Finite Group Databasebeta

← #14289355

Subgroups — #14289355

Order 1920.

628 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#66051C211yesmaximal, characteristic
2C5×#5076C211yesmaximal, characteristic, complemented
3#11746880C212yesmaximal, complemented
4#11746365C211yesmaximal, characteristic, complemented
5#11745835C212yesmaximal, complemented
6#10602059—31nomaximal, Hall
7C2×C3×D4×D5—22no—
8C3×C5×#127C2211yescharacteristic
9C2×C5×#214—22no—
10C5×#869C2211yescharacteristic, complemented
11C3×#4084—22no—
12C3×#4083—22no—
13C3×C4×D20C2212yes—
14C4⋊(C3⋊#168)C2212yescomplemented
15C4×C5×C3⋊C8C2211yescharacteristic, complemented
16#90986—22no—
17#90964—22no—
18#71907—51nomaximal, Hall
19#66051D311yescharacteristic
20C5×#492—31no—
21#65373—32no—
22#64764—31no—
23#64679—32no—
24C23×C3×D5—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C2×C5×Dic6—21no—
28C2×C3×C22⋊D5—24no—
29C3×D4×D5—44no—
30C3×D4×D5—44no—
31C2×C3×D20D412yes—
32C2×C3×C4×D5—22no—
33C3×C42×C5C2311yescharacteristic
34C2×C3⋊#168—22no—
35C5×#214—44no—
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C3×C22⋊Dic5—22no—
39C3×#685—22no—
40C3×C4⋊Dic5D412yes—
41C3×D42—51no—
42#5076D511yescharacteristic, complemented
43#5008—52no—
44#4544—51no—
45D4⋊(C3⋊C8)—52no—
46C2×D4×D5—22no—
47C2×C5×SD16—62no—
48C5×C4⋊Q8—31no—
49C5×#127C2×D311yescharacteristic
50#4084—22no—
51#4083—22no—
52C4×D20C2×D312yes—
53C4×C5×C8—31no—
54#3941—62no—
55#3940—62no—
56C4⋊#168—32no—
57#1629—151noSylow
58C23×C3×C5—22no—
59C22×C3×D5—22no—
60C22×C3×D5—48no—
61C22×C3×D5—82no—
62C3×C5×D4—42no—
63C3×C5×D4—42no—
64C3×C5×D4—42no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C2×C5×Dic3—41no—
68C5×Dic6—42no—
69C3×C22⋊D5—48no—
70C2×C3×Dic5—22no—
71C3×D20—22no—
72C3×D20SD1614yescomplemented
73C3×C4×D5—42no—
74C3×C4×D5—42no—
75C3⋊#168—42no—
76C5×C3⋊C8—22no—
77C22×C3×D4—102no—
78C3×#127C2×D511yescharacteristic
79C3×#121—102no—
80C3×#120—102no—
81C3×C4×D4—52no—
82C2×#214—22no—
83#869C2×D511yescharacteristic, complemented
84#832—102no—
85#808—102no—
86C4⋊(C3⋊C8)—52no—
87C4×C3⋊C8C2×D511yescharacteristic, complemented
88C23×D5—22no—
89C2×C5×Q8—61no—
90C2×C5×D4—22no—
91C2×C5×D4#6712yes—
92C2×C22⋊D5—24no—
93D4×D5—44no—
94D4×D5—44no—
95C2×D20#6712yes—
96C2×C4×D5—22no—
97C5×SD16—124no—
98C2×C5×C8—61no—
99C5×C4⋊C4—62no—
100C42×C5C22×D311yescharacteristic
101C22⋊Dic5—22no—
102#685—22no—
103C4⋊Dic5#6712yes—
104C2×#168—62no—
105D42—51no—
106#492—31no—
107#476—152no—
108#331—151no—
109D4⋊C8—152no—
110C22×C3×C5—44no—
111C22×C3×C5—42no—
112C22×C3×C5#12011yescharacteristic
113C2×C3×D5—24no—
114C2×C3×D5—42no—
115C2×C3×D5—42no—
116C2×C3×D5—88no—
117C3×C4×C5—21no—
118C3×C4×C5C2×SD1612yes—
119C3×C4×C5AGL(1,ℤ/8)12yes—
120C3×Dic5—42no—
121C5×Dic3—81no—
122C24×C3—102no—
123C2×C3×D4—22no—
124C2×C3×D4—52no—
125C2×C3×D4—104no—
126C2×C3×D4—204no—
127C2×C3×D4—204no—
128C2×C3×D4C22⋊D512yes—
129C22×C3×C4—102no—
130C2×Dic6—21no—
131C3×C4⋊C4—52no—
132C3×C22⋊C4—102no—
133C3×C22⋊C4—102no—
134C3×C42C22×D511yescharacteristic
135#214—44no—
136C4⋊Dic3—22no—
137C2×C3⋊C8—21no—
138C2×C3⋊C8—102no—
139C23×C5—22no—
140C22×D5—22no—
141C22×D5—48no—
142C22×D5—82no—
