Finite Group Databasebeta

← #11753613

Subgroups — #11753613

Order 960.

384 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91778C211yesmaximal, characteristic, complemented
2C5×#890C211yesmaximal, characteristic, complemented
3C3×#4044C211yesmaximal, characteristic
4#91470C211yesmaximal, characteristic, complemented
5#91430C211yesmaximal, characteristic
6#91430C211yesmaximal, characteristic
7#91394C211yesmaximal, characteristic
8#91388C211yesmaximal, characteristic, complemented
9#91363C211yesmaximal, characteristic
10#91362C211yesmaximal, characteristic
11#91361C211yesmaximal, characteristic
12#91339C211yesmaximal, characteristic, complemented
13#91336C211yesmaximal, characteristic, complemented
14#91324C211yesmaximal, characteristic, complemented
15#91323C211yesmaximal, characteristic, complemented
16#66030—31nomaximal, Hall
17C2×#1204C2211yescharacteristic
18C2×#1204C2211yescharacteristic
19C2×D5×Dic3C2211yescharacteristic
20C3×C5×C4⋊C4C2211yescharacteristic
21C4⋊Dic15C2211yescharacteristic
22#6712C2211yescharacteristic
23#6712C2211yescharacteristic
24#6712C2211yescharacteristic
25#6712C2211yescharacteristic
26C4×Dic15C2211yescharacteristic
27C5×C4⋊Dic3C2211yescharacteristic
28C5×C4⋊Dic3C2211yescharacteristic
29C5×C4⋊Dic3C2211yescharacteristic
30C5×Dic3⋊C4C2211yescharacteristic
31C5×Dic3⋊C4C2211yescharacteristic
32C4×C5×Dic3C2211yescharacteristic
33C3×#685C2211yescharacteristic
34C3×#685C2211yescharacteristic
35C3×#685C2211yescharacteristic
36C3×C4⋊Dic5C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×C4×Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46#6665C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5701—51nomaximal, Hall
53C5×#125—31no—
54#4044—31no—
55#4044—31no—
56#4044D311yescharacteristic
57#4042—31no—
58#4042—31no—
59#4038—31no—
60#4036—31no—
61#4035—31no—
62#4035—31no—
63#4035—31no—
64#4034—31no—
65#4033—31no—
66#4022—31no—
67C4×Dic10—31no—
68C22×C3×D5C2311yescharacteristic
69C2×C3×C4×C5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×Dic15C2311yescharacteristic
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×C5×Dic3C2311yescharacteristic
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C3×Dic5C2311yescharacteristic
81C2×C3×Dic5C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83#1204—22no—
84#1204—22no—
85D5×Dic3—22no—
86C3×#126—51no—
87#890D511yescharacteristic, complemented
88#889—51no—
89#889—51no—
90#889—51no—
91#888—51no—
92#887—51no—
93#879—51no—
94#879—51no—
95#879—51no—
96#878—51no—
97#878—51no—
98#877—51no—
99#870—51no—
100C4×Dic6—51no—
101C2×C4×D5—31no—
102C2×Dic10—31no—
103C2×Dic10—31no—
104C5×C4⋊C4—31no—
105C5×C4⋊C4—31no—
106C5×C4⋊C4—31no—
107C5×C4⋊C4—31no—
108C5×C4⋊C4—31no—
109C5×C4⋊C4C2×D311yescharacteristic
110C42×C5—31no—
111#685—31no—
