Finite Group Databasebeta

← #14439610

Subgroups — #14439610

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#908C211yesmaximal, characteristic, complemented
2C2×C3×#4054C211yesmaximal, characteristic, complemented
3#11754604C211yesmaximal, characteristic, complemented
4#11754600C211yesmaximal, characteristic, complemented
5C2×#91297C211yesmaximal, characteristic, complemented
6C22×#6652C211yesmaximal, characteristic, complemented
7#11751223C211yesmaximal, characteristic, complemented
8#11748015C212yesmaximal, complemented
9#11748013C212yesmaximal, complemented
10#11748012C212yesmaximal, complemented
11#11747977C212yesmaximal, complemented
12#10615671—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91815C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C5×#908—24no—
21C2×C5×D24C2212yescomplemented
22C2×C5×#204C2212yescomplemented
23C3×#4054—24no—
24C2×C3×D40C2212yescomplemented
25C2×C3×#677C2212yescomplemented
26#91568—22no—
27#91563—22no—
28#91463C2212yescomplemented
29#91463C2212yescomplemented
30#91456—22no—
31#91449—22no—
32#91370C2212yescomplemented
33#91368C2212yescomplemented
34C2×#6661C2211yescharacteristic, complemented
35C2×#6656C2211yescharacteristic, complemented
36C2×#6655C2211yescharacteristic, complemented
37#91297—24no—
38C2×#6652—24no—
39C2×#6652C2212yes—
40C2×#6652C2212yes—
41C2×#6652C2211yescharacteristic, complemented
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83940—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66164—31no—
47C2×#4096—31no—
48#66139—31no—
49C22×#686—31no—
50C2×#4054D311yescharacteristic, complemented
51#65465—32no—
52#65457—32no—
53#65443—32no—
54#65440—32no—
55#65411—31no—
56C23×C5×D3—21no—
57C23×C3×D5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×C5×#67—21no—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12—22no—
63C2×C5×D12—22no—
64C2×C5×D12—21no—
65C2×C5×D12C2312yes—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20—22no—
73C2×C3×D20—22no—
74C2×C3×D20—21no—
75C2×C3×D20C2311yescharacteristic
76C2×C3×D20C2312yes—
77C2×C3×C4×D5—21no—
78C2×C3×Dic10C2311yescharacteristic
79C2×#1201—24no—
80C2×#1201—24no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83#6719D412yes—
84C4⋊Dic15D412yes—
85C4×Dic15C2312yes—
86C2×C3⋊#168D414yescomplemented
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2311yescharacteristic
89C5×D24—24no—
90C5×#204—24no—
91C3×D40—24no—
92C3×#677—24no—
93(C2×D3)⋊Dic5—24no—
94#6665—24no—
95#6661—22no—
96#6656—22no—
97#6655—22no—
98#6652—24no—
99#6652—24no—
100#6652—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5830—51no—
103C2×#950—51no—
104#5805—51no—
105C22×#213—51no—
106C2×#908D511yescharacteristic, complemented
107#5176—52no—
108#5168—52no—
109#5154—52no—
110#5151—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C22×C5×D4—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16C2×D311yescharacteristic
120#4099—62no—
121#4096—64no—
122#4093—32no—
123C2×#689—31no—
124C2×#688—31no—
125#4086—32no—
126#4086—32no—
127#4084—62no—
128#4083—62no—
129#4082—32no—
130C2×#687—31no—
131C2×#686—32no—
132C2×#686—32no—
133C2×#686—31no—
134C2×#686—64no—
135#4076—62no—
136#4072—31no—
137C22×#168—31no—
138#4054—24no—
139C2×D40C2×D312yescomplemented
140C2×#677C2×D312yescomplemented
