Finite Group Databasebeta

← #11752629

Subgroups — #11752629

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
1C4×Dic30C211yesmaximal, characteristic, complemented
2C5×#876C211yesmaximal, characteristic
3C3×#4016C211yesmaximal, characteristic, complemented
4#91436C211yesmaximal, characteristic
5#91432C211yesmaximal, characteristic
6#91400C211yesmaximal, characteristic
7#91382C211yesmaximal, characteristic, complemented
8#91367C211yesmaximal, characteristic
9#91346C211yesmaximal, characteristic, complemented
10#91342C211yesmaximal, characteristic
11#91341C211yesmaximal, characteristic
12#91339C211yesmaximal, characteristic, complemented
13#91334C211yesmaximal, characteristic, complemented
14#91328C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#66035—31nomaximal, Hall
17C2×Dic30C2211yescharacteristic
18C2×#1204C2211yescharacteristic
19C2×D3×Dic5C2211yescharacteristic
20C3×C42×C5C2211yescharacteristic
21C4⋊Dic15C2211yescharacteristic
22#6712C2211yescharacteristic
23#6712C2211yescharacteristic
24C4×Dic15C2211yescharacteristic
25C4×Dic15C2211yescharacteristic
26C5×(C2×D3)⋊C4C2211yescharacteristic
27C5×(C2×D3)⋊C4C2211yescharacteristic
28C5×(C2×D3)⋊C4C2211yescharacteristic
29C5×Dic3⋊C4C2211yescharacteristic
30C5×Dic3⋊C4C2211yescharacteristic
31C5×Dic3⋊C4C2211yescharacteristic
32C3×C4⋊Dic5C2211yescharacteristic
33C3×C4⋊Dic5C2211yescharacteristic
34C3×#683C2211yescharacteristic
35C3×#683C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×#683C2211yescharacteristic
38Dic3⋊Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40#6669C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5696—51nomaximal, Hall
53C5×#126—31no—
54#4036—31no—
55#4035—31no—
56#4035—31no—
57#4035—31no—
58#4034—31no—
59#4033—31no—
60#4025—31no—
61#4025—31no—
62#4025—31no—
63#4024—31no—
64#4024—31no—
65#4023—31no—
66#4016D311yescharacteristic, complemented
67C4×Dic10—31no—
68C22×C5×D3C2311yescharacteristic
69C2×C3×C4×C5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×Dic15C2311yescharacteristic
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76Dic30—22no—
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C3×Dic5C2311yescharacteristic
81C2×C3×Dic5C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84#1204—22no—
85D3×Dic5—22no—
86C3×#125—51no—
87#898—51no—
88#898—51no—
89#898—51no—
90#896—51no—
91#896—51no—
92#892—51no—
93#890—51no—
94#889—51no—
95#889—51no—
96#889—51no—
97#888—51no—
98#887—51no—
99#876D511yescharacteristic
100C4×Dic6—51no—
101C22×Dic5—31no—
102C2×Dic10—31no—
103C2×Dic10—31no—
104C5×C4⋊C4—31no—
105C5×C4⋊C4—31no—
106C5×C4⋊C4—31no—
107C5×C22⋊C4—31no—
108C5×C22⋊C4—31no—
109C5×C22⋊C4—31no—
110C42×C5C2×D311yescharacteristic
111C22⋊Dic5—31no—
112C22⋊Dic5—31no—
113C22⋊Dic5—31no—
114C4⋊Dic5—31no—
115C4⋊Dic5—31no—
116C4⋊Dic5—31no—
117C4⋊Dic5C2×D311yescharacteristic
118C4⋊Dic5C2×D311yescharacteristic
119#683—31no—
120#683—31no—
121#683—31no—
122#683—31no—
123#683—31no—
124#683—31no—
125#683—31no—
126#683—31no—
127#683C2×D311yescharacteristic
128#683C2×D311yescharacteristic
129#683C2×D311yescharacteristic
130#683C2×D311yescharacteristic
131C4×Dic5—31no—
132C4×Dic5—31no—
133C4×Dic5—31no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136#541—151noSylow
137C22×C3×C5C2411yescharacteristic
138C2×C5×D3—21no—
139C2×C5×D3—21no—
140C2×C5×D3—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—
151C3×Dic5—21no—
152C5×Dic3—21no—
153C5×Dic3—21no—
154C5×Dic3—21no—
155C2×C4×D3—51no—
156C2×Dic6—51no—
157C2×Dic6—51no—
158C3×C4⋊C4—51no—
159C3×C4⋊C4—51no—
160C3×C4⋊C4—51no—
161C3×C4⋊C4—51no—
162C3×C4⋊C4—51no—
163C3×C4⋊C4—51no—
164C3×C42C2×D511yescharacteristic
165(C2×D3)⋊C4—51no—
166(C2×D3)⋊C4—51no—
167(C2×D3)⋊C4—51no—
168(C2×D3)⋊C4C2×D511yescharacteristic
