Finite Group Databasebeta

← #11752787

Subgroups — #11752787

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#91768C211yesmaximal, characteristic
2C5×#878C211yesmaximal, characteristic
3C3×#4025C211yesmaximal, characteristic
4#91575C211yesmaximal, characteristic
5#91531C211yesmaximal, characteristic
6#91531C211yesmaximal, characteristic
7#91529C211yesmaximal, characteristic
8#91384C211yesmaximal, characteristic, complemented
9#91378C211yesmaximal, characteristic, complemented
10#91346C211yesmaximal, characteristic, complemented
11#91343C211yesmaximal, characteristic, complemented
12#91336C211yesmaximal, characteristic, complemented
13Dic5×Dic6C211yesmaximal, characteristic, complemented
14#91329C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#65959—31nomaximal, Hall
17C22×C5×Dic3C2211yescharacteristic
18C2×C5×Dic6C2211yescharacteristic
19C2×#1204C2211yescharacteristic
20C3×C5×C22⋊C4C2211yescharacteristic
21#6719C2211yescharacteristic
22#6719C2211yescharacteristic
23C4⋊Dic15C2211yescharacteristic
24#6712C2211yescharacteristic
25#6712C2211yescharacteristic
26C4×Dic15C2211yescharacteristic
27C5×#217C2211yescharacteristic
28C5×C4⋊Dic3C2211yescharacteristic
29C5×Dic3⋊C4C2211yescharacteristic
30C5×Dic3⋊C4C2211yescharacteristic
31C3×C22⋊Dic5C2211yescharacteristic
32C3×C22⋊Dic5C2211yescharacteristic
33C3×C4⋊Dic5C2211yescharacteristic
34C3×#683C2211yescharacteristic
35C3×#683C2211yescharacteristic
36C3×C4×Dic5C2211yescharacteristic
37Dic3⋊Dic5C2211yescharacteristic
38Dic3⋊Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48Dic3×Dic5C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5701—51nomaximal, Hall
53C5×C22⋊Q8—31no—
54Q8×Dic5—31no—
55#4090—31no—
56#4072—31no—
57#4070—31no—
58#4036—31no—
59#4036—31no—
60#4036—31no—
61#4035—31no—
62#4035—31no—
63#4033—31no—
64#4025—31no—
65#4025—31no—
66#4025—31no—
67#4025D311yescharacteristic
68C23×C3×C5C2311yescharacteristic
69C2×C3×C4×C5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×Dic15C2311yescharacteristic
72C2×Dic15C2311yescharacteristic
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×C5×Dic3—22no—
76C2×C5×Dic3C2311yescharacteristic
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C5×Dic6—22no—
81C2×C3×Dic5C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85#1204—22no—
86C3×#126—51no—
87#890—51no—
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#878D511yescharacteristic
98#877—51no—
99#870—51no—
100C4×Dic6—51no—
101C2×C5×Q8—31no—
102C22×C4×C5—31no—
103C2×Dic10—31no—
104C5×C4⋊C4—31no—
105C5×C4⋊C4—31no—
106C5×C4⋊C4—31no—
107C5×C22⋊C4—31no—
108C5×C22⋊C4C2×D311yescharacteristic
109C22⋊Dic5—31no—
110C22⋊Dic5—31no—
111C22⋊Dic5C2×D311yescharacteristic
112C22⋊Dic5C2×D311yescharacteristic
113C4⋊Dic5—31no—
114C4⋊Dic5—31no—
115C4⋊Dic5—31no—
116C4⋊Dic5—31no—
117C4⋊Dic5—31no—
118C4⋊Dic5—31no—
119C4⋊Dic5C2×D311yescharacteristic
120#683—31no—
121#683—31no—
122#683—31no—
123#683—31no—
124#683—31no—
125#683—31no—
126#683—31no—
127#683—31no—
128#683C2×D311yescharacteristic
129#683C2×D311yescharacteristic
130C4×Dic5—31no—
131C4×Dic5—31no—
132C4×Dic5—31no—
133C4×Dic5—31no—
134C4×Dic5—31no—
135C4×Dic5C2×D311yescharacteristic
136#541—151noSylow
137C22×C3×C5—21no—
138C22×C3×C5—21no—
139C22×C3×C5—21no—
140C22×C3×C5C2411yescharacteristic
141C3×C4×C5—21no—
142C3×C4×C5—21no—
143Dic15—21no—
144Dic15—21no—
145Dic15—21no—
146Dic15—21no—
147C3×Dic5—21no—
148C3×Dic5—21no—
149C3×Dic5—21no—
150C3×Dic5—21no—
151C5×Dic3—21no—
152C5×Dic3—21no—
153C5×Dic3—21no—
154C5×Dic3#4112yes—
155C22×Dic3C2×D511yescharacteristic
156C2×Dic6—51no—
157C2×Dic6C2×D511yescharacteristic
158C3×C4⋊C4—51no—
159C3×C4⋊C4—51no—
160C3×C4⋊C4—51no—
161C3×C22⋊C4—51no—
162C3×C22⋊C4—51no—
163C3×C22⋊C4C2×D511yescharacteristic
164C3×C42—51no—
165#217—51no—
166#217—51no—
167#217C2×D511yescharacteristic
168C4⋊Dic3—51no—
169C4⋊Dic3—51no—
170C4⋊Dic3—51no—
171C4⋊Dic3—51no—