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—22no—
146C22×C5×D3—21no—
147C22×C5×D3—42no—
148C22×C5×D3—82no—
149C22×C3×D5—22no—
150C22×C3×D5—21no—
151C22×C3×D5—42no—
152C22×C3×D5—82no—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15C2×D414yes—
158C5×#67—42no—
159C2×C5×Dic3—21no—
160C5×D12—21no—
161C5×D12—22no—
162C5×D12—21no—
163C5×D12—22no—
164C5×D12—42no—
165C4×C5×D3—42no—
166C5×Dic6—21no—
167C5×Dic6—21no—
168C3×C22⋊D5—42no—
169C2×C3×Dic5—21no—
170C3×D20—22no—
171C3×D20—21no—
172C3×D20—22no—
173C3×D20—21no—
174C3×D20—42no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178#1201—84no—
179#1201—84no—
180C3×C5×C8C2×D414yes—
181C3⋊#168C2×D412yes—
182C3⋊#168C2×D412yes—
183C2×C3×#41—51no—
184C22×C3×D4—51no—
185C2×#235C2×D511yescharacteristic
186C22×D12C2×D511yescharacteristic
187C3×AGL(1,ℤ/8)—104no—
188C2×C3×SD16—52no—
189C2×C3×D8—52no—
190C2×C3×M16C2×D511yescharacteristic
191#953—102no—
192#950—104no—
193#947—52no—
194C2×#216—51no—
195C2×#215—51no—
196#940—52no—
197#940—52no—
198#938—102no—
199#937—102no—
200#936—52no—
201C2×#214—51no—
202C2×#213—51no—
203C2×#213—52no—
204C2×#213—52no—
205C2×#213—104no—
206#930—102no—
207#926—51no—
208C22×C3⋊C8—51no—
209#908—24no—
210C2×D24C2×D512yescomplemented
211C2×#204C2×D512yescomplemented
212#815—52no—
213C8×Dic3—52no—
214C24×C5—61no—
215C23×D5—21no—
216C5×#41—62no—
217C5×#41—62no—
218C2×C5×Q8—31no—
219C2×C5×D4—31no—
220C2×C5×D4—32no—
221C2×C5×D4—61no—
222C2×C5×D4—62no—
223C2×C5×D4—61no—
224C2×C5×D4—62no—
225C22×C4×C5—61no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—21no—
228C2×C22⋊D5—64no—
229C2×C22⋊D5—64no—
230#709—22no—
231#709—22no—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—21no—
235C2×D20C22×D312yes—
236C2×D20C22×D311yescharacteristic
237C2×C4×D5—21no—
238C2×Dic10C22×D311yescharacteristic
239C5×SD16—64no—
240C5×D8—64no—
241C5×M16#6714yescomplemented
242C2×C5×C8C22×D312yes—
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—62no—
246#688—62no—
247#687—62no—
248#686—62no—
249#686—64no—
250#686—64no—
251#685—64no—
252C4⋊Dic5—32no—
253C4×Dic5—32no—
254C2×#168—34no—
255C2×#168—31no—
256C2×#168—31no—
257D40—24no—
258#677—24no—
259C2×AGL(1,ℤ/8)—31no—
260C2×AGL(1,ℤ/8)—51no—
261C2×#135—151no—
262C22×D8—151no—
263#535—151no—
264#535—151no—
265#496—152no—
266#496—152no—
267#495—152no—
268#493—152no—
269#405—151no—
270C22×C3×C5—22no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×C5×D3—41no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C5×D3—44no—
277C2×C5×D3—84no—
278C2×C3×D5—41no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—44no—
282C2×C3×D5—84no—
283C3×C4×C5#12712yes—
284C3×C4×C5C22×D411yescharacteristic
285C3×C4×C5C22×D411yescharacteristic
286Dic15—24no—
287C3×Dic5—41no—
288C5×Dic3—41no—
289C24×C3—101no—
290C23×D3—21no—
291C3×#41—102no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—52no—
295C2×C3×D4—51no—
296C2×C3×D4—101no—
297C2×C3×D4—102no—
298C2×C3×D4—101no—
299C2×C3×D4—102no—
300C22×C3×C4—101no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—21no—
303C2×#67—104no—
304C2×#67—104no—
305#235—22no—
306#235—22no—
307C2×D12—22no—
308C2×D12—22no—
309C2×D12—21no—
310C2×D12C22×D512yes—
311C2×D12C22×D511yescharacteristic
312C2×C4×D3—21no—
313C2×Dic6C22×D511yescharacteristic
314C3×SD16—104no—
