Finite Group Databasebeta

← #11753457

Subgroups — #11753457

Order 960.

444 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91778C211yesmaximal, characteristic, complemented
2C5×#896C211yesmaximal, characteristic
3C3×#4033C211yesmaximal, characteristic, complemented
4#91417C211yesmaximal, characteristic
5#91410C211yesmaximal, characteristic
6#91398C211yesmaximal, characteristic
7#91398C211yesmaximal, characteristic
8C4×D3×Dic5C211yesmaximal, characteristic
9#91382C211yesmaximal, characteristic, complemented
10#91352C211yesmaximal, characteristic
11Dic5×Dic6C211yesmaximal, characteristic, complemented
12#91329C211yesmaximal, characteristic, complemented
13#91327C211yesmaximal, characteristic, complemented
14#91323C211yesmaximal, characteristic, complemented
15#91323C211yesmaximal, characteristic, complemented
16#65956—31nomaximal, Hall
17C2×C4×C5×D3C2211yescharacteristic
18C2×C5×Dic6C2211yescharacteristic
19C2×C3×Dic10C2211yescharacteristic
20C2×#1204C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×D3×Dic5C2211yescharacteristic
23C2×D3×Dic5C2211yescharacteristic
24C3×C5×C4⋊C4C2211yescharacteristic
25C4⋊Dic15C2211yescharacteristic
26#6712C2211yescharacteristic
27#6712C2211yescharacteristic
28#6712C2211yescharacteristic
29#6712C2211yescharacteristic
30C4×Dic15C2211yescharacteristic
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×(C2×D3)⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C3×#683C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×C4×Dic5C2211yescharacteristic
38C3×C4×Dic5C2211yescharacteristic
39C3×C4×Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48Dic3×Dic5C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5578—51nomaximal, Hall
53C5×C22⋊Q8—31no—
54Q8×Dic5—31no—
55#4090—31no—
56#4070—31no—
57C2×C4×Dic5—31no—
58#4035—31no—
59#4035—31no—
60#4034—31no—
61#4033—31no—
62#4033—31no—
63#4033D311yescharacteristic, complemented
64#4024—31no—
65#4024—31no—
66#4023—31no—
67#4023—31no—
68C22×C5×D3C2311yescharacteristic
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
79C4×C5×D3—22no—
80C5×Dic6—22no—
81C2×C3×Dic5C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C3×Dic10—22no—
86#1204—22no—
87#1204—22no—
88D3×Dic5—22no—
89D3×Dic5Q814yescomplemented
90C3×C4×Q8—51no—
91#946—51no—
92#944—51no—
93#897—51no—
94#896—51no—
95#896D511yescharacteristic
96#889—51no—
97#889—51no—
98#888—51no—
99#872—51no—
100#872—51no—
101C42×D3—51no—
102C4×Dic6—51no—
103C4×Dic6—51no—
104C4×Dic6—51no—
105C2×C5×Q8—31no—
106C22×C4×C5—31no—
107C22×Dic5—31no—
108C22×Dic5—31no—
109C2×Dic10—31no—
110C2×Dic10—31no—
111C2×Dic10C2×D311yescharacteristic
112C5×C4⋊C4—31no—
113C5×C4⋊C4—31no—
114C5×C4⋊C4C2×D311yescharacteristic
115C5×C22⋊C4—31no—
116C5×C22⋊C4—31no—
117C22⋊Dic5—31no—
118C22⋊Dic5—31no—
119C4⋊Dic5—31no—
120C4⋊Dic5—31no—
121C4⋊Dic5—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
