Finite Group Databasebeta

← #14289356

Subgroups — #14289356

Order 1920.

628 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 92 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
1#11756476C211yesmaximal, characteristic
2C5×#5076C211yesmaximal, characteristic, complemented
3#11746885C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5#11745838C212yesmaximal, complemented
6#10602059—31nomaximal, Hall
7C2×D4×D15—22no—
8C3×C5×#127C2211yescharacteristic
9#91827—22no—
10#91826—22no—
11C4×D60C2212yes—
12C2×C5×#214—22no—
13C5×#869C2211yescharacteristic, complemented
14C4×C5×C3⋊C8C2211yescharacteristic, complemented
15C3×C4⋊#168C2212yescomplemented
16#90985—22no—
17#90969—22no—
18#68391—51nomaximal, Hall
19#66051—31no—
20C5×#492—31no—
21#65373—32no—
22#64764D311yescharacteristic, complemented
23#64679—32no—
24C23×D15—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C2×#1220—24no—
28D4×D15—44no—
29D4×D15—44no—
30C2×D60D412yes—
31C2×C4×D15—22no—
32C2×C5×Dic6—21no—
33C3×C42×C5C2311yescharacteristic
34#6719—22no—
35#6714—22no—
36C4⋊Dic15D412yes—
37C5×#214—44no—
38C5×C4⋊Dic3—22no—
39C2×C5×C3⋊C8—21no—
40C2×C3×#168—22no—
41#5717—51no—
42#5076D511yescharacteristic, complemented
43#4842—52no—
44C3×#331—51no—
45#4483—52no—
46C2×D4×D5—62no—
47C2×C5×SD16—62no—
48C5×C4⋊Q8—31no—
49C5×#127C2×D311yescharacteristic
50#4084—62no—
51#4083—62no—
52C4×D20—32no—
53C4×C5×C8—31no—
54#3941—62no—
55#3940—62no—
56C4⋊#168C2×D312yescomplemented
57#1629—151noSylow
58C23×C3×C5—22no—
59C22×D15—22no—
60C22×D15—48no—
61C22×D15—82no—
62C3×C5×D4—42no—
63C3×C5×D4—42no—
64C3×C5×D4—42no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67#1220—48no—
68C2×Dic15—22no—
69D60—22no—
70D60SD1614yescomplemented
71C4×D15—42no—
72C4×D15—42no—
73C2×C5×Dic3—41no—
74C5×Dic6—42no—
75C3×#168—42no—
76C5×C3⋊C8—22no—
77C2×D3×D4—102no—
78C3×#127C2×D511yescharacteristic
79#938—102no—
80#937—102no—
81C2×#214—22no—
82C4×D12—52no—
83#869C2×D511yescharacteristic, complemented
84C3×C4⋊C8—52no—
85#821—102no—
86#817—102no—
87C4×C3⋊C8C2×D511yescharacteristic, complemented
88C23×D5—62no—
89C2×C5×Q8—61no—
90C2×C5×D4—22no—
91C2×C5×D4D1212yes—
92C2×C22⋊D5—64no—
93D4×D5—124no—
94D4×D5—124no—
95C2×D20—32no—
96C2×C4×D5—62no—
97C5×SD16—124no—
98C2×C5×C8—61no—
99C5×C4⋊C4—62no—
100C42×C5C22×D311yescharacteristic
101C22⋊Dic5—62no—
102#685—62no—
103C4⋊Dic5—32no—
104C2×#168—22no—
105D42—151no—
106#492—31no—
107#476—152no—
108#331—51no—
109D4⋊C8—152no—
110C22×C3×C5—44no—
111C22×C3×C5—42no—
112C22×C3×C5#12011yescharacteristic
113C2×D15—24no—
114C2×D15—42no—
115C2×D15—42no—
116C2×D15—88no—
117C3×C4×C5—21no—
118C3×C4×C5C2×SD1612yes—
119C3×C4×C5AGL(1,ℤ/8)12yes—
120Dic15—42no—
121C5×Dic3—81no—
122C23×D3—102no—
123C2×C3×D4—22no—
124C2×C3×D4C22⋊D512yes—
125C2×#67—104no—
126D3×D4—204no—
127D3×D4—204no—
128C2×D12—52no—
129C2×C4×D3—102no—
130C2×Dic6—21no—
131C2×C3×C8—102no—
132C3×C42C22×D511yescharacteristic
133#217—102no—
134#214—44no—
135(C2×D3)⋊C4—102no—
136C4⋊Dic3—22no—
137C4⋊Dic3—52no—
138C2×C3⋊C8—21no—
139C23×C5—22no—
140C22×D5—62no—
141C22×D5—128no—
142C22×D5—242no—
143C5×Q8—122no—
144C5×D4—42no—
145C5×D4—42no—
146C5×D4—42no—
