Finite Group Databasebeta

← #14425746

Subgroups — #14425746

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757146C211yesmaximal, characteristic, complemented
2C3×C5×#535C211yesmaximal, characteristic, complemented
3#11756564C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11751133C218yesmaximal, complemented
6#11751107C212yesmaximal, complemented
7#10615127—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×C3×C5×D4C2211yescharacteristic, complemented
10#92101—22no—
11#92100—22no—
12#41×D15—24no—
13#92098—21no—
14#92095—21no—
15#92095C2214yes—
16C2×#6817—22no—
17C2×#6817C2212yes—
18C3×C5×#127—21no—
19C3×C5×#124—21no—
20C3×C5×#121—22no—
21C3×C5×#120C2214yescomplemented
22C3×C5×#117C2211yescharacteristic, complemented
23#91842C2218yescomplemented
24#91829—22no—
25#91827—24no—
26#91825—22no—
27#91815C2212yescomplemented
28#91118C2214yescomplemented
29#91090C2218yescomplemented
30#83396—51nomaximal, Hall
31#66283—31no—
32C5×#535D311yescharacteristic, complemented
33#66139—32no—
34#65529—31no—
35#65321—38no—
36#65295—32no—
37C24×C3×C5C2312yes—
38C3×C5×#41—22no—
39C3×C5×#41—22no—
40C2×C3×C5×Q8D411yescharacteristic, complemented
41C2×C3×C5×D4—24no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4D411yescharacteristic, complemented
47C2×C3×C5×D4C2312yes—
48C22×C3×C4×C5D412yescomplemented
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220—24no—
51C2×#1220—28no—
52C2×#1220C2314yes—
53#6821—24no—
54Q8×D15—24no—
55#6819—24no—
56#6819—28no—
57D4×D15—24no—
58D4×D15—28no—
59#6817—24no—
60#6817—24no—
61#6817—22no—
62#6817—24no—
63#6817—22no—
64#6817—22no—
65#6817—22no—
66C2×D60—22no—
67C2×D60D412yescomplemented
68C2×C4×D15—24no—
69C2×C4×D15D414yescomplemented
70C2×Dic30—22no—
71C2×Dic30D412yescomplemented
72C3×C5×C4⋊C4—21no—
73C3×C5×C22⋊C4—24no—
74C3×C5×C22⋊C4C2312yes—
75C3×C42×C5—21no—
76#6719—28no—
77#6719C2314yes—
78C4⋊Dic15—22no—
79C4×Dic15—22no—
80#5964—51no—
81C3×#535D511yescharacteristic, complemented
82#5805—52no—
83#5240—51no—
84#5032—58no—
85#5006—52no—
86C2×C5×#41C2×D311yescharacteristic
87C22×C5×D4C2×D311yescharacteristic, complemented
88#4150—62no—
89#4149—62no—
90D5×#41—64no—
91#4147—61no—
92#4144—34no—
93#4144—61no—
94C2×#709—32no—
95C2×#709—62no—
96C5×#127—21no—
97C5×#124—21no—
98C5×#121—22no—
99C5×#120C2×D314yescomplemented
100C5×#117C2×D311yescharacteristic, complemented
101#4099—38no—
102#4086—62no—
103#4084—64no—
104#4082—62no—
105#4072—32no—
106#3966—34no—
107#3938—38no—
108#3027—151noSylow
109C23×C3×C5—24no—
110C23×C3×C5—22no—
111C23×C3×C5—82no—
112C23×C3×C5C2×D412yes—
113C23×C3×C5C2411yescharacteristic
114C22×D15—24no—
115C22×D15C2×D414yes—
116C3×C5×Q8—22no—
117C3×C5×D4—24no—
118C3×C5×D4—22no—
119C3×C5×D4—41no—
120C3×C5×D4—42no—
121C3×C5×D4—41no—
122C3×C5×D4—84no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131#1220—28no—
132#1220—24no—
133#1220—24no—
134#1220—88no—
135C2×Dic15—24no—
136C2×Dic15—24no—
137C2×Dic15C2×D414yes—
138D60—24no—
139D60—22no—
140D60—22no—
141C4×D15—28no—
142C4×D15—24no—
