Finite Group Databasebeta

← #11755007

Subgroups — #11755007

Order 960.

540 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#711C211yesmaximal, characteristic
2C22×#1204C211yesmaximal, characteristic, complemented
3#91824C211yesmaximal, characteristic, complemented
4C5×#935C211yesmaximal, characteristic, complemented
5#91574C212yesmaximal, complemented
6#91537C211yesmaximal, characteristic, complemented
7#91536C211yesmaximal, characteristic, complemented
8#91534C212yesmaximal, complemented
9#91528C211yesmaximal, characteristic, complemented
10#91349C212yesmaximal, complemented
11#91327C212yesmaximal, complemented
12#65982—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic
14C22×Dic15C2211yescharacteristic
15C22×C5×Dic3C2211yescharacteristic
16C2×C3×C22⋊D5C2211yescharacteristic
17C2×C3×C22⋊D5C2211yescharacteristic
18C22×C3×Dic5C2211yescharacteristic
19C22×C3×Dic5C2211yescharacteristic
20C3×#711—24no—
21C2×C3×C4×D5C2211yescharacteristic
22C2×C3×Dic10C2211yescharacteristic
23C2×#1204—24no—
24C2×#1204C2212yes—
25C2×#1204C2212yes—
26#6719C2211yescharacteristic
27#6719C2212yes—
28#6712C2212yes—
29C5×#217C2211yescharacteristic
30C5×#217C2212yes—
31C5×Dic3⋊C4C2212yes—
32Dic3⋊Dic5C2212yes—
33#6669C2212yes—
34#6668C2212yes—
35#6665C2212yes—
36#6665C2212yes—
37Dic3×Dic5C2212yes—
38#5825—51nomaximal, Hall
39C2×#711D311yescharacteristic
40C22×Dic10—31no—
41C5×#123—31no—
42#4081—31no—
43#4075—31no—
44#4042—32no—
45#4034—32no—
46#4032—31no—
47#4031—32no—
48#4024—32no—
49#4023—31no—
50C23×C3×C5C2311yescharacteristic
51C23×C3×C5C2311yescharacteristic
52C22×C3×D5C2311yescharacteristic
53C3×C5×D4—22no—
54C2×C3×C4×C5C2311yescharacteristic
55C2×Dic15—22no—
56C2×Dic15C2312yes—
57C2×Dic15C2312yes—
58C2×C5×Dic3—22no—
59C2×C5×Dic3C2312yes—
60C2×C5×Dic3C2312yes—
61C3×C22⋊D5—22no—
62C3×C22⋊D5—22no—
63C2×C3×Dic5—22no—
64C2×C3×Dic5D414yes—
65C2×C3×Dic5C2311yescharacteristic
66C2×C3×Dic5C2311yescharacteristic
67C2×C3×Dic5C2311yescharacteristic
68C3×C4×D5—22no—
69C3×Dic10—22no—
70#1204—24no—
71#1204—24no—
72C2×C3×#41—51no—
73C22×Dic6—51no—
74#944—52no—
75#936—52no—
76#935—51no—
77#935—51no—
78#935—51no—
79#935D511yescharacteristic, complemented
80#926—51no—
81#924—52no—
82#924—52no—
83C2×C5×D4C2×D311yescharacteristic
84C22×C4×C5—31no—
85C2×C22⋊D5C2×D311yescharacteristic
86C2×C22⋊D5C2×D311yescharacteristic
87C22×Dic5—31no—
88C22×Dic5C2×D311yescharacteristic
89C22×Dic5C2×D311yescharacteristic
90#711—24no—
91C2×C4×D5C2×D311yescharacteristic
92C2×Dic10—32no—
93C2×Dic10—32no—
94C2×Dic10—64no—
95C2×Dic10C2×D311yescharacteristic
96C5×C4⋊C4—32no—
97C5×C22⋊C4—31no—
98C5×C22⋊C4—32no—
99C22⋊Dic5—31no—
100C22⋊Dic5—32no—
101#685—32no—
102#685—32no—
103C4⋊Dic5—32no—
104#683—32no—
105#683—32no—
106#683—32no—
107C4×Dic5—32no—
108#536—151noSylow
109C22×C3×C5—22no—
110C22×C3×C5—21no—
111C22×C3×C5—22no—
112C22×C3×C5C2×D412yes—
113C22×C3×C5C2411yescharacteristic
114C2×C3×D5—21no—
115C2×C3×D5—22no—
116C3×C4×C5—21no—
117Dic15—22no—
118Dic15—22no—
119C3×Dic5—21no—
120C3×Dic5C2×D412yes—
121C3×Dic5C2×D412yes—
122C5×Dic3—22no—
123C5×Dic3—22no—
124C3×#41—104no—
125C2×C3×Q8—51no—
126C2×C3×D4—51no—
127C2×C3×D4—51no—
128C2×C3×D4C2×D511yescharacteristic
129C22×C3×C4—51no—
130C22×C3×C4—51no—
131C22×C3×C4—51no—
132C22×Dic3—51no—
133C22×Dic3C2×D511yescharacteristic
134C2×Dic6—52no—
135C2×Dic6—52no—
136C2×Dic6—104no—
137#217—52no—
138#217—51no—
139#217—52no—
140#217—52no—
141#217C2×D512yes—
142#217C2×D511yescharacteristic
143C4⋊Dic3—52no—
144Dic3⋊C4—52no—
145Dic3⋊C4—52no—
146Dic3⋊C4—52no—
147Dic3⋊C4C2×D512yes—
148C4×Dic3—52no—
149C23×C5C22×D311yescharacteristic
150C23×C5C22×D311yescharacteristic
151C22×D5C22×D311yescharacteristic
