Finite Group Databasebeta

← #11753422

Subgroups — #11753422

Order 960.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6768C211yesmaximal, characteristic
2C2×D3×Dic10C211yesmaximal, characteristic, complemented
3#91785C211yesmaximal, characteristic, complemented
4C5×#894C211yesmaximal, characteristic, complemented
5C3×#4034C211yesmaximal, characteristic, complemented
6#91436C211yesmaximal, characteristic, complemented
7#91432C211yesmaximal, characteristic, complemented
8#91427C211yesmaximal, characteristic, complemented
9#91423C211yesmaximal, characteristic, complemented
10#91398C211yesmaximal, characteristic, complemented
11#91377C211yesmaximal, characteristic, complemented
12#91351C211yesmaximal, characteristic, complemented
13#91350C211yesmaximal, characteristic, complemented
14#91327C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65982—31nomaximal, Hall
17C2×C4×D15C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C2×C5×D12C2211yescharacteristic
20C2×C4×C5×D3C2211yescharacteristic
21C2×C3×Dic10C2211yescharacteristic
22C2×C3×Dic10C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1204C2211yescharacteristic
25C2×#1203C2211yescharacteristic
26C2×#1203C2211yescharacteristic
27C2×D3×Dic5C2211yescharacteristic
28C2×D3×Dic5C2211yescharacteristic
29C2×D3×Dic5C2211yescharacteristic
30#6768—24no—
31D3×Dic10—24no—
32C3×C5×C4⋊C4C2211yescharacteristic
33#6714C2211yescharacteristic
34#6714C2211yescharacteristic
35#6712C2211yescharacteristic
36#6712C2211yescharacteristic
37C5×(C2×D3)⋊C4C2211yescharacteristic
38C5×(C2×D3)⋊C4C2211yescharacteristic
39C5×(C2×D3)⋊C4C2211yescharacteristic
40C5×Dic3⋊C4C2211yescharacteristic
41C3×C4⋊Dic5C2211yescharacteristic
42C3×#683C2211yescharacteristic
43C3×#683C2211yescharacteristic
44C3×C4×Dic5C2211yescharacteristic
45Dic3⋊Dic5C2211yescharacteristic
46#6669C2211yescharacteristic
47#6669C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50(C2×D3)⋊Dic5C2211yescharacteristic
51(C2×D3)⋊Dic5C2211yescharacteristic
52(C2×D3)⋊Dic5C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5724—51nomaximal, Hall
55C2×#711—31no—
56C22×Dic10—31no—
57C5×#123—31no—
58#4081—31no—
59#4075—31no—
60#4042—31no—
61#4042—31no—
62#4034—31no—
63#4034D311yescharacteristic, complemented
64#4032—31no—
65#4031—31no—
66#4031—31no—
67#4024—31no—
68#4024—31no—
69#4023—31no—
70C22×D15C2311yescharacteristic
71C22×C5×D3C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C4×D15—22no—
80Dic30—22no—
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C5×D12—22no—
84C4×C5×D3—22no—
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C3×Dic10—22no—
90C3×Dic10—22no—
91#1204—22no—
92#1204—22no—
93#1203—22no—
94#1203—22no—
95D3×Dic5—22no—
96D3×Dic5—22no—
97D3×Dic5D414yes—
98C2×#239—51no—
99C2×D3×Q8—51no—
100C3×C4⋊Q8—51no—
101#947—51no—
102#944—51no—
103#896—51no—
104#896—51no—
105#896—51no—
106#896—51no—
107#894—51no—
108#894—51no—
109#894—51no—
110#894D511yescharacteristic, complemented
111#875—51no—
112#872—51no—
113C2×C5×D4—31no—
114C22×C4×C5—31no—
115C2×C22⋊D5—31no—
116C2×C22⋊D5—31no—
117C22×Dic5—31no—
118C22×Dic5—31no—
119C22×Dic5—31no—
120#711—64no—
121C2×C4×D5—31no—
122C2×Dic10—31no—
123C2×Dic10—31no—
124C2×Dic10—31no—
125C2×Dic10—64no—
126C2×Dic10C2×D311yescharacteristic
