Finite Group Databasebeta

← #14439398

Subgroups — #14439398

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#135C211yesmaximal, characteristic, complemented
2#11756589C211yesmaximal, characteristic, complemented
3#11756584C211yesmaximal, characteristic, complemented
4C2×#91840C211yesmaximal, characteristic, complemented
5C2×#91838C211yesmaximal, characteristic, complemented
6C22×#6706C211yesmaximal, characteristic, complemented
7#11751291C212yesmaximal, complemented
8#11751276C212yesmaximal, complemented
9#11751269C212yesmaximal, complemented
10#11751255C212yesmaximal, complemented
11#11751202C211yesmaximal, characteristic, complemented
12#10615636—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×C5×#41C2211yescharacteristic
15C22×D60C2211yescharacteristic
16C22×Dic30C2211yescharacteristic
17C3×C5×#135—24no—
18C2×C3×C5×Q16C2211yescharacteristic, complemented
19C2×C3×C5×SD16C2211yescharacteristic, complemented
20C2×C3×C5×SD16C2211yescharacteristic, complemented
21C2×C3×C5×D8C2211yescharacteristic, complemented
22C22×C3×C5×C8C2211yescharacteristic
23#91840—24no—
24#91838—24no—
25#91836C2212yes—
26#91833C2212yescomplemented
27C2×#6718C2212yescomplemented
28C2×#6717C2212yes—
29#91829C2212yes—
30#91826—22no—
31#91825C2212yescomplemented
32#91824—22no—
33C2×#6716C2212yescomplemented
34C2×#6715C2212yes—
35#91819—22no—
36#91815C2211yescharacteristic
37#91813—22no—
38C2×#6710C2211yescharacteristic
39C2×#6706—24no—
40C2×#6706C2212yes—
41C2×#6706C2212yes—
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83905—51nomaximal, Hall
45C2×C5×#135D311yescharacteristic, complemented
46#66164—31no—
47#66159—31no—
48C2×#4097—31no—
49C2×#4095—31no—
50C22×#677—31no—
51#65479—32no—
52#65464—32no—
53#65457—32no—
54#65443—32no—
55#65390—31no—
56C23×D15—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C3×C5×#41—22no—
61C2×C3×C5×Q8C2311yescharacteristic
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4—21no—
64C2×C3×C5×D4—21no—
65C2×C3×C5×D4C2311yescharacteristic
66C2×C3×C5×D4C2311yescharacteristic
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5C2311yescharacteristic
70C2×#1220—24no—
71C22×Dic15—21no—
72C2×D60—22no—
73C2×D60—22no—
74C2×D60—21no—
75C2×D60C2312yes—
76C2×Dic30—22no—
77C2×Dic30—22no—
78C2×Dic30—21no—
79C2×Dic30C2312yes—
80C3×C5×Q16—22no—
81C3×C5×SD16—22no—
82C3×C5×SD16—22no—
83C3×C5×D8—22no—
84C2×C3×C5×C8D414yescomplemented
85C2×C3×C5×C8C2311yescharacteristic
86C2×C3×C5×C8C2311yescharacteristic
87#6719—24no—
88#6719D412yes—
89#6718—24no—
90#6717—24no—
91#6716—24no—
92#6715—24no—
93#6714—24no—
94C4⋊Dic15D412yes—
95#6712—24no—
96C4×Dic15C2312yes—
97#6710D414yescomplemented
98C2×C3⋊#168C2312yes—
99#6706—24no—
100#6706—24no—
101C2×C3×#135D511yescharacteristic, complemented
102#5830—51no—
103#5825—51no—
104C2×#951—51no—
105C2×#949—51no—
106C22×#204—51no—
107#5190—52no—
108#5175—52no—
109#5168—52no—
110#5154—52no—
111#5101—51no—
112C2×C5×#41C2×D311yescharacteristic
113C2×C5×#41C2×D311yescharacteristic
114C22×D20—31no—
115C22×Dic10—31no—
116C5×#135—24no—
117C2×C5×Q16C2×D311yescharacteristic, complemented
118C2×C5×SD16C2×D311yescharacteristic, complemented
119C2×C5×SD16C2×D311yescharacteristic, complemented
120C2×C5×D8C2×D311yescharacteristic, complemented
121C22×C5×C8C2×D311yescharacteristic
122#4097—64no—
123#4095—64no—
124#4093—32no—
125#4090—32no—
