Finite Group Databasebeta

← C2×AGL(1,𝔽5)×C42⋊C3 #14512513

Subgroups — C2×AGL(1,𝔽5)×C42⋊C3 #14512513

Order 1920.

504 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 40 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×D5×C42⋊C3C211yesmaximal, characteristic
2AGL(1,𝔽5)×C42⋊C3C212yesmaximal, direct product factor
3C2×C42×AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
4C2×A4×AGL(1,𝔽5)—41nomaximal
5C2×C5×C42⋊C3C411yescharacteristic, complemented
6D5×C42⋊C3C411yescharacteristic, complemented
7D5×C42⋊C3C2211yescharacteristic
8C2×C4×C42⋊C3—51nomaximal, Hall
9C22×C4×AGL(1,𝔽5)—31no—
10C22×C4×AGL(1,𝔽5)—31no—
11C2×C42×D5C2×C311yescharacteristic
12C42×AGL(1,𝔽5)—32no—
13C42×AGL(1,𝔽5)C2×C312yescomplemented
14C2×D5×A4—41no—
15A4×AGL(1,𝔽5)—42no—
16C5×C42⋊C3C2×C411yescharacteristic, complemented
17C22×C42⋊C3—51no—
18C4×C42⋊C3—52no—
19C23×AGL(1,𝔽5)—31no—
20C23×AGL(1,𝔽5)A411yescharacteristic
21C22×C4×D5—31no—
22C2×C4×AGL(1,𝔽5)—32no—
23C2×C4×AGL(1,𝔽5)—32no—
24C2×C4×AGL(1,𝔽5)—34no—
25C2×C4×AGL(1,𝔽5)—34no—
26C2×C4×AGL(1,𝔽5)—32no—
27C2×C4×AGL(1,𝔽5)—34no—
28C2×C4×AGL(1,𝔽5)—32no—
29C2×C4×AGL(1,𝔽5)—32no—
30C2×C4×AGL(1,𝔽5)—32no—
31C2×C42×C5C3×C411yescharacteristic, complemented
32C2×C4×Dic5—31no—
33C42×D5—31no—
34C42×D5—31no—
35C42×D5C3×C411yescharacteristic, complemented
36C42×D5C22×C311yescharacteristic
37C2×C43—51noSylow
38C2×C5×A4—41no—
39C2×C3×AGL(1,𝔽5)—161no—
40D5×A4—41no—
41D5×A4—41no—
42C2×C4×A4—201no—
43C2×C42⋊C3—51no—
44C2×C42⋊C3—51no—
45C2×C42⋊C3AGL(1,𝔽5)11yescharacteristic, direct product factor
46C23×D5C2×A411yescharacteristic
47C22×AGL(1,𝔽5)—32no—
48C22×AGL(1,𝔽5)—32no—
49C22×AGL(1,𝔽5)—34no—
50C22×AGL(1,𝔽5)—34no—
51C22×AGL(1,𝔽5)—32no—
52C22×AGL(1,𝔽5)—31no—
53C22×AGL(1,𝔽5)—31no—
54C22×AGL(1,𝔽5)—32no—
55C22×AGL(1,𝔽5)C2×A412yes—
56C22×C4×C5—31no—
57C22×Dic5—31no—
58C2×C4×D5—32no—
59C2×C4×D5—32no—
60C2×C4×D5—32no—
61C2×C4×D5—32no—
62C2×C4×D5—31no—
63C2×C4×D5—31no—
64C2×C4×D5—31no—
65C2×C4×D5—31no—
66C4×AGL(1,𝔽5)—38no—
67C4×AGL(1,𝔽5)—38no—
68C4×AGL(1,𝔽5)—34no—
69C4×AGL(1,𝔽5)—34no—
70C4×AGL(1,𝔽5)—34no—
71C4×AGL(1,𝔽5)—34no—
72C42×C5—31no—
73C42×C5C2×C3×C411yescharacteristic, complemented
74C4×Dic5—32no—
75C4×Dic5—31no—
76C4×Dic5—31no—
77C22×C42—51no—
78C22×C42—151no—
79C22×C42—151no—
80C43—52no—
81C43—152no—
