Finite Group Databasebeta

← #11756315

Subgroups — #11756315

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
1C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2#91826C211yesmaximal, characteristic
3#91824C211yesmaximal, characteristic, complemented
4#91818C211yesmaximal, characteristic, complemented
5C4×#1220C211yesmaximal, characteristic, complemented
6C2×#6714C211yesmaximal, characteristic, complemented
7#91813C211yesmaximal, characteristic, complemented
8#91787C211yesmaximal, characteristic, complemented
9#91785C211yesmaximal, characteristic, complemented
10#91774C211yesmaximal, characteristic, complemented
11#91772C211yesmaximal, characteristic, complemented
12C22⋊C4×D15C211yesmaximal, characteristic, complemented
13#91766C211yesmaximal, characteristic, complemented
14#91765C211yesmaximal, characteristic, complemented
15#91761C211yesmaximal, characteristic, complemented
16#65890—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C22×C3×C4×C5C2211yescharacteristic
20C22×C3×C4×C5C2211yescharacteristic, complemented
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C22×Dic15C2211yescharacteristic
24C2×C4×D15C2211yescharacteristic
25C2×C4×D15C2211yescharacteristic
26C2×Dic30C2211yescharacteristic, complemented
27C3×C5×C4⋊C4C2211yescharacteristic, complemented
28C3×C5×C22⋊C4C2211yescharacteristic
29C3×C5×C22⋊C4C2211yescharacteristic, complemented
30C3×C42×C5C2211yescharacteristic, complemented
31#6719C2211yescharacteristic
32#6719C2211yescharacteristic
33#6719C2211yescharacteristic, complemented
34#6719C2211yescharacteristic, complemented
35#6714C2211yescharacteristic
36#6714C2211yescharacteristic
37#6714C2211yescharacteristic
38#6714C2211yescharacteristic
39#6714C2211yescharacteristic
40#6714C2211yescharacteristic
41#6714C2211yescharacteristic
42#6714C2211yescharacteristic
43C4⋊Dic15C2211yescharacteristic, complemented
44#6712C2211yescharacteristic, complemented
45#6712C2211yescharacteristic, complemented
46#6712C2211yescharacteristic, complemented
47#6712C2211yescharacteristic, complemented
48#6712C2211yescharacteristic, complemented
49#6712C2211yescharacteristic, complemented
50C4×Dic15C2211yescharacteristic, complemented
51C4×Dic15C2211yescharacteristic, complemented
52#5556—51nomaximal, Hall
53C4×C5×D4D311yescharacteristic, complemented
54#4083—31no—
55#4081—31no—
56#4075—31no—
57C4×C22⋊D5—31no—
58C2×#685—31no—
59#4070—31no—
60#4044—31no—
61#4042—31no—
62#4031—31no—
63#4029—31no—
64D5×C22⋊C4—31no—
65#4023—31no—
66#4022—31no—
67#4018—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×D15—22no—
71C22×D15—22no—
72C22×D15—41no—
73C22×D15C2311yescharacteristic
74C22×D15C2311yescharacteristic
75C3×C5×D4—22no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80C2×C3×C4×C5C2311yescharacteristic
81C2×C3×C4×C5C2311yescharacteristic
82C2×C3×C4×C5C2311yescharacteristic
83#1220—22no—
84#1220—41no—
85C2×Dic15—22no—
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C2×Dic15C2311yescharacteristic
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C2×Dic15C2311yescharacteristic
92C4×D15—22no—
93C4×D15—41no—
94Dic30—41no—
95C3×C4×D4D511yescharacteristic, complemented
96#937—51no—
97#935—51no—
98#929—51no—
99C4×#67—51no—
100C2×(C2×D3)⋊C4—51no—
101#924—51no—
102#898—51no—
103#896—51no—
104#885—51no—
105#883—51no—
106D3×C22⋊C4—51no—
107#877—51no—
108#876—51no—
109#872—51no—
110C23×D5—31no—
111C2×C5×D4C2×D311yescharacteristic
112C22×C4×C5C2×D311yescharacteristic
113C22×C4×C5C2×D311yescharacteristic, complemented
114C2×C22⋊D5—31no—
115C2×C22⋊D5—31no—
116C22×Dic5—31no—
117C2×C4×D5—31no—
118C2×C4×D5—31no—
119C2×Dic10—31no—