126C2×#689—32no—
127C2×#688—32no—
128#4086—32no—
129#4083—62no—
130#4082—32no—
131#4081—62no—
132C2×#687—32no—
133C2×#686—32no—
134#4076—62no—
135#4072—31no—
136#4070—62no—
137C2×#681—31no—
138C2×#677—32no—
139C2×#677—32no—
140C2×#677—64no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5—21no—
146C23×C3×C5C2×D411yescharacteristic
147C22×D15—22no—
148C22×D15—42no—
149C22×D15—82no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×Q8—21no—
153C3×C5×Q8—21no—
154C3×C5×D4—21no—
155C3×C5×D4—21no—
156C3×C5×D4—21no—
157C3×C5×D4—21no—
158C3×C5×D4—42no—
159C3×C5×D4—42no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—42no—
163C2×C3×C4×C5—42no—
164C2×C3×C4×C5C2×D411yescharacteristic
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5C2411yescharacteristic
168#1220—84no—
169C2×Dic15—22no—
170C2×Dic15—42no—
171C2×Dic15C2×D414yes—
172D60—22no—
173D60—22no—
174D60—42no—
175Dic30—22no—
176Dic30—22no—
177Dic30—42no—
178C3×C5×C8C2×D412yes—
179C3×C5×C8C2×D412yes—
180C3⋊#168C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C2×C3×#41C2×D511yescharacteristic
183C22×D12—51no—
184C22×Dic6—51no—
185C3×#135—24no—
186C2×C3×Q16C2×D511yescharacteristic, complemented
187C2×C3×SD16C2×D511yescharacteristic, complemented
188C2×C3×SD16C2×D511yescharacteristic, complemented
189C2×C3×D8C2×D511yescharacteristic, complemented
190C22×C3×C8C2×D511yescharacteristic
191#951—104no—
192#949—104no—
193#947—52no—
194#944—52no—
195C2×#216—52no—
196C2×#215—52no—
197#940—52no—
198#937—102no—
199#936—52no—
200#935—102no—
201C2×#214—52no—
202C2×#213—52no—
203#930—102no—
204#926—51no—
205#924—102no—
206C2×#208—51no—
207C2×#204—52no—
208C2×#204—52no—
209C2×#204—104no—
210#815—52no—
211C8×Dic3—52no—
212C23×D5—61no—
213C5×#41—22no—
214C5×#41—22no—
215C5×#41—22no—
216C5×#41—22no—
217C2×C5×Q8C22×D311yescharacteristic
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4—21no—
221C2×C5×D4C22×D311yescharacteristic
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—64no—
227C22×Dic5—61no—
228C2×D20—32no—
229C2×D20—62no—
230C2×D20—62no—
231C2×D20—61no—
232C2×Dic10—32no—
233C2×Dic10—62no—
234C2×Dic10—62no—
235C2×Dic10—61no—
236C5×Q16—22no—
237C5×SD16—22no—
238C5×SD16—22no—
239C5×D8—22no—
240C2×C5×C8#6714yescomplemented
241C2×C5×C8C22×D311yescharacteristic
242C2×C5×C8C22×D311yescharacteristic
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—64no—
246#688—64no—
247#687—64no—
248#686—64no—
249#685—64no—
250C4⋊Dic5—32no—
251#683—64no—
252C4×Dic5—32no—
253#681—34no—
254C2×#168—32no—
255#677—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135D1511yescharacteristic, complemented
260C22×SD16—151no—
261#536—151no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5—42no—
273C22×C3×C5#12712yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×D15—42no—
276C2×D15—44no—
277C2×D15—84no—
278C3×C4×C5—41no—
279C3×C4×C5—41no—
280C3×C4×C5#12712yes—
281C3×C4×C5C22×D411yescharacteristic
282C3×C4×C5C22×D411yescharacteristic
283Dic15—24no—
284Dic15—42no—
285C23×D3—101no—
286C3×#41—22no—
287C3×#41—22no—
288C3×#41—22no—
289C3×#41—22no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×Q8C22×D511yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4C22×D511yescharacteristic
295C2×C3×D4C22×D511yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—104no—
300C22×Dic3—101no—
301C2×D12—52no—
302C2×D12—102no—
303C2×D12—102no—