143C5×Q8—122no—
144C5×D4—42no—
145C5×D4—42no—
146C5×D4—42no—
147C2×C4×C5—121no—
148C2×C4×C5C2×#6711yescharacteristic
149C2×C4×C5C2×#6712yes—
150C22⋊D5—48no—
151C2×Dic5—22no—
152D20—22no—
153D20#21414yescomplemented
154C4×D5—42no—
155C4×D5—42no—
156C5×C8—62no—
157#168—122no—
158C22×D4—102no—
159C2×SD16—62no—
160C4⋊Q8—31no—
161#127D3×D511yescharacteristic
162#121—102no—
163#120—102no—
164C4×D4—52no—
165#106—302no—
166C4⋊C8—152no—
167#102—302no—
168C4×C8—31no—
169C2×C3×C5—82no—
170C2×C3×C5#45012yes—
171C2×C3×C5#45311yescharacteristic
172C3×D5—44no—
173C23×C3—22no—
174C23×C3—102no—
175C23×C3—208no—
176C23×C3—402no—
177C3×D4—42no—
178C3×D4—42no—
179C3×D4—42no—
180C3×D4—54no—
181C3×D4—102no—
182C3×D4—208no—
183C2×C3×C4—102no—
184C2×C3×C4—202no—
185C2×C3×C4—202no—
186C2×C3×C4D4×D512yes—
187C2×C3×C4C2×C22⋊D511yescharacteristic
188C2×Dic3—41no—
189Dic6—42no—
190C3⋊C8—22no—
191C3⋊C8—202no—
192C22×C5—44no—
193C22×C5—42no—
194C22×C5#95311yescharacteristic
195C2×D5—24no—
196C2×D5—42no—
197C2×D5—42no—
198C2×D5—88no—
199C4×C5—21no—
200C4×C5—241no—
201C4×C5#93212yes—
202C4×C5C2×#21412yes—
203Dic5—42no—
204C24—102no—
205C2×Q8—61no—
206C2×D4—22no—
207C2×D4—52no—
208C2×D4—104no—
209C2×D4—204no—
210C2×D4—204no—
211C2×D4#120112yes—
212C22×C4—102no—
213SD16—124no—
214C2×C8—61no—
215C2×C8—302no—
216C4⋊C4—52no—
217C4⋊C4—62no—
218C22⋊C4—102no—
219C22⋊C4—102no—
220C42C2×D3×D511yescharacteristic
221C3×C5#162911yescharacteristic, complemented, Hall
222C22×C3—42no—
223C22×C3—44no—
224C22×C3—104no—
225C22×C3—202no—
226C22×C3—202no—
227C22×C3—408no—
228C22×C3#408311yescharacteristic
229C3×C4—21no—
230C3×C4—202no—
231C3×C4D5×SD1612yes—
232C3×C4#406012yes—
233Dic3—81no—
234C2×C5—82no—
235C2×C5#521812yes—
236C2×C5#524111yescharacteristic
237D5—44no—
238C23—22no—
239C23—102no—
240C23—208no—
241C23—402no—
242Q8—122no—
243D4—42no—
244D4—42no—
245D4—42no—
246D4—54no—
247D4—102no—
248D4—208no—
249C2×C4—102no—
250C2×C4—121no—
251C2×C4—202no—
252C2×C4—202no—
253C2×C4C2×#120111yescharacteristic
254C2×C4D5×#6712yes—
255C8—62no—
256C8—602no—
257C2×C3—82no—
258C2×C3—204no—
259C2×C3#6536611yescharacteristic
260C2×C3#6545812yes—
261C5#7190711yescharacteristic, complemented, Sylow
262C22—42no—
263C22—44no—
264C22—104no—
265C22—202no—
266C22—202no—
267C22—408no—
268C22#9156311yescharacteristic
269C4—21no—
270C4—202no—
271C4—241no—
272C4D5×#21412yes—
273C4#9149112yes—
274C3#1060205911yescharacteristic, complemented, Sylow
275C2—82no—
276C2—204no—
277C2#1174904412yes—
278C2#1174913711yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC3×#66051C2
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. #11746880C2semidirect
4. #11746365C2semidirect
5. #11745835C2semidirect
10. C5×#869C22semidirect
14. C4⋊(C3⋊#168)C22semidirect
15. C4×C5×C3⋊C8C22semidirect
42. #5076D5semidirect
72. C3×D20SD16semidirect
83. #869C2×D5semidirect
87. C4×C3⋊C8C2×D5semidirect
153. D20#214semidirect
221. C3×C5#1629semidirect
261. C5#71907semidirect
274. C3#10602059semidirect

Maximal subgroups

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

subgroupindex
C3×#660512
C5×#50762
#117468802
#117463652
#117458352
#106020593
#719075