143C4×D15—24no—
144Dic30—24no—
145Dic30—22no—
146Dic30—22no—
147C2×C3×#41C2×D511yescharacteristic
148C22×C3×D4C2×D511yescharacteristic, complemented
149#1010—102no—
150#1009—102no—
151D3×#41—104no—
152#1007—101no—
153#1004—54no—
154#1004—101no—
155C2×#235—52no—
156C2×#235—102no—
157C3×#127—21no—
158C3×#124—21no—
159C3×#121—22no—
160C3×#120C2×D514yescomplemented
161C3×#117C2×D511yescharacteristic, complemented
162#953—58no—
163#940—102no—
164#938—104no—
165#936—102no—
166#926—52no—
167#834—54no—
168#806—58no—
169C24×C5C22×D312yes—
170C5×#41—22no—
171C5×#41—22no—
172C2×C5×Q8#6711yescharacteristic, complemented
173C2×C5×D4—24no—
174C2×C5×D4—22no—
175C2×C5×D4—22no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4#6711yescharacteristic, complemented
179C2×C5×D4C22×D312yes—
180C22×C4×C5#6712yescomplemented
181C22×C4×C5C22×D311yescharacteristic
182C2×C22⋊D5—34no—
183C2×C22⋊D5—64no—
184C2×C22⋊D5—68no—
185#713—64no—
186Q8×D5—64no—
187#711—68no—
188#711—64no—
189D4×D5—68no—
190D4×D5—64no—
191#709—64no—
192#709—64no—
193#709—62no—
194#709—62no—
195#709—62no—
196#709—62no—
197#709—64no—
198C2×D20—32no—
199C2×D20—62no—
200C2×C4×D5—34no—
201C2×C4×D5—64no—
202C2×Dic10—32no—
203C2×Dic10—62no—
204C5×C4⋊C4—21no—
205C5×C22⋊C4—24no—
206C5×C22⋊C4C22×D312yes—
207C42×C5—21no—
208C22⋊Dic5—34no—
209C22⋊Dic5—68no—
210C4⋊Dic5—62no—
211C4×Dic5—62no—
212#585—151no—
213#535—152no—
214#535D1511yescharacteristic, complemented
215B(4,𝔽2)—158no—
216#410—151no—
217#410—152no—
218C22×C3×C5—22no—
219C22×C3×C5—41no—
220C22×C3×C5—42no—
221C22×C3×C5—48no—
222C22×C3×C5—44no—
223C22×C3×C5—42no—
224C22×C3×C5C22×D412yes—
225C22×C3×C5C22×D411yescharacteristic
226C2×D15—24no—
227C2×D15—44no—
228C2×D15—84no—
229C3×C4×C5—22no—
230C3×C4×C5—42no—
231C3×C4×C5#12011yescharacteristic
232C3×C4×C5#12012yes—
233C3×C4×C5#12011yescharacteristic
234Dic15—24no—
235Dic15—44no—
236C24×C3C22×D512yes—
237C3×#41—22no—
238C3×#41—22no—
239C2×C3×Q8C22⋊D511yescharacteristic, complemented
240C2×C3×D4—24no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4C22⋊D511yescharacteristic, complemented
246C2×C3×D4C22×D512yes—
247C22×C3×C4C22⋊D512yescomplemented
248C22×C3×C4C22×D511yescharacteristic
249C2×#67—54no—
250C2×#67—104no—
251C2×#67—108no—
252#239—104no—
253D3×Q8—104no—
254#237—108no—
255#237—104no—
256D3×D4—108no—
257D3×D4—104no—
258#235—104no—
259#235—104no—
260#235—102no—
261#235—102no—
262#235—102no—
263#235—102no—
264#235—104no—
265C2×D12—52no—
266C2×D12—102no—
267C2×C4×D3—54no—
268C2×C4×D3—104no—
269C2×Dic6—52no—
270C2×Dic6—102no—
271C3×C4⋊C4—21no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4C22×D512yes—
274C3×C42—21no—
275#217—54no—
276#217—108no—
277C4⋊Dic3—102no—
278C4×Dic3—102no—
279C23×C5—24no—
280C23×C5—22no—
281C23×C5—82no—
282C23×C5C2×#6712yes—
283C23×C5C23×D311yescharacteristic
284C22×D5—34no—
285C22×D5—64no—
286C5×Q8—22no—
287C5×D4—24no—
288C5×D4—22no—
289C5×D4—41no—
290C5×D4—42no—
291C5×D4—41no—
292C5×D4—84no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5D3×D412yes—