304C2×D12—101no—
305C2×Dic6—52no—
306C2×Dic6—102no—
307C2×Dic6—102no—
308C2×Dic6—101no—
309C3×Q16—22no—
310C3×SD16—22no—
311C3×SD16—22no—
312C3×D8—22no—
313C2×C3×C8C22⋊D514yescomplemented
314C2×C3×C8C22×D511yescharacteristic
315C2×C3×C8C22×D511yescharacteristic
316#217—52no—
317#217—104no—
318#216—104no—
319#215—104no—
320#214—104no—
321#213—104no—
322(C2×D3)⋊C4—104no—
323C4⋊Dic3—52no—
324Dic3⋊C4—104no—
325C4×Dic3—52no—
326#208—54no—
327C2×C3⋊C8—52no—
328#204—104no—
329#204—104no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5D3×D411yescharacteristic
333C22×D5—62no—
334C22×D5—122no—
335C22×D5—242no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×Q8—21no—
339C5×Q8—21no—
340C5×D4—21no—
341C5×D4—21no—
342C5×D4—21no—
343C5×D4—21no—
344C5×D4—42no—
345C5×D4—42no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
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—244no—
355C2×Dic5—34no—
356C2×Dic5—62no—
357C2×Dic5—122no—
358D20—62no—
359D20—62no—
360D20—122no—
361Dic10—62no—
362Dic10—62no—
363Dic10—122no—
364C5×C8C2×#6712yes—
365C5×C8C2×#6712yes—
366#168—34no—
367C2×#41C2×D1511yescharacteristic
368C2×#41C2×D1511yescharacteristic
369C22×Q8—151no—
370C22×D4—151no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—24no—
374C2×Q16—152no—
375C2×Q16C2×D1511yescharacteristic, complemented
376C2×SD16—152no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—304no—
381C2×SD16C2×D1511yescharacteristic, complemented
382C2×SD16C2×D1511yescharacteristic, complemented
383C2×D8—152no—
384C2×D8C2×D1511yescharacteristic, complemented
385C2×M16—151no—
386C22×C8C2×D1511yescharacteristic
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—151no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5—81no—
401C2×C3×C5C2×#12711yescharacteristic
402C2×C3×C5#57712yes—
403D15—82no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3D4×D511yescharacteristic
407C22×D3—102no—
408C22×D3—202no—
409C22×D3—402no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—21no—
413C3×Q8—21no—
414C3×D4—21no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—21no—
418C3×D4—42no—
419C3×D4—42no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4D4×D512yes—
425C2×C3×C4D4×D511yescharacteristic
426C2×C3×C4C2×C22⋊D512yes—
427C2×C3×C4C23×D511yescharacteristic
428#67—404no—
429C2×Dic3—54no—
430C2×Dic3—102no—
431C2×Dic3—202no—
432D12—102no—
433D12—102no—
434D12—202no—
435Dic6—102no—
436Dic6—102no—
437Dic6—202no—
438C3×C8C2×C22⋊D512yes—
439C3×C8C2×C22⋊D512yes—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5#94012yes—
447C22×C5C2×D3×D411yescharacteristic
448C2×D5—124no—
449C2×D5—122no—
450C2×D5—244no—
451C4×C5—41no—
452C4×C5—41no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—64no—
457Dic5—122no—
458C24—301no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—22no—
463C2×Q8—152no—
464C2×Q8—301no—
465C2×Q8—302no—
466C2×Q8—302no—
467C2×Q8C22×D1511yescharacteristic
468C2×Q8C22×D1511yescharacteristic
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—152no—
472C2×D4—304no—
473C2×D4—302no—
474C2×D4—301no—
475C2×D4—302no—
476C2×D4C22×D1511yescharacteristic
477C2×D4C22×D1511yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—301no—
481C22×C4C22×D1511yescharacteristic
482Q16—22no—
483Q16—304no—
484SD16—22no—
485SD16—22no—
486SD16—304no—
487SD16—304no—
488SD16—304no—
489SD16—304no—