82C2×C3×D5—161no—
83C5×A4—41no—
84C3×AGL(1,𝔽5)—162no—
85C22×A4—201no—
86C4×A4—202no—
87C42⋊C3C2×AGL(1,𝔽5)11yescharacteristic, direct product factor
88C23×C5C4×A411yescharacteristic
89C22×D5—31no—
90C22×D5—31no—
91C22×D5—31no—
92C22×D5—31no—
93C22×D5C4×A411yescharacteristic
94C22×D5C22×A411yescharacteristic
95C2×AGL(1,𝔽5)—34no—
96C2×AGL(1,𝔽5)—38no—
97C2×AGL(1,𝔽5)—38no—
98C2×AGL(1,𝔽5)—34no—
99C2×AGL(1,𝔽5)—34no—
100C2×AGL(1,𝔽5)—32no—
101C2×AGL(1,𝔽5)—31no—
102C2×AGL(1,𝔽5)—32no—
103C2×AGL(1,𝔽5)—32no—
104C2×AGL(1,𝔽5)—32no—
105C2×AGL(1,𝔽5)C42⋊C311yescharacteristic, direct product factor
106C2×C4×C5—32no—
107C2×C4×C5—32no—
108C2×C4×C5—31no—
109C2×C4×C5—31no—
110C2×Dic5—32no—
111C2×Dic5—32no—
112C2×Dic5—31no—
113C2×Dic5—31no—
114C4×D5—32no—
115C4×D5—32no—
116C4×D5—32no—
117C4×D5—32no—
118C4×D5—32no—
119C4×D5—32no—
120C4×D5—32no—
121C4×D5—32no—
122C23×C4—51no—
123C23×C4—151no—
124C23×C4—151no—
125C2×C42—51no—
126C2×C42—51no—
127C2×C42—151no—
128C2×C42—151no—
129C2×C42—151no—
130C2×C42—152no—
131C2×C42—152no—
132C2×C42—152no—
133C2×C42—152no—
134C2×C42—152no—
135C2×C42—154no—
136C2×C42—154no—
137C2×C42—154no—
138C2×C42—152no—
139C2×C42C3×AGL(1,𝔽5)11yescharacteristic, complemented
140C2×C3×C5—161no—
141C3×D5—161no—
142C3×D5—161no—
143C2×A4—41no—
144C2×A4—201no—
145C2×A4—201no—
146C2×C3×C4—801no—
147C22×C5—31no—
148C22×C5—31no—
149C22×C5C2×C4×A411yescharacteristic
150C2×D5—32no—
151C2×D5—31no—
152C2×D5—31no—
153C2×D5—31no—
154C2×D5—31no—
155C2×D5—31no—
156C2×D5—31no—
157C2×D5—31no—
158C2×D5C2×C42⋊C311yescharacteristic
159AGL(1,𝔽5)—38no—
160AGL(1,𝔽5)—32no—
161AGL(1,𝔽5)C2×C42⋊C312yesdirect product factor
162C4×C5—32no—
163C4×C5—32no—
164Dic5—32no—
165Dic5—32no—
166C24—51no—
167C22×C4—31no—
168C22×C4—52no—
169C22×C4—151no—
170C22×C4—151no—
171C22×C4—151no—
172C22×C4—151no—
173C22×C4—152no—
174C22×C4—152no—
175C22×C4—152no—
176C22×C4—152no—
177C22×C4—151no—
178C22×C4—152no—
179C22×C4—152no—
180C22×C4—152no—
181C22×C4—154no—
182C22×C4—154no—
183C22×C4—151no—
184C22×C4—152no—
185C22×C4—151no—
186C42—31no—
187C42—151no—
188C42—151no—
189C42—152no—
190C42—154no—
191C42—154no—
192C42—158no—
193C42—158no—
194C42—154no—
195C42—154no—
196C42C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
197C3×C5—161noHall
198C22×C3—801no—