297C2×C4×C5D3×D412yes—
298C2×C4×C5C2×#6712yes—
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C2×#6711yescharacteristic
301C22⋊D5—68no—
302C22⋊D5—64no—
303C22⋊D5—64no—
304C22⋊D5—248no—
305C2×Dic5—34no—
306C2×Dic5—64no—
307C2×Dic5—64no—
308D20—64no—
309D20—62no—
310D20—62no—
311C4×D5—68no—
312C4×D5—64no—
313C4×D5—64no—
314Dic10—64no—
315Dic10—62no—
316Dic10—62no—
3172−1+4—302no—
3182−1+4—301no—
319H(5,𝔽2)—154no—
320H(5,𝔽2)—302no—
321H(5,𝔽2)—301no—
322C2×#41—152no—
323C2×#41—304no—
324C2×#41—302no—
325C2×#41C2×D1511yescharacteristic
326C22×D4C2×D1511yescharacteristic, complemented
327#127—21no—
328#127—302no—
329#124—21no—
330#124—302no—
331#121—22no—
332#121—304no—
333#120—158no—
334#120C2×D1514yescomplemented
335#117—152no—
336#117C2×D1511yescharacteristic, complemented
337#99—154no—
338#99—158no—
339C2×C3×C5—22no—
340C2×C3×C5—21no—
341C2×C3×C5—42no—
342C2×C3×C5—82no—
343C2×C3×C5C2×#12011yescharacteristic
344D15—44no—
345C23×C3—24no—
346C23×C3—22no—
347C23×C3—82no—
348C23×C3C2×C22⋊D512yes—
349C23×C3C23×D511yescharacteristic
350C22×D3—54no—
351C22×D3—104no—
352C3×Q8—22no—
353C3×D4—24no—
354C3×D4—22no—
355C3×D4—41no—
356C3×D4—42no—
357C3×D4—41no—
358C3×D4—84no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4D4×D512yes—
363C2×C3×C4D4×D512yes—
364C2×C3×C4C2×C22⋊D512yes—
365C2×C3×C4C2×C22⋊D511yescharacteristic
366C2×C3×C4C2×C22⋊D511yescharacteristic
367#67—108no—
368#67—104no—
369#67—104no—
370#67—408no—
371C2×Dic3—54no—
372C2×Dic3—104no—
373C2×Dic3—104no—
374D12—104no—
375D12—102no—
376D12—102no—
377C4×D3—108no—
378C4×D3—104no—
379C4×D3—104no—
380Dic6—104no—
381Dic6—102no—
382Dic6—102no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—42no—
386C22×C5—48no—
387C22×C5—44no—
388C22×C5—42no—
389C22×C5C2×D3×D412yes—
390C22×C5C22×#6711yescharacteristic
391C2×D5—64no—
392C2×D5—124no—
393C2×D5—244no—
394C4×C5—22no—
395C4×C5—42no—
396C4×C5#93711yescharacteristic
397C4×C5#93712yes—
398C4×C5#93711yescharacteristic
399Dic5—64no—
400Dic5—124no—
401C24C22×D1512yes—
402#41—22no—
403#41—22no—
404#41—304no—
405#41—304no—
406#41—308no—
407#41—304no—
408#41—304no—
409#41—302no—
410#41—302no—
411#41—302no—
412#41—302no—
413#41—304no—
414C2×Q8—152no—
415C2×Q8—302no—
416C2×Q8—304no—
417C2×Q8#122011yescharacteristic, complemented
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—154no—
424C2×D4—152no—
425C2×D4—302no—
426C2×D4—308no—
427C2×D4—304no—
428C2×D4—304no—
429C2×D4—308no—
430C2×D4#122011yescharacteristic, complemented
431C2×D4C22×D1512yes—
432C22×C4—154no—
433C22×C4—304no—
434C22×C4#122012yescomplemented
435C22×C4C22×D1511yescharacteristic
436C4⋊C4—21no—
437C4⋊C4—302no—
438C22⋊C4—24no—
439C22⋊C4—154no—
440C22⋊C4—308no—
441C22⋊C4C22×D1512yes—
442C42—21no—
443C42—302no—
444C3×C5#302711yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—42no—
448C22×C3—48no—
449C22×C3—44no—
450C22×C3—42no—
451C22×C3C2×D4×D512yes—
452C22×C3C22×C22⋊D511yescharacteristic
453C2×D3—104no—
454C2×D3—204no—
455C2×D3—404no—
456C3×C4—22no—
457C3×C4—42no—