131#683C2×D311yescharacteristic
132C4×Dic5—31no—
133C4×Dic5—31no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5C2×D311yescharacteristic
138C4×Dic5C2×D311yescharacteristic
139C4×Dic5C2×D311yescharacteristic
140#533—151noSylow
141C22×C3×C5C2411yescharacteristic
142C2×C5×D3—21no—
143C2×C5×D3—21no—
144C2×C5×D3C2×Q812yes—
145C3×C4×C5—21no—
146C3×C4×C5—21no—
147C3×C4×C5—21no—
148Dic15—21no—
149Dic15—21no—
150Dic15—21no—
151Dic15C2×Q812yes—
152C3×Dic5—21no—
153C3×Dic5—21no—
154C3×Dic5C2×Q812yes—
155C3×Dic5#4112yes—
156C5×Dic3—21no—
157C5×Dic3—21no—
158C5×Dic3#4112yes—
159C2×C3×Q8—51no—
160C2×C4×D3—51no—
161C2×C4×D3—51no—
162C2×C4×D3C2×D511yescharacteristic
163C2×Dic6—51no—
164C2×Dic6—51no—
165C2×Dic6C2×D511yescharacteristic
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4C2×D511yescharacteristic
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172(C2×D3)⋊C4—51no—
173(C2×D3)⋊C4—51no—
174(C2×D3)⋊C4C2×D511yescharacteristic
175(C2×D3)⋊C4C2×D511yescharacteristic
176C4⋊Dic3—51no—
177C4⋊Dic3—51no—
178C4⋊Dic3—51no—
179Dic3⋊C4—51no—
180Dic3⋊C4—51no—
181Dic3⋊C4—51no—
182Dic3⋊C4—51no—
183Dic3⋊C4—51no—
184Dic3⋊C4—51no—
185Dic3⋊C4—51no—
186Dic3⋊C4—51no—
187Dic3⋊C4C2×D511yescharacteristic
188Dic3⋊C4C2×D511yescharacteristic
189C4×Dic3—51no—
190C4×Dic3—51no—
191C4×Dic3—51no—
192C4×Dic3—51no—
193C4×Dic3—51no—
194C23×C5—31no—
195C5×Q8—62no—
196C2×C4×C5—31no—
197C2×C4×C5—31no—
198C2×C4×C5—31no—
199C2×C4×C5—62no—
200C2×C4×C5C22×D311yescharacteristic
201C2×C4×C5C22×D311yescharacteristic
202C2×C4×C5C22×D311yescharacteristic
203C2×Dic5—31no—
204C2×Dic5—34no—
205C2×Dic5—31no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—62no—
209C2×Dic5C22×D311yescharacteristic
210C2×Dic5C22×D311yescharacteristic
211C2×Dic5C22×D311yescharacteristic
212C2×Dic5C22×D311yescharacteristic
213Dic10—22no—
214Dic10—62no—
215Dic10—62no—
216C4⋊Q8—151no—
217C4⋊Q8—151no—
218#125—151no—
219#125—151no—
220C22⋊Q8—31no—
221C22⋊Q8—151no—
222C22⋊Q8—151no—
223C22⋊Q8—151no—
224C4×Q8—51no—
225C4×Q8—151no—
226C4×Q8—151no—
227C4×Q8—151no—
228#117—151no—
229#117—151no—
230C2×C42—151no—
231C2×C3×C5C22×Q811yescharacteristic
232C2×C3×C5C2×#4111yescharacteristic
233C2×C3×C5C2×#4111yescharacteristic
234C5×D3—22no—
235C22×D3C22×D511yescharacteristic
236C3×Q8—102no—
237C2×C3×C4—51no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4C22×D511yescharacteristic
242C2×C3×C4C22×D511yescharacteristic
243C2×C3×C4C22×D511yescharacteristic
244C2×Dic3—51no—
245C2×Dic3—51no—
246C2×Dic3—51no—
247C2×Dic3—51no—
248C2×Dic3C22×D511yescharacteristic
249C2×Dic3C22×D511yescharacteristic
250C2×Dic3C22×D511yescharacteristic
251C4×D3—22no—
252C4×D3—54no—
253C4×D3—102no—
254Dic6—22no—
255Dic6—102no—
256Dic6—102no—
257C22×C5—32no—
258C22×C5—61no—
259C22×C5—61no—
260C22×C5C23×D311yescharacteristic
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—32no—
