Finite Group Databasebeta

← #14439293

Subgroups — #14439293

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#137C211yesmaximal, characteristic, complemented
2#11756591C211yesmaximal, characteristic, complemented
3C2×#91838C211yesmaximal, characteristic, complemented
4C2×#91836C211yesmaximal, characteristic, complemented
5C2×#91831C211yesmaximal, characteristic, complemented
6C2×#91797C211yesmaximal, characteristic, complemented
7#11751292C212yesmaximal, complemented
8#11751291C212yesmaximal, complemented
9#11751277C212yesmaximal, complemented
10#11751269C212yesmaximal, complemented
11M16×Dic15C211yesmaximal, characteristic, complemented
12#10615704—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×C5×Q8C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C22×D60C2211yescharacteristic
17C3×C5×#137—24no—
18C2×C3×C5×Q16C2212yescomplemented
19C2×C3×C5×SD16C2212yescomplemented
20C2×C3×C5×M16C2211yescharacteristic
21#91838—24no—
22#91836—22no—
23#91836C2212yes—
24#91836C2212yes—
25#91836C2211yescharacteristic, complemented
26#91833C2211yescharacteristic, complemented
27C2×#6718C2212yescomplemented
28#91831—24no—
29C2×#6717C2212yes—
30C2×#6717C2212yescomplemented
31#91829C2211yescharacteristic, complemented
32#91828—22no—
33#91825C2211yescharacteristic, complemented
34C2×#6715C2212yes—
35C4×#1220—22no—
36C2×#6714—22no—
37C2×C4×Dic15C2211yescharacteristic
38C2×#6710C2211yescharacteristic
39#91797—24no—
40C2×D120C2212yes—
41C2×#6706C2212yes—
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83973—51nomaximal, Hall
45C2×C5×#137D311yescharacteristic, complemented
46#66166—31no—
47C2×#4095—31no—
48C2×#4093—31no—
49C2×#4088—31no—
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65457—32no—
55M16×Dic5—31no—
56C23×D15—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8—21no—
60C2×C3×C5×Q8—22no—
61C2×C3×C5×Q8—22no—
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×Q8C2312yes—
64C2×C3×C5×D4—21no—
65C2×C3×C5×D4C2311yescharacteristic
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5C2311yescharacteristic
69C2×#1220—21no—
70C2×#1220—22no—
71C22×Dic15D412yes—
72#6817—22no—
73#6817—22no—
74C2×D60—22no—
75C2×D60—22no—
76C2×D60—21no—
77C2×D60C2312yes—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C3×C5×Q16—24no—
82C3×C5×SD16—24no—
83C3×C5×M16D414yescomplemented
84C2×C3×C5×C8C2312yes—
85#6719—22no—
86#6718—24no—
87#6717—24no—
88#6717—24no—
89#6715—24no—
90#6714—24no—
91#6714—24no—
92#6714—22no—
93#6712—22no—
94C4×Dic15D412yes—
95C4×Dic15C2311yescharacteristic
96C4×Dic15C2311yescharacteristic
97#6710D414yescomplemented
98C2×C3⋊#168C2312yes—
99D120—24no—
100#6706—24no—
101C2×C3×#137D511yescharacteristic, complemented
102#5832—51no—
103C2×#949—51no—
104C2×#947—51no—
105C2×#942—51no—
106C2×#908—51no—
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5168—52no—
111Dic3×M16—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C22×D20—31no—
116C5×#137—24no—
117C2×C5×Q16C2×D312yescomplemented
118C2×C5×SD16C2×D312yescomplemented
119C2×C5×M16C2×D311yescharacteristic
120#4095—64no—
121#4093—32no—
122#4093—32no—
123#4093—31no—
124#4093—62no—
125#4090—31no—
126C2×#689—32no—
127#4088—64no—
128C2×#688—32no—
129C2×#688—32no—
130#4086—31no—
131#4085—62no—
132#4082—31no—
133C2×#686—32no—
