Finite Group Databasebeta

← #14289067

Subgroups — #14289067

Order 1920.

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

normal subgroups only

This group has 480 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
1C5×#5734C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11747037C212yesmaximal, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745836C212yesmaximal, complemented
6#10602720—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×#6717—22no—
9#91763C2211yescharacteristic
10C5×#947—22no—
11C5×#895—22no—
12C5×#892—22no—
13C4×C5×D12C2212yes—
14C2×#6654—22no—
15C4×C3⋊#168C2211yescharacteristic
16C3×C4⋊#168C2212yes—
17#90969—22no—
18#68491—51nomaximal, Hall
19C5×#555—31no—
20#65374—31no—
21#65304—32no—
22#64766D311yescharacteristic, complemented
23D4⋊#168—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60—21no—
27C2×C5×D12—22no—
28C2×C5×D12D412yes—
29C2×C4×C5×D3—22no—
30C3×C5×C4⋊C4—22no—
31C3×C42×C5C2311yescharacteristic
32#6717—44no—
33C2×C3⋊#168—21no—
34C5×(C2×D3)⋊C4—24no—
35C5×(C2×D3)⋊C4—22no—
36C5×C4⋊Dic3D412yes—
37C4×C5×Dic3—22no—
38C2×C3×#168—22no—
39#6654—44no—
40#5734D511yescharacteristic, complemented
41#5085—51no—
42#4843—52no—
43C3×#333—51no—
44#4483—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46C5×#124—62no—
47C5×#121—62no—
48C4×C5×D4—32no—
49C5×#117—62no—
50C2×#688—62no—
51C2×#686—62no—
52#4020—31no—
53#3941—62no—
54C4⋊#168C2×D312yes—
55C4×#168—31no—
56#1624—151noSylow
57C22×D15—41no—
58C22×C5×D3—22no—
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63D60—42no—
64D60—42no—
65D60—42no—
66C2×C5×Dic3—22no—
67C5×D12—22no—
68C5×D12—22no—
69C5×D12—82no—
70C4×C5×D3—42no—
71C4×C5×D3—42no—
72C3⋊#168—22no—
73C3×#168—42no—
74C3×C4⋊Q8C2×D511yescharacteristic
75#947—22no—
76C2×#215—102no—
77C2×D24—102no—
78#895—22no—
79#892—22no—
80#874—51no—
81C4×D12C2×D512yes—
82C3×C4⋊C8—52no—
83#821—102no—
84C4×C3⋊C8—51no—
85C2×C5×Q8D1212yes—
86C2×C5×D4—32no—
87C2×C5×D4—62no—
88C22×C4×C5—62no—
89C2×D20—61no—
90C2×D20—62no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—32no—
93C5×C22⋊C4—64no—
94C5×C22⋊C4—62no—
95C42×C5—62no—
96C42×C5C22×D311yescharacteristic
97#688—124no—
98#686—124no—
99C2×#168—22no—
100C2×#168—61no—
101#555—31no—
102#492—151no—
103#459—152no—
104#333—51no—
105D4⋊C8—152no—
106C22×C3×C5#12011yescharacteristic
107C2×D15—82no—
108C2×D15—81no—
109C2×C5×D3—42no—
110C2×C5×D3—42no—
111C2×C5×D3—42no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5#13512yes—
115C3×C4×C5AGL(1,ℤ/8)12yes—
116C5×Dic3—42no—
117C2×C3×Q8C22⋊D512yes—
118C2×D12—22no—
119C2×D12—102no—
120C2×D12—101no—
121C2×D12C22⋊D512yes—
122C2×C4×D3—22no—
123C2×C3×C8—102no—
124C3×C4⋊C4—22no—
125C3×C42C22×D511yescharacteristic
126#215—204no—
127(C2×D3)⋊C4—24no—
128(C2×D3)⋊C4—22no—
129C4⋊Dic3C22⋊D512yes—
130C4×Dic3—22no—
131C2×C3⋊C8—101no—
132D24—204no—
