Finite Group Databasebeta

← #14308960

Subgroups — #14308960

Order 1920.

492 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 118 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×#5500C211yesmaximal, characteristic
2#11751074C211yesmaximal, characteristic
3#11748417C212yesmaximal
4C3×#64750C211yesmaximal, characteristic
5#11745975C212yesmaximal
6#10602698—31nomaximal, Hall
7C22×Dic30C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C4×Dic15C2211yescharacteristic
10C5×#926C2212yes—
11C5×#924—22no—
12C5×#890—22no—
13C5×#888—22no—
14C2×C3×#681C2212yes—
15#91115—22no—
16#90975—22no—
17#90975—22no—
18#68998—51nomaximal, Hall
19C5×#544—31no—
20#65293—32no—
21#65263—31no—
22#64752—32no—
23#64750D311yescharacteristic
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C22×Dic15—21no—
27C22×Dic15—21no—
28C2×Dic30—22no—
29C2×Dic30—22no—
30C2×Dic30—21no—
31C2×Dic30Q812yescomplemented
32C2×C5×Dic6—22no—
33C3×C5×C4⋊C4—22no—
34C4×Dic15—22no—
35C5×#217—22no—
36C5×C4⋊Dic3—22no—
37C5×C4⋊Dic3D412yes—
38C5×C4⋊Dic3D412yes—
39C5×Dic3⋊C4—24no—
40C4×C5×Dic3—22no—
41C3×#681—22no—
42C3×#681—22no—
43C2×C3×#168—22no—
44#5500D511yescharacteristic
45#5120—52no—
46#4973—51no—
47C3×#343—51no—
48#4555—52no—
49C22×Dic10—31no—
50C5×C4⋊Q8—62no—
51C5×#125—62no—
52C5×C22⋊Q8—62no—
53C5×#117—32no—
54C2×C5×C4⋊C4C2×D311yescharacteristic
55C2×C4×Dic5—31no—
56C2×#681C2×D312yes—
57#3963—62no—
58#3942—62no—
59#3942—62no—
60#2028—151noSylow
61C23×C3×C5C2×D411yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5C2×Q811yescharacteristic
66C2×C3×C4×C5#4112yes—
67C2×C3×C4×C5#4111yescharacteristic
68C2×Dic15—22no—
69C2×Dic15—22no—
70C2×Dic15—41no—
71C2×Dic15—41no—
72C2×Dic15—41no—
73C2×Dic15—41no—
74Dic30—24no—
75Dic30—42no—
76C2×C5×Dic3—22no—
77C2×C5×Dic3—22no—
78C5×Dic6—82no—
79C3×#168—42no—
80C22×Dic6—51no—
81C2×C3×M16—52no—
82C2×C3×C4⋊C4C2×D511yescharacteristic
83#926C2×D512yes—
84#924—22no—
85C2×C4×Dic3—51no—
86#890—22no—
87#888—22no—
88C3⋊#95—102no—
89#816—102no—
90#816—102no—
91C2×C5×Q8—62no—
92C22×C4×C5D1212yes—
93C22×C4×C5C22×D311yescharacteristic
94C22×Dic5—61no—
95C22×Dic5—61no—
96C2×Dic10—32no—
97C2×Dic10—62no—
98C2×Dic10—62no—
99C2×Dic10—61no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—32no—
102C5×C4⋊C4—32no—
103C5×C4⋊C4—62no—
104C5×C4⋊C4—64no—
105C5×C22⋊C4—62no—
106C42×C5—62no—
107C4×Dic5—62no—
108#681—22no—
109#681—22no—
110C2×#168—22no—
111#544—31no—
112#419—152no—
113#391—151no—
114#343—51no—
115#339—152no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5#12011yescharacteristic
119C22×C3×C5C22⋊Q811yescharacteristic
120C22×C3×C5#12411yescharacteristic
121C3×C4×C5—42no—
122C3×C4×C5C22⋊Q812yes—
123C3×C4×C5#12412yes—
124Dic15—42no—
125Dic15—42no—
126C5×Dic3—42no—
127C5×Dic3—42no—
128C22×C3×C4C22⋊D512yes—
129C22×C3×C4C22×D511yescharacteristic
130C22×Dic3—101no—
131C22×Dic3—101no—
132C2×Dic6—22no—
133C2×Dic6—52no—
134C2×Dic6—102no—
135C2×Dic6—102no—
136C2×Dic6—101no—
137C3×M16—102no—
138C3×M16—102no—
139C2×C3×C8—102no—
140C3×C4⋊C4—22no—
141#217—22no—
142C4⋊Dic3—22no—
143C4⋊Dic3C22⋊D512yes—
144C4⋊Dic3C22⋊D512yes—
145Dic3⋊C4—24no—
146C4×Dic3—22no—
147C4×Dic3—102no—
148C23×C5C2×D1211yescharacteristic
149C5×Q8—242no—
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5—62no—
