Finite Group Databasebeta

← #14301508

Subgroups — #14301508

Order 1920.

648 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C2×C5×#944C211yesmaximal, characteristic
2C3×#66146C211yesmaximal, characteristic
3C2×#91120C211yesmaximal, characteristic
4#11748407C212yesmaximal
5#11745974C212yesmaximal
6#10602577—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×C5×Dic6C2211yescharacteristic
9C2×#6710C2212yes—
10C5×#944—22no—
11C5×#944C414yescomplemented
12C2×C5×Dic3⋊C4—22no—
13C2×C4×C5×Dic3C2211yescharacteristic
14C3×Q8×Dic5—24no—
15C3×#4072—22no—
16C3×#4072C2212yes—
17#91120—22no—
18#90972—24no—
19#71660—51nomaximal, Hall
20C2×C5×C4⋊Q8—31no—
21#66146D311yescharacteristic
22C2×#3968—31no—
23#65514—32no—
24#64743—32no—
25C2×C3×C5×Q8—22no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8C2×C412yes—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5D412yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×C5×Dic3—21no—
32C22×C5×Dic3—21no—
33C2×C5×Dic6—22no—
34C2×C5×Dic6—22no—
35C2×C5×Dic6—21no—
36C2×C5×Dic6C2×C412yes—
37#6710—22no—
38#6710—22no—
39C2×C3⋊#168—22no—
40C5×Dic3⋊C4—28no—
41C4×C5×Dic3—21no—
42C4×C5×Dic3C2×C412yes—
43C3×C22⋊Dic5—22no—
44C3×C4⋊Dic5—24no—
45C3×C4⋊Dic5D414yes—
46C3×C4×Dic5—24no—
47C3×C4×Dic5—22no—
48C3×#519—51no—
49C2×#944D511yescharacteristic
50C2×#836—51no—
51#5004—52no—
52#4532—52no—
53C22×C5×Q8—31no—
54C22×C5×Q8C2×D311yescharacteristic
55C5×C4⋊Q8—34no—
56C5×C4⋊Q8—62no—
57C2×C5×C4⋊C4—62no—
58C2×C42×C5—31no—
59Q8×Dic5—24no—
60#4072—22no—
61#4072C2×D312yes—
62C2×#681—32no—
63#3968—62no—
64#3967—64no—
65#1886—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C3×C5×Q8—24no—
68C3×C5×Q8—24no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5C22⋊C414yes—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5#4112yes—
76C2×C5×Dic3—24no—
77C2×C5×Dic3—22no—
78C2×C5×Dic3—22no—
79C2×C5×Dic3—41no—
80C2×C5×Dic3—41no—
81C5×Dic6—24no—
82C5×Dic6—42no—
83C2×C3×Dic5—24no—
84C3⋊#168—42no—
85C22×C3×Q8C2×D511yescharacteristic
86C22×Dic6C2×D511yescharacteristic
87C3×C4×Q8—104no—
88C3×#117—52no—
89C3×#117—102no—
90#944—22no—
91#944Dic514yescomplemented
92C2×Dic3⋊C4—22no—
93C2×C4×Dic3C2×D511yescharacteristic
94C2×#208—52no—
95#836—102no—
96#810—104no—
97C2×C5×Q8—22no—
98C2×C5×Q8—22no—
99C2×C5×Q8—32no—
100C2×C5×Q8—61no—
101C2×C5×Q8—62no—
102C2×C5×Q8—62no—
103C2×C5×Q8C4×D312yes—
104C2×C5×Q8D1212yes—
105C22×C4×C5—61no—
106C22×C4×C5—61no—
107C22×C4×C5#6712yes—
108C22×C4×C5C22×D311yescharacteristic
109C5×C4⋊C4—68no—
110C42×C5—32no—
111C42×C5—61no—
112C22⋊Dic5—22no—
113C4⋊Dic5—24no—
114C4⋊Dic5#6714yes—
115C4×Dic5—24no—
116C4×Dic5—22no—
117#681—62no—
118#681—62no—
119C2×#168—62no—
120C2×C4⋊Q8—31no—
121#519—51no—
122#419—152no—
123C2×#101—151no—
124#339—152no—
125C22×C3×C5—22no—
126C22×C3×C5C2×C22⋊C411yescharacteristic
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5#12311yescharacteristic
129C3×C4×C5—24no—
130C3×C4×C5C4×D412yes—
131C3×C4×C5#12112yes—
132C3×Dic5—44no—
133C5×Dic3—24no—
134C5×Dic3—42no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8C2×Dic512yes—
138C2×C3×Q8C22⋊D512yes—
139C22×C3×C4C22⋊D512yes—
140C22×C3×C4C22×D511yescharacteristic
141C22×Dic3—21no—
142C22×Dic3—21no—
143C2×Dic6—22no—
144C2×Dic6—22no—
145C2×Dic6—21no—
146C2×Dic6C2×Dic512yes—
147C3×C4⋊C4—54no—
148C3×C4⋊C4—104no—
149C3×C22⋊C4—102no—
150C3×C42—104no—
151C3×C42—102no—
152Dic3⋊C4—28no—
153C4×Dic3—21no—
154C4×Dic3C2×Dic512yes—