112#685—31no—
113#685—31no—
114#685C2×D311yescharacteristic
115#685C2×D311yescharacteristic
116#685C2×D311yescharacteristic
117C4⋊Dic5—31no—
118C4⋊Dic5—31no—
119C4⋊Dic5—31no—
120C4⋊Dic5C2×D311yescharacteristic
121#683—31no—
122#683—31no—
123#683—31no—
124#683—31no—
125#683—31no—
126#683—31no—
127#683—31no—
128#683—31no—
129#683—31no—
130#683C2×D311yescharacteristic
131C4×Dic5—31no—
132C4×Dic5—31no—
133C4×Dic5—31no—
134C4×Dic5—31no—
135C4×Dic5C2×D311yescharacteristic
136#541—151noSylow
137C22×C3×C5C2411yescharacteristic
138C2×C3×D5—21no—
139C2×C3×D5—21no—
140C2×C3×D5—21no—
141C3×C4×C5—21no—
142C3×C4×C5—21no—
143C3×C4×C5—21no—
144Dic15—21no—
145Dic15—21no—
146Dic15—21no—
147Dic15#4112yes—
148C3×Dic5—21no—
149C3×Dic5—21no—
150C3×Dic5—21no—
151C5×Dic3—21no—
152C5×Dic3—21no—
153C5×Dic3—21no—
154C5×Dic3—21no—
155C22×Dic3—51no—
156C2×Dic6—51no—
157C2×Dic6—51no—
158C3×C4⋊C4—51no—
159C3×C4⋊C4—51no—
160C3×C4⋊C4C2×D511yescharacteristic
161C3×C22⋊C4—51no—
162C3×C22⋊C4—51no—
163C3×C22⋊C4—51no—
164C3×C42—51no—
165#217—51no—
166#217—51no—
167#217—51no—
168C4⋊Dic3—51no—
169C4⋊Dic3—51no—
170C4⋊Dic3C2×D511yescharacteristic
171C4⋊Dic3C2×D511yescharacteristic
172C4⋊Dic3C2×D511yescharacteristic
173Dic3⋊C4—51no—
174Dic3⋊C4—51no—
175Dic3⋊C4—51no—
176Dic3⋊C4—51no—
177Dic3⋊C4—51no—
178Dic3⋊C4—51no—
179Dic3⋊C4—51no—
180Dic3⋊C4—51no—
181Dic3⋊C4—51no—
182Dic3⋊C4—51no—
183Dic3⋊C4C2×D511yescharacteristic
184Dic3⋊C4C2×D511yescharacteristic
185C4×Dic3—51no—
186C4×Dic3—51no—
187C4×Dic3—51no—
188C4×Dic3—51no—
189C4×Dic3C2×D511yescharacteristic
190C22×D5C22×D311yescharacteristic
191C2×C4×C5—31no—
192C2×C4×C5—31no—
193C2×C4×C5—31no—
194C2×C4×C5—31no—
195C2×C4×C5C22×D311yescharacteristic
196C2×C4×C5C22×D311yescharacteristic
197C2×C4×C5C22×D311yescharacteristic
198C2×Dic5—31no—
199C2×Dic5—31no—
200C2×Dic5—31no—
201C2×Dic5—31no—
202C2×Dic5C22×D311yescharacteristic
203C2×Dic5C22×D311yescharacteristic
204C2×Dic5C22×D311yescharacteristic
205C4×D5—62no—
206Dic10—62no—
207Dic10—62no—
208C4⋊Q8—151no—
209#126—51no—
210#126—151no—
211#126—151no—
212#126—151no—
213#125—31no—
214#125—151no—
215#125—151no—
216#125—151no—
217#125—151no—
218C22⋊Q8—151no—
219C22⋊Q8—151no—
220C4×Q8—151no—
221C4×Q8—151no—
222#117—151no—
223C2×C3×C5C2×#4111yescharacteristic
224C2×C3×C52−1+411yescharacteristic
225C2×C3×C52−1+411yescharacteristic
226C3×D5—41no—
227C23×C3—51no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4C22×D511yescharacteristic
232C2×C3×C4C22×D511yescharacteristic
233C2×C3×C4C22×D511yescharacteristic
234C2×Dic3—51no—
235C2×Dic3—51no—
236C2×Dic3—51no—
237C2×Dic3—51no—
238C2×Dic3—102no—
239C2×Dic3C22×D511yescharacteristic
240C2×Dic3C22×D511yescharacteristic
241C2×Dic3C22×D511yescharacteristic
242C2×Dic3C22×D511yescharacteristic
243Dic6—102no—
244Dic6—102no—
