Finite Group Databasebeta

← #14439589

Subgroups — #14439589

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
1#11756564C211yesmaximal, characteristic, complemented
2C22×C5×#213C211yesmaximal, characteristic, complemented
3C2×C3×#4078C211yesmaximal, characteristic, complemented
4#11754604C211yesmaximal, characteristic, complemented
5C2×#91311C211yesmaximal, characteristic, complemented
6C2×#91304C211yesmaximal, characteristic, complemented
7#11749096C212yesmaximal, complemented
8#11749095C212yesmaximal, complemented
9#11749077C212yesmaximal, complemented
10#11749075C212yesmaximal, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10615561—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17#91842—22no—
18#91829C2212yescomplemented
19#91827—22no—
20#91825C2212yescomplemented
21#91815C2211yescharacteristic
22C2×C5×#213—24no—
23C2×C5×#213C2212yes—
24C2×C5×#213C2212yes—
25C22×C5×C3⋊C8C2211yescharacteristic
26C2×C3×#687C2212yescomplemented
27C3×#4078—24no—
28C2×C3×#686C2212yescomplemented
29C2×C3×#681C2211yescharacteristic
30#91568—22no—
31#91463C2212yescomplemented
32#91449—22no—
33#91370C2212yescomplemented
34C2×#6662C2211yescharacteristic, complemented
35C2×#6659C2212yescomplemented
36C2×#6658C2211yescharacteristic, complemented
37#91311—24no—
38C2×#6657C2211yescharacteristic, complemented
39#91304—24no—
40C2×#6654C2212yescomplemented
41C2×#6653C2211yescharacteristic, complemented
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83940—51nomaximal, Hall
45C22×C5×D8—31no—
46#66139—31no—
47#66139—31no—
48C2×#4078—31no—
49C2×#4078D311yescharacteristic, complemented
50C2×#4050—31no—
51#65444—32no—
52#65443—32no—
53#65443—32no—
54#65440—32no—
55#65390—31no—
56C24×C3×C5—21no—
57C23×C5×D3—21no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C2×#1220—24no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C2×C5×D12—22no—
71C2×C5×D12—22no—
72C2×C5×D12—21no—
73C2×C5×D12C2312yes—
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1201—24no—
81#6719—24no—
82#6719D412yes—
83C4⋊Dic15D412yes—
84C4×Dic15C2312yes—
85C5×#213—24no—
86C5×#213—24no—
87C2×C5×C3⋊C8D414yescomplemented
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C5×C3⋊C8C2311yescharacteristic
90C3×#687—24no—
91C3×#686—24no—
92C3×#681D414yescomplemented
93C2×C3×#168C2312yes—
94(C2×D3)⋊Dic5—24no—
95#6662—22no—
96#6659—24no—
97#6658—22no—
98#6657—22no—
99#6654—24no—
100#6653—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5830—51no—
103C2×#950—51no—
104#5805—51no—
105C22×#213D511yescharacteristic, complemented
106C2×#908—51no—
107#5176—52no—
108#5168—52no—
109#5154—52no—
110#5151—52no—
111#5122—51no—
112C22×C5×D4—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C2×#709C2×D311yescharacteristic
116C2×C5×D8—32no—
117C2×C5×D8—32no—
118C2×C5×D8—64no—
119C22×C5×C8—31no—
120#4099—62no—
121#4099—62no—
122#4086—32no—
123#4086—32no—
124#4084—62no—
125#4084—62no—
126#4082—32no—
127#4082—32no—
128C2×#687—32no—
129C2×#687C2×D312yescomplemented
130#4078—24no—
131#4078—64no—
132C2×#686—32no—
133C2×#686C2×D312yescomplemented
134#4072—31no—
135C2×#681C2×D311yescharacteristic
136C2×Dic20—31no—
137#4050—64no—
138C2×D40—31no—
139C2×#677—31no—
140C2×#677—31no—
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—21no—
149C22×C5×D3—22no—
150C22×C5×D3—42no—
151C22×C5×D3—82no—
152C22×C3×D5—21no—
153C3×C5×D4—22no—
154C3×C5×D4—22no—
155C3×C5×D4—42no—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2411yescharacteristic
160#1220—42no—
161#1220—84no—
162C2×Dic15—21no—
163C2×Dic15C2×D414yes—