199A4—41no—
200C3×C4—802no—
201C2×C5—31no—
202C2×C5—31no—
203C2×C5C4×C42⋊C311yescharacteristic, complemented
204D5—31no—
205D5—31no—
206D5C4×C42⋊C311yescharacteristic, complemented
207D5C22×C42⋊C311yescharacteristic
208C23—51no—
209C23—51no—
210C23—151no—
211C23—151no—
212C23—151no—
213C23—151no—
214C23A4×AGL(1,𝔽5)11yescharacteristic
215C2×C4—32no—
216C2×C4—32no—
217C2×C4—31no—
218C2×C4—31no—
219C2×C4—51no—
220C2×C4—152no—
221C2×C4—152no—
222C2×C4—152no—
223C2×C4—152no—
224C2×C4—152no—
225C2×C4—152no—
226C2×C4—152no—
227C2×C4—152no—
228C2×C4—152no—
229C2×C4—152no—
230C2×C4—152no—
231C2×C4—152no—
232C2×C4—151no—
233C2×C4—154no—
234C2×C4—158no—
235C2×C4—152no—
236C2×C4—154no—
237C2×C4—158no—
238C2×C4—154no—
239C2×C4—151no—
240C2×C4—151no—
241C2×C4—152no—
242C2×C3—161no—
243C2×C3—801no—
244C2×C3—801no—
245C5C2×C4×C42⋊C311yescharacteristic, complemented, Sylow
246C22—31no—
247C22—31no—
248C22—51no—
249C22—151no—
250C22—151no—
251C22—151no—
252C22—151no—
253C22—151no—
254C22—151no—
255C22—152no—
256C22—151no—
257C22C2×A4×AGL(1,𝔽5)11yescharacteristic
258C4—32no—
259C4—32no—
260C4—52no—
261C4—152no—
262C4—152no—
263C4—152no—
264C4—158no—
265C3—161noSylow
266C2—31no—
267C2—31no—
268C2—51no—
269C2—51no—
270C2—151no—
271C2—151no—
272C2AGL(1,𝔽5)×C42⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×C42⋊C3
commutator, hypocenterC42×C5C2×C3×C4
FrattiniC22C2×A4×AGL(1,𝔽5)
FittingC2×C42×C5C3×C4
socleC23×C5C4×A4
prime radicalC2×D5×C42⋊C3C2
cosocleC42×D5C22×C3
LCSG ▷ C42×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. AGL(1,𝔽5)×C42⋊C3C2direct (N × H)
3. C2×C42×AGL(1,𝔽5)C3semidirect
5. C2×C5×C42⋊C3C4semidirect
6. D5×C42⋊C3C4semidirect
13. C42×AGL(1,𝔽5)C2×C3semidirect
16. C5×C42⋊C3C2×C4semidirect
31. C2×C42×C5C3×C4semidirect
35. C42×D5C3×C4semidirect
45. C2×C42⋊C3AGL(1,𝔽5)direct (N × H)
73. C42×C5C2×C3×C4semidirect
87. C42⋊C3C2×AGL(1,𝔽5)direct (N × H)
105. C2×AGL(1,𝔽5)C42⋊C3direct (N × H)
139. C2×C42C3×AGL(1,𝔽5)semidirect
161. AGL(1,𝔽5)C2×C42⋊C3direct (N × H)
196. C42C2×C3×AGL(1,𝔽5)semidirect
203. C2×C5C4×C42⋊C3semidirect
206. D5C4×C42⋊C3semidirect
245. C5C2×C4×C42⋊C3semidirect
272. C2AGL(1,𝔽5)×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C42⋊C32
AGL(1,𝔽5)×C42⋊C32
C2×C42×AGL(1,𝔽5)3
C2×A4×AGL(1,𝔽5)4
C2×C4×C42⋊C35