Finite Group Databasebeta

← #14308962

Subgroups — #14308962

Order 1920.

492 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 116 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#11756259C211yesmaximal, characteristic
2C5×#4973C211yesmaximal, characteristic
3#11748409C212yesmaximal
4C3×#64750C211yesmaximal, characteristic
5#11745976C212yesmaximal
6#10600466—31nomaximal, Hall
7C22×C5×Dic6C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9#91815C2212yes—
10#91813—22no—
11#91779—22no—
12#91777—22no—
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×#681C2212yes—
15C5×C3⋊#95—22no—
16#90973—22no—
17#90973—22no—
18#68998—51nomaximal, Hall
19#65834—31no—
20C5×#391—31no—
21#65514—32no—
22#64750D311yescharacteristic
23#64743—32no—
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C2×Dic30—22no—
27C22×C5×Dic3—21no—
28C22×C5×Dic3—21no—
29C2×C5×Dic6—22no—
30C2×C5×Dic6—22no—
31C2×C5×Dic6—21no—
32C2×C5×Dic6Q812yescomplemented
33C3×C5×C4⋊C4—22no—
34#6719—22no—
35C4⋊Dic15—22no—
36C4⋊Dic15D412yes—
37C4⋊Dic15D412yes—
38#6712—24no—
39C4×Dic15—22no—
40C4×C5×Dic3—22no—
41C3×#681—22no—
42C3×#681—22no—
43C2×C3×#168—22no—
44#5500—51no—
45#5120—52no—
46#4973D511yescharacteristic
47C3×#343—51no—
48#4555—52no—
49C22×C5×Q8—31no—
50C2×C5×C4⋊C4C2×D311yescharacteristic
51C2×C42×C5—31no—
52#4072—32no—
53#4070—62no—
54C2×#681C2×D312yes—
55#4036—62no—
56#4034—62no—
57C5×#95—62no—
58#3967—62no—
59#3967—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—
70Dic30—82no—
71C2×C5×Dic3—22no—
72C2×C5×Dic3—22no—
73C2×C5×Dic3—41no—
74C2×C5×Dic3—41no—
75C2×C5×Dic3—41no—
76C2×C5×Dic3—41no—
77C5×Dic6—24no—
78C5×Dic6—42no—
79C3×#168—42no—
80C22×Dic6C2×D511yescharacteristic
81C2×C3×M16—52no—
82C2×C3×C4⋊C4C2×D511yescharacteristic
83#926—52no—
84#924—102no—
85C2×C4×Dic3C2×D511yescharacteristic
86#890—102no—
87#888—102no—
88C3⋊#95—22no—
89#816—102no—
90#816—102no—
91C2×C5×Q8—32no—
92C2×C5×Q8—61no—
93C2×C5×Q8—62no—
94C2×C5×Q8—62no—
95C22×C4×C5—61no—
96C22×C4×C5—61no—
97C22×C4×C5D1212yes—
98C22×C4×C5C22×D311yescharacteristic
99C2×Dic10—62no—
100C5×C4⋊C4—22no—
101C42×C5—62no—
102C22⋊Dic5—62no—
103C4⋊Dic5—32no—
104C4⋊Dic5—32no—
105C4⋊Dic5—62no—
106#683—64no—
107C4×Dic5—62no—
108#681—22no—
109#681—22no—
110C2×#168—22no—
111#544—151no—
112#419—152no—
113#391—31no—
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—21no—
131C22×Dic3—21no—
132C2×Dic6—22no—
133C2×Dic6—22no—
134C2×Dic6—21no—
135C2×Dic6—102no—
136C2×Dic6Dic1012yescomplemented
137C3×M16—102no—
138C3×M16—102no—
139C2×C3×C8—102no—
140C3×C4⋊C4—22no—
141#217—102no—
142C4⋊Dic3—52no—
143C4⋊Dic3—52no—
144C4⋊Dic3—102no—
145Dic3⋊C4—104no—
146C4×Dic3—22no—
147C4×Dic3—102no—
148C23×C5C2×D1211yescharacteristic
149C5×Q8—64no—
150C5×Q8—122no—
151C2×C4×C5—22no—
152C2×C4×C5—42no—
153C2×C4×C5—62no—
154C2×C4×C5—62no—
155C2×C4×C5—121no—
156C2×C4×C5—121no—
157C2×C4×C5—121no—
158C2×C4×C5—121no—
159C2×C4×C5#23512yes—
160C2×C4×C5D3×D412yes—
161C2×C4×C5#23711yescharacteristic
162C2×C4×C5D3×Q811yescharacteristic
163C2×Dic5—62no—
164C2×Dic5—62no—
165Dic10—242no—
166#168—42no—
167C22×Q8—31no—
168C2×M16—52no—
169C4⋊Q8—302no—
170#125—302no—
171C22⋊Q8—302no—
172#117—152no—
173C2×C4⋊C4D3×D511yescharacteristic
174C2×C42—31no—
175#103—302no—
176#103—302no—
177#95—62no—
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×C4C2×Dic1011yescharacteristic
187C2×C3×C4#70911yescharacteristic
188C2×C3×C4D4×D512yes—
189C2×C3×C4#71112yes—
190C2×Dic3—22no—
191C2×Dic3—22no—
192C2×Dic3—41no—
193C2×Dic3—41no—
194C2×Dic3—41no—
195C2×Dic3—41no—
196C2×Dic3—102no—
197C2×Dic3—102no—
198Dic6—24no—
199Dic6—42no—
200Dic6—402no—
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—32no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8—62no—
218C2×Q8—302no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4#120312yes—
222C22×C4C2×D3×D511yescharacteristic
223M16—102no—
224M16—102no—
225C2×C8—102no—
226C4⋊C4—22no—
227C4⋊C4—152no—
228C4⋊C4—152no—
229C4⋊C4—302no—
230C4⋊C4—304no—
231C22⋊C4—302no—
232C42—62no—
233C42—302no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#407011yescharacteristic
238C22×C3#408211yescharacteristic
239C22×C3#408311yescharacteristic
240C3×C4—42no—
241C3×C4#402412yes—
242C3×C4#403112yes—
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—64no—
254Q8—122no—
255Q8—1202no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—62no—
259C2×C4—62no—
260C2×C4—121no—
261C2×C4—121no—
262C2×C4—121no—
263C2×C4—121no—
264C2×C4—302no—
265C2×C4—302no—
266C2×C4#676511yescharacteristic
267C2×C4D3×Dic1011yescharacteristic
268C2×C4#677212yes—
269C2×C4#679012yes—
270C8—202no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6523611yescharacteristic
274C2×C3#6535011yescharacteristic
275C2×C3#6538411yescharacteristic
276C5#6899811yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9136511yescharacteristic
280C22#9137311yescharacteristic
281C22#9157311yescharacteristic
282C4—42no—
283C4—122no—
284C4—122no—
285C4—602no—
286C4—602no—
287C4#9143212yes—
288C4#9146212yes—
289C3#1060046611yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1174879511yescharacteristic
293C2#1174915011yescharacteristic
294C2#1174939611yescharacteristic
subgroupG/H
centerC22#91573
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
32. C2×C5×Dic6Q8semidirect
136. C2×Dic6Dic10semidirect
234. C3×C5#2028semidirect
276. C5#68998semidirect
289. C3#10600466semidirect

Maximal subgroups

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

subgroupindex
#117562592
C5×#49732
#117484092
C3×#647502
#117459762
#106004663
#689985