245C22×C5C23×D311yescharacteristic
246C2×D5—21no—
247C2×D5—21no—
248C2×D5—21no—
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—61no—
253C4×C5—61no—
254C4×C5—61no—
255C4×C5—61no—
256Dic5—21no—
257Dic5—21no—
258Dic5—21no—
259Dic5—32no—
260Dic5—61no—
261Dic5—61no—
262Dic5—61no—
263C2×Q8—151no—
264C2×Q8—151no—
265C22×C4—151no—
266C4⋊C4—31no—
267C4⋊C4—31no—
268C4⋊C4—31no—
269C4⋊C4—31no—
270C4⋊C4—31no—
271C4⋊C4—51no—
272C4⋊C4—51no—
273C4⋊C4—151no—
274C4⋊C4—151no—
275C4⋊C4—151no—
276C4⋊C4—151no—
277C4⋊C4—151no—
278C4⋊C4—151no—
279C4⋊C4—151no—
280C4⋊C4—151no—
281C4⋊C4—151no—
282C4⋊C4—151no—
283C4⋊C4—151no—
284C4⋊C4—151no—
285C4⋊C4D3×D511yescharacteristic
286C22⋊C4—51no—
287C22⋊C4—51no—
288C22⋊C4—51no—
289C22⋊C4—151no—
290C22⋊C4—151no—
291C22⋊C4—151no—
292C42—31no—
293C42—51no—
294C42—151no—
295C42—151no—
296C42—151no—
297C42—151no—
298C3×C5#54111yescharacteristic, complemented, Hall
299C22×C3—101no—
300C22×C3—101no—
301C22×C3—101no—
302C22×C3C23×D511yescharacteristic
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—101no—
307C3×C4—101no—
308C3×C4—101no—
309Dic3—21no—
310Dic3—21no—
311Dic3—21no—
312Dic3—21no—
313Dic3—52no—
314Dic3—101no—
315Dic3—101no—
316Dic3—101no—
317C2×C5D3×#4111yescharacteristic
318C2×C5#101011yescharacteristic
319C2×C5#101011yescharacteristic
320D5—41no—
321C23—51no—
322Q8—302no—
323Q8—302no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—51no—
329C2×C4—51no—
330C2×C4—51no—
331C2×C4—151no—
332C2×C4—151no—
333C2×C4—151no—
334C2×C4—151no—
335C2×C4—302no—
336C2×C4C2×D3×D511yescharacteristic
337C2×C4C2×D3×D511yescharacteristic
338C2×C4C2×D3×D511yescharacteristic
339C2×C3—201no—
340C2×C3#414711yescharacteristic
341C2×C3D5×#4111yescharacteristic
342C2×C3#415011yescharacteristic
343C5#570111yescharacteristic, complemented, Sylow
344C22—101no—
345C22—101no—
346C22—101no—
347C22C22×D3×D511yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—61no—
352C4—61no—
353C4—61no—
354C4—61no—
355C4—101no—
356C4—101no—
357C4—101no—
358C4—152no—
359C4—301no—
360C4—301no—
361C4—301no—
362C3#6603011yescharacteristic, complemented, Sylow
363C2—201no—
364C2#9200011yescharacteristic
365C2#9202011yescharacteristic
366C2#9203411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC22×C3×D5C23
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #91778C2semidirect
2. C5×#890C2semidirect
4. #91470C2semidirect
8. #91388C2semidirect
12. #91339C2semidirect
13. #91336C2semidirect
14. #91324C2semidirect
15. #91323C2semidirect
87. #890D5semidirect
298. C3×C5#541semidirect
343. C5#5701semidirect
362. C3#66030semidirect

Maximal subgroups

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

subgroupindex
#917782
C5×#8902
C3×#40442
#914702
#914302
#913942
#913882
#913632
#913622
#913612
#913392
#913362
#913242
#913232
#660303
#57015