169(C2×D3)⋊C4C2×D511yescharacteristic
170(C2×D3)⋊C4C2×D511yescharacteristic
171C4⋊Dic3—51no—
172C4⋊Dic3—51no—
173C4⋊Dic3—51no—
174C4⋊Dic3—51no—
175Dic3⋊C4—51no—
176Dic3⋊C4—51no—
177Dic3⋊C4—51no—
178Dic3⋊C4—51no—
179Dic3⋊C4—51no—
180Dic3⋊C4—51no—
181Dic3⋊C4—51no—
182Dic3⋊C4C2×D511yescharacteristic
183Dic3⋊C4C2×D511yescharacteristic
184Dic3⋊C4C2×D511yescharacteristic
185C4×Dic3—51no—
186C4×Dic3—51no—
187C4×Dic3—51no—
188C4×Dic3—51no—
189C4×Dic3—51no—
190C23×C5—31no—
191C2×C4×C5—31no—
192C2×C4×C5—31no—
193C2×C4×C5—31no—
194C2×C4×C5C22×D311yescharacteristic
195C2×C4×C5C22×D311yescharacteristic
196C2×C4×C5C22×D311yescharacteristic
197C2×Dic5—31no—
198C2×Dic5—31no—
199C2×Dic5—31no—
200C2×Dic5—31no—
201C2×Dic5—62no—
202C2×Dic5C22×D311yescharacteristic
203C2×Dic5C22×D311yescharacteristic
204C2×Dic5C22×D311yescharacteristic
205C2×Dic5C22×D311yescharacteristic
206Dic10—62no—
207Dic10—62no—
208C4⋊Q8—151no—
209#126—31no—
210#126—151no—
211#126—151no—
212#126—151no—
213#125—51no—
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
226C5×D3—41no—
227C22×D3C22×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×C3×C4C22×D511yescharacteristic
235C2×Dic3—51no—
236C2×Dic3—51no—
237C2×Dic3—51no—
238C2×Dic3—51no—
239C2×Dic3C22×D511yescharacteristic
240C2×Dic3C22×D511yescharacteristic
241C2×Dic3C22×D511yescharacteristic
242C4×D3—102no—
243Dic6—102no—
244Dic6—102no—
245C22×C5—61no—
246C22×C5—61no—
247C22×C5—61no—
248C22×C5C23×D311yescharacteristic
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—61no—
253C4×C5—61no—
254C4×C5—61no—
255Dic5—21no—
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—51no—
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—51no—
273C4⋊C4—51no—
274C4⋊C4—51no—
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—31no—
288C22⋊C4—31no—
289C22⋊C4—151no—
290C22⋊C4—151no—
291C22⋊C4—151no—
292C42—151no—
293C42—151no—
294C42—151no—
295C42—151no—
296C42—151no—
297C42D3×D511yescharacteristic
298C3×C5#54111yescharacteristic, complemented, Hall
299C22×C3C23×D511yescharacteristic
300C2×D3—21no—
301C2×D3—21no—
302C2×D3—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—101no—
307C3×C4—101no—
308C3×C4—101no—
309C3×C4—101no—
310Dic3—21no—
311Dic3—21no—
312Dic3—21no—
313Dic3—52no—
314Dic3—101no—
315Dic3—101no—
316Dic3—101no—
317C2×C5—121no—
318C2×C5#100711yescharacteristic
319C2×C5D3×#4111yescharacteristic
320C2×C5#101011yescharacteristic
321C23—31no—
322Q8—302no—
323Q8—302no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—51no—
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×C3D5×#4111yescharacteristic
340C2×C3#415011yescharacteristic
341C2×C3#415011yescharacteristic
342D3—41no—
343C5#569611yescharacteristic, complemented, Sylow
344C22—61no—
345C22—61no—
346C22—61no—
347C22C22×D3×D511yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—61no—
352C4—61no—
353C4—61no—
354C4—101no—
355C4—101no—
356C4—101no—
357C4—101no—
358C4—152no—
359C4—301no—
360C4—301no—
361C4—301no—
362C3#6603511yescharacteristic, complemented, Sylow
363C2—121no—
364C2#9200111yescharacteristic
365C2#9200411yescharacteristic
366C2#9201611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radicalC22×C5×D3C23
hypercenterC42D3×D5
hypocenterC3×C5#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×Dic30C2semidirect
3. C3×#4016C2semidirect
7. #91382C2semidirect
9. #91346C2semidirect
12. #91339C2semidirect
13. #91334C2semidirect
14. #91328C2semidirect
15. #91325C2semidirect
66. #4016D3semidirect
298. C3×C5#541semidirect
343. C5#5696semidirect
362. C3#66035semidirect

Maximal subgroups

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

subgroupindex
C4×Dic302
C5×#8762
C3×#40162
#914362
#914322
#914002
#913822
#913672
#913462
#913422
#913412
#913392
#913342
#913282
#913252
#660353
#56965