Finite Group Databasebeta

← #11754303

Subgroups — #11754303

Order 960.

540 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#709C211yesmaximal, characteristic
2C2×D5×Dic6C211yesmaximal, characteristic, complemented
3#91813C211yesmaximal, characteristic, complemented
4C5×#924C211yesmaximal, characteristic, complemented
5#91548C212yesmaximal, complemented
6#91534C212yesmaximal, complemented
7#91407C212yesmaximal, complemented
8#91360C211yesmaximal, characteristic, complemented
9#91359C211yesmaximal, characteristic, complemented
10#91358C211yesmaximal, characteristic, complemented
11#91327C212yesmaximal, complemented
12#65962—31nomaximal, Hall
13C22×C3×C4×C5C2211yescharacteristic
14C2×Dic30C2211yescharacteristic
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×C22⋊D5C2211yescharacteristic
17C2×C3×C22⋊D5C2211yescharacteristic
18C3×#709—24no—
19C2×C3×D20C2211yescharacteristic
20C2×C3×C4×D5C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×C3×Dic10C2211yescharacteristic
23C2×#1204C2212yes—
24C2×D5×Dic3C2212yes—
25D5×Dic6—24no—
26#6719C2212yes—
27C4⋊Dic15C2211yescharacteristic
28#6712C2212yes—
29C5×#217C2212yes—
30C5×C4⋊Dic3C2211yescharacteristic
31C5×Dic3⋊C4C2212yes—
32Dic3⋊Dic5C2212yes—
33#6669C2212yes—
34#6665C2212yes—
35#6665C2212yes—
36#6665C2212yes—
37Dic3×Dic5C2212yes—
38#5825—51nomaximal, Hall
39C2×Q8×D5—31no—
40C2×#709D311yescharacteristic
41C5×C22⋊Q8—31no—
42#4092—31no—
43#4070—31no—
44#4043—31no—
45#4040—32no—
46#4038—31no—
47#4034—32no—
48#4031—32no—
49#4029—32no—
50C23×C3×C5C2311yescharacteristic
51C22×C3×D5C2311yescharacteristic
52C22×C3×D5C2311yescharacteristic
53C2×C3×C4×C5—22no—
54C2×C3×C4×C5C2311yescharacteristic
55C2×C3×C4×C5C2311yescharacteristic
56C2×Dic15C2312yes—
57C2×Dic15C2312yes—
58Dic30—22no—
59C2×C5×Dic3C2312yes—
60C2×C5×Dic3C2312yes—
61C5×Dic6—22no—
62C3×C22⋊D5—22no—
63C3×C22⋊D5—22no—
64C2×C3×Dic5C2311yescharacteristic
65C2×C3×Dic5C2311yescharacteristic
66C3×D20—22no—
67C3×C4×D5—22no—
68C3×C4×D5D414yes—
69C3×Dic10—22no—
70#1204—24no—
71D5×Dic3—24no—
72C2×C3×#41—51no—
73C22×Dic6—51no—
74#944—52no—
75#936—52no—
76#935—52no—
77#935—52no—
78#926—51no—
79#924—51no—
80#924—51no—
81#924—51no—
82#924D511yescharacteristic, complemented
83C2×C5×Q8—31no—
84C22×C4×C5C2×D311yescharacteristic
85C2×C22⋊D5C2×D311yescharacteristic
86C2×C22⋊D5C2×D311yescharacteristic
87Q8×D5—64no—
88#709—24no—
89C2×D20C2×D311yescharacteristic
90C2×C4×D5—32no—
91C2×C4×D5C2×D311yescharacteristic
92C2×C4×D5C2×D311yescharacteristic
93C2×Dic10—31no—
94C2×Dic10—32no—
95C2×Dic10C2×D311yescharacteristic
96C5×C4⋊C4—32no—
97C5×C4⋊C4—31no—
