Finite Group Databasebeta

← #11753911

Subgroups — #11753911

Order 960.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91787C211yesmaximal, characteristic, complemented
2C5×#894C211yesmaximal, characteristic, complemented
3C3×#4043C211yesmaximal, characteristic, complemented
4#91475C211yesmaximal, characteristic
5D3×#685C211yesmaximal, characteristic, complemented
6D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#91440C211yesmaximal, characteristic, complemented
8#91435C211yesmaximal, characteristic, complemented
9#91427C211yesmaximal, characteristic, complemented
10#91414C211yesmaximal, characteristic, complemented
11#91410C211yesmaximal, characteristic, complemented
12#91394C211yesmaximal, characteristic, complemented
13#91345C211yesmaximal, characteristic, complemented
14#91338C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65992—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×C5×D12C2211yescharacteristic
19C2×C4×C5×D3C2211yescharacteristic
20C2×C3×C4×D5C2211yescharacteristic
21C2×C3×Dic10C2211yescharacteristic, complemented
22C2×#1203C2211yescharacteristic
23C2×#1201C2211yescharacteristic
24C2×D3×Dic5C2211yescharacteristic
25C2×D3×Dic5C2211yescharacteristic, complemented
26C2×D5×Dic3C2211yescharacteristic
27C3×C5×C4⋊C4C2211yescharacteristic, complemented
28#6714C2211yescharacteristic
29#6714C2211yescharacteristic
30#6714C2211yescharacteristic
31C4⋊Dic15C2211yescharacteristic, complemented
32#6712C2211yescharacteristic, complemented
33C4×Dic15C2211yescharacteristic, complemented
34C5×(C2×D3)⋊C4C2211yescharacteristic
35C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C5×Dic3⋊C4C2211yescharacteristic, complemented
38C3×#685C2211yescharacteristic
39C3×#685C2211yescharacteristic
40C3×C4⋊Dic5C2211yescharacteristic, complemented
41C3×C4⋊Dic5C2211yescharacteristic, complemented
42Dic3⋊Dic5C2211yescharacteristic, complemented
43#6668C2211yescharacteristic, complemented
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49#6665C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5637—51nomaximal, Hall
53C5×#123—31no—
54#4083—31no—
55D4×Dic5—31no—
56C2×#685—31no—
57#4072—31no—
58#4044—31no—
59#4044—31no—
60#4043D311yescharacteristic, complemented
61#4038—31no—
62#4032—31no—
63#4031—31no—
64#4029—31no—
65#4027—31no—
66D5×C22⋊C4—31no—
67#4024—31no—
68C22×D15C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×D3×D5—22no—
73C2×D3×D5—22no—
74C2×D3×D5—41no—
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C5×D12—22no—
84C4×C5×D3—22no—
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C3×C4×D5—41no—
89C3×Dic10—41no—
90#1203—41no—
91#1201—22no—
92D3×Dic5—41no—
93D3×Dic5—41no—
94D5×Dic3—22no—
95C3×C22⋊Q8—51no—
96#947—51no—
97#946—51no—
98C4×#67—51no—
99C2×(C2×D3)⋊C4—51no—
100#898—51no—
101#898—51no—
102#894—51no—
103#894D511yescharacteristic, complemented
104#893—51no—
105#892—51no—
106#886—51no—
107#882—51no—
108D3×C22⋊C4—51no—
109#877—51no—
110C23×D5—31no—
111C2×C5×D4—31no—
112C22×C4×C5—31no—
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C22×Dic5—31no—
116C22×Dic5—31no—
117C2×C4×D5—31no—
118C2×C4×D5C2×D311yescharacteristic
119C2×Dic10C2×D311yescharacteristic, complemented
120C5×C4⋊C4—31no—
121C5×C4⋊C4C2×D311yescharacteristic, complemented
122C5×C22⋊C4—31no—
123C5×C22⋊C4—31no—
124C5×C22⋊C4—31no—
125C22⋊Dic5—31no—
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134#685C2×D311yescharacteristic
135#685C2×D311yescharacteristic
136C4⋊Dic5—31no—
137C4⋊Dic5—31no—