147C2×C4×C5—121no—
148C2×C4×C5C2×D1211yescharacteristic
149C2×C4×C5D3×D412yes—
150C22⋊D5—128no—
151C2×Dic5—62no—
152D20—34no—
153D20—62no—
154C4×D5—122no—
155C4×D5—122no—
156C5×C8—62no—
157#168—42no—
158C22×D4—302no—
159C2×SD16—62no—
160C4⋊Q8—31no—
161#127D3×D511yescharacteristic
162#121—302no—
163#120—302no—
164C4×D4—152no—
165#106—302no—
166C4⋊C8—52no—
167#102—302no—
168C4×C8—31no—
169C2×C3×C5—82no—
170C2×C3×C5#45012yes—
171C2×C3×C5#45311yescharacteristic
172D15—44no—
173C23×C3—22no—
174C22×D3—102no—
175C22×D3—208no—
176C22×D3—402no—
177C3×D4—42no—
178C3×D4—42no—
179C3×D4—42no—
180C2×C3×C4D4×D512yes—
181C2×C3×C4C2×C22⋊D511yescharacteristic
182#67—208no—
183C2×Dic3—41no—
184C2×Dic3—102no—
185D12—54no—
186D12—102no—
187C4×D3—202no—
188C4×D3—202no—
189Dic6—42no—
190C3×C8—202no—
191C3⋊C8—22no—
192C22×C5—42no—
193C22×C5—44no—
194C22×C5#88211yescharacteristic
195C2×D5—64no—
196C2×D5—122no—
197C2×D5—122no—
198C2×D5—248no—
199C4×C5—21no—
200C4×C5—241no—
201C4×C5#91112yes—
202C4×C5D3×SD1612yes—
203Dic5—122no—
204C24—302no—
205C2×Q8—61no—
206C2×D4—22no—
207C2×D4—152no—
208C2×D4—304no—
209C2×D4—604no—
210C2×D4—604no—
211C2×D4#120312yes—
212C22×C4—302no—
213SD16—124no—
214C2×C8—61no—
215C2×C8—102no—
216C4⋊C4—62no—
217C4⋊C4—152no—
218C22⋊C4—302no—
219C22⋊C4—302no—
220C42C2×D3×D511yescharacteristic
221C3×C5#162911yescharacteristic, complemented, Hall
222C22×C3—42no—
223C22×C3—44no—
224C22×C3#408311yescharacteristic
225C2×D3—104no—
226C2×D3—202no—
227C2×D3—202no—
228C2×D3—408no—
229C3×C4—21no—
230C3×C4D5×SD1612yes—
231C3×C4#406012yes—
232Dic3—81no—
233Dic3—202no—
234C2×C5—82no—
235C2×C5#474711yescharacteristic
236C2×C5#477612yes—
237D5—124no—
238C23—22no—
239C23—302no—
240C23—608no—
241C23—1202no—
242Q8—122no—
243D4—42no—
244D4—42no—
245D4—42no—
246D4—154no—
247D4—302no—
248D4—608no—
249C2×C4—121no—
250C2×C4—302no—
251C2×C4—602no—
252C2×C4—602no—
253C2×C4C2×#120311yescharacteristic
254C2×C4#679012yes—
255C8—62no—
256C8—202no—
257C2×C3—82no—
258C2×C3#6536611yescharacteristic
259C2×C3#6545812yes—
260D3—204no—
261C5#6839111yescharacteristic, complemented, Sylow
262C22—42no—
263C22—44no—
264C22—304no—
265C22—602no—
266C22—602no—
267C22—1208no—
268C22#9157311yescharacteristic
269C4—21no—
270C4—241no—
271C4—602no—
272C4#9148712yes—
273C4#9149812yes—
274C3#1060205911yescharacteristic, complemented, Sylow
275C2—82no—
276C2—604no—
277C2#1174906212yes—
278C2#1174914311yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radical#11756476C2
hypercenter#127D3×D5
hypocenterC3×C5#1629
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C5×#5076C2semidirect
3. #11746885C2semidirect
4. C3×#64764C2semidirect
5. #11745838C2semidirect
13. C5×#869C22semidirect
14. C4×C5×C3⋊C8C22semidirect
15. C3×C4⋊#168C22semidirect
22. #64764D3semidirect
42. #5076D5semidirect
56. C4⋊#168C2×D3semidirect
70. D60SD16semidirect
83. #869C2×D5semidirect
87. C4×C3⋊C8C2×D5semidirect
221. C3×C5#1629semidirect
261. C5#68391semidirect
274. C3#10602059semidirect

Maximal subgroups

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

subgroupindex
#117564762
C5×#50762
#117468852
C3×#647642
#117458382
#106020593
#683915