Finite Group Databasebeta

← Dic5×#120⋊C3 #14512241

Subgroups — Dic5×#120⋊C3 #14512241

Order 1920.

508 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 44 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
1Dic5×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C5×#120⋊C3C211yesmaximal, characteristic
3#65536⋊C3C211yesmaximal, characteristic, complemented
4Dic5×#120C311yesmaximal, characteristic, complemented, Hall
5C2×C5×C22⋊A4C2211yescharacteristic
6C2×A4×Dic5—41nomaximal
7C5×#120⋊C3C412yescomplemented
8C4×#120⋊C3—51nomaximal, Hall
9C24×Dic5C2×C311yescharacteristic, complemented
10C2×C5×#120C2×C311yescharacteristic
11C2×D4×Dic5—31no—
12#65536C2×C311yescharacteristic, complemented
13#65509—31no—
14#65239—31no—
15C22⋊C4×Dic5—31no—
16C5×C22⋊A4C2×C411yescharacteristic, complemented
17C22×C5×A4—41no—
18A4×Dic5—41no—
19A4×Dic5—41no—
20A4×Dic5—82no—
21C4×C22⋊A4—51no—
22C2×#120⋊C3D511yescharacteristic
23#379⋊C3—51no—
24C25×C5C22×C311yescharacteristic
25C22×C5×D4—31no—
26C23×Dic5—31no—
27C23×Dic5—31no—
28C23×Dic5—62no—
29C23×Dic5—62no—
30C23×Dic5A411yescharacteristic, complemented
31C5×#120—32no—
32C5×#120C3×C412yescomplemented
33C2×C5×C22⋊C4—31no—
34C2×C22⋊Dic5—31no—
35C2×C22⋊Dic5—31no—
36C2×C22⋊Dic5—31no—
37D4×Dic5—62no—
38D4×Dic5—62no—
39C2×C4⋊Dic5—31no—
40C2×C4×Dic5—31no—
41#3963—32no—
42C4×#120—51noSylow
43C2×C5×A4—42no—
44C2×C5×A4—41no—
45C2×C5×A4—82no—
46C2×C3×Dic5—161no—
47C2×C22⋊A4C2×D511yescharacteristic
48C2×C4×A4—201no—
49#120⋊C3Dic512yesdirect product factor
50C24×C5—31no—
51C24×C5—31no—
52C24×C5—62no—
53C24×C5—62no—
54C24×C5C2×C3×C411yescharacteristic, complemented
55C24×C5C2×A411yescharacteristic
56C2×C5×D4—32no—
57C2×C5×D4—32no—
58C2×C5×D4—62no—
59C2×C5×D4—62no—
60C22×C4×C5—31no—
61C22×Dic5—22no—
62C22×Dic5—32no—
63C22×Dic5—32no—
64C22×Dic5—31no—
65C22×Dic5—31no—
66C22×Dic5—61no—
67C22×Dic5—62no—
68C22×Dic5—62no—
69C22×Dic5—64no—
70C22×Dic5—61no—
71C22×Dic5—62no—
72C22×Dic5—62no—
73C22×Dic5—64no—
74C22×Dic5—62no—
75C22×Dic5—62no—
76C22×Dic5C2×A411yescharacteristic
77C22×Dic5C2×A411yescharacteristic
78C5×C22⋊C4—32no—
79C5×C22⋊C4—32no—
80C22⋊Dic5—62no—
81C22⋊Dic5—62no—
82C22⋊Dic5—62no—
83C4⋊Dic5—62no—
84C4×Dic5—61no—
85C4×Dic5—61no—
86C24×C4—51no—
87C2×#120C3×D511yescharacteristic
88C2×C4×D4—151no—
89#386—151no—
90#385—151no—
91#379—51no—
92C4×C22⋊C4—151no—
93C22×C3×C5—161no—
94C5×A4—41no—
95C5×A4—82no—
96C3×Dic5—161no—
97C3×Dic5—161no—
98C22⋊A4C2×Dic511yescharacteristic, complemented
99C22×A4—41no—
100C4×A4—201no—
101C4×A4—201no—
102C4×A4—402no—
103C23×C5—22no—
104C23×C5—32no—
105C23×C5—32no—
106C23×C5—31no—
107C23×C5—31no—
108C23×C5—62no—
109C23×C5—62no—
110C23×C5—61no—
111C23×C5—62no—
112C23×C5—62no—
113C23×C5—62no—
114C23×C5—64no—
115C23×C5—61no—
116C23×C5—62no—
117C23×C5—62no—
118C23×C5—64no—
119C23×C5C4×A412yescomplemented
120C23×C5C22×A411yescharacteristic
121C5×D4—64no—
122C5×D4—64no—
123C2×C4×C5—32no—
124C2×C4×C5—61no—
125C2×C4×C5—61no—
126C2×Dic5—31no—
127C2×Dic5—31no—
128C2×Dic5—32no—
129C2×Dic5—41no—
130C2×Dic5—62no—
131C2×Dic5—64no—
132C2×Dic5—61no—
133C2×Dic5—62no—
134C2×Dic5—64no—
135C2×Dic5—62no—
136C2×Dic5—62no—
137C2×Dic5—62no—
138C2×Dic5—61no—
139C2×Dic5—62no—
140C2×Dic5—121no—
141C25C2×C3×D511yescharacteristic
142C22×D4—31no—
143C23×C4—51no—
144C23×C4—151no—
145C23×C4—151no—
146C23×C4—302no—
147C23×C4—302no—
148#120—32no—
149#120C3×Dic512yescomplemented
150C4×D4—302no—
151C4×D4—302no—
152C2×C4⋊C4—151no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—151no—