127C2×Dic10C2×D311yescharacteristic
128C5×C4⋊C4—31no—
129C5×C4⋊C4C2×D311yescharacteristic
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C5×C22⋊C4—31no—
133C22⋊Dic5—31no—
134C22⋊Dic5—31no—
135C22⋊Dic5—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140C4⋊Dic5—31no—
141C4⋊Dic5C2×D311yescharacteristic
142#683—31no—
143#683—31no—
144#683—31no—
145#683—31no—
146#683C2×D311yescharacteristic
147#683C2×D311yescharacteristic
148C4×Dic5—31no—
149C4×Dic5C2×D311yescharacteristic
150#536—151noSylow
151C22×C3×C5C2411yescharacteristic
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C2×C5×D3—21no—
156C2×C5×D3—21no—
157C2×C5×D3—21no—
158C2×C5×D3—21no—
159C2×C5×D3—21no—
160C2×C5×D3C2×D412yes—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164Dic15—21no—
165Dic15—21no—
166Dic15C2×D412yes—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5C2×D412yes—
171C5×Dic3—21no—
172C5×Dic3—21no—
173C2×C3×Q8—51no—
174C2×C3×Q8—51no—
175#239—104no—
176D3×Q8—104no—
177C2×D12—51no—
178C2×D12—51no—
179C2×D12C2×D511yescharacteristic
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×C4×D3—51no—
183C2×C4×D3—51no—
184C2×C4×D3C2×D511yescharacteristic
185C2×Dic6—51no—
186C2×Dic6—51no—
187C2×Dic6—51no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4C2×D511yescharacteristic
192C3×C42—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4—51no—
195(C2×D3)⋊C4—51no—
196(C2×D3)⋊C4—51no—
197(C2×D3)⋊C4—51no—
198(C2×D3)⋊C4—51no—
199(C2×D3)⋊C4—51no—
200(C2×D3)⋊C4C2×D511yescharacteristic
201(C2×D3)⋊C4C2×D511yescharacteristic
202(C2×D3)⋊C4C2×D511yescharacteristic
203Dic3⋊C4—51no—
204Dic3⋊C4—51no—
205Dic3⋊C4—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4—51no—
208Dic3⋊C4C2×D511yescharacteristic
209C4×Dic3—51no—
210C23×C5—31no—
211C23×C5—31no—
212C22×D5—31no—
213C5×D4—62no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—62no—
217C2×C4×C5C22×D311yescharacteristic
218C2×C4×C5C22×D311yescharacteristic
219C2×C4×C5C22×D311yescharacteristic
220C22⋊D5—62no—
221C22⋊D5—62no—
222C2×Dic5—31no—
223C2×Dic5—34no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—62no—
227C2×Dic5—62no—
228C2×Dic5C22×D311yescharacteristic
229C2×Dic5C22×D311yescharacteristic
230C2×Dic5C22×D311yescharacteristic
231C2×Dic5C22×D311yescharacteristic
232C4×D5—62no—
233Dic10—22no—
234Dic10—22no—
235Dic10—62no—
236Dic10—62no—
237Dic10—62no—
238C2×#41—151no—
239C22×Q8—151no—
240C4⋊Q8—51no—
241C4⋊Q8—151no—
242#124—151no—
243#124—151no—
244#123—31no—
245#123—151no—
246#123—151no—
247#123—151no—
248C22⋊Q8—151no—
249C22⋊Q8—151no—
250C22⋊Q8—151no—
251C22⋊Q8—151no—
252#117—151no—
253C2×C3×C5C22×D411yescharacteristic
254C2×C3×C52−1+411yescharacteristic
255C2×C3×C52−1+411yescharacteristic
256D15—41no—
257C5×D3—22no—
258C5×D3—41no—
259C22×D3—51no—
260C22×D3C22×D511yescharacteristic
261C22×D3C22×D511yescharacteristic
262C3×Q8—102no—
263C3×Q8—102no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4C22×D511yescharacteristic
269C2×C3×C4C22×D511yescharacteristic
270C2×C3×C4C22×D511yescharacteristic
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3C22×D511yescharacteristic
275C2×Dic3C22×D511yescharacteristic
276D12—22no—
277D12—102no—
278D12—102no—
279C4×D3—22no—
280C4×D3—54no—
281C4×D3—102no—
282C4×D3—102no—
283C4×D3—102no—
284Dic6—102no—
