Finite Group Databasebeta

← #14301504

Subgroups — #14301504

Order 1920.

648 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 160 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
1#11756571C211yesmaximal, characteristic
2C2×C3×#4090C211yesmaximal, characteristic
3C2×C5×#836C211yesmaximal, characteristic
4#11748400C212yesmaximal
5#11745978C212yesmaximal
6#10600896—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×C3×Dic10C2211yescharacteristic
9Q8×Dic15—24no—
10#91815—22no—
11#91815C2212yes—
12C2×C5×#208C2212yes—
13C3×#4090—22no—
14C3×#4090C414yescomplemented
15C2×C3×#683—22no—
16C2×C3×C4×Dic5C2211yescharacteristic
17C5×#836—22no—
18#90971—24no—
19#71784—51nomaximal, Hall
20#66146—31no—
21C2×#4090D311yescharacteristic
22C2×C5×#101—31no—
23#65409—32no—
24#64775—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×C3×Dic5—21no—
32C22×C3×Dic5—21no—
33C2×C3×Dic10—22no—
34C2×C3×Dic10—22no—
35C2×C3×Dic10—21no—
36C2×C3×Dic10C2×C412yes—
37#6719—22no—
38C4⋊Dic15—24no—
39C4⋊Dic15D414yes—
40C4×Dic15—24no—
41C4×Dic15—22no—
42C5×#208—22no—
43C5×#208—22no—
44C2×C5×C3⋊C8—22no—
45C3×#683—28no—
46C3×C4×Dic5—21no—
47C3×C4×Dic5C2×C412yes—
48C2×C3×C4⋊Q8—51no—
49#5812—51no—
50C2×#836D511yescharacteristic
51#5225—52no—
52#4523—52no—
53C22×C5×Q8C2×D311yescharacteristic
54C22×Dic10C2×D311yescharacteristic
55C2×C5×M16—32no—
56Q8×Dic5—64no—
57#4090—22no—
58#4090Dic314yescomplemented
59#4072—32no—
60#4072—62no—
61C2×#683—22no—
62C2×C4×Dic5C2×D311yescharacteristic
63C5×#101—62no—
64#3948—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×Dic15—24no—
77C2×C3×Dic5—24no—
78C2×C3×Dic5—22no—
79C2×C3×Dic5—22no—
80C2×C3×Dic5—41no—
81C2×C3×Dic5—41no—
82C3×Dic10—24no—
83C3×Dic10—42no—
84C5×C3⋊C8—42no—
85C22×C3×Q8—51no—
86C22×C3×Q8C2×D511yescharacteristic
87C3×C4⋊Q8—54no—
88C3×C4⋊Q8—102no—
89C2×C3×C4⋊C4—102no—
90C2×C3×C42—51no—
91Q8×Dic3—104no—
92#926—52no—
93#926—102no—
94C2×#208C2×D512yes—
95#836—22no—
96#835—104no—
97C2×C5×Q8—22no—
98C2×C5×Q8—22no—
99C2×C5×Q8C2×Dic312yes—
100C2×C5×Q8#6712yes—
101C22×C4×C5#6712yes—
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—21no—
104C22×Dic5—21no—
105C2×Dic10—22no—
106C2×Dic10—22no—
107C2×Dic10—21no—
108C2×Dic10C2×Dic312yes—
109C5×M16—62no—
110C5×M16—62no—
111C2×C5×C8—62no—
112C22⋊Dic5—62no—
113C4⋊Dic5—34no—
114C4⋊Dic5—64no—
115#683—28no—
116C4×Dic5—21no—
117C4×Dic5—64no—
118C4×Dic5—62no—
119C4×Dic5C2×Dic312yes—
120C2×C4⋊Q8—51no—
121#519—151no—
122#419—152no—
123C2×#101—31no—
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—
132Dic15—44no—
133C3×Dic5—24no—
134C3×Dic5—42no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8—52no—
138C2×C3×Q8—101no—
139C2×C3×Q8—102no—
140C2×C3×Q8—102no—
141C2×C3×Q8C4×D512yes—
142C2×C3×Q8C22⋊D512yes—
143C22×C3×C4—101no—
144C22×C3×C4—101no—
145C22×C3×C4D2012yes—
146C22×C3×C4C22×D511yescharacteristic
147C3×C4⋊C4—108no—
148C3×C42—52no—
149C3×C42—101no—
150#217—102no—
151C4⋊Dic3—54no—
152C4⋊Dic3—104no—
153C4×Dic3—104no—
154C4×Dic3—102no—
155#208—22no—
156#208—22no—
157C2×C3⋊C8—22no—
158C23×C5C2×#6711yescharacteristic
159C5×Q8—24no—
160C5×Q8—24no—
161C2×C4×C5—22no—
162C2×C4×C5—22no—
163C2×C4×C5#21714yes—
164C2×C4×C5D3×D412yes—
165C2×C4×C5#23712yes—