134C4×C22⋊D5—62no—
135C2×#685—62no—
136C2×C4×Dic5—31no—
137C2×#681—31no—
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3153—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—21no—
148C22×D15—44no—
149C22×D15—42no—
150C3×C5×Q8—21no—
151C3×C5×Q8—22no—
152C3×C5×Q8—22no—
153C3×C5×Q8—21no—
154C3×C5×Q8—42no—
155C3×C5×D4—21no—
156C3×C5×D4—21no—
157C3×C5×D4—42no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—42no—
161C2×C3×C4×C5—42no—
162C2×C3×C4×C5C2×D411yescharacteristic
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5C2411yescharacteristic
166#1220—44no—
167#1220—42no—
168C2×Dic15—21no—
169C2×Dic15—42no—
170C2×Dic15C2×D412yes—
171C2×Dic15C2×D412yes—
172D60—22no—
173D60—21no—
174D60—22no—
175D60—21no—
176D60—42no—
177C4×D15—42no—
178Dic30—21no—
179Dic30—21no—
180C3×C5×C8C2×D414yes—
181C3⋊#168C2×D414yes—
182C2×C3×#41C2×D511yescharacteristic
183C22×C3×Q8C2×D511yescharacteristic
184C2×#235—51no—
185C22×D12—51no—
186C3×#137—24no—
187C2×C3×Q16C2×D512yescomplemented
188C2×C3×SD16C2×D512yescomplemented
189C2×C3×M16C2×D511yescharacteristic
190#949—104no—
191#947—52no—
192#947—52no—
193#947—51no—
194#947—102no—
195#944—51no—
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199C2×#215—52no—
200#940—51no—
201#939—102no—
202#936—51no—
203C2×#213—52no—
204C4×#67—102no—
205C2×(C2×D3)⋊C4—102no—
206C2×C4×Dic3—51no—
207C2×#208—51no—
208#908—104no—
209C2×D24—52no—
210C2×#204—52no—
211#815—52no—
212C8×Dic3—52no—
213C23×D5—61no—
214C5×#41—22no—
215C5×#41—22no—
216C2×C5×Q8—21no—
217C2×C5×Q8—22no—
218C2×C5×Q8—22no—
219C2×C5×Q8C22×D312yes—
220C2×C5×Q8C22×D311yescharacteristic
221C2×C5×D4—21no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—62no—
227C2×C22⋊D5—61no—
228C22×Dic5—32no—
229#709—62no—
230#709—62no—
231C2×D20—32no—
232C2×D20—31no—
233C2×D20—62no—
234C2×D20—62no—
235C2×D20—61no—
236C2×C4×D5—61no—
237C2×Dic10—31no—
238C5×Q16—24no—
239C5×SD16—24no—
240C5×M16#6714yescomplemented
241C2×C5×C8C22×D312yes—
242C22⋊Dic5—62no—
243#689—64no—
244#688—64no—
245#688—64no—
246#686—64no—
247#685—64no—
248#685—64no—
249#685—62no—
250#683—62no—
251C4×Dic5—32no—
252C4×Dic5—31no—
253C4×Dic5—31no—
254#681—34no—
255C2×#168—32no—
256D40—64no—
257#677—64no—
258C2×#137—151no—
259C2×#137D1511yescharacteristic, complemented
260C2×AGL(1,ℤ/8)—151no—
261C2×AGL(1,ℤ/8)—151no—
262#532—151no—
263C2×#124—151no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—151no—
269C22×C3×C5—22no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—41no—
275C2×D15—42no—
276C2×D15—42no—
277C2×D15—44no—
278C2×D15—84no—
279C3×C4×C5—41no—
280C3×C4×C5—42no—
281C3×C4×C5#12712yes—
282C3×C4×C5C22×D411yescharacteristic
283C3×C4×C5C22×D411yescharacteristic
284Dic15—22no—
285Dic15—22no—
286Dic15—41no—
287C23×D3—101no—
288C3×#41—22no—
289C3×#41—22no—
290C2×C3×Q8—21no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×Q8C22×D512yes—
295C2×C3×D4—21no—
296C2×C3×D4C22×D511yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—102no—
301C2×#67—101no—
302C22×Dic3—52no—
303#235—102no—
304#235—102no—
305C2×D12—52no—
306C2×D12—51no—
307C2×D12—102no—
308C2×D12—102no—
309C2×D12—101no—
310C2×C4×D3—101no—
311C2×Dic6—51no—
312C3×Q16—24no—
313C3×SD16—24no—
314C3×M16C22⋊D514yescomplemented
315C2×C3×C8C22×D512yes—
316#217—102no—
