C2211yescharacteristic
7A4⋊#170C414yesdirect product factor
8C4×C3⋊#170—41nomaximal
9C4×A4⋊C8—51nomaximal, Hall
10C22×C4×Dic5D311yescharacteristic
11C2×C22⋊#170—32no—
12C2×C4×#170—31no—
13C2×C4×#170—31no—
14#64918—32no—
15C22×C5×A4C2×C411yescharacteristic
16C4×C5×A4C812yescomplemented
17C2×C3⋊#170—42no—
18A4×Dic5C812yescomplemented
19A4×Dic5C2×C412yes—
20C3×C4×Dic5—41no—
21C42×A4—51no—
22C2×A4⋊C8—52no—
23C23×C4×C5Dic311yescharacteristic
24C23×Dic5Dic311yescharacteristic
25C23×Dic5C2×D311yescharacteristic
26C22×#170—32no—
27C22×#170—32no—
28C2×C4×Dic5—31no—
29C2×C4×Dic5—31no—
30C2×C4×Dic5—31no—
31C2×C4×Dic5—31no—
32C22⋊#170—34no—
33C22⋊#170—34no—
34C4×#170—61no—
35C4×#170—61no—
36C4×#170—61no—
37C4×#170—61no—
38C4×C22⋊C8—151noSylow
39C2×C5×A4C4211yescharacteristic
40C2×C5×A4C2×C811yescharacteristic
41C2×C5×A4C2×C811yescharacteristic
42C2×C3×C4×C5—41no—
43C2×C3×Dic5—41no—
44C2×C3×Dic5—41no—
45C3⋊#170—44no—
46C2×C4×A4—51no—
47C2×C4×A4—51no—
48C2×C4×A4AGL(1,𝔽5)11yescharacteristic
49A4⋊C8—54no—
50C4×C3⋊C8—201no—
51C24×C5C2×Dic311yescharacteristic
52C22×C4×C5—31no—
53C22×C4×C5—32no—
54C22×C4×C5—31no—
55C22×C4×C5C3⋊C812yescomplemented
56C22×Dic5—31no—
57C22×Dic5—31no—
58C22×Dic5—32no—
59C22×Dic5—31no—
60C22×Dic5—32no—
61C22×Dic5—31no—
62C22×Dic5C3⋊C812yescomplemented
63C22×Dic5C4×D312yes—
64C2×#170—34no—
65C2×#170—34no—
66C2×#170—62no—
67C2×#170—62no—
68C2×#170—62no—
69C2×#170—62no—
70C4×Dic5—31no—
71C4×Dic5—31no—
72C4×Dic5—31no—
73C4×Dic5—61no—
74C4×Dic5S411yescharacteristic
75C22×C42—51no—
76C2×C22⋊C8—152no—
77C2×C4×C8—151no—
78C2×C4×C8—151no—
79#336—152no—
80C22×C3×C5—41no—
81C5×A4C4×C811yescharacteristic, complemented
82C3×C4×C5—42no—
83C3×Dic5—42no—
84C3×Dic5—42no—
85C22×A4C2×AGL(1,𝔽5)11yescharacteristic
86C4×A4—52no—
87C4×A4—52no—
88C4×A4#17012yescomplemented
89C3×C42—201no—
90C2×C3⋊C8—202no—
91C23×C5—31no—
92C23×C5—31no—
93C23×C5—31no—
94C23×C5—31no—
95C23×C5C2×C3⋊C811yescharacteristic
96C23×C5C2×C3⋊C811yescharacteristic
97C23×C5C4×Dic311yescharacteristic
98C2×C4×C5—31no—
99C2×C4×C5—32no—
100C2×C4×C5—32no—
101C2×C4×C5—32no—
102C2×C4×C5—61no—
103C2×C4×C5SL(2,ℤ/4)11yescharacteristic
104C2×Dic5—31no—
105C2×Dic5—31no—
106C2×Dic5—32no—
107C2×Dic5—32no—
108C2×Dic5—32no—
109C2×Dic5—32no—
110C2×Dic5—32no—
111C2×Dic5—32no—
112C2×Dic5—61no—
113C2×Dic5—61no—
114C2×Dic5SL(2,ℤ/4)11yescharacteristic
115C2×Dic5C2×S411yescharacteristic
116#170—64no—
117#170—64no—
118C23×C4—51no—
119C23×C4—51no—
120C23×C4ΓL(1,𝔽16)11yescharacteristic
121C22×C8—152no—
122C22×C8—152no—
123C2×C42—151no—
124C2×C42—151no—
125C2×C42—151no—
126C2×C42—151no—
127C22⋊C8—154no—
128C22⋊C8—154no—
129C4×C8—301no—
130C4×C8—301no—
131C4×C8—301no—
132C4×C8—301no—
133C2×C3×C5—41no—
134C2×C3×C5—41no—
135C2×C3×C5—41no—
136C2×A4D5⋊C811yescharacteristic
137C2×A4C4×AGL(1,𝔽5)11yescharacteristic
138C2×A4C2×#17011yescharacteristic
139C2×C3×C4—41no—
140C2×C3×C4—201no—
141C2×C3×C4—201no—
142C3⋊C8—204no—
143C22×C5—31no—
144C22×C5—31no—
145C22×C5—31no—
