Finite Group Databasebeta

← #14289066

Subgroups — #14289066

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
2C3×#65374C211yesmaximal, characteristic, complemented
3#11747033C212yesmaximal, complemented
4#11746367C211yesmaximal, characteristic, complemented
5#11745837C212yesmaximal, complemented
6#10602720—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C5×#947—22no—
9C5×#895—22no—
10C5×#892—22no—
11C4×C5×D12C2212yes—
12C2×C3×#688—22no—
13C3×#4020C2211yescharacteristic
14C2×#6652—22no—
15C4⋊(C3⋊#168)C2212yes—
16C3×C4×#168C2211yescharacteristic
17#90964—22no—
18#71265—51nomaximal, Hall
19C5×#555—31no—
20#65374D311yescharacteristic, complemented
21#65304—32no—
22#64766—31no—
23D4⋊#168—32no—
24C2×C3×C5×Q8D412yes—
25C2×C5×D12—22no—
26C2×C5×D12D412yes—
27C2×C4×C5×D3—22no—
28C2×C3×D20—21no—
29C2×C3×D20—22no—
30C3×C5×C4⋊C4—22no—
31C3×C42×C5C2311yescharacteristic
32C2×C3⋊#168—22no—
33C5×(C2×D3)⋊C4—24no—
34C5×(C2×D3)⋊C4—22no—
35C5×C4⋊Dic3D412yes—
36C4×C5×Dic3—22no—
37C3×#688—44no—
38C2×C3×#168—21no—
39#6652—44no—
40#5734D511yescharacteristic, complemented
41C3×#492—51no—
42#5072—52no—
43#4546—51no—
44#4459—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46C5×#124—62no—
47C5×#121—62no—
48C4×C5×D4—32no—
49C5×#117—62no—
50C2×#688—22no—
51C2×#686—62no—
52#4020C2×D311yescharacteristic
53#3941—62no—
54C4⋊#168—32no—
55C4×#168C2×D311yescharacteristic
56#1624—151noSylow
57C22×C5×D3—22no—
58C22×C3×D5—41no—
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C2×C5×Dic3—22no—
64C5×D12—22no—
65C5×D12—22no—
66C5×D12—82no—
67C4×C5×D3—42no—
68C4×C5×D3—42no—
69C3×D20—42no—
70C3×D20—42no—
71C3×D20—42no—
72C3⋊#168—42no—
73C3×#168—22no—
74C2×C3×SD16—102no—
75C3×C4⋊Q8C2×D511yescharacteristic
76C3×#127—51no—
77#947—22no—
78C2×#213—102no—
79#895—22no—
80#892—22no—
81C4×D12C2×D512yes—
82C3×C4×C8—51no—
83#832—102no—
84C4⋊(C3⋊C8)—52no—
85C2×C5×Q8#6712yes—
86C2×C5×D4—32no—
87C2×C5×D4—62no—
88C22×C4×C5—62no—
89C2×D20—22no—
90C2×D20—21no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—32no—
93C5×C22⋊C4—64no—
94C5×C22⋊C4—62no—
95C42×C5—62no—
96C42×C5C22×D311yescharacteristic
97#688—44no—
98#686—124no—
99C2×#168—21no—
100C2×#168—62no—
101#555—31no—
102#492—51no—
103#459—152no—
104#333—151no—
105D4⋊C8—152no—
106C22×C3×C5#12011yescharacteristic
107C2×C5×D3—42no—
108C2×C5×D3—42no—
109C2×C5×D3—42no—
110C2×C3×D5—82no—
111C2×C3×D5—81no—
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×C3×D4—102no—
119C2×C3×D4—101no—
120C2×D12—22no—
121C2×D12C22⋊D512yes—
122C2×C4×D3—22no—
123C3×SD16—204no—
124C2×C3×C8—101no—
125C3×C4⋊C4—22no—
126C3×C42C22×D511yescharacteristic
127#213—204no—
128(C2×D3)⋊C4—24no—
129(C2×D3)⋊C4—22no—
130C4⋊Dic3C22⋊D512yes—
131C4×Dic3—22no—
