Finite Group Databasebeta

← #11756352

Subgroups — #11756352

Order 960.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#120C211yesmaximal, characteristic, complemented
2#91842C211yesmaximal, characteristic, complemented
3C2×#6719C211yesmaximal, characteristic, complemented
4#91828C211yesmaximal, characteristic, complemented
5#91828C211yesmaximal, characteristic, complemented
6#91827C211yesmaximal, characteristic, complemented
7#91825C211yesmaximal, characteristic, complemented
8#91824C211yesmaximal, characteristic, complemented
9D4×Dic15C211yesmaximal, characteristic, complemented
10#91774C211yesmaximal, characteristic, complemented
11#91772C211yesmaximal, characteristic, complemented
12#91770C211yesmaximal, characteristic, complemented
13#91768C211yesmaximal, characteristic, complemented
14#91768C211yesmaximal, characteristic, complemented
15#91767C211yesmaximal, characteristic, complemented
16#65927—31nomaximal, Hall
17C24×C3×C5C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic
20C2×C3×C5×D4C2211yescharacteristic
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C2×#1220C2211yescharacteristic
24C2×#1220C2211yescharacteristic, complemented
25C22×Dic15C2211yescharacteristic
26C22×Dic15C2211yescharacteristic
27C22×Dic15C2211yescharacteristic, complemented
28C2×C4×D15C2211yescharacteristic, complemented
29C2×Dic30C2211yescharacteristic, complemented
30C3×C5×C22⋊C4C2211yescharacteristic
31C3×C5×C22⋊C4C2211yescharacteristic
32C3×C5×C22⋊C4C2211yescharacteristic
33#6719C2211yescharacteristic
34#6719C2211yescharacteristic
35#6719C2211yescharacteristic
36#6719C2211yescharacteristic
37#6719C2211yescharacteristic
38#6719C2211yescharacteristic
39#6719C2211yescharacteristic
40#6719C2211yescharacteristic, complemented
41#6719C2211yescharacteristic, complemented
42#6714C2211yescharacteristic, complemented
43#6714C2211yescharacteristic, complemented
44C4⋊Dic15C2211yescharacteristic, complemented
45C4⋊Dic15C2211yescharacteristic, complemented
46#6712C2211yescharacteristic, complemented
47#6712C2211yescharacteristic, complemented
48#6712C2211yescharacteristic, complemented
49#6712C2211yescharacteristic, complemented
50C4×Dic15C2211yescharacteristic, complemented
51C4×Dic15C2211yescharacteristic, complemented
52#5593—51nomaximal, Hall
53C5×#120D311yescharacteristic, complemented
54#4099—31no—
55C2×C22⋊Dic5—31no—
56#4085—31no—
57#4085—31no—
58#4084—31no—
59#4082—31no—
60#4081—31no—
61D4×Dic5—31no—
62#4031—31no—
63#4029—31no—
64#4027—31no—
65#4025—31no—
66#4025—31no—
67#4024—31no—
68C23×C3×C5—22no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5C2311yescharacteristic
72C23×C3×C5C2311yescharacteristic
73C23×C3×C5C2311yescharacteristic
74C23×C3×C5C2311yescharacteristic
75C22×D15C2311yescharacteristic
76C3×C5×D4—22no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C2×C3×C4×C5C2311yescharacteristic
80C2×C3×C4×C5C2311yescharacteristic
81C2×C3×C4×C5C2311yescharacteristic
82#1220—22no—
83#1220—41no—
84#1220—41no—
85#1220—41no—
86C2×Dic15—41no—
87C2×Dic15—41no—
88C2×Dic15—41no—
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C2×Dic15C2311yescharacteristic
92C2×Dic15C2311yescharacteristic
93C2×Dic15C2311yescharacteristic
94C2×Dic15C2311yescharacteristic
95C2×Dic15C2311yescharacteristic
96C4×D15—41no—
97Dic30—41no—
98C3×#120D511yescharacteristic, complemented
99#953—51no—
100C2×#217—51no—
101#939—51no—
102#939—51no—
103#938—51no—
104#936—51no—
105#935—51no—
106D4×Dic3—51no—
107#885—51no—
108#883—51no—
109#67⋊C4—51no—
110#879—51no—
111#879—51no—
112#878—51no—
113C24×C5C2×D311yescharacteristic
114C2×C5×D4C2×D311yescharacteristic
115C2×C5×D4C2×D311yescharacteristic