120C5×C4⋊C4C2×D311yescharacteristic, complemented
121C5×C22⋊C4C2×D311yescharacteristic
122C5×C22⋊C4C2×D311yescharacteristic, complemented
123C42×C5C2×D311yescharacteristic, complemented
124C22⋊Dic5—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#685—31no—
135#685—31no—
136C4⋊Dic5—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683—31no—
142#683—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145#551—151noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#4112yes—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—44no—
159C2×D15#4112yes—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165Dic15—21no—
166Dic15—21no—
167Dic15—21no—
168Dic15—21no—
169Dic15—21no—
170Dic15—21no—
171C23×D3—51no—
172C2×C3×D4C2×D511yescharacteristic
173C22×C3×C4C2×D511yescharacteristic
174C22×C3×C4C2×D511yescharacteristic, complemented
175C2×#67—51no—
176C2×#67—51no—
177C22×Dic3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×Dic6—51no—
181C3×C4⋊C4C2×D511yescharacteristic, complemented
182C3×C22⋊C4C2×D511yescharacteristic
183C3×C22⋊C4C2×D511yescharacteristic, complemented
184C3×C42C2×D511yescharacteristic, complemented
185#217—51no—
186#217—51no—
187#217—51no—
188#217—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)⋊C4—51no—
196(C2×D3)⋊C4—51no—
197C4⋊Dic3—51no—
198Dic3⋊C4—51no—
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C23×C5C22×D311yescharacteristic
207C23×C5C22×D311yescharacteristic
208C22×D5—31no—
209C22×D5—31no—
210C22×D5—62no—
211C22×D5—62no—
212C22×D5—121no—
213C5×D4—22no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5C22×D311yescharacteristic
217C2×C4×C5C22×D311yescharacteristic
218C2×C4×C5C22×D311yescharacteristic
219C2×C4×C5C22×D311yescharacteristic
220C2×C4×C5C22×D311yescharacteristic
221C22⋊D5—62no—
222C22⋊D5—121no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—31no—
227C2×Dic5—31no—
228C2×Dic5—31no—
229C2×Dic5—62no—
230C4×D5—62no—
231C4×D5—121no—
232Dic10—121no—
233#126—151no—
234#126—151no—
235#124—151no—
236#123—151no—
237#123—151no—
238#123—151no—
239C22⋊Q8—151no—
240C22⋊Q8—151no—
241#120—151no—
242C4×D4—151no—
243C4×D4D1511yescharacteristic, complemented
244#117—151no—
245#117—151no—
246C2×C22⋊C4—151no—
247C2×C22⋊C4—151no—
248C2×C3×C5—22no—
249C2×C3×C5—41no—
250C2×C3×C5C2×#4111yescharacteristic
251C2×C3×C5C2×#4111yescharacteristic
252C2×C3×C5H(5,𝔽2)11yescharacteristic
253D15—22no—
254D15—41no—
255C23×C3C22×D511yescharacteristic
256C23×C3C22×D511yescharacteristic
257C22×D3—51no—
258C22×D3—51no—
259C22×D3—102no—
260C22×D3—102no—
261C22×D3—201no—
262C3×D4—22no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4C22×D511yescharacteristic
266C2×C3×C4C22×D511yescharacteristic
267C2×C3×C4C22×D511yescharacteristic
268C2×C3×C4C22×D511yescharacteristic
269C2×C3×C4C22×D511yescharacteristic
270#67—102no—
271#67—201no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—51no—
275C2×Dic3—51no—
276C2×Dic3—51no—
277C2×Dic3—51no—
278C2×Dic3—102no—
279C4×D3—102no—
280C4×D3—201no—
281Dic6—201no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5#23512yes—
288C22×C5C23×D311yescharacteristic
289C2×D5—32no—
290C2×D5—61no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C2×D5—61no—
295C2×D5—124no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—21no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5—61no—
305Dic5—61no—
306Dic5—61no—
307C24—151no—
308C2×Q8—151no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4C2×D1511yescharacteristic
312C22×C4—151no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4C2×D1511yescharacteristic
316C22×C4C2×D1511yescharacteristic, complemented
317C4⋊C4—151no—