98C5×C22⋊C4—32no—
99C22⋊Dic5—32no—
100#685—32no—
101#685—32no—
102#685—32no—
103C4⋊Dic5—31no—
104C4⋊Dic5—32no—
105#683—32no—
106#683—32no—
107C4×Dic5—32no—
108#536—151noSylow
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5—21no—
112C22×C3×C5C2411yescharacteristic
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5—21no—
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5C2×D412yes—
119C3×C4×C5—21no—
120C3×C4×C5C2×D412yes—
121Dic15—22no—
122Dic15—22no—
123C3×Dic5—21no—
124C3×Dic5C2×D412yes—
125C5×Dic3—22no—
126C5×Dic3—22no—
127C3×#41—104no—
128C2×C3×Q8—51no—
129C2×C3×D4—51no—
130C2×C3×D4—51no—
131C2×C3×D4—51no—
132C22×C3×C4—51no—
133C22×C3×C4—51no—
134C22×C3×C4C2×D511yescharacteristic
135C22×Dic3—52no—
136C2×Dic6—51no—
137C2×Dic6—52no—
138C2×Dic6—104no—
139C2×Dic6C2×D511yescharacteristic
140#217—52no—
141#217—52no—
142#217—52no—
143#217—52no—
144#217C2×D512yes—
145C4⋊Dic3—51no—
146C4⋊Dic3C2×D511yescharacteristic
147Dic3⋊C4—52no—
148Dic3⋊C4—52no—
149Dic3⋊C4—52no—
150Dic3⋊C4C2×D512yes—
151C4×Dic3—52no—
152C23×C5C22×D311yescharacteristic
153C22×D5C22×D311yescharacteristic
154C22×D5C22×D311yescharacteristic
155C5×Q8—62no—
156C2×C4×C5—22no—
157C2×C4×C5—32no—
158C2×C4×C5—32no—
159C2×C4×C5C22×D311yescharacteristic
160C2×C4×C5C22×D311yescharacteristic
161C22⋊D5—22no—
162C22⋊D5—22no—
163C2×Dic5—32no—
164C2×Dic5—32no—
165C2×Dic5C22×D311yescharacteristic
166C2×Dic5C22×D311yescharacteristic
167D20—22no—
168C4×D5—22no—
169C4×D5—64no—
170C4×D5#6714yes—
171Dic10—22no—
172Dic10—62no—
173Dic10—64no—
174C2×#41—51no—
175C22×Q8—151no—
176C4⋊Q8—152no—
177#124—152no—
178#123—152no—
179#123—152no—
180C22⋊Q8—31no—
181C22⋊Q8—151no—
182C22⋊Q8—151no—
183C22⋊Q8—151no—
184#117—151no—
185C2×C3×C5—41no—
186C2×C3×C5C22×D411yescharacteristic
187C2×C3×C52−1+411yescharacteristic
188C2×C3×C52−1+411yescharacteristic
189C3×D5—22no—
190C3×D5—41no—
191C23×C3—51no—
192C23×C3—51no—
193C23×C3C22×D511yescharacteristic
194C3×Q8—102no—
195C3×D4—102no—
196C3×D4—102no—
197C3×D4—102no—
198C2×C3×C4—22no—
199C2×C3×C4—51no—
200C2×C3×C4—54no—
201C2×C3×C4—51no—
202C2×C3×C4—102no—
203C2×C3×C4C22×D511yescharacteristic
204C2×C3×C4C22×D511yescharacteristic
205C2×Dic3—52no—
206C2×Dic3—52no—
207C2×Dic3—104no—
208C2×Dic3C22×D512yes—
209C2×Dic3C22×D512yes—
210Dic6—22no—
211Dic6—104no—
212Dic6—102no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5C23×D311yescharacteristic
217C2×D5—21no—
218C2×D5—21no—
219C2×D5—21no—
220C2×D5—21no—
221C2×D5—21no—
222C2×D5C2×#6712yes—
223C4×C5—21no—
224C4×C5—62no—
225C4×C5—62no—
226C4×C5C2×#6712yes—
227Dic5—21no—
228Dic5—62no—
