Finite Group Databasebeta

← Dic5×#127⋊C3 #14512252

Subgroups — Dic5×#127⋊C3 #14512252

Order 1920.

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

normal subgroups only

This group has 388 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
1C2×C5×#127⋊C3C211yesmaximal, characteristic
2Dic5×C42⋊C3C211yesmaximal, characteristic, complemented
3#65224⋊C3C211yesmaximal, characteristic, complemented
4Dic5×#127C311yesmaximal, characteristic, complemented, Hall
5C2×A4×Dic5—41nomaximal
6C5×#127⋊C3C412yescomplemented
7C2×C5×C42⋊C3C2211yescharacteristic
8C4×#127⋊C3—51nomaximal, Hall
9C2×C5×#127C2×C311yescharacteristic
10C2×D4×Dic5—31no—
11C2×D4×Dic5—31no—
12#65510—31no—
13#65510—31no—
14#65224C2×C311yescharacteristic, complemented
15C42×Dic5C2×C311yescharacteristic, complemented
16C22×C5×A4—41no—
17A4×Dic5—41no—
18A4×Dic5—41no—
19C5×C42⋊C3C2×C411yescharacteristic, complemented
20C2×#127⋊C3D511yescharacteristic
21#384⋊C3—51no—
22C4×C42⋊C3—51no—
23C22×C5×D4—31no—
24C22×C5×D4—31no—
25C23×Dic5—31no—
26C23×Dic5A411yescharacteristic
27C5×#127—32no—
28C5×#127C3×C412yescomplemented
29C2×C42×C5C22×C311yescharacteristic
30C2×C22⋊Dic5—32no—
31C2×C22⋊Dic5—31no—
32C2×C22⋊Dic5—31no—
33D4×Dic5—62no—
34D4×Dic5—62no—
35D4×Dic5—62no—
36D4×Dic5—62no—
37C2×C4⋊Dic5—31no—
38C2×C4⋊Dic5—31no—
39C2×C4×Dic5—31no—
40C2×C4×Dic5—31no—
41C4×#127—51noSylow
42C2×C5×A4—42no—
43C2×C5×A4—41no—
44C2×C3×Dic5—161no—
45C2×C4×A4—201no—
46#127⋊C3Dic512yesdirect product factor
47C2×C42⋊C3C2×D511yescharacteristic
48C24×C5—31no—
49C24×C5C2×A411yescharacteristic
50C2×C5×D4—32no—
51C2×C5×D4—32no—
52C2×C5×D4—32no—
53C2×C5×D4—32no—
54C2×C5×D4—62no—
55C2×C5×D4—62no—
56C2×C5×D4—62no—
57C2×C5×D4—62no—
58C22×C4×C5—31no—
59C22×Dic5—31no—
60C22×Dic5—31no—
61C22×Dic5—61no—
62C22×Dic5—61no—
63C22×Dic5—62no—
64C22×Dic5—62no—
65C22×Dic5—61no—
66C22×Dic5—61no—
67C22×Dic5C2×A411yescharacteristic
68C22×Dic5C2×A411yescharacteristic
69C42×C5—31no—
70C42×C5C2×C3×C411yescharacteristic, complemented
71C22⋊Dic5—62no—
72C22⋊Dic5—62no—
73C22⋊Dic5—64no—
74C4⋊Dic5—62no—
75C4⋊Dic5—62no—
76C4×Dic5—32no—
77C4×Dic5—32no—
78C4×Dic5—62no—
79C2×#127C3×D511yescharacteristic
80C2×C4×D4—151no—
81C2×C4×D4—151no—
82#390—151no—
83#390—151no—
84#384—51no—
85C43—51no—
86C22×C3×C5—161no—
87C5×A4—41no—
88C3×Dic5—161no—
89C3×Dic5—161no—
90C22×A4—41no—
91C4×A4—201no—
92C4×A4—201no—
93C42⋊C3C2×Dic511yescharacteristic, complemented
94C23×C5—32no—
95C23×C5—61no—
96C23×C5—61no—
97C23×C5—61no—
98C23×C5—62no—
99C23×C5—61no—
100C23×C5—62no—
101C23×C5C4×A412yes—
102C23×C5C22×A411yescharacteristic
103C5×D4—64no—
104C5×D4—64no—
105C5×D4—64no—
106C5×D4—64no—
107C2×C4×C5—32no—
108C2×C4×C5—32no—
109C2×C4×C5—31no—
110C2×C4×C5—31no—
111C2×Dic5—31no—
112C2×Dic5—31no—
113C2×Dic5—32no—
114C2×Dic5—41no—
115C2×Dic5—61no—
116C2×Dic5—62no—
117C2×Dic5—61no—
118C2×Dic5—62no—
119C2×Dic5—121no—
120C2×Dic5—121no—
121C2×Dic5—122no—
122C2×Dic5—121no—
123C22×D4—31no—
124C22×D4—31no—
125C23×C4—51no—
126C23×C4—151no—
127#127—32no—
128#127C3×Dic512yescomplemented
129C4×D4—302no—
130C4×D4—302no—