265C4×C5—61no—
266C4×C5—61no—
267Dic5—21no—
268Dic5—21no—
269Dic5—32no—
270Dic5—61no—
271Dic5—61no—
272Dic5—61no—
273Dic5#23512yes—
274Dic5D3×Q812yes—
275C2×Q8—31no—
276C2×Q8—51no—
277C2×Q8—151no—
278C2×Q8—151no—
279C22×C4—31no—
280C22×C4—151no—
281C22×C4—151no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—51no—
285C4⋊C4—51no—
286C4⋊C4—151no—
287C4⋊C4—151no—
288C4⋊C4—151no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—151no—
292C4⋊C4—151no—
293C4⋊C4—151no—
294C4⋊C4—151no—
295C4⋊C4—151no—
296C4⋊C4—151no—
297C4⋊C4D3×D511yescharacteristic
298C22⋊C4—31no—
299C22⋊C4—31no—
300C22⋊C4—151no—
301C22⋊C4—151no—
302C42—51no—
303C42—51no—
304C42—51no—
305C42—151no—
306C42—151no—
307C42—151no—
308C42—151no—
309C42—151no—
310C3×C5#53311yescharacteristic, complemented, Hall
311C22×C3C23×D511yescharacteristic
312C2×D3—21no—
313C2×D3—21no—
314C2×D3Q8×D512yes—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—52no—
319C3×C4—52no—
320C3×C4—101no—
321C3×C4—101no—
322Dic3—21no—
323Dic3—21no—
324Dic3—52no—
325Dic3—101no—
326Dic3—101no—
327Dic3—101no—
328Dic3#71112yes—
329C2×C5—62no—
330C2×C5C2×#23511yescharacteristic
331C2×C5C2×D3×Q811yescharacteristic
332C2×C5D3×#4111yescharacteristic
333C23—31no—
334Q8—62no—
335Q8—102no—
336Q8—302no—
337Q8—302no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—51no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—62no—
346C2×C4—154no—
347C2×C4—151no—
348C2×C4—151no—
349C2×C4—151no—
350C2×C4—151no—
351C2×C4—302no—
352C2×C4C2×D3×D511yescharacteristic
353C2×C4C2×D3×D511yescharacteristic
354C2×C4C2×D3×D511yescharacteristic
355C2×C3C2×#71111yescharacteristic
356C2×C3C2×Q8×D511yescharacteristic
357C2×C3D5×#4111yescharacteristic
358D3—22no—
359C5#557811yescharacteristic, complemented, Sylow
360C22—32no—
361C22—61no—
362C22—61no—
363C22C22×D3×D511yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—32no—
368C4—52no—
369C4—52no—
370C4—61no—
371C4—61no—
372C4—101no—
373C4—101no—
374C4—152no—
375C4—301no—
376C4—301no—
377C4—301no—
378C3#6595611yescharacteristic, complemented, Sylow
379C2—62no—
380C2D5×#23511yescharacteristic
381C2D3×#71111yescharacteristic
382C2D3×Q8×D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC22×C5×D3C23
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#533
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
3. C3×#4033C2semidirect
9. #91382C2semidirect
11. Dic5×Dic6C2semidirect
12. #91329C2semidirect
13. #91327C2semidirect
14. #91323C2semidirect
15. #91323C2semidirect
63. #4033D3semidirect
89. D3×Dic5Q8semidirect
310. C3×C5#533semidirect
359. C5#5578semidirect
378. C3#65956semidirect

Maximal subgroups

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

subgroupindex
#917782
C5×#8962
C3×#40332
#914172
#914102
#913982
C4×D3×Dic52
#913822
#913522
Dic5×Dic62
#913292
#913272
#913232
#659563
#55785