133C23×C5—62no—
134C22×D5—121no—
135C5×Q8—42no—
136C5×D4—62no—
137C5×D4—62no—
138C5×D4—242no—
139C2×C4×C5—22no—
140C2×C4×C5—62no—
141C2×C4×C5—122no—
142C2×C4×C5—122no—
143C2×C4×C5C2×D1211yescharacteristic
144C2×C4×C5D3×D412yes—
145D20—122no—
146D20—122no—
147D20—122no—
148#168—42no—
149#168—62no—
150C2×SD16—302no—
151C2×D8—302no—
152C4⋊Q8D3×D511yescharacteristic
153#127—151no—
154#124—62no—
155#121—62no—
156C4×D4—32no—
157#117—62no—
158C4⋊C8—52no—
159#102—302no—
160C4×C8—151no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163D15—161no—
164C5×D3—82no—
165C22×D3—22no—
166C22×D3—201no—
167C3×Q8—42no—
168C2×C3×C4—22no—
169C2×C3×C4C2×C22⋊D511yescharacteristic
170C2×C3×C4C2×C22⋊D512yes—
171C2×Dic3—22no—
172D12—22no—
173D12—22no—
174D12—82no—
175D12—202no—
176D12—202no—
177D12—202no—
178C4×D3—42no—
179C4×D3—42no—
180C3×C8—202no—
181C3⋊C8—102no—
182C22×C5—122no—
183C22×C5—122no—
184C22×C5—122no—
185C22×C5#88211yescharacteristic
186C2×D5—241no—
187C2×D5—242no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5—122no—
191C4×C5#91412yes—
192C4×C5#91912yes—
193C2×Q8#120312yes—
194C2×D4—32no—
195C2×D4—62no—
196C2×D4—301no—
197C2×D4—302no—
198C22×C4—62no—
199SD16—604no—
200D8—604no—
201C2×C8—102no—
202C2×C8—301no—
203C4⋊C4—22no—
204C4⋊C4—32no—
205C22⋊C4—64no—
206C22⋊C4—62no—
207C42—62no—
208C42C2×D3×D511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3#409911yescharacteristic
211C2×D3—42no—
212C2×D3—42no—
213C2×D3—42no—
214C2×D3—402no—
215C2×D3—401no—
216C3×C4—21no—
217C3×C4—42no—
218C3×C4#409512yes—
219C3×C4#409612yes—
220Dic3—42no—
221C2×C5—242no—
222C2×C5#474711yescharacteristic
223C2×C5#481012yes—
224D5—481no—
225C23—62no—
226C23—601no—
227Q8—42no—
228D4—62no—
229D4—62no—
230D4—242no—
231D4—602no—
232D4—602no—
233D4—602no—
234C2×C4—22no—
235C2×C4—62no—
236C2×C4—122no—
237C2×C4—122no—
238C2×C4C2×#120311yescharacteristic
239C2×C4D3×C22⋊D512yes—
240C8—202no—
241C8—302no—
242C2×C3#6552712yes—
243C2×C3#6553011yescharacteristic
244D3—82no—
245D3—801no—
246C5#6849111yescharacteristic, complemented, Sylow
247C22—122no—
248C22—122no—
249C22—122no—
250C22—1201no—
251C22—1202no—
252C22#9157011yescharacteristic
253C4—21no—
254C4—42no—
255C4—122no—
256C4#9150412yes—
257C4#9151912yes—
258C3#1060272011yescharacteristic, complemented, Sylow
259C2—242no—
260C2—2401no—
261C2#1174914111yescharacteristic
262C2#1174928212yes—
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5734C2semidirect
2. #11751186C2semidirect
3. #11747037C2semidirect
4. C3×#64766C2semidirect
5. #11745836C2semidirect
22. #64766D3semidirect
40. #5734D5semidirect
209. C3×C5#1624semidirect
246. C5#68491semidirect
258. C3#10602720semidirect

Maximal subgroups

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

subgroupindex
C5×#57342
#117511862
#117470372
C3×#647662
#117458362
#106027203
#684915