138C4⋊Dic5C2×D311yescharacteristic, complemented
139C4⋊Dic5C2×D311yescharacteristic, complemented
140#683—31no—
141#683—31no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145#551—151noSylow
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×C5×D3—21no—
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C2×C5×D3—21no—
154C2×C5×D3—21no—
155C2×C5×D3#4112yes—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5#4112yes—
159D3×D5—44no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163Dic15—21no—
164Dic15—21no—
165Dic15—21no—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C5×Dic3—21no—
170C5×Dic3—21no—
171C23×D3—51no—
172C2×C3×Q8—51no—
173C22×C3×C4—51no—
174C2×#67—51no—
175C22×Dic3—51no—
176C2×D12—51no—
177C2×D12C2×D511yescharacteristic
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×C4×D3C2×D511yescharacteristic
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4C2×D511yescharacteristic, complemented
184C3×C22⋊C4—51no—
185C3×C22⋊C4—51no—
186#217—51no—
187(C2×D3)⋊C4—51no—
188(C2×D3)⋊C4—51no—
189(C2×D3)⋊C4—51no—
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4—51no—
195(C2×D3)⋊C4C2×D511yescharacteristic
196(C2×D3)⋊C4C2×D511yescharacteristic, complemented
197(C2×D3)⋊C4C2×D511yescharacteristic, complemented
198C4⋊Dic3—51no—
199C4⋊Dic3—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4C2×D511yescharacteristic, complemented
203C4×Dic3—51no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C23×C5—31no—
207C23×C5—31no—
208C22×D5—31no—
209C22×D5—62no—
210C22×D5—62no—
211C22×D5—121no—
212C22×D5C22×D311yescharacteristic
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—121no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—121no—
226C2×Dic5—121no—
227C2×Dic5C22×D311yescharacteristic
228C2×Dic5C22×D311yescharacteristic
229C2×Dic5C22×D311yescharacteristic
230C4×D5—41no—
231C4×D5—62no—
232Dic10—41no—
233#126—151no—
234#126—151no—
235#124—151no—
236#123—31no—
237#123—151no—
238#123—151no—
239C22⋊Q8—51no—
240C22⋊Q8—151no—
241#120—151no—
242C4×D4—151no—
243C4×D4—151no—
244#117—151no—
245#117—151no—
246C2×C22⋊C4—151no—
247C2×C22⋊C4—151no—
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5H(5,𝔽2)11yescharacteristic
251D15—41no—
252C3×D5—22no—
253C5×D3—22no—
254C5×D3—41no—
255C23×C3—51no—
256C22×D3—51no—
257C22×D3—102no—
258C22×D3—102no—
259C22×D3—201no—
260C22×D3C22×D511yescharacteristic
261C22×D3C22×D511yescharacteristic
262C3×Q8—201no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—201no—
267C2×C3×C4C22×D511yescharacteristic
268C2×C3×C4C22×D511yescharacteristic
269C2×C3×C4C22×D511yescharacteristic
270#67—102no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—102no—
275C2×Dic3C22×D511yescharacteristic
276C2×Dic3C22×D511yescharacteristic
277D12—22no—
278D12—201no—
279C4×D3—22no—
280C4×D3—201no—
281C4×D3—201no—
282C22×C5—32no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5—61no—
286C22×C5—61no—
287C22×C5—61no—
288C22×C5C23×D311yescharacteristic
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C2×D5—124no—
295C2×D5#23912yes—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—61no—
300C4×C5—61no—
301Dic5—21no—
302Dic5—21no—
303Dic5—21no—
304Dic5—61no—
305Dic5—61no—
306Dic5—61no—
307C24—151no—
308C2×Q8—51no—
309C2×D4—31no—
310C2×D4—151no—
311C2×D4—151no—
312C22×C4—31no—
313C22×C4—51no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—51no—
319C4⋊C4—51no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4D3×D511yescharacteristic, complemented