318C4⋊C4—151no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4C2×D1511yescharacteristic, complemented
325C22⋊C4—151no—
326C22⋊C4—151no—
327C22⋊C4—151no—
328C22⋊C4—151no—
329C22⋊C4—151no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C22⋊C4C2×D1511yescharacteristic
338C22⋊C4C2×D1511yescharacteristic, complemented
339C42—151no—
340C42—151no—
341C42C2×D1511yescharacteristic, complemented
342C3×C5#55111yescharacteristic, complemented, Hall
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3#70912yes—
349C22×C3C23×D511yescharacteristic
350C2×D3—52no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C2×D3—101no—
355C2×D3—101no—
356C2×D3—204no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365Dic3—101no—
366Dic3—101no—
367Dic3—101no—
368C2×C5—22no—
369C2×C5—41no—
370C2×C5C2×#23511yescharacteristic
371C2×C5#100411yescharacteristic
372C2×C5D3×#4111yescharacteristic
373D5—62no—
374D5—121no—
375C23—151no—
376C23—151no—
377C23—302no—
378C23—302no—
379C23—601no—
380C23C22×D1511yescharacteristic
381C23C22×D1511yescharacteristic
382Q8—601no—
383D4—22no—
384D4—302no—
385D4—601no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—302no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4C22×D1511yescharacteristic
398C2×C4C22×D1511yescharacteristic
399C2×C4C22×D1511yescharacteristic
400C2×C4C22×D1511yescharacteristic
401C2×C4C22×D1511yescharacteristic
402C2×C3—22no—
403C2×C3—41no—
404C2×C3C2×#70911yescharacteristic
405C2×C3#414411yescharacteristic
406C2×C3D5×#4111yescharacteristic
407D3—102no—
408D3—201no—
409C5#555611yescharacteristic, complemented, Sylow
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—152no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22—301no—
420C22—301no—
421C22—604no—
422C22#681712yes—
423C22C23×D1511yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—301no—
430C4—301no—
431C4—301no—
432C4—301no—
433C4—301no—
434C4—301no—
435C3#6589011yescharacteristic, complemented, Sylow
436C2—22no—
437C2—41no—
438C2—302no—
439C2—601no—
440C2C2×#681711yescharacteristic
441C2#9209511yescharacteristic
442C2#41×D1511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C4×C5×D4C2
prime radical#91826C2
hypercenterC4×D4D15
hypocenterC3×C5#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×C5×D4C2semidirect
3. #91824C2semidirect
4. #91818C2semidirect
5. C4×#1220C2semidirect
6. C2×#6714C2semidirect
7. #91813C2semidirect
8. #91787C2semidirect
9. #91785C2semidirect
10. #91774C2semidirect
11. #91772C2semidirect
12. C22⋊C4×D15C2semidirect
13. #91766C2semidirect
14. #91765C2semidirect
15. #91761C2semidirect
20. C22×C3×C4×C5C22semidirect
26. C2×Dic30C22semidirect
27. C3×C5×C4⋊C4C22semidirect
29. C3×C5×C22⋊C4C22semidirect
30. C3×C42×C5C22semidirect
33. #6719C22semidirect
34. #6719C22semidirect
43. C4⋊Dic15C22semidirect
44. #6712C22semidirect
45. #6712C22semidirect
46. #6712C22semidirect
47. #6712C22semidirect
48. #6712C22semidirect
49. #6712C22semidirect
50. C4×Dic15C22semidirect
51. C4×Dic15C22semidirect
53. C4×C5×D4D3semidirect
95. C3×C4×D4D5semidirect
113. C22×C4×C5C2×D3semidirect
120. C5×C4⋊C4C2×D3semidirect
122. C5×C22⋊C4C2×D3semidirect
123. C42×C5C2×D3semidirect
174. C22×C3×C4C2×D5semidirect
181. C3×C4⋊C4C2×D5semidirect
183. C3×C22⋊C4C2×D5semidirect
184. C3×C42C2×D5semidirect
243. C4×D4D15semidirect
316. C22×C4C2×D15semidirect
324. C4⋊C4C2×D15semidirect
338. C22⋊C4C2×D15semidirect
341. C42C2×D15semidirect
342. C3×C5#551semidirect
409. C5#5556semidirect
435. C3#65890semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×D42
#918262
#918242
#918182
C4×#12202
C2×#67142
#918132
#917872
#917852
#917742
#917722
C22⋊C4×D152
#917662
#917652
#917612
#658903
#55565