315C3×D8—104no—
316C3×M16C22⋊D514yescomplemented
317C2×C3×C8C22×D512yes—
318#217—52no—
319#217—104no—
320#216—102no—
321#215—102no—
322#214—102no—
323#213—104no—
324#213—104no—
325#213—102no—
326(C2×D3)⋊C4—104no—
327C4⋊Dic3—52no—
328C4×Dic3—52no—
329C2×C3⋊C8—54no—
330C2×C3⋊C8—51no—
331C2×C3⋊C8—51no—
332D24—24no—
333#204—24no—
334C23×C5—62no—
335C23×C5—61no—
336C23×C5—122no—
337C23×C5—242no—
338C23×C5D3×D411yescharacteristic
339C22×D5—22no—
340C22×D5—21no—
341C22×D5—42no—
342C22×D5—82no—
343C5×Q8—61no—
344C5×Q8—61no—
345C5×D4—62no—
346C5×D4—61no—
347C5×D4—61no—
348C5×D4—62no—
349C5×D4—122no—
350C5×D4—122no—
351C2×C4×C5—61no—
352C2×C4×C5—122no—
353C2×C4×C5D3×D411yescharacteristic
354C2×C4×C5D3×D412yes—
355C2×C4×C5C2×#6712yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—42no—
358C22⋊D5—244no—
359C22⋊D5—244no—
360C2×Dic5—21no—
361C2×Dic5—34no—
362D20—22no—
363D20—21no—
364D20—22no—
365D20—21no—
366D20—42no—
367C4×D5—42no—
368Dic10—21no—
369Dic10—21no—
370C5×C8C2×#6714yes—
371#168—32no—
372#168—32no—
373C2×#41—31no—
374C2×#41—51no—
375C22×D4—31no—
376C22×D4—51no—
377AGL(1,ℤ/8)—64no—
378AGL(1,ℤ/8)—104no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—32no—
382C2×SD16—52no—
383C2×SD16—151no—
384C2×SD16—151no—
385C2×D8—32no—
386C2×D8—52no—
387C2×D8—152no—
388C2×D8—152no—
389C2×D8—151no—
390C2×D8—304no—
391C2×M16D3×D511yescharacteristic
392C22×C8—151no—
393#127—152no—
394#127—152no—
395#124—152no—
396#124—152no—
397#121—302no—
398#121—302no—
399#120—302no—
400#120—302no—
401#117—151no—
402#97—152no—
403C4×C8—152no—
404C2×C3×C5—22no—
405C2×C3×C5C2×#12711yescharacteristic
406C2×C3×C5#57612yes—
407C3×D5—81no—
408C3×D5—82no—
409C5×D3—81no—
410C5×D3—82no—
411C23×C3—102no—
412C23×C3—101no—
413C23×C3—202no—
414C23×C3—402no—
415C23×C3D4×D511yescharacteristic
416C22×D3—22no—
417C22×D3—21no—
418C22×D3—42no—
419C22×D3—82no—
420C3×Q8—101no—
421C3×Q8—101no—
422C3×D4—102no—
423C3×D4—101no—
424C3×D4—101no—
425C3×D4—102no—
426C3×D4—202no—
427C3×D4—202no—
428C2×C3×C4—101no—
429C2×C3×C4—202no—
430C2×C3×C4D4×D512yes—
431C2×C3×C4D4×D511yescharacteristic
432C2×C3×C4C2×C22⋊D512yes—
433C2×C3×C4C23×D511yescharacteristic
434#67—42no—
435#67—404no—
436#67—404no—
437C2×Dic3—21no—
438C2×Dic3—54no—
439D12—22no—
440D12—21no—
441D12—22no—
442D12—21no—
443D12—42no—
444C4×D3—42no—
445Dic6—21no—
446Dic6—21no—
447C3×C8C2×C22⋊D514yes—
448C3⋊C8—52no—
449C3⋊C8—52no—
450C22×C5—22no—
451C22×C5—122no—
452C22×C5—124no—
453C22×C5—121no—
454C22×C5—122no—
455C22×C5—244no—
456C22×C5#94012yes—
457C22×C5C2×D3×D411yescharacteristic
458C2×D5—42no—
459C2×D5—44no—
460C2×D5—41no—
461C2×D5—42no—
462C2×D5—84no—
463C4×C5—121no—
464C4×C5#94012yes—
465C4×C5C2×D3×D411yescharacteristic
466C4×C5C22×#6711yescharacteristic
467Dic5—41no—
468Dic5—64no—
469C24—61no—
470C24—101no—
471#41—62no—
472#41—62no—
473#41—102no—
474#41—102no—
475C2×Q8—31no—
476C2×Q8—51no—
477C2×D4—32no—
478C2×D4—31no—
479C2×D4—52no—
480C2×D4—51no—
481C2×D4—61no—
482C2×D4—62no—
483C2×D4—61no—
484C2×D4—62no—
485C2×D4—101no—
486C2×D4—102no—
487C2×D4—101no—
488C2×D4—102no—
489C2×D4—304no—
490C2×D4—304no—
491C22×C4—61no—
492C22×C4—101no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—64no—
496SD16—104no—
497SD16—302no—
498SD16—302no—
499D8—64no—
500D8—104no—
501D8—304no—