285Dic6—102no—
286Dic6—102no—
287C22×C5—32no—
288C22×C5—61no—
289C22×C5—61no—
290C22×C5—61no—
291C22×C5—61no—
292C22×C5—61no—
293C22×C5C23×D311yescharacteristic
294C2×D5—61no—
295C2×D5—61no—
296C2×D5—61no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—61no—
301C4×C5—61no—
302Dic5—21no—
303Dic5—21no—
304Dic5—21no—
305Dic5—32no—
306Dic5—61no—
307Dic5—61no—
308Dic5D3×D412yes—
309#41—304no—
310C2×Q8—51no—
311C2×Q8—51no—
312C2×Q8—151no—
313C2×Q8—151no—
314C2×Q8—151no—
315C2×Q8—304no—
316C2×D4—31no—
317C2×D4—151no—
318C2×D4—151no—
319C22×C4—31no—
320C22×C4—151no—
321C22×C4—151no—
322C22×C4—151no—
323C22×C4—151no—
324C4⋊C4—31no—
325C4⋊C4—51no—
326C4⋊C4—51no—
327C4⋊C4—51no—
328C4⋊C4—151no—
329C4⋊C4—151no—
330C4⋊C4—151no—
331C4⋊C4—151no—
332C4⋊C4—151no—
333C4⋊C4D3×D511yescharacteristic
334C22⋊C4—31no—
335C22⋊C4—31no—
336C22⋊C4—31no—
337C22⋊C4—151no—
338C22⋊C4—151no—
339C22⋊C4—151no—
340C22⋊C4—151no—
341C22⋊C4—151no—
342C22⋊C4—151no—
343C22⋊C4—151no—
344C42—51no—
345C42—151no—
346C3×C5#53611yescharacteristic, complemented, Hall
347C22×C3C23×D511yescharacteristic
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—101no—
354C2×D3—101no—
355C2×D3—101no—
356C2×D3D4×D512yes—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—52no—
361C3×C4—101no—
362C3×C4—101no—
363C3×C4—101no—
364Dic3—21no—
365Dic3—21no—
366Dic3—52no—
367Dic3—101no—
368Dic3—101no—
369C2×C5—62no—
370C2×C5—121no—
371C2×C5C2×D3×D411yescharacteristic
372C2×C5#100711yescharacteristic
373C2×C5#100711yescharacteristic
374D5—121no—
375C23—31no—
376C23—31no—
377C23—151no—
378Q8—102no—
379Q8—102no—
380Q8—302no—
381Q8—302no—
382Q8—302no—
383D4—62no—
384D4—302no—
385D4—302no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—62no—
393C2×C4—154no—
394C2×C4—151no—
395C2×C4—151no—
396C2×C4—151no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4C2×D3×D511yescharacteristic
401C2×C4C2×D3×D511yescharacteristic
402C2×C4C2×D3×D511yescharacteristic
403C2×C3C2×D4×D511yescharacteristic
404C2×C3#415011yescharacteristic
405C2×C3#415011yescharacteristic
406D3—22no—
407D3—41no—
408D3—201no—
409C5#572411yescharacteristic, complemented, Sylow
410C22—32no—
411C22—61no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—52no—
424C4—61no—
425C4—61no—
426C4—101no—
427C4—101no—
428C4—101no—
429C4—152no—
430C4—301no—
431C4—301no—
432C3#6598211yescharacteristic, complemented, Sylow
433C2—62no—
434C2—121no—
435C2—601no—
436C2#9200411yescharacteristic
437C2D3×D4×D511yescharacteristic
438C2#9203011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#6768C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic10C2semidirect
3. #91785C2semidirect
4. C5×#894C2semidirect
5. C3×#4034C2semidirect
6. #91436C2semidirect
7. #91432C2semidirect
8. #91427C2semidirect
9. #91423C2semidirect
10. #91398C2semidirect
11. #91377C2semidirect
12. #91351C2semidirect
13. #91350C2semidirect
14. #91327C2semidirect
15. #91326C2semidirect
63. #4034D3semidirect
110. #894D5semidirect
346. C3×C5#536semidirect
409. C5#5724semidirect
432. C3#65982semidirect

Maximal subgroups

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

subgroupindex
C2×#67682
C2×D3×Dic102
#917852
C5×#8942
C3×#40342
#914362
#914322
#914272
#914232
#913982
#913772
#913512
#913502
#913272
#913262
#659823
#57245