317#216—104no—
318#215—104no—
319#215—104no—
320#213—104no—
321(C2×D3)⋊C4—104no—
322(C2×D3)⋊C4—104no—
323(C2×D3)⋊C4—102no—
324Dic3⋊C4—102no—
325C4×Dic3—52no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328#208—54no—
329C2×C3⋊C8—52no—
330D24—104no—
331#204—104no—
332C23×C5—21no—
333C23×C5D3×D411yescharacteristic
334C22×D5—62no—
335C22×D5—61no—
336C22×D5—124no—
337C22×D5—122no—
338C5×Q8—21no—
339C5×Q8—22no—
340C5×Q8—22no—
341C5×Q8—21no—
342C5×Q8—42no—
343C5×D4—21no—
344C5×D4—21no—
345C5×D4—42no—
346C2×C4×C5—21no—
347C2×C4×C5—22no—
348C2×C4×C5—42no—
349C2×C4×C5—42no—
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5D3×D412yes—
352C2×C4×C5C2×#6712yes—
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—124no—
355C22⋊D5—122no—
356C2×Dic5—32no—
357C2×Dic5—32no—
358C2×Dic5—61no—
359C2×Dic5—122no—
360D20—62no—
361D20—61no—
362D20—62no—
363D20—61no—
364D20—122no—
365C4×D5—122no—
366Dic10—61no—
367Dic10—61no—
368C5×C8C2×#6714yes—
369#168—34no—
370C2×#41—151no—
371C2×#41C2×D1511yescharacteristic
372C22×Q8C2×D1511yescharacteristic
373C22×D4—151no—
374#137—24no—
375#137—304no—
376AGL(1,ℤ/8)—304no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—152no—
379C2×Q16C2×D1512yescomplemented
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16C2×D1512yescomplemented
384C2×D8—152no—
385C2×D8—152no—
386C2×M16—151no—
387C2×M16C2×D1511yescharacteristic
388C4⋊Q8—151no—
389#127—151no—
390#124—152no—
391#124—152no—
392#124—151no—
393#124—151no—
394#124—302no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—302no—
398C2×C42—151no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5—81no—
403C2×C3×C5C2×#12711yescharacteristic
404C2×C3×C5#57512yes—
405D15—81no—
406D15—82no—
407C23×C3—21no—
408C23×C3D4×D511yescharacteristic
409C22×D3—102no—
410C22×D3—101no—
411C22×D3—204no—
412C22×D3—202no—
413C3×Q8—21no—
414C3×Q8—22no—
415C3×Q8—22no—
416C3×Q8—21no—
417C3×Q8—42no—
418C3×D4—21no—
419C3×D4—21no—
420C3×D4—42no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4D4×D512yes—
426C2×C3×C4D4×D511yescharacteristic
427C2×C3×C4C2×C22⋊D512yes—
428C2×C3×C4C23×D511yescharacteristic
429#67—204no—
430#67—202no—
431C2×Dic3—52no—
432C2×Dic3—52no—
433C2×Dic3—101no—
434C2×Dic3—202no—
435D12—102no—
436D12—101no—
437D12—102no—
438D12—101no—
439D12—202no—
440C4×D3—202no—
441Dic6—101no—
442Dic6—101no—
443C3×C8C2×C22⋊D514yes—
444C3⋊C8—54no—
445C22×C5—22no—
446C22×C5—42no—
447C22×C5—41no—
448C22×C5#94012yes—
449C22×C5C2×D3×D411yescharacteristic
450C2×D5—122no—
451C2×D5—124no—
452C2×D5—121no—
453C2×D5—122no—
454C2×D5—244no—
455C4×C5—41no—
456C4×C5—42no—
457C4×C5#94012yes—
458C4×C5C2×D3×D411yescharacteristic
459C4×C5C22×#6711yescharacteristic
460Dic5—62no—
461Dic5—62no—
462Dic5—121no—
463C24—301no—
464#41—22no—
465#41—22no—
466#41—302no—
467#41—302no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—151no—
472C2×Q8C22×D1512yes—
473C2×Q8C22×D1511yescharacteristic
474C2×D4—21no—
475C2×D4—152no—
476C2×D4—151no—
477C2×D4—302no—
478C2×D4—301no—
479C2×D4—302no—
480C2×D4—301no—
481C2×D4—302no—
482C2×D4C22×D1511yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—152no—
486C22×C4—301no—
487C22×C4C22×D1511yescharacteristic
488Q16—24no—
489Q16—304no—
490SD16—24no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—304no—