490D8—22no—
491D8—304no—
492M16—154no—
493C2×C8—152no—
494C2×C8#122014yescomplemented
495C2×C8C22×D1511yescharacteristic
496C2×C8C22×D1511yescharacteristic
497C4⋊C4—152no—
498C4⋊C4—304no—
499C22⋊C4—152no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—152no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3#408612yes—
510C22×C3C2×D4×D511yescharacteristic
511C2×D3—204no—
512C2×D3—202no—
513C2×D3—404no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C22×C22⋊D511yescharacteristic
519Dic3—104no—
520Dic3—202no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5—81no—
524C2×C5#577012yes—
525C2×C5C2×#94011yescharacteristic
526D5—242no—
527C23—21no—
528C23—21no—
529C23—302no—
530C23—602no—
531C23—1202no—
532C23D4×D1511yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—302no—
538Q8—302no—
539Q8—602no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—42no—
545D4—42no—
546D4—302no—
547D4—302no—
548D4—602no—
549D4—1204no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—154no—
555C2×C4—302no—
556C2×C4—602no—
557C2×C4D4×D1511yescharacteristic
558C2×C4D4×D1512yes—
559C2×C4C2×#122012yes—
560C2×C4C23×D1511yescharacteristic
561C8—154no—
562C8C2×#122012yes—
563C8C2×#122012yes—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3—81no—
567C2×C3#6610412yes—
568C2×C3C2×#408611yescharacteristic
569D3—402no—
570C5#8390511yescharacteristic, complemented, Sylow
571C22—22no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—42no—
576C22—602no—
577C22—604no—
578C22—1204no—
579C22#9182912yes—
580C22C2×D4×D1511yescharacteristic
581C4—41no—
582C4—41no—
583C4—304no—
584C4—602no—
585C4#9182912yes—
586C4C2×D4×D1511yescharacteristic
587C4C22×#122011yescharacteristic
588C3#1061563611yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—81no—
592C2—1202no—
593C2#1175652912yes—
594C2C2×#9182911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#135C2
socleC22×C3×C5C22×D4
hypercenterC2×#135D15
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#135C2semidirect
2. #11756589C2semidirect
3. #11756584C2semidirect
4. C2×#91840C2semidirect
5. C2×#91838C2semidirect
6. C22×#6706C2semidirect
7. #11751291C2semidirect
8. #11751276C2semidirect
9. #11751269C2semidirect
10. #11751255C2semidirect
11. #11751202C2semidirect
18. C2×C3×C5×Q16C22semidirect
19. C2×C3×C5×SD16C22semidirect
20. C2×C3×C5×SD16C22semidirect
21. C2×C3×C5×D8C22semidirect
26. #91833C22semidirect
27. C2×#6718C22semidirect
31. #91825C22semidirect
33. C2×#6716C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
45. C2×C5×#135D3semidirect
84. C2×C3×C5×C8D4semidirect
97. #6710D4semidirect
101. C2×C3×#135D5semidirect
117. C2×C5×Q16C2×D3semidirect
118. C2×C5×SD16C2×D3semidirect
119. C2×C5×SD16C2×D3semidirect
120. C2×C5×D8C2×D3semidirect
186. C2×C3×Q16C2×D5semidirect
187. C2×C3×SD16C2×D5semidirect
188. C2×C3×SD16C2×D5semidirect
189. C2×C3×D8C2×D5semidirect
240. C2×C5×C8#67semidirect
259. C2×#135D15semidirect
313. C2×C3×C8C22⋊D5semidirect
375. C2×Q16C2×D15semidirect
381. C2×SD16C2×D15semidirect
382. C2×SD16C2×D15semidirect
384. C2×D8C2×D15semidirect
494. C2×C8#1220semidirect
503. C3×C5#3154semidirect
570. C5#83905semidirect
588. C3#10615636semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1352
#117565892
#117565842
C2×#918402
C2×#918382
C22×#67062
#117512912
#117512762
#117512692
#117512552
#117512022
#106156363
#839055