155#208—102no—
156#208—102no—
157C2×C3⋊C8—102no—
158C23×C5C2×#6711yescharacteristic
159C5×Q8—24no—
160C5×Q8—24no—
161C5×Q8—64no—
162C5×Q8—122no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—64no—
166C2×C4×C5—62no—
167C2×C4×C5—62no—
168C2×C4×C5—121no—
169C2×C4×C5—121no—
170C2×C4×C5(C2×D3)⋊C414yes—
171C2×C4×C5C2×C4×D311yescharacteristic
172C2×C4×C5C2×D1211yescharacteristic
173C2×C4×C5#23512yes—
174C2×C4×C5C2×#6712yes—
175C2×Dic5—24no—
176#168—122no—
177C22×Q8—31no—
178C22×Q8D3×D511yescharacteristic
179C2×M16—152no—
180C4⋊Q8—34no—
181C4⋊Q8—62no—
182C4×Q8—104no—
183#117—52no—
184#117—102no—
185C2×C4⋊C4—62no—
186C2×C42—31no—
187#103—304no—
188#101—302no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#38611yescharacteristic
192C2×C3×C5#45612yes—
193C23×C3C2×C22⋊D511yescharacteristic
194C3×Q8—24no—
195C3×Q8—24no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—104no—
199C2×C3×C4C22⋊Dic514yes—
200C2×C3×C4D4×D512yes—
201C2×C3×C4#71112yes—
202C2×C3×C4C22×Dic511yescharacteristic
203C2×C3×C4C2×C22⋊D511yescharacteristic
204C2×Dic3—24no—
205C2×Dic3—22no—
206C2×Dic3—22no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209Dic6—24no—
210Dic6—42no—
211C3⋊C8—202no—
212C22×C5—22no—
213C22×C5C2×(C2×D3)⋊C411yescharacteristic
214C22×C5#92911yescharacteristic
215C22×C5#95311yescharacteristic
216C4×C5—24no—
217C4×C5—64no—
218C4×C5—122no—
219C4×C5C4×#6712yes—
220C4×C5#93012yes—
221Dic5—44no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—32no—
225C2×Q8—61no—
226C2×Q8—62no—
227C2×Q8—62no—
228C2×Q8D3×Dic512yes—
229C2×Q8#120312yes—
230C22×C4—61no—
231C22×C4—61no—
232C22×C4#120112yes—
233C22×C4C2×D3×D511yescharacteristic
234M16—302no—
235M16—302no—
236C2×C8—302no—
237C4⋊C4—54no—
238C4⋊C4—68no—
239C4⋊C4—104no—
240C22⋊C4—102no—
241C42—32no—
242C42—61no—
243C42—104no—
244C42—102no—
245C3×C5#188611yescharacteristic, complemented, Hall
246C22×C3—22no—
247C22×C3#408111yescharacteristic
248C22×C3#408311yescharacteristic
249C22×C3C2×C22⋊Dic511yescharacteristic
250C3×C4—24no—
251C3×C4—204no—
252C3×C4D4×Dic512yes—
253C3×C4#408512yes—
254Dic3—24no—
255Dic3—42no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#521311yescharacteristic
259C2×C5#524612yes—
260C23C2×#120111yescharacteristic
261Q8—24no—
262Q8—24no—
263Q8—64no—
264Q8—122no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—64no—
268C2×C4—62no—
269C2×C4—62no—
270C2×C4—104no—
271C2×C4—121no—
272C2×C4—121no—
273C2×C4(C2×D3)⋊Dic514yes—
274C2×C4C2×D3×Dic511yescharacteristic
275C2×C4#678212yes—
276C2×C4C2×#120311yescharacteristic
277C2×C4D5×#6712yes—
278C8—602no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3#6538412yes—
282C2×C3#6550911yescharacteristic
283C5#7166011yescharacteristic, complemented, Sylow
284C22—22no—
285C22C2×(C2×D3)⋊Dic511yescharacteristic
286C22#9153911yescharacteristic
287C22#9156311yescharacteristic
288C4—24no—
289C4—64no—
290C4—122no—
291C4—204no—
292C4Dic5×#6712yes—
293C4#9156612yes—
294C3#1060257711yescharacteristic, complemented, Sylow
295C2—21no—
296C2—21no—
297C2#1174939012yes—
298C2#1174949211yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1886
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
11. C5×#944C4semidirect
91. #944Dic5semidirect
245. C3×C5#1886semidirect
283. C5#71660semidirect
294. C3#10602577semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9442
C3×#661462
C2×#911202
#117484072
#117459742
#106025773
#716605