166C2×C4×C5C22×Dic311yescharacteristic
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5—24no—
169C2×Dic5—22no—
170C2×Dic5—22no—
171C2×Dic5—41no—
172C2×Dic5—41no—
173C2×Dic5—64no—
174Dic10—24no—
175Dic10—42no—
176C5×C8—122no—
177C22×Q8—51no—
178C22×Q8D3×D511yescharacteristic
179C2×M16—32no—
180C4⋊Q8—54no—
181C4⋊Q8—102no—
182C4×Q8—304no—
183#117—152no—
184#117—302no—
185C2×C4⋊C4—102no—
186C2×C42—51no—
187#103—304no—
188#101—62no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#38611yescharacteristic
192C2×C3×C5#45612yes—
193C23×C3C2×D2011yescharacteristic
194C3×Q8—24no—
195C3×Q8—24no—
196C3×Q8—104no—
197C3×Q8—202no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—104no—
201C2×C3×C4—102no—
202C2×C3×C4—102no—
203C2×C3×C4—201no—
204C2×C3×C4—201no—
205C2×C3×C4#68514yes—
206C2×C3×C4C2×C4×D511yescharacteristic
207C2×C3×C4D4×D512yes—
208C2×C3×C4#71112yes—
209C2×C3×C4C2×C22⋊D511yescharacteristic
210C2×Dic3—104no—
211C3⋊C8—42no—
212C22×C5—22no—
213C22×C5#93511yescharacteristic
214C22×C5#93711yescharacteristic
215C22×C5C2×#21711yescharacteristic
216C4×C5—24no—
217C4×C5D4×Dic312yes—
218C4×C5#93912yes—
219Dic5—24no—
220Dic5—42no—
221Dic5—124no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—52no—
225C2×Q8—101no—
226C2×Q8—102no—
227C2×Q8—102no—
228C2×Q8D5×Dic312yes—
229C2×Q8#120112yes—
230C22×C4—101no—
231C22×C4—101no—
232C22×C4#120212yes—
233C22×C4C2×D3×D511yescharacteristic
234M16—62no—
235M16—62no—
236C2×C8—62no—
237C4⋊C4—108no—
238C4⋊C4—154no—
239C4⋊C4—304no—
240C22⋊C4—302no—
241C42—52no—
242C42—101no—
243C42—304no—
244C42—302no—
245C3×C5#188611yescharacteristic, complemented, Hall
246C22×C3—22no—
247C22×C3#402811yescharacteristic
248C22×C3#403211yescharacteristic
249C22×C3C2×#68511yescharacteristic
250C3×C4—24no—
251C3×C4—104no—
252C3×C4—202no—
253C3×C4#402712yes—
254C3×C4#408512yes—
255Dic3—204no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#509512yes—
259C2×C5#522011yescharacteristic
260C23C2×#120211yescharacteristic
261Q8—24no—
262Q8—24no—
263Q8—104no—
264Q8—202no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—104no—
268C2×C4—102no—
269C2×C4—102no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4—304no—
273C2×C4#666514yes—
274C2×C4C2×D5×Dic311yescharacteristic
275C2×C4#678012yes—
276C2×C4C2×#120111yescharacteristic
277C2×C4#679012yes—
278C8—122no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3#6504112yes—
282C2×C3#6524711yescharacteristic
283C5#7178411yescharacteristic, complemented, Sylow
284C22—22no—
285C22C2×#666511yescharacteristic
286C22#9153711yescharacteristic
287C22#9157211yescharacteristic
288C4—24no—
289C4—104no—
290C4—202no—
291C4—604no—
292C4#9155912yes—
293C4#9157112yes—
294C3#1060089611yescharacteristic, complemented, Sylow
295C2—21no—
296C2—21no—
297C2#1174939512yes—
298C2#1174950011yescharacteristic
subgroupG/H
centerC22#91572
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
14. C3×#4090C4semidirect
58. #4090Dic3semidirect
245. C3×C5#1886semidirect
283. C5#71784semidirect
294. C3#10600896semidirect

Maximal subgroups

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

subgroupindex
#117565712
C2×C3×#40902
C2×C5×#8362
#117484002
#117459782
#106008963
#717845