229Dic5—62no—
230Dic5C2×#6712yes—
231#41—104no—
232C2×Q8—31no—
233C2×Q8—51no—
234C2×Q8—152no—
235C2×Q8—151no—
236C2×Q8—304no—
237C2×D4—51no—
238C2×D4—51no—
239C2×D4—51no—
240C22×C4—51no—
241C22×C4—51no—
242C22×C4—152no—
243C22×C4D3×D511yescharacteristic
244C4⋊C4—31no—
245C4⋊C4—32no—
246C4⋊C4—152no—
247C4⋊C4—152no—
248C4⋊C4—151no—
249C4⋊C4—152no—
250C22⋊C4—32no—
251C22⋊C4—152no—
252C22⋊C4—152no—
253C22⋊C4—152no—
254C22⋊C4—152no—
255C42—152no—
256C3×C5#53611yescharacteristic, complemented, Hall
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—52no—
261C22×C3—101no—
262C22×C3—101no—
263C22×C3—101no—
264C22×C3—101no—
265C22×C3—101no—
266C22×C3C23×D511yescharacteristic
267C3×C4—21no—
268C3×C4—52no—
269C3×C4—101no—
270C3×C4D4×D512yes—
271Dic3—22no—
272Dic3—22no—
273Dic3—102no—
274Dic3—102no—
275C2×C5—41no—
276C2×C5#101011yescharacteristic
277C2×C5#101011yescharacteristic
278C2×C5C22×#6711yescharacteristic
279D5—22no—
280D5—41no—
281C23—51no—
282C23—51no—
283C23C2×D3×D511yescharacteristic
284Q8—62no—
285Q8—102no—
286Q8—304no—
287Q8—302no—
288D4—102no—
289D4—102no—
290D4—102no—
291C2×C4—22no—
292C2×C4—32no—
293C2×C4—32no—
294C2×C4—51no—
295C2×C4—54no—
296C2×C4—51no—
297C2×C4—102no—
298C2×C4—152no—
299C2×C4—152no—
300C2×C4—304no—
301C2×C4C2×D3×D511yescharacteristic
302C2×C4C2×D3×D511yescharacteristic
303C2×C3—41no—
304C2×C3—102no—
305C2×C3—201no—
306C2×C3C2×D4×D511yescharacteristic
307C2×C3#414711yescharacteristic
308C2×C3#415011yescharacteristic
309C5#582511yescharacteristic, complemented, Sylow
310C22—21no—
311C22—21no—
312C22—21no—
313C22—52no—
314C22—101no—
315C22—101no—
316C22—101no—
317C22—101no—
318C22—101no—
319C22C22×D3×D511yescharacteristic
320C4—21no—
321C4—52no—
322C4—62no—
323C4—62no—
324C4—101no—
325C4—302no—
326C4—302no—
327C4D5×#6712yes—
328C3#6596211yescharacteristic, complemented, Sylow
329C2—41no—
330C2—102no—
331C2—201no—
332C2#9200011yescharacteristic
333C2#9200111yescharacteristic
334C2C2×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
prime radicalC2×C3×#709C2
hypercenterC22×C4D3×D5
hypocenterC3×C5#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5×Dic6C2semidirect
3. #91813C2semidirect
4. C5×#924C2semidirect
5. #91548C2semidirect
6. #91534C2semidirect
7. #91407C2semidirect
8. #91360C2semidirect
9. #91359C2semidirect
10. #91358C2semidirect
11. #91327C2semidirect
82. #924D5semidirect
256. C3×C5#536semidirect
309. C5#5825semidirect
328. C3#65962semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#7092
C2×D5×Dic62
#918132
C5×#9242
#915482
#915342
#914072
#913602
#913592
#913582
#913272
#659623
#58255