Finite Group Databasebeta

← C2×A4×Dic20 #14514136

Subgroups — C2×A4×Dic20 #14514136

Order 1920.

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

normal subgroups only

This group has 688 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
1C2×A4×Dic10C212yesmaximal
2C2×C5×C8×A4C211yesmaximal, characteristic
3A4×Dic20C214yesmaximal, direct product factor
4C23×Dic20C311yesmaximal, characteristic, complemented, Hall
5C2×C4×C5×A4C2211yescharacteristic
6C2×A4×Dic5—22no—
7A4×Dic10—22no—
8A4×Dic10C2214yes—
9C2×C3×Dic20—41nomaximal
10C5×C8×A4C2212yes—
11C2×A4×Q16—51nomaximal, Hall
12C23×Dic10C2×C312yes—
13C23×C5×C8C2×C311yescharacteristic
14C22×Dic20—31no—
15C22×Dic20—32no—
16C22×Dic20—34no—
17C22×Dic20—31no—
18C22×Dic20C2×C314yescomplemented
19C22×C5×A4D411yescharacteristic
20C2×C3×Dic10—42no—
21C4×C5×A4D411yescharacteristic
22C4×C5×A4C2311yescharacteristic
23A4×Dic5—24no—
24C2×C3×C5×C8—41no—
25C3×Dic20—44no—
26C2×Q8×A4—52no—
27A4×Q16—54no—
28C2×C8×A4D511yescharacteristic
29C23×C4×C5C22×C311yescharacteristic
30C23×Dic5—22no—
31C22×Dic10—22no—
32C22×Dic10—32no—
33C22×Dic10—32no—
34C22×Dic10—34no—
35C22×Dic10—62no—
36C22×Dic10—62no—
37C22×Dic10C22×C314yes—
38C22×C5×C8—31no—
39C22×C5×C8—31no—
40C22×C5×C8—32no—
41C22×C5×C8C22×C312yes—
42C2×Dic20—32no—
43C2×Dic20—38no—
44C2×Dic20—34no—
45C2×Dic20—32no—
46C2×Dic20—31no—
47C2×Dic20—34no—
48C2×Dic20—34no—
49C2×Dic20—38no—
50C2×Dic20—34no—
51C2×Dic20A411yescharacteristic, direct product factor
52C23×Q16—51noSylow
53C2×C5×A4Q1612yescomplemented
54C2×C5×A4C2×D411yescharacteristic
55C2×C3×C4×C5—41no—
56C2×C3×Dic5—82no—
57C3×Dic10—44no—
58C3×Dic10—82no—
59C3×C5×C8—42no—
60Q8×A4—54no—
61Q8×A4—102no—
62C2×C4×A4—102no—
63C2×C4×A4C2×D511yescharacteristic
64C2×C3×Q16—201no—
65C8×A4C2×D512yes—
66C24×C5C3×D411yescharacteristic
67C22×C4×C5—31no—
68C22×C4×C5—31no—
69C22×C4×C5—31no—
70C22×C4×C5—31no—
71C22×C4×C5C3×D411yescharacteristic
72C22×C4×C5C23×C311yescharacteristic
73C22×Dic5—24no—
74C22×Dic5—62no—
75C22×Dic5—64no—
76C22×Dic5—62no—
77C2×Dic10—34no—
78C2×Dic10—32no—
79C2×Dic10—34no—
80C2×Dic10—34no—
81C2×Dic10—34no—
82C2×Dic10—62no—
83C2×Dic10—62no—
84C2×Dic10—62no—
85C2×Dic10—68no—
86C2×Dic10—62no—
87C2×Dic10—64no—
88C2×Dic10—62no—
89C2×Dic10—62no—
90C2×Dic10—64no—
91C2×Dic10C2×A412yes—
92C2×C5×C8—32no—
93C2×C5×C8—31no—
94C2×C5×C8—32no—
95C2×C5×C8—32no—
96C2×C5×C8—32no—
97C2×C5×C8C2×A411yescharacteristic
98Dic20—38no—
99Dic20—38no—
100Dic20—34no—
101Dic20C2×A414yesdirect product factor
102C23×Q8—52no—
103C22×Q16—54no—
104C22×Q16—151no—
105C22×Q16—151no—
106C22×Q16—154no—
107C22×Q16—152no—
108C23×C8C3×D511yescharacteristic
109C22×C3×C5—41no—
110C5×A4C2×Q1611yescharacteristic, complemented
111C3×C4×C5—41no—
112C3×C4×C5—41no—
113C3×Dic5—84no—
114C22×A4D2011yescharacteristic
115C2×C3×Q8—202no—
116C4×A4—104no—
117C4×A4D2011yescharacteristic
118C4×A4C22×D511yescharacteristic
119C3×Q16—204no—
120C2×C3×C8—41no—
121C23×C5—31no—
122C23×C5—32no—
123C23×C5—31no—
124C23×C5C3×Q1612yescomplemented
125C23×C5C2×C3×D411yescharacteristic
126C2×C4×C5—32no—
127C2×C4×C5—31no—
128C2×C4×C5—31no—
129C2×C4×C5—31no—
130C2×C4×C5—31no—
131C2×C4×C5—31no—
132C2×C4×C5—31no—
133C2×C4×C5—31no—
134C2×C4×C5C22×A411yescharacteristic
135C2×Dic5—22no—
136C2×Dic5—64no—
137C2×Dic5—64no—
138C2×Dic5—64no—
139C2×Dic5—62no—
140C2×Dic5—64no—
141Dic10—22no—
142Dic10—34no—
143Dic10—64no—
144Dic10—64no—
145Dic10—64no—
146Dic10—62no—
147Dic10—64no—
148Dic10C22×A414yes—
149C5×C8—32no—
150C5×C8C22×A412yes—
151C22×Q8—54no—
152C22×Q8—102no—
153C22×Q8—152no—
154C22×Q8—152no—