116C2×C5×D4C2×D311yescharacteristic
117C2×C22⋊D5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5—31no—
121C22×Dic5—31no—
122C22×Dic5—31no—
123C22×Dic5—31no—
124C2×C4×D5—31no—
125C2×Dic10—31no—
126C5×C22⋊C4C2×D311yescharacteristic
127C5×C22⋊C4C2×D311yescharacteristic
128C5×C22⋊C4C2×D311yescharacteristic
129C22⋊Dic5—31no—
130C22⋊Dic5—31no—
131C22⋊Dic5—31no—
132C22⋊Dic5—31no—
133C22⋊Dic5—31no—
134C22⋊Dic5—31no—
135C22⋊Dic5—31no—
136C22⋊Dic5—31no—
137C22⋊Dic5—31no—
138#685—31no—
139#685—31no—
140C4⋊Dic5—31no—
141C4⋊Dic5—31no—
142#683—31no—
143#683—31no—
144#683—31no—
145#683—31no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148#538—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5—21no—
160C22×C3×C5—44no—
161C22×C3×C5#4112yes—
162C22×C3×C5C2411yescharacteristic
163C2×D15—21no—
164C2×D15—21no—
165C2×D15—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169Dic15—21no—
170Dic15—21no—
171Dic15—21no—
172Dic15—21no—
173Dic15—21no—
174Dic15—21no—
175Dic15—21no—
176C24×C3C2×D511yescharacteristic
177C2×C3×D4C2×D511yescharacteristic
178C2×C3×D4C2×D511yescharacteristic
179C2×C3×D4C2×D511yescharacteristic
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67—51no—
184C22×Dic3—51no—
185C22×Dic3—51no—
186C22×Dic3—51no—
187C2×C4×D3—51no—
188C2×Dic6—51no—
189C3×C22⋊C4C2×D511yescharacteristic
190C3×C22⋊C4C2×D511yescharacteristic
191C3×C22⋊C4C2×D511yescharacteristic
192#217—51no—
193#217—51no—
194#217—51no—
195#217—51no—
196#217—51no—
197#217—51no—
198#217—51no—
199#217—51no—
200#217—51no—
201(C2×D3)⋊C4—51no—
202(C2×D3)⋊C4—51no—
203C4⋊Dic3—51no—
204C4⋊Dic3—51no—
205Dic3⋊C4—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4—51no—
208Dic3⋊C4—51no—
209C4×Dic3—51no—
210C4×Dic3—51no—
211C23×C5—22no—
212C23×C5—41no—
213C23×C5—41no—
214C23×C5C22×D311yescharacteristic
215C23×C5C22×D311yescharacteristic
216C23×C5C22×D311yescharacteristic
217C23×C5C22×D311yescharacteristic
218C22×D5—31no—
219C5×D4—22no—
220C5×D4—41no—
221C5×D4—41no—
222C2×C4×C5C22×D311yescharacteristic
223C2×C4×C5C22×D311yescharacteristic
224C2×C4×C5C22×D311yescharacteristic
225C22⋊D5—62no—
226C22⋊D5—121no—
227C22⋊D5—121no—
228C22⋊D5—121no—
229C2×Dic5—31no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238C2×Dic5—121no—
239C4×D5—121no—
240Dic10—121no—
241#126—151no—
242#126—151no—
243#124—151no—
244#124—151no—
245#123—151no—
246#123—151no—
247C22⋊Q8—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#120—151no—
252#120D1511yescharacteristic, complemented
253C4×D4—151no—
254C4×D4—151no—
255C2×C22⋊C4—151no—
256C2×C3×C5—22no—
257C2×C3×C5—41no—
258C2×C3×C5—41no—
259C2×C3×C5—41no—
260C2×C3×C5C2×#4111yescharacteristic
261C2×C3×C5H(5,𝔽2)11yescharacteristic
262C2×C3×C5H(5,𝔽2)11yescharacteristic
263D15—41no—
264C23×C3—22no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3C22×D511yescharacteristic
268C23×C3C22×D511yescharacteristic
269C23×C3C22×D511yescharacteristic
270C23×C3C22×D511yescharacteristic
271C22×D3—51no—
272C3×D4—22no—
273C3×D4—41no—
274C3×D4—41no—
275C2×C3×C4C22×D511yescharacteristic
276C2×C3×C4C22×D511yescharacteristic
277C2×C3×C4C22×D511yescharacteristic
278#67—102no—
279#67—201no—
280#67—201no—
281#67—201no—
282C2×Dic3—51no—
283C2×Dic3—51no—
284C2×Dic3—51no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—51no—
289C2×Dic3—201no—
290C2×Dic3—201no—
291C2×Dic3—201no—
292C4×D3—201no—
293Dic6—201no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—44no—
306C22×C5#23712yes—
307C22×C5C23×D311yescharacteristic
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—61no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—21no—
314Dic5—61no—
315Dic5—61no—
316Dic5—61no—
317Dic5—61no—
318Dic5—61no—