132C2×C3⋊C8—102no—
133C23×C5—62no—
134C22×D5—41no—
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×C5D3×D412yes—
144C2×C4×C5C2×#6711yescharacteristic
145D20—42no—
146D20—42no—
147D20—42no—
148#168—22no—
149#168—122no—
150C2×SD16—102no—
151C2×D8—302no—
152C4⋊Q8D3×D511yescharacteristic
153#127—51no—
154#124—62no—
155#121—62no—
156C4×D4—32no—
157#117—62no—
158C4⋊C8—152no—
159#102—302no—
160C4×C8—51no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163C3×D5—161no—
164C5×D3—82no—
165C23×C3—201no—
166C22×D3—22no—
167C3×Q8—42no—
168C3×D4—202no—
169C3×D4—202no—
170C3×D4—202no—
171C2×C3×C4—22no—
172C2×C3×C4C2×C22⋊D511yescharacteristic
173C2×C3×C4C2×C22⋊D512yes—
174C2×Dic3—22no—
175D12—22no—
176D12—22no—
177D12—82no—
178C4×D3—42no—
179C4×D3—42no—
180C3×C8—102no—
181C3⋊C8—202no—
182C22×C5—122no—
183C22×C5—122no—
184C22×C5—122no—
185C22×C5#93711yescharacteristic
186C2×D5—82no—
187C2×D5—81no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5—122no—
191C4×C5#91412yes—
192C4×C5#91612yes—
193C2×Q8#120112yes—
194C2×D4—32no—
195C2×D4—62no—
196C2×D4—101no—
197C2×D4—102no—
198C22×C4—62no—
199SD16—204no—
200D8—604no—
201C2×C8—101no—
202C2×C8—302no—
203C4⋊C4—22no—
204C4⋊C4—32no—
205C22⋊C4—64no—
206C22⋊C4—62no—
207C42—62no—
208C42C2×D3×D511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3—402no—
211C22×C3—401no—
212C22×C3#409911yescharacteristic
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—42no—
216C3×C4—21no—
217C3×C4—42no—
218C3×C4#409512yes—
219C3×C4#409612yes—
220Dic3—42no—
221C2×C5—242no—
222C2×C5#507711yescharacteristic
223C2×C5#517212yes—
224D5—161no—
225C23—62no—
226C23—201no—
227Q8—42no—
228D4—62no—
229D4—62no—
230D4—202no—
231D4—202no—
232D4—202no—
233D4—242no—
234C2×C4—22no—
235C2×C4—62no—
236C2×C4—122no—
237C2×C4—122no—
238C2×C4C2×#120111yescharacteristic
239C2×C4D3×C22⋊D512yes—
240C8—102no—
241C8—602no—
242C2×C3—801no—
243C2×C3#6552712yes—
244C2×C3#6553011yescharacteristic
245D3—82no—
246C5#7126511yescharacteristic, complemented, Sylow
247C22—122no—
248C22—122no—
249C22—122no—
250C22—401no—
251C22—402no—
252C22#9156811yescharacteristic
253C4—21no—
254C4—42no—
255C4—122no—
256C4#9150412yes—
257C4#9151712yes—
258C3#1060272011yescharacteristic, complemented, Sylow
259C2—242no—
260C2—801no—
261C2#1174914011yescharacteristic
262C2#1174928112yes—
subgroupG/H
centerC22#91568
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. C3×#65374C2semidirect
3. #11747033C2semidirect
4. #11746367C2semidirect
5. #11745837C2semidirect
20. #65374D3semidirect
40. #5734D5semidirect
209. C3×C5#1624semidirect
246. C5#71265semidirect
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
C3×#653742
#117470332
#117463672
#117458372
#106027203
#712655