458C3×C4#408311yescharacteristic
459C3×C4#408312yes—
460C3×C4#408311yescharacteristic
461Dic3—104no—
462Dic3—204no—
463C2×C5—22no—
464C2×C5—21no—
465C2×C5—42no—
466C2×C5—82no—
467C2×C5C2×#93711yescharacteristic
468D5—124no—
469C23—24no—
470C23—22no—
471C23—82no—
472C23—154no—
473C23—304no—
474C23C2×#122012yes—
475C23C23×D1511yescharacteristic
476Q8—22no—
477Q8—304no—
478Q8—302no—
479Q8—302no—
480D4—24no—
481D4—22no—
482D4—41no—
483D4—41no—
484D4—42no—
485D4—84no—
486D4—304no—
487D4—308no—
488D4—304no—
489D4—304no—
490D4—302no—
491D4—302no—
492D4—1208no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—154no—
497C2×C4—308no—
498C2×C4—304no—
499C2×C4—304no—
500C2×C4—304no—
501C2×C4—304no—
502C2×C4D4×D1512yes—
503C2×C4D4×D1512yes—
504C2×C4C2×#122012yes—
505C2×C4C2×#122011yescharacteristic
506C2×C4C2×#122011yescharacteristic
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—82no—
511C2×C3C2×#408311yescharacteristic
512D3—204no—
513C5#8339611yescharacteristic, complemented, Sylow
514C22—22no—
515C22—41no—
516C22—42no—
517C22—44no—
518C22—48no—
519C22—42no—
520C22—304no—
521C22—604no—
522C22—1204no—
523C22C2×D4×D1512yes—
524C22C22×#122011yescharacteristic
525C4—22no—
526C4—42no—
527C4—304no—
528C4—604no—
529C4#9182611yescharacteristic
530C4#9182611yescharacteristic
531C4#9182612yes—
532C3#1061512711yescharacteristic, complemented, Sylow
533C2—21no—
534C2—22no—
535C2—42no—
536C2—82no—
537C2—604no—
538C2C2×#9182611yescharacteristic
subgroupG/H
centerC2C2×#91826
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC3×C5×#535C2
socleC2×C3×C5C2×#120
hypercenter#535D15
hypocenterC3×C5#3027
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #11757146C2semidirect
2. C3×C5×#535C2semidirect
3. #11756564C2semidirect
4. #11751341C2semidirect
5. #11751133C2semidirect
6. #11751107C2semidirect
9. C22×C3×C5×D4C22semidirect
21. C3×C5×#120C22semidirect
22. C3×C5×#117C22semidirect
23. #91842C22semidirect
27. #91815C22semidirect
28. #91118C22semidirect
29. #91090C22semidirect
32. C5×#535D3semidirect
40. C2×C3×C5×Q8D4semidirect
46. C2×C3×C5×D4D4semidirect
48. C22×C3×C4×C5D4semidirect
67. C2×D60D4semidirect
69. C2×C4×D15D4semidirect
71. C2×Dic30D4semidirect
81. C3×#535D5semidirect
87. C22×C5×D4C2×D3semidirect
99. C5×#120C2×D3semidirect
100. C5×#117C2×D3semidirect
148. C22×C3×D4C2×D5semidirect
160. C3×#120C2×D5semidirect
161. C3×#117C2×D5semidirect
172. C2×C5×Q8#67semidirect
178. C2×C5×D4#67semidirect
180. C22×C4×C5#67semidirect
214. #535D15semidirect
239. C2×C3×Q8C22⋊D5semidirect
245. C2×C3×D4C22⋊D5semidirect
247. C22×C3×C4C22⋊D5semidirect
326. C22×D4C2×D15semidirect
334. #120C2×D15semidirect
336. #117C2×D15semidirect
417. C2×Q8#1220semidirect
430. C2×D4#1220semidirect
434. C22×C4#1220semidirect
444. C3×C5#3027semidirect
513. C5#83396semidirect
532. C3#10615127semidirect

Maximal subgroups

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

subgroupindex
#117571462
C3×C5×#5352
#117565642
#117513412
#117511332
#117511072
#106151273
#833965