502D8—304no—
503D8—302no—
504M16#120114yescomplemented
505C2×C8—154no—
506C2×C8—151no—
507C2×C8—151no—
508C2×C8C2×D3×D512yes—
509C4⋊C4—152no—
510C22⋊C4—152no—
511C22⋊C4—304no—
512C22⋊C4—304no—
513C42—152no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—202no—
517C22×C3—204no—
518C22×C3—201no—
519C22×C3—202no—
520C22×C3—404no—
521C22×C3#408612yes—
522C22×C3C2×D4×D511yescharacteristic
523C2×D3—42no—
524C2×D3—44no—
525C2×D3—41no—
526C2×D3—42no—
527C2×D3—84no—
528C3×C4—201no—
529C3×C4#408612yes—
530C3×C4C2×D4×D511yescharacteristic
531C3×C4C22×C22⋊D511yescharacteristic
532Dic3—41no—
533Dic3—104no—
534C2×C5—22no—
535C2×C5—242no—
536C2×C5—241no—
537C2×C5#577412yes—
538C2×C5C2×#94011yescharacteristic
539D5—82no—
540D5—81no—
541C23—62no—
542C23—61no—
543C23—102no—
544C23—101no—
545C23—122no—
546C23—202no—
547C23—242no—
548C23—402no—
549C23#677711yescharacteristic
550Q8—61no—
551Q8—61no—
552Q8—101no—
553Q8—101no—
554D4—62no—
555D4—61no—
556D4—61no—
557D4—62no—
558D4—102no—
559D4—101no—
560D4—101no—
561D4—102no—
562D4—122no—
563D4—122no—
564D4—202no—
565D4—202no—
566D4—1204no—
567D4—1204no—
568C2×C4—61no—
569C2×C4—101no—
570C2×C4—122no—
571C2×C4—154no—
572C2×C4—202no—
573C2×C4#677711yescharacteristic
574C2×C4#677712yes—
575C2×C4C2×#120112yes—
576C2×C4C22×D3×D511yescharacteristic
577C8—152no—
578C8—152no—
579C8C2×#120114yes—
580C2×C3—22no—
581C2×C3—402no—
582C2×C3—401no—
583C2×C3#6610812yes—
584C2×C3C2×#408611yescharacteristic
585D3—82no—
586D3—81no—
587C5#8394011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—122no—
590C22—124no—
591C22—121no—
592C22—122no—
593C22—202no—
594C22—204no—
595C22—201no—
596C22—202no—
597C22—244no—
598C22—404no—
599C22#9146312yes—
600C22C2×#677711yescharacteristic
601C4—121no—
602C4—201no—
603C4—304no—
604C4#9146312yes—
605C4C2×#677711yescharacteristic
606C4C22×#120111yescharacteristic
607C3#1061567111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—242no—
610C2—241no—
611C2—402no—
612C2—401no—
613C2#1175403812yes—
614C2C2×#9146311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5#3155
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C5×#908C2semidirect
2. C2×C3×#4054C2semidirect
3. #11754604C2semidirect
4. #11754600C2semidirect
5. C2×#91297C2semidirect
6. C22×#6652C2semidirect
7. #11751223C2semidirect
8. #11748015C2semidirect
9. #11748013C2semidirect
10. #11748012C2semidirect
11. #11747977C2semidirect
21. C2×C5×D24C22semidirect
22. C2×C5×#204C22semidirect
24. C2×C3×D40C22semidirect
25. C2×C3×#677C22semidirect
28. #91463C22semidirect
29. #91463C22semidirect
32. #91370C22semidirect
33. #91368C22semidirect
34. C2×#6661C22semidirect
35. C2×#6656C22semidirect
36. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
50. C2×#4054D3semidirect
81. C3×C5×M16D4semidirect
86. C2×C3⋊#168D4semidirect
106. C2×#908D5semidirect
139. C2×D40C2×D3semidirect
140. C2×#677C2×D3semidirect
210. C2×D24C2×D5semidirect
211. C2×#204C2×D5semidirect
241. C5×M16#67semidirect
316. C3×M16C22⋊D5semidirect
504. M16#1201semidirect
514. C3×C5#3155semidirect
587. C5#83940semidirect
607. C3#10615671semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9082
C2×C3×#40542
#117546042
#117546002
C2×#912972
C22×#66522
#117512232
#117480152
#117480132
#117480122
#117479772
#106156713
#839405