152C5×D4—22no—
153C2×C4×C5—32no—
154C2×C4×C5—32no—
155C2×C4×C5—62no—
156C2×C4×C5C22×D311yescharacteristic
157C22⋊D5—22no—
158C22⋊D5—22no—
159C2×Dic5—22no—
160C2×Dic5—32no—
161C2×Dic5—32no—
162C2×Dic5—62no—
163C2×Dic5#6714yes—
164C2×Dic5C22×D311yescharacteristic
165C2×Dic5C22×D311yescharacteristic
166C2×Dic5C22×D311yescharacteristic
167C4×D5—22no—
168Dic10—22no—
169Dic10—64no—
170Dic10—64no—
171C2×#41—51no—
172C22×Q8—151no—
173C4⋊Q8—152no—
174#124—152no—
175#123—31no—
176#123—151no—
177#123—151no—
178#123—151no—
179C22⋊Q8—152no—
180C22⋊Q8—152no—
181#117—151no—
182C2×C3×C5—22no—
183C2×C3×C5—41no—
184C2×C3×C5C22×D411yescharacteristic
185C2×C3×C52−1+412yes—
186C3×D5—41no—
187C23×C3—51no—
188C23×C3C22×D511yescharacteristic
189C23×C3C22×D511yescharacteristic
190C3×Q8—102no—
191C3×D4—22no—
192C3×D4—102no—
193C3×D4—102no—
194C2×C3×C4—54no—
195C2×C3×C4—51no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—102no—
199C2×C3×C4—102no—
200C2×C3×C4C22×D511yescharacteristic
201C2×Dic3—22no—
202C2×Dic3—52no—
203C2×Dic3—52no—
204C2×Dic3—102no—
205C2×Dic3C22×D512yes—
206C2×Dic3C22×D512yes—
207Dic6—104no—
208Dic6—104no—
209C22×C5—22no—
210C22×C5—22no—
211C22×C5—21no—
212C22×C5C2×#6712yes—
213C22×C5C23×D311yescharacteristic
214C2×D5—22no—
215C2×D5—21no—
216C4×C5—21no—
217C4×C5—62no—
218C4×C5—62no—
219Dic5—21no—
220Dic5—62no—
221Dic5—62no—
222Dic5C2×#6712yes—
223Dic5C2×#6712yes—
224#41—104no—
225C2×Q8—51no—
226C2×Q8—152no—
227C2×Q8—152no—
228C2×Q8—304no—
229C2×D4—51no—
230C2×D4—51no—
231C2×D4D3×D511yescharacteristic
232C22×C4—31no—
233C22×C4—51no—
234C22×C4—51no—
235C22×C4—51no—
236C22×C4—151no—
237C4⋊C4—32no—
238C4⋊C4—152no—
239C4⋊C4—152no—
240C4⋊C4—152no—
241C4⋊C4—152no—
242C22⋊C4—31no—
243C22⋊C4—32no—
244C22⋊C4—152no—
245C22⋊C4—152no—
246C22⋊C4—151no—
247C22⋊C4—152no—
248C42—152no—
249C3×C5#53611yescharacteristic, complemented, Hall
250C22×C3—22no—
251C22×C3—21no—
252C22×C3—22no—
253C22×C3—101no—
254C22×C3—102no—
255C22×C3D4×D512yes—
256C22×C3C23×D511yescharacteristic
257C3×C4—21no—
258C3×C4—52no—
259C3×C4—52no—
260C3×C4—101no—
261Dic3—22no—
262Dic3—22no—
263Dic3—102no—
264Dic3—102no—
265C2×C5—22no—
266C2×C5—41no—
267C2×C5#101012yes—
268C2×C5C22×#6711yescharacteristic
269D5—41no—
270C23—51no—
271C23C2×D3×D511yescharacteristic
272C23C2×D3×D511yescharacteristic
273Q8—102no—
274Q8—304no—
275Q8—304no—
276D4—22no—
277D4—102no—
278D4—102no—
279C2×C4—32no—
280C2×C4—32no—
281C2×C4—54no—
282C2×C4—51no—
283C2×C4—51no—
284C2×C4—51no—
285C2×C4—62no—
286C2×C4—102no—
287C2×C4—102no—
288C2×C4—152no—
289C2×C4—152no—
290C2×C4—302no—
291C2×C4C2×D3×D511yescharacteristic
292C2×C3—22no—
293C2×C3—41no—
294C2×C3—201no—
295C2×C3C2×D4×D511yescharacteristic
296C2×C3#415012yes—
297C5#582511yescharacteristic, complemented, Sylow
298C22—22no—
299C22—22no—
300C22—21no—
301C22—102no—
302C22—101no—
303C22D5×#6712yes—
304C22C22×D3×D511yescharacteristic
305C4—21no—
306C4—52no—
307C4—52no—
308C4—62no—
309C4—62no—
310C4—101no—
311C4—302no—
312C4—302no—
313C3#6598211yescharacteristic, complemented, Sylow
314C2—22no—
315C2—41no—
316C2—201no—
317C2#9202012yes—
318C2C2×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC2×C3×#711C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×#1204C2semidirect
3. #91824C2semidirect
4. C5×#935C2semidirect
5. #91574C2semidirect
6. #91537C2semidirect
7. #91536C2semidirect
8. #91534C2semidirect
9. #91528C2semidirect
10. #91349C2semidirect
11. #91327C2semidirect
79. #935D5semidirect
249. C3×C5#536semidirect
297. C5#5825semidirect
313. C3#65982semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#7112
C22×#12042
#918242
C5×#9352
#915742
#915372
#915362
#915342
#915282
#913492
#913272
#659823
#58255