Finite Group Databasebeta

← #14289360

Subgroups — #14289360

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
2#11751177C211yesmaximal, characteristic, complemented
3#11746881C212yesmaximal, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5#11745834C212yesmaximal, complemented
6#10599184—31nomaximal, Hall
7C2×C3×D4×D5—22no—
8C3×C5×#127C2211yescharacteristic
9C2×#6716—22no—
10#91758C2211yescharacteristic, complemented
11C3×#4084—22no—
12C3×#4083—22no—
13C3×C4×D20C2212yes—
14C4×C3⋊#168C2211yescharacteristic, complemented
15C5×C4⋊(C3⋊C8)C2212yescomplemented
16#90987—22no—
17#90965—22no—
18#71907—51nomaximal, Hall
19#66051D311yescharacteristic
20#65365—31no—
21#65131—32no—
22C5×#331—31no—
23#64703—32no—
24C23×C3×D5—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C2×Dic30—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
34#6716—44no—
35C4⋊Dic15—22no—
36C2×C3⋊#168—21no—
37C2×C5×C3⋊C8—22no—
38C3×C22⋊Dic5—22no—
39C3×#685—22no—
40C3×C4⋊Dic5D412yes—
41C3×D42—51no—
42#5076—51no—
43#5008—52no—
44#4544D511yescharacteristic, complemented
45D4⋊(C3⋊C8)—52no—
46C2×D4×D5—22no—
47C5×#127C2×D311yescharacteristic
48#4084—22no—
49#4083—22no—
50C2×#687—62no—
51C4×D20C2×D312yes—
52#4015—31no—
53C5×C4⋊C8—32no—
54#3953—62no—
55#3949—62no—
56C4×#168—31no—
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×Dic15—41no—
68Dic30—42no—
69C3×C22⋊D5—48no—
70C2×C3×Dic5—22no—
71C3×D20—22no—
72C3×D20SD1614yescomplemented
73C3×C4×D5—42no—
74C3×C4×D5—42no—
75C3⋊#168—22no—
76C5×C3⋊C8—42no—
77C22×C3×D4—102no—
78C3×#127C2×D511yescharacteristic
79C3×#121—102no—
80C3×#120—102no—
81C3×C4×D4—52no—
82C2×#214—102no—
83#869—51no—
84#832—102no—
85#808—102no—
86C4⋊(C3⋊C8)C2×D512yescomplemented
87C4×C3⋊C8—51no—
88C23×D5—22no—
89C2×C5×D4—22no—
90C2×C5×D4#6712yes—
91C2×C22⋊D5—24no—
92D4×D5—44no—
93D4×D5—44no—
94C2×D20#6712yes—
95C2×C4×D5—22no—
96C2×Dic10—61no—
97C2×C5×C8—62no—
98C42×C5C22×D311yescharacteristic
99C22⋊Dic5—22no—
100#687—124no—
101#685—22no—
102C4⋊Dic5—62no—
103C4⋊Dic5#6712yes—
104C2×#168—61no—
105D42—51no—
106#492—151no—
107#476—152no—
108#331—31no—
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—
120Dic15—81no—
121C3×Dic5—42no—
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×D4D2012yes—
129C22×C3×C4—102no—
130C2×Dic6—101no—
131C3×C4⋊C4—52no—
132C3×C22⋊C4—102no—
133C3×C22⋊C4—102no—
134C3×C42C22×D511yescharacteristic
135#214—204no—
136C4⋊Dic3—102no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8—101no—
139C23×C5—22no—
140C22×D5—22no—
141C22×D5—48no—
142C22×D5—82no—
143C5×D4—42no—
144C5×D4—42no—
145C5×D4—42no—
146C2×C4×C5C2×#6711yescharacteristic
147C2×C4×C5C2×#6712yes—
148C22⋊D5—48no—
149C2×Dic5—22no—
150C2×Dic5—121no—
151D20—22no—
152D20#21414yescomplemented
153C4×D5—42no—
154C4×D5—42no—
155Dic10—122no—
156C5×C8—122no—
157#168—62no—
158C22×D4—102no—
159C2×SD16—302no—
160C4⋊Q8—151no—
161#127D3×D511yescharacteristic
162#121—102no—
163#120—102no—
164C4×D4—52no—
165#106—302no—
166C4⋊C8—32no—
167#102—302no—
168C4×C8—151no—
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×C4C2×D2011yescharacteristic
187C2×C3×C4D4×D512yes—
188C2×Dic3—201no—
189Dic6—202no—
190C3⋊C8—42no—
191C3⋊C8—102no—
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#93212yes—
201C4×C5C2×#21412yes—
202Dic5—42no—
203Dic5—241no—
204C24—102no—
205C2×Q8—301no—
206C2×D4—22no—
207C2×D4—52no—
208C2×D4—104no—
209C2×D4—204no—
210C2×D4—204no—
211C2×D4#120212yes—
212C22×C4—102no—
213SD16—604no—
214C2×C8—62no—
215C2×C8—301no—
216C4⋊C4—52no—
217C4⋊C4—302no—
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#402811yescharacteristic
229C3×C4—21no—
230C3×C4—202no—
231C3×C4#405712yes—
232C3×C4D5×SD1612yes—
233Dic3—401no—
234C2×C5—82no—
235C2×C5#521812yes—
236C2×C5#524111yescharacteristic
237D5—44no—
238C23—22no—
239C23—102no—
240C23—208no—
241C23—402no—
242Q8—602no—
243D4—42no—
244D4—42no—
245D4—42no—
246D4—54no—
247D4—102no—
248D4—208no—
249C2×C4—102no—
250C2×C4—202no—
251C2×C4—202no—
252C2×C4—601no—
253C2×C4C2×#120211yescharacteristic
254C2×C4D5×#6712yes—
255C8—122no—
256C8—302no—
257C2×C3—82no—
258C2×C3—204no—
259C2×C3#6503611yescharacteristic
260C2×C3#6506512yes—
261C5#7190711yescharacteristic, complemented, Sylow
262C22—42no—
263C22—44no—
264C22—104no—
265C22—202no—
266C22—202no—
267C22—408no—
268C22#9156411yescharacteristic
269C4—21no—
270C4—202no—
271C4—1201no—
272C4D5×#21412yes—
273C4#9148912yes—
274C3#1059918411yescharacteristic, complemented, Sylow
275C2—82no—
276C2—204no—
277C2#1174904512yes—
278C2#1174913811yescharacteristic
subgroupG/H
centerC22#91564
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. #11751177C2semidirect
3. #11746881C2semidirect
4. C5×#4544C2semidirect
5. #11745834C2semidirect
10. #91758C22semidirect
14. C4×C3⋊#168C22semidirect
15. C5×C4⋊(C3⋊C8)C22semidirect
44. #4544D5semidirect
72. C3×D20SD16semidirect
86. C4⋊(C3⋊C8)C2×D5semidirect
152. D20#214semidirect
221. C3×C5#1629semidirect
261. C5#71907semidirect
274. C3#10599184semidirect

Maximal subgroups

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

subgroupindex
C3×#660512
#117511772
#117468812
C5×#45442
#117458342
#105991843
#719075