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×Dic3—51no—
190C23×C5C22×D311yescharacteristic
191C5×Q8—62no—
192C2×C4×C5—31no—
193C2×C4×C5—31no—
194C2×C4×C5—31no—
195C2×C4×C5—31no—
196C2×C4×C5—62no—
197C2×C4×C5C22×D311yescharacteristic
198C2×C4×C5C22×D311yescharacteristic
199C2×Dic5—31no—
200C2×Dic5—31no—
201C2×Dic5—31no—
202C2×Dic5—31no—
203C2×Dic5C22×D311yescharacteristic
204C2×Dic5C22×D311yescharacteristic
205C2×Dic5C22×D311yescharacteristic
206C2×Dic5C22×D311yescharacteristic
207Dic10—62no—
208C4⋊Q8—151no—
209#126—51no—
210#126—151no—
211#126—151no—
212#126—151no—
213#125—151no—
214#125—151no—
215#125—151no—
216#125—151no—
217#125—151no—
218C22⋊Q8—31no—
219C22⋊Q8—151no—
220C4×Q8—151no—
221C4×Q8—151no—
222#117—151no—
223C2×C3×C5—41no—
224C2×C3×C5C2×#4111yescharacteristic
225C2×C3×C52−1+411yescharacteristic
226C2×C3×C52−1+411yescharacteristic
227C23×C3C22×D511yescharacteristic
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4C22×D511yescharacteristic
233C2×C3×C4C22×D511yescharacteristic
234C2×Dic3—22no—
235C2×Dic3—51no—
236C2×Dic3—51no—
237C2×Dic3—51no—
238C2×Dic3—51no—
239C2×Dic3C22×D511yescharacteristic
240C2×Dic3C22×D511yescharacteristic
241C2×Dic3C22×D511yescharacteristic
242C2×Dic3C22×D511yescharacteristic
243Dic6—22no—
244Dic6—102no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5C23×D311yescharacteristic
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—32no—
252C4×C5—61no—
253C4×C5—61no—
254C4×C5—61no—
255Dic5—21no—
256Dic5—21no—
257Dic5—21no—
258Dic5—21no—
259Dic5—61no—
260Dic5—61no—
261Dic5—61no—
262Dic5—61no—
263C2×Q8—31no—
264C2×Q8—151no—
265C22×C4—31no—
266C4⋊C4—31no—
267C4⋊C4—31no—
268C4⋊C4—31no—
269C4⋊C4—51no—
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—151no—
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⋊C4—151no—
286C22⋊C4—31no—
287C22⋊C4—51no—
288C22⋊C4—51no—
289C22⋊C4—151no—
290C22⋊C4—151no—
291C22⋊C4D3×D511yescharacteristic
292C42—51no—
293C42—151no—
294C42—151no—
295C42—151no—
296C42—151no—
297C42—151no—
298C3×C5#54111yescharacteristic, complemented, Hall
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3C23×D511yescharacteristic
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—101no—
306C3×C4—101no—
307C3×C4—101no—
308C3×C4—101no—
309Dic3—21no—
310Dic3—21no—
311Dic3—21no—
312Dic3—101no—
313Dic3—101no—
314Dic3—101no—
315Dic3—101no—
316Dic3#71112yes—
317C2×C5—41no—
318C2×C5D3×#4111yescharacteristic
319C2×C5#101011yescharacteristic
320C2×C5#101011yescharacteristic
321C23C2×D3×D511yescharacteristic
322Q8—62no—
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—51no—
332C2×C4—62no—
333C2×C4—151no—
334C2×C4—151no—
335C2×C4—151no—
336C2×C4—151no—
337C2×C4C2×D3×D511yescharacteristic
338C2×C4C2×D3×D511yescharacteristic
339C2×C3—41no—
340C2×C3C2×#71111yescharacteristic
341C2×C3#414711yescharacteristic
342C2×C3#415011yescharacteristic
343C5#570111yescharacteristic, complemented, Sylow
344C22—21no—
345C22—21no—
346C22—21no—
347C22C22×D3×D511yescharacteristic
348C4—21no—
349C4—21no—
350C4—32no—
351C4—61no—
352C4—61no—
353C4—61no—
354C4—101no—
355C4—101no—
356C4—101no—
357C4—101no—
358C4—301no—
359C4—301no—
360C4—301no—
361C4—301no—
362C3#6595911yescharacteristic, complemented, Sylow
363C2—41no—
364C2#9200011yescharacteristic
365C2#9202011yescharacteristic
366C2D3×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC23×C3×C5C23
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #91384C2semidirect
9. #91378C2semidirect
10. #91346C2semidirect
11. #91343C2semidirect
12. #91336C2semidirect
13. Dic5×Dic6C2semidirect
14. #91329C2semidirect
15. #91325C2semidirect
298. C3×C5#541semidirect
343. C5#5701semidirect
362. C3#65959semidirect

Maximal subgroups

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

subgroupindex
#917682
C5×#8782
C3×#40252
#915752
#915312
#915292
#913842
#913782
#913462
#913432
#913362
Dic5×Dic62
#913292
#913252
#659593
#57015