319Dic5—61no—
320Dic5—61no—
321C24C2×D1511yescharacteristic
322C2×Q8—151no—
323C2×D4—151no—
324C2×D4—151no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4C2×D1511yescharacteristic
328C2×D4C2×D1511yescharacteristic
329C2×D4C2×D1511yescharacteristic
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—151no—
335C4⋊C4—151no—
336C4⋊C4—151no—
337C4⋊C4—151no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C22⋊C4—151no—
341C22⋊C4—151no—
342C22⋊C4—151no—
343C22⋊C4—151no—
344C22⋊C4—151no—
345C22⋊C4—151no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4C2×D1511yescharacteristic
352C22⋊C4C2×D1511yescharacteristic
353C22⋊C4C2×D1511yescharacteristic
354C42—151no—
355C42—151no—
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—44no—
369C22×C3#71112yes—
370C22×C3C23×D511yescharacteristic
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—101no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377Dic3—101no—
378Dic3—101no—
379Dic3—101no—
380Dic3—101no—
381Dic3—101no—
382Dic3—101no—
383Dic3—101no—
384C2×C5—22no—
385C2×C5—41no—
386C2×C5—41no—
387C2×C5—41no—
388C2×C5C2×#23711yescharacteristic
389C2×C5#100411yescharacteristic
390C2×C5#100411yescharacteristic
391D5—121no—
392C23—22no—
393C23—41no—
394C23—41no—
395C23—151no—
396C23C22×D1511yescharacteristic
397C23C22×D1511yescharacteristic
398C23C22×D1511yescharacteristic
399C23C22×D1511yescharacteristic
400Q8—601no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—302no—
405D4—601no—
406D4—601no—
407D4—601no—
408C2×C4—151no—
409C2×C4—151no—
410C2×C4—151no—
411C2×C4—151no—
412C2×C4—151no—
413C2×C4—151no—
414C2×C4—151no—
415C2×C4—601no—
416C2×C4—601no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4C22×D1511yescharacteristic
420C2×C4C22×D1511yescharacteristic
421C2×C4C22×D1511yescharacteristic
422C2×C3—22no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3C2×#71111yescharacteristic
427C2×C3#414411yescharacteristic
428C2×C3#414411yescharacteristic
429D3—201no—
430C5#559311yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—44no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22#681912yes—
447C22C23×D1511yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—301no—
452C4—301no—
453C4—301no—
454C4—301no—
455C4—301no—
456C4—301no—
457C4—301no—
458C3#6592711yescharacteristic, complemented, Sylow
459C2—22no—
460C2—41no—
461C2—41no—
462C2—41no—
463C2—601no—
464C2C2×#681911yescharacteristic
465C2#9209511yescharacteristic
466C2#9209511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#120C2
hypercenter#120D15
hypocenterC3×C5#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C3×C5×#120C2semidirect
2. #91842C2semidirect
3. C2×#6719C2semidirect
4. #91828C2semidirect
5. #91828C2semidirect
6. #91827C2semidirect
7. #91825C2semidirect
8. #91824C2semidirect
9. D4×Dic15C2semidirect
10. #91774C2semidirect
11. #91772C2semidirect
12. #91770C2semidirect
13. #91768C2semidirect
14. #91768C2semidirect
15. #91767C2semidirect
24. C2×#1220C22semidirect
27. C22×Dic15C22semidirect
28. C2×C4×D15C22semidirect
29. C2×Dic30C22semidirect
40. #6719C22semidirect
41. #6719C22semidirect
42. #6714C22semidirect
43. #6714C22semidirect
44. C4⋊Dic15C22semidirect
45. C4⋊Dic15C22semidirect
46. #6712C22semidirect
47. #6712C22semidirect
48. #6712C22semidirect
49. #6712C22semidirect
50. C4×Dic15C22semidirect
51. C4×Dic15C22semidirect
53. C5×#120D3semidirect
98. C3×#120D5semidirect
252. #120D15semidirect
356. C3×C5#538semidirect
430. C5#5593semidirect
458. C3#65927semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1202
#918422
C2×#67192
#918282
#918272
#918252
#918242
D4×Dic152
#917742
#917722
#917702
#917682
#917672
#659273
#55935