325C22⋊C4—31no—
326C22⋊C4—31no—
327C22⋊C4—31no—
328C22⋊C4—51no—
329C22⋊C4—51no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C22⋊C4—151no—
338C22⋊C4—151no—
339C42—151no—
340C42—151no—
341C42—151no—
342C3×C5#55111yescharacteristic, complemented, Hall
343C22×C3—52no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3C23×D511yescharacteristic
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—101no—
353C2×D3—101no—
354C2×D3—101no—
355C2×D3—204no—
356C2×D3#71112yes—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—101no—
363Dic3—21no—
364Dic3—21no—
365Dic3—101no—
366Dic3—101no—
367Dic3—101no—
368C2×C5—62no—
369C2×C5—121no—
370C2×C5#100411yescharacteristic
371C2×C5C2×#23911yescharacteristic
372C2×C5D3×#4111yescharacteristic
373D5—22no—
374D5—121no—
375C23—31no—
376C23—31no—
377C23—51no—
378C23—151no—
379C23—302no—
380C23—302no—
381C23—601no—
382Q8—201no—
383D4—62no—
384D4—302no—
385D4—601no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—62no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—201no—
396C2×C4—302no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4C2×D3×D511yescharacteristic
400C2×C4C2×D3×D511yescharacteristic
401C2×C4C2×D3×D511yescharacteristic
402C2×C3—102no—
403C2×C3C2×#71111yescharacteristic
404C2×C3D5×#4111yescharacteristic
405C2×C3#414911yescharacteristic
406D3—22no—
407D3—41no—
408D3—201no—
409C5#563711yescharacteristic, complemented, Sylow
410C22—32no—
411C22—52no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—61no—
417C22—101no—
418C22—101no—
419C22—301no—
420C22—301no—
421C22—301no—
422C22—604no—
423C22C22×D3×D511yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—61no—
428C4—61no—
429C4—101no—
430C4—101no—
431C4—101no—
432C4—301no—
433C4—301no—
434C4—301no—
435C3#6599211yescharacteristic, complemented, Sylow
436C2—62no—
437C2—102no—
438C2—121no—
439C2—601no—
440C2#9201711yescharacteristic
441C2D3×#71111yescharacteristic
442C2D5×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radical#91475C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#551
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. #91787C2semidirect
2. C5×#894C2semidirect
3. C3×#4043C2semidirect
5. D3×#685C2semidirect
6. D5×(C2×D3)⋊C4C2semidirect
7. #91440C2semidirect
8. #91435C2semidirect
9. #91427C2semidirect
10. #91414C2semidirect
11. #91410C2semidirect
12. #91394C2semidirect
13. #91345C2semidirect
14. #91338C2semidirect
15. #91326C2semidirect
21. C2×C3×Dic10C22semidirect
25. C2×D3×Dic5C22semidirect
27. C3×C5×C4⋊C4C22semidirect
31. C4⋊Dic15C22semidirect
32. #6712C22semidirect
33. C4×Dic15C22semidirect
35. C5×(C2×D3)⋊C4C22semidirect
36. C5×(C2×D3)⋊C4C22semidirect
37. C5×Dic3⋊C4C22semidirect
40. C3×C4⋊Dic5C22semidirect
41. C3×C4⋊Dic5C22semidirect
42. Dic3⋊Dic5C22semidirect
43. #6668C22semidirect
48. (C2×D3)⋊Dic5C22semidirect
50. Dic3×Dic5C22semidirect
51. Dic3×Dic5C22semidirect
60. #4043D3semidirect
103. #894D5semidirect
119. C2×Dic10C2×D3semidirect
121. C5×C4⋊C4C2×D3semidirect
138. C4⋊Dic5C2×D3semidirect
139. C4⋊Dic5C2×D3semidirect
183. C3×C4⋊C4C2×D5semidirect
196. (C2×D3)⋊C4C2×D5semidirect
197. (C2×D3)⋊C4C2×D5semidirect
202. Dic3⋊C4C2×D5semidirect
324. C4⋊C4D3×D5semidirect
342. C3×C5#551semidirect
409. C5#5637semidirect
435. C3#65992semidirect

Maximal subgroups

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

subgroupindex
#917872
C5×#8942
C3×#40432
#914752
D3×#6852
D5×(C2×D3)⋊C42
#914402
#914352
#914272
#914142
#914102
#913942
#913452
#913382
#913262
#659923
#56375