155C22×Q8—154no—
156C22×Q8—302no—
157C22×Q8—302no—
158C23×C4—102no—
159C23×C4C2×C3×D511yescharacteristic
160C2×Q16—51no—
161C2×Q16—154no—
162C2×Q16—154no—
163C2×Q16—152no—
164C2×Q16—158no—
165C2×Q16—152no—
166C2×Q16—154no—
167C2×Q16—154no—
168C2×Q16—158no—
169C2×Q16—151no—
170C22×C8—31no—
171C22×C8—31no—
172C22×C8—32no—
173C22×C8C2×C3×D512yes—
174C2×C3×C5—41no—
175C2×C3×C5—42no—
176C2×A4Dic2012yesdirect product factor
177C2×A4C2×D2011yescharacteristic
178C3×Q8—204no—
179C3×Q8—402no—
180C2×C3×C4—41no—
181C2×C3×C4—402no—
182C3×C8—42no—
183C22×C5—32no—
184C22×C5—31no—
185C22×C5—32no—
186C22×C5—31no—
187C22×C5—31no—
188C22×C5—32no—
189C22×C5—32no—
190C22×C5C2×C3×Q1611yescharacteristic, complemented
191C22×C5D4×A411yescharacteristic
192C4×C5—31no—
193C4×C5—31no—
194C4×C5D4×A411yescharacteristic
195C4×C5C23×A411yescharacteristic
196Dic5—24no—
197Dic5—64no—
198C24C3×D2011yescharacteristic
199C2×Q8—52no—
200C2×Q8—154no—
201C2×Q8—154no—
202C2×Q8—154no—
203C2×Q8—154no—
204C2×Q8—152no—
205C2×Q8—302no—
206C2×Q8—302no—
207C2×Q8—302no—
208C2×Q8—304no—
209C2×Q8—302no—
210C2×Q8—304no—
211C2×Q8—302no—
212C2×Q8—308no—
213C2×Q8—302no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—104no—
219C22×C4—302no—
220C22×C4—304no—
221C22×C4—302no—
222C22×C4C3×D2011yescharacteristic
223C22×C4C22×C3×D511yescharacteristic
224Q16—54no—
225Q16—158no—
226Q16—158no—
227Q16—154no—
228C2×C8—32no—
229C2×C8—31no—
230C2×C8—32no—
231C2×C8—32no—
232C2×C8—32no—
233C2×C8D5×A411yescharacteristic
234C3×C5—41noHall
235C22×C3—41no—
236A4C2×Dic2011yescharacteristic, direct product factor
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—404no—
240C2×C5—32no—
241C2×C5—31no—
242C2×C5—31no—
243C2×C5A4×Q1612yescomplemented
244C2×C5C2×D4×A411yescharacteristic
245C23—31no—
246C23—32no—
247C23—31no—
248C23C3×Dic2012yescomplemented
249C23C2×C3×D2011yescharacteristic
250Q8—54no—
251Q8—102no—
252Q8—154no—
253Q8—304no—
254Q8—304no—
255Q8—304no—
256Q8—304no—
257Q8—302no—
258C2×C4—32no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—31no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—102no—
267C2×C4—304no—
268C2×C4—304no—
269C2×C4—304no—
270C2×C4—302no—
271C2×C4—304no—
272C2×C4C2×D5×A411yescharacteristic
273C8—32no—
274C8C2×D5×A412yes—
275C2×C3—41no—
276C2×C3—42no—
277C5C2×A4×Q1611yescharacteristic, complemented, Sylow
278C22—32no—
279C22—31no—
280C22—32no—
281C22—31no—
282C22—31no—
283C22—32no—
284C22—32no—
285C22C2×C3×Dic2011yescharacteristic, complemented
286C22A4×D2011yescharacteristic
287C4—31no—
288C4—31no—
289C4—104no—
290C4—304no—
291C4A4×D2011yescharacteristic
292C4C22×D5×A411yescharacteristic
293C3—41noSylow
294C2—31no—
295C2—32no—
296C2—31no—
297C2A4×Dic2012yesdirect product factor
298C2C2×A4×D2011yescharacteristic
subgroupG/H
centerC22A4×D20
commutator, cosocleC22×C4×C5C23×C3
FrattiniC4C22×D5×A4
FittingC23×C5×C8C2×C3
socleC24×C5C3×D4
prime radicalC22×C5×A4D4
hypercenterC2×C8D5×A4
hypocenterC22×C5C2×C3×Q16
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. A4×Dic20C2direct (N × H)
4. C23×Dic20C3semidirect
18. C22×Dic20C2×C3semidirect
51. C2×Dic20A4direct (N × H)
53. C2×C5×A4Q16semidirect
101. Dic20C2×A4direct (N × H)
110. C5×A4C2×Q16semidirect
124. C23×C5C3×Q16semidirect
176. C2×A4Dic20direct (N × H)
190. C22×C5C2×C3×Q16semidirect
236. A4C2×Dic20direct (N × H)
243. C2×C5A4×Q16semidirect
248. C23C3×Dic20semidirect
277. C5C2×A4×Q16semidirect
285. C22C2×C3×Dic20semidirect
297. C2A4×Dic20direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×Dic102
C2×C5×C8×A42
A4×Dic202
C23×Dic203
C2×C3×Dic204
C2×A4×Q165