153C2×C4×C5—62no—
154C2×C4×C5#23512yes—
155C2×C4×C5D3×D412yes—
156C2×C4×C5#23711yescharacteristic
157C2×C4×C5D3×Q811yescharacteristic
158C2×Dic5—62no—
159C2×Dic5—62no—
160C2×Dic5—121no—
161C2×Dic5—121no—
162C2×Dic5—121no—
163C2×Dic5—121no—
164Dic10—64no—
165Dic10—122no—
166#168—42no—
167C22×Q8—151no—
168C2×M16—52no—
169C4⋊Q8—62no—
170#125—62no—
171C22⋊Q8—62no—
172#117—32no—
173C2×C4⋊C4D3×D511yescharacteristic
174C2×C42—151no—
175#103—302no—
176#103—302no—
177#95—302no—
178C2×C3×C5—21no—
179C2×C3×C5—21no—
180C2×C3×C5#39311yescharacteristic
181C2×C3×C5#45511yescharacteristic
182C2×C3×C5#45611yescharacteristic
183C23×C3C2×C22⋊D511yescharacteristic
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4Q8×D511yescharacteristic
187C2×C3×C4#71311yescharacteristic
188C2×C3×C4#71312yes—
189C2×C3×C4C2×C22⋊D512yes—
190C2×Dic3—22no—
191C2×Dic3—22no—
192C2×Dic3—102no—
193C2×Dic3—102no—
194C2×Dic3—201no—
195C2×Dic3—201no—
196C2×Dic3—201no—
197C2×Dic3—201no—
198Dic6—82no—
199Dic6—104no—
200Dic6—202no—
201C3×C8—202no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#87511yescharacteristic
205C22×C5#88211yescharacteristic
206C22×C5#89711yescharacteristic
207C4×C5—42no—
208C4×C5—122no—
209C4×C5—122no—
210C4×C5#88512yes—
211C4×C5#89612yes—
212Dic5—122no—
213Dic5—122no—
214C2×Q8—62no—
215C2×Q8—152no—
216C2×Q8—301no—
217C2×Q8—302no—
218C2×Q8—302no—
219C22×C4—301no—
220C22×C4—301no—
221C22×C4#120312yes—
222C22×C4C2×D3×D511yescharacteristic
223M16—102no—
224M16—102no—
225C2×C8—102no—
226C4⋊C4—22no—
227C4⋊C4—32no—
228C4⋊C4—32no—
229C4⋊C4—62no—
230C4⋊C4—64no—
231C22⋊C4—62no—
232C42—62no—
233C42—302no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#409211yescharacteristic
238C22×C3#409311yescharacteristic
239C22×C3#409911yescharacteristic
240C3×C4—42no—
241C3×C4#409212yes—
242C3×C4#409312yes—
243Dic3—42no—
244Dic3—42no—
245Dic3—202no—
246Dic3—202no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#467311yescharacteristic
250C2×C5#474611yescharacteristic
251C2×C5#475211yescharacteristic
252C23C2×#120311yescharacteristic
253Q8—242no—
254Q8—304no—
255Q8—602no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—62no—
259C2×C4—62no—
260C2×C4—302no—
261C2×C4—302no—
262C2×C4—601no—
263C2×C4—601no—
264C2×C4—601no—
265C2×C4—601no—
266C2×C4#676611yescharacteristic
267C2×C4D15⋊Q811yescharacteristic
268C2×C4#677312yes—
269C2×C4D3×C22⋊D512yes—
270C8—202no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6552011yescharacteristic
274C2×C3#6553111yescharacteristic
275C2×C3#6553511yescharacteristic
276C5#6899811yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9137511yescharacteristic
280C22#9138311yescharacteristic
281C22#9157011yescharacteristic
282C4—42no—
283C4—122no—
284C4—122no—
285C4—602no—
286C4—602no—
287C4#9142412yes—
288C4#9145512yes—
289C3#1060269811yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1174878411yescharacteristic
293C2#1174914811yescharacteristic
294C2#1174939411yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. C2×Dic30Q8semidirect
234. C3×C5#2028semidirect
276. C5#68998semidirect
289. C3#10602698semidirect

Maximal subgroups

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

subgroupindex
C5×#55002
#117510742
#117484172
C3×#647502
#117459752
#106026983
#689985