146C22×C5—31no—
147C22×C5—31no—
148C22×C5—31no—
149C22×C5—31no—
150C22×C5—31no—
151C22×C5—31no—
152C22×C5—61no—
153C22×C5C4×C3⋊C811yescharacteristic, complemented
154C22×C5C2×SL(2,ℤ/4)11yescharacteristic
155C4×C5—32no—
156C4×C5A4⋊C812yescomplemented
157Dic5—32no—
158Dic5—32no—
159Dic5A4⋊C812yescomplemented
160Dic5C4×S412yes—
161C24C2×ΓL(1,𝔽16)11yescharacteristic
162C22×C4—31no—
163C22×C4—31no—
164C22×C4—32no—
165C22×C4—52no—
166C22×C4—52no—
167C22×C4—151no—
168C22×C4—151no—
169C22×C4—152no—
170C22×C4—151no—
171C22×C4—151no—
172C22×C4—152no—
173C22×C4C3⋊#17012yescomplemented
174C2×C8—154no—
175C2×C8—154no—
176C2×C8—302no—
177C2×C8—302no—
178C2×C8—302no—
179C2×C8—302no—
180C42—51no—
181C42—151no—
182C42—151no—
183C42—151no—
184C42—301no—
185C3×C5—41noHall
186C22×C3—41no—
187A4C4×#17011yescharacteristic, complemented
188C3×C4—42no—
189C3×C4—202no—
190C3×C4—202no—
191C2×C5—31no—
192C2×C5—31no—
193C2×C5—31no—
194C2×C5—31no—
195C2×C5C2×A4⋊C811yescharacteristic
196C2×C5C2×A4⋊C811yescharacteristic
197C2×C5C4×SL(2,ℤ/4)11yescharacteristic
198C23—31no—
199C23—31no—
200C23—31no—
201C23—31no—
202C23D5⋊(C3⋊C8)11yescharacteristic
203C23C4×ΓL(1,𝔽16)11yescharacteristic
204C23C2×C3⋊#17011yescharacteristic
205C2×C4—31no—
206C2×C4—32no—
207C2×C4—32no—
208C2×C4—32no—
209C2×C4—51no—
210C2×C4—51no—
211C2×C4—61no—
212C2×C4—152no—
213C2×C4—152no—
214C2×C4—152no—
215C2×C4—152no—
216C2×C4—151no—
217C2×C4—151no—
218C2×C4—152no—
219C2×C4—152no—
220C2×C4—301no—
221C2×C4—301no—
222C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
223C8—304no—
224C8—304no—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3—41no—
228C5C4×A4⋊C811yescharacteristic, complemented, Sylow
229C22—31no—
230C22—31no—
231C22—31no—
232C22—31no—
233C22—31no—
234C22—31no—
235C22—31no—
236C22—31no—
237C22—31no—
238C22—61no—
239C22C4×C3⋊#17011yescharacteristic, complemented
240C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
241C4—32no—
242C4—52no—
243C4—52no—
244C4—152no—
245C4—152no—
246C4A4⋊#17012yesdirect product factor
247C3—41noSylow
248C2—31no—
249C2—31no—
250C2—31no—
251C2—31no—
252C2D5⋊(A4⋊C8)11yescharacteristic
253C2C4×A4⋊AGL(1,𝔽5)11yescharacteristic
254C2C2×A4⋊#17011yescharacteristic
subgroupG/H
center, hypercenterC2×C4A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×A4C4×C8
FrattiniC22C2×A4⋊AGL(1,𝔽5)
FittingC23×C4×C5Dic3
socleC24×C5C2×Dic3
prime radicalC22×C5×A4C2×C4
cosocleC2×A4×Dic5C22
LCSG ▷ C5×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
7. A4⋊#170C4direct (N × H)
16. C4×C5×A4C8semidirect
18. A4×Dic5C8semidirect
55. C22×C4×C5C3⋊C8semidirect
62. C22×Dic5C3⋊C8semidirect
81. C5×A4C4×C8semidirect
88. C4×A4#170semidirect
153. C22×C5C4×C3⋊C8semidirect
156. C4×C5A4⋊C8semidirect
159. Dic5A4⋊C8semidirect
173. C22×C4C3⋊#170semidirect
187. A4C4×#170semidirect
228. C5C4×A4⋊C8semidirect
239. C22C4×C3⋊#170semidirect
246. C4A4⋊#170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4⋊#1702
C4×A4×Dic52
C4×C22⋊#1703
C4×C3⋊#1704
C4×A4⋊C85