131C4×D4—302no—
132C4×D4—302no—
133C2×C4⋊C4—151no—
134C2×C4⋊C4—151no—
135C2×C22⋊C4—151no—
136C2×C22⋊C4—152no—
137C2×C22⋊C4—151no—
138C2×C42—151no—
139C2×C42—151no—
140C2×C42C2×C3×D511yescharacteristic
141C2×C3×C5—162no—
142C2×C3×C5—161no—
143C2×A4—42no—
144C2×A4—41no—
145C2×C3×C4—801no—
146C22×C5—31no—
147C22×C5—31no—
148C22×C5—41no—
149C22×C5—62no—
150C22×C5—62no—
151C22×C5—64no—
152C22×C5—121no—
153C22×C5—121no—
154C22×C5—122no—
155C22×C5—121no—
156C22×C5C2×C4×A411yescharacteristic
157C4×C5—32no—
158C4×C5—32no—
159Dic5—31no—
160Dic5—41no—
161Dic5—62no—
162Dic5—121no—
163Dic5#127⋊C311yescharacteristic, direct product factor
164C24—31no—
165C24D5×A411yescharacteristic
166C2×D4—32no—
167C2×D4—32no—
168C2×D4—32no—
169C2×D4—32no—
170C2×D4—62no—
171C2×D4—62no—
172C2×D4—62no—
173C2×D4—62no—
174C22×C4—31no—
175C22×C4—51no—
176C22×C4—51no—
177C22×C4—151no—
178C22×C4—151no—
179C22×C4—301no—
180C22×C4—301no—
181C22×C4—302no—
182C22×C4—302no—
183C22×C4—301no—
184C22×C4—301no—
185C4⋊C4—302no—
186C4⋊C4—302no—
187C22⋊C4—302no—
188C22⋊C4—302no—
189C22⋊C4—304no—
190C42—31no—
191C42—152no—
192C42—152no—
193C42—302no—
194C42C2×C3×Dic511yescharacteristic, complemented
195C3×C5—161noHall
196C22×C3—161no—
197A4—41no—
198C3×C4—801no—
199C3×C4—801no—
200C2×C5—31no—
201C2×C5—31no—
202C2×C5—42no—
203C2×C5—122no—
204C2×C5C2×#127⋊C311yescharacteristic
205C23—32no—
206C23—61no—
207C23—61no—
208C23—61no—
209C23—62no—
210C23—61no—
211C23—62no—
212C23A4×Dic512yes—
213C23C2×D5×A411yescharacteristic
214D4—64no—
215D4—64no—
216D4—64no—
217D4—64no—
218C2×C4—32no—
219C2×C4—32no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—151no—
223C2×C4—151no—
224C2×C4—152no—
225C2×C4—201no—
226C2×C4—301no—
227C2×C4—302no—
228C2×C4—301no—
229C2×C4—302no—
230C2×C4—601no—
231C2×C4—601no—
232C2×C4—601no—
233C2×C4—602no—
234C2×C3—162no—
235C2×C3—161no—
236C5C4×#127⋊C311yescharacteristic, complemented, Sylow
237C22—31no—
238C22—31no—
239C22—41no—
240C22—62no—
241C22—62no—
242C22—64no—
243C22—121no—
244C22—121no—
245C22—122no—
246C22—121no—
247C22C2×A4×Dic511yescharacteristic
248C4—32no—
249C4—32no—
250C4—51no—
251C4—151no—
252C4—201no—
253C4—302no—
254C4—601no—
255C3—161noSylow
256C2—31no—
257C2—31no—
258C2—42no—
259C2—122no—
260C2D5×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D5×#127⋊C3
commutator, hypocenterC42×C5C2×C3×C4
FrattiniC23C2×D5×A4
FittingC2×C5×#127C2×C3
socleC23×C5C22×A4
prime radicalC2×C5×#127⋊C3C2
cosocleC2×C42×C5C22×C3
LCSG ▷ C42×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic5×C42⋊C3C2semidirect
3. #65224⋊C3C2semidirect
4. Dic5×#127C3semidirect
6. C5×#127⋊C3C4semidirect
14. #65224C2×C3semidirect
15. C42×Dic5C2×C3semidirect
19. C5×C42⋊C3C2×C4semidirect
28. C5×#127C3×C4semidirect
46. #127⋊C3Dic5direct (N × H)
70. C42×C5C2×C3×C4semidirect
93. C42⋊C3C2×Dic5semidirect
128. #127C3×Dic5semidirect
163. Dic5#127⋊C3direct (N × H)
194. C42C2×C3×Dic5semidirect
236. C5C4×#127⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#127⋊C32
Dic5×C42⋊C32
#65224⋊C32
Dic5×#1273
C2×A4×Dic54
C4×#127⋊C35