155C2×C22⋊C4—151no—
156C2×C22⋊C4—151no—
157C2×C42—151no—
158#95—152no—
159C2×C3×C5—162no—
160C2×C3×C5—161no—
161C2×A4—42no—
162C2×A4—41no—
163C2×A4—82no—
164C2×C3×C4—801no—
165C22×C5—22no—
166C22×C5—31no—
167C22×C5—31no—
168C22×C5—32no—
169C22×C5—32no—
170C22×C5—41no—
171C22×C5—62no—
172C22×C5—62no—
173C22×C5—64no—
174C22×C5—62no—
175C22×C5—62no—
176C22×C5—62no—
177C22×C5—62no—
178C22×C5—62no—
179C22×C5—64no—
180C22×C5—62no—
181C22×C5—121no—
182C22×C5C2×C4×A411yescharacteristic
183C4×C5—62no—
184Dic5—31no—
185Dic5—41no—
186Dic5—62no—
187Dic5—121no—
188Dic5#120⋊C311yescharacteristic, direct product factor
189C24—31no—
190C24—31no—
191C24—62no—
192C24—62no—
193C24C2×C3×Dic511yescharacteristic, complemented
194C24D5×A411yescharacteristic
195C2×D4—32no—
196C2×D4—32no—
197C2×D4—62no—
198C2×D4—62no—
199C22×C4—31no—
200C22×C4—51no—
201C22×C4—51no—
202C22×C4—102no—
203C22×C4—152no—
204C22×C4—152no—
205C22×C4—151no—
206C22×C4—151no—
207C22×C4—301no—
208C22×C4—302no—
209C22×C4—302no—
210C22×C4—304no—
211C22×C4—301no—
212C22×C4—302no—
213C22×C4—302no—
214C22×C4—304no—
215C22×C4—302no—
216C22×C4—302no—
217C4⋊C4—302no—
218C22⋊C4—32no—
219C22⋊C4—32no—
220C22⋊C4—302no—
221C22⋊C4—302no—
222C22⋊C4—302no—
223C42—301no—
224C42—301no—
225C3×C5—161noHall
226C22×C3—161no—
227A4—41no—
228A4—82no—
229C3×C4—801no—
230C3×C4—801no—
231C2×C5—31no—
232C2×C5—31no—
233C2×C5—42no—
234C2×C5—62no—
235C2×C5—62no—
236C2×C5C2×#120⋊C311yescharacteristic
237C23—22no—
238C23—32no—
239C23—32no—
240C23—31no—
241C23—31no—
242C23—62no—
243C23—62no—
244C23—61no—
245C23—62no—
246C23—62no—
247C23—62no—
248C23—64no—
249C23—61no—
250C23—62no—
251C23—62no—
252C23—64no—
253C23A4×Dic512yescomplemented
254C23C2×D5×A411yescharacteristic
255D4—64no—
256D4—64no—
257C2×C4—32no—
258C2×C4—61no—
259C2×C4—61no—
260C2×C4—151no—
261C2×C4—151no—
262C2×C4—152no—
263C2×C4—201no—
264C2×C4—302no—
265C2×C4—302no—
266C2×C4—304no—
267C2×C4—301no—
268C2×C4—302no—
269C2×C4—304no—
270C2×C4—302no—
271C2×C4—302no—
272C2×C4—301no—
273C2×C4—302no—
274C2×C4—601no—
275C2×C3—162no—
276C2×C3—161no—
277C5C4×#120⋊C311yescharacteristic, complemented, Sylow
278C22—22no—
279C22—31no—
280C22—31no—
281C22—32no—
282C22—32no—
283C22—41no—
284C22—62no—
285C22—62no—
286C22—62no—
287C22—62no—
288C22—64no—
289C22—62no—
290C22—62no—
291C22—62no—
292C22—64no—
293C22—62no—
294C22—121no—
295C22C2×A4×Dic511yescharacteristic
296C4—51no—
297C4—62no—
298C4—151no—
299C4—201no—
300C4—302no—
301C4—601no—
302C3—161noSylow
303C2—31no—
304C2—31no—
305C2—42no—
306C2—62no—
307C2—62no—
308C2D5×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D5×#120⋊C3
commutator, hypocenterC24×C5C2×C3×C4
FrattiniC23C2×D5×A4
FittingC2×C5×#120C2×C3
socleC23×C5C22×A4
prime radicalC2×C5×#120⋊C3C2
cosocleC25×C5C22×C3
LCSG ▷ C24×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. Dic5×C22⋊A4C2semidirect
3. #65536⋊C3C2semidirect
4. Dic5×#120C3semidirect
7. C5×#120⋊C3C4semidirect
9. C24×Dic5C2×C3semidirect
12. #65536C2×C3semidirect
16. C5×C22⋊A4C2×C4semidirect
30. C23×Dic5A4semidirect
32. C5×#120C3×C4semidirect
49. #120⋊C3Dic5direct (N × H)
54. C24×C5C2×C3×C4semidirect
98. C22⋊A4C2×Dic5semidirect
119. C23×C5C4×A4semidirect
149. #120C3×Dic5semidirect
188. Dic5#120⋊C3direct (N × H)
193. C24C2×C3×Dic5semidirect
253. C23A4×Dic5semidirect
277. C5C4×#120⋊C3semidirect

Maximal subgroups

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

subgroupindex
Dic5×C22⋊A42
C2×C5×#120⋊C32
#65536⋊C32
Dic5×#1203
C2×A4×Dic54
C4×#120⋊C35