495D8—304no—
496M16—154no—
497M16#122014yescomplemented
498C2×C8—152no—
499C2×C8C22×D1512yes—
500C4⋊C4—302no—
501C22⋊C4—304no—
502C22⋊C4—304no—
503C22⋊C4—302no—
504C22⋊C4—302no—
505C42—152no—
506C42—151no—
507C42—151no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—42no—
511C22×C3—41no—
512C22×C3#408612yes—
513C22×C3C2×D4×D511yescharacteristic
514C2×D3—202no—
515C2×D3—204no—
516C2×D3—201no—
517C2×D3—202no—
518C2×D3—404no—
519C3×C4—41no—
520C3×C4—42no—
521C3×C4#408612yes—
522C3×C4C2×D4×D511yescharacteristic
523C3×C4C22×C22⋊D511yescharacteristic
524Dic3—102no—
525Dic3—102no—
526Dic3—201no—
527C2×C5—22no—
528C2×C5—81no—
529C2×C5#577712yes—
530C2×C5C2×#94011yescharacteristic
531D5—242no—
532D5—241no—
533C23—21no—
534C23—302no—
535C23—301no—
536C23—604no—
537C23—602no—
538C23D4×D1511yescharacteristic
539Q8—21no—
540Q8—22no—
541Q8—22no—
542Q8—21no—
543Q8—42no—
544Q8—301no—
545Q8—301no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—302no—
550D4—301no—
551D4—301no—
552D4—302no—
553D4—604no—
554D4—602no—
555D4—602no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—152no—
561C2×C4—152no—
562C2×C4—301no—
563C2×C4—602no—
564C2×C4—602no—
565C2×C4D4×D1511yescharacteristic
566C2×C4D4×D1512yes—
567C2×C4C2×#122012yes—
568C2×C4C23×D1511yescharacteristic
569C8—154no—
570C8C2×#122014yes—
571C2×C3—22no—
572C2×C3—81no—
573C2×C3#6611112yes—
574C2×C3C2×#408611yescharacteristic
575D3—402no—
576D3—401no—
577C5#8397311yescharacteristic, complemented, Sylow
578C22—22no—
579C22—41no—
580C22—42no—
581C22—601no—
582C22—602no—
583C22—602no—
584C22—604no—
585C22—1204no—
586C22#9182912yes—
587C22C2×D4×D1511yescharacteristic
588C4—41no—
589C4—42no—
590C4—302no—
591C4—302no—
592C4—601no—
593C4#9182912yes—
594C4C2×D4×D1511yescharacteristic
595C4C22×#122011yescharacteristic
596C3#1061570411yescharacteristic, complemented, Sylow
597C2—22no—
598C2—81no—
599C2—1202no—
600C2—1201no—
601C2#1175653612yes—
602C2C2×#9182911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
hypercenterC2×#137D15
hypocenterC3×C5#3153
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#137C2semidirect
2. #11756591C2semidirect
3. C2×#91838C2semidirect
4. C2×#91836C2semidirect
5. C2×#91831C2semidirect
6. C2×#91797C2semidirect
7. #11751292C2semidirect
8. #11751291C2semidirect
9. #11751277C2semidirect
10. #11751269C2semidirect
11. M16×Dic15C2semidirect
18. C2×C3×C5×Q16C22semidirect
19. C2×C3×C5×SD16C22semidirect
25. #91836C22semidirect
26. #91833C22semidirect
27. C2×#6718C22semidirect
30. C2×#6717C22semidirect
31. #91829C22semidirect
33. #91825C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
45. C2×C5×#137D3semidirect
83. C3×C5×M16D4semidirect
97. #6710D4semidirect
101. C2×C3×#137D5semidirect
117. C2×C5×Q16C2×D3semidirect
118. C2×C5×SD16C2×D3semidirect
187. C2×C3×Q16C2×D5semidirect
188. C2×C3×SD16C2×D5semidirect
240. C5×M16#67semidirect
259. C2×#137D15semidirect
314. C3×M16C22⋊D5semidirect
379. C2×Q16C2×D15semidirect
383. C2×SD16C2×D15semidirect
497. M16#1220semidirect
508. C3×C5#3153semidirect
577. C5#83973semidirect
596. C3#10615704semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1372
#117565912
C2×#918382
C2×#918362
C2×#918312
C2×#917972
#117512922
#117512912
#117512772
#117512692
M16×Dic152
#106157043
#839735