164D60—21no—
165D60—21no—
166C4×D15—42no—
167Dic30—21no—
168Dic30—21no—
169C5×D12—22no—
170C5×D12—22no—
171C5×D12—42no—
172C3×C22⋊D5—42no—
173C2×C3×Dic5—21no—
174C3×D20—21no—
175C3×D20—21no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10—21no—
179#1201—84no—
180C3×#168C2×D414yes—
181C5×C3⋊C8C2×D412yes—
182C5×C3⋊C8C2×D412yes—
183C2×C3×#41—51no—
184C22×C3×D4C2×D511yescharacteristic
185C2×#235—51no—
186C22×D12C2×D511yescharacteristic
187C3×AGL(1,ℤ/8)—104no—
188C2×C3×SD16—52no—
189C2×C3×D8—52no—
190C2×C3×M16—51no—
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—24no—
203C2×#213—51no—
204C2×#213C2×D512yes—
205C2×#213C2×D512yes—
206#930—102no—
207#926—51no—
208C22×C3⋊C8C2×D511yescharacteristic
209#908—104no—
210C2×D24—52no—
211C2×#204—52no—
212#815—52no—
213C8×Dic3—52no—
214C24×C5—21no—
215C24×C5—61no—
216C2×C5×D4—22no—
217C2×C5×D4—21no—
218C2×C5×D4—22no—
219C2×C5×D4—32no—
220C2×C5×D4—62no—
221C2×C5×D4—61no—
222C2×C5×D4—62no—
223C2×C5×D4C22×D312yes—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C2×C22⋊D5—64no—
227C2×C22⋊D5—64no—
228C2×C22⋊D5—61no—
229#709—22no—
230#709—22no—
231#709—62no—
232#709—62no—
233C2×D20—31no—
234C2×D20C22×D311yescharacteristic
235C2×C4×D5—21no—
236C2×C4×D5—61no—
237C2×Dic10—31no—
238C2×Dic10C22×D311yescharacteristic
239C5×D8—64no—
240C5×D8—64no—
241C2×C5×C8—34no—
242C2×C5×C8—31no—
243C2×C5×C8—31no—
244C22⋊Dic5—32no—
245C22⋊Dic5—64no—
246C22⋊Dic5—64no—
247#687—24no—
248#687—64no—
249#686—24no—
250#686—64no—
251C4⋊Dic5—32no—
252C4×Dic5—32no—
253#681#6714yescomplemented
254C2×#168C22×D312yes—
255Dic20—62no—
256D40—62no—
257#677—62no—
258#677—62no—
259C2×AGL(1,ℤ/8)—51no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—151no—
262C22×D8—31no—
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—42no—
272C22×C3×C5—44no—
273C22×C3×C5—84no—
274C22×C3×C5#12712yes—
275C22×C3×C5C22×D411yescharacteristic
276C2×D15—41no—
277C2×D15—42no—
278C2×C5×D3—42no—
279C2×C5×D3—44no—
280C2×C5×D3—84no—
281C2×C3×D5—41no—
282C2×C3×D5—42no—
283C3×C4×C5#12712yes—
284C3×C4×C5C22×D411yescharacteristic
285C3×C4×C5C22×D411yescharacteristic
286Dic15—24no—
287Dic15—41no—
288C3×Dic5—41no—
289C24×C3—21no—
290C23×D3—21no—
291C3×#41—102no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—22no—
295C2×C3×D4—21no—
296C2×C3×D4—22no—
297C2×C3×D4—51no—
298C2×C3×D4—101no—
299C2×C3×D4C22×D512yes—
300C22×C3×C4—101no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—104no—
303C2×#67—104no—
304C2×#67—101no—
305#235—102no—
306#235—102no—
307C2×D12—22no—
308C2×D12—22no—
309C2×D12—21no—
310C2×D12—51no—
311C2×D12C22×D512yes—
312C2×C4×D3—101no—
313C2×Dic6—51no—
314C3×SD16—104no—
315C3×D8—104no—
316C3×M16—54no—
317C2×C3×C8—52no—
318#217—52no—
319#217—104no—
320#216—102no—
321#215—102no—
322#214—102no—
323#213—24no—
324#213—24no—
325#213—102no—
326(C2×D3)⋊C4—104no—
327C4⋊Dic3—52no—
328C4×Dic3—52no—
329C2×C3⋊C8C22⋊D514yescomplemented
330C2×C3⋊C8C22×D511yescharacteristic
331C2×C3⋊C8C22×D511yescharacteristic
332D24—104no—
333#204—104no—
334C23×C5—22no—
335C23×C5—42no—
336C23×C5—62no—
337C23×C5—82no—
338C23×C5—122no—
339C23×C5—242no—
340C23×C5D3×D411yescharacteristic
341C22×D5—21no—
342C22×D5—61no—
343C5×D4—22no—
344C5×D4—22no—
345C5×D4—42no—
346C5×D4—62no—
347C5×D4—62no—
348C5×D4—122no—
349C2×C4×C5D3×D412yes—
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5C2×#6712yes—
352C2×C4×C5C23×D311yescharacteristic
353C22⋊D5—42no—
354C22⋊D5—122no—
355C22⋊D5—244no—
356C22⋊D5—244no—
357C2×Dic5—21no—
358C2×Dic5—34no—
359C2×Dic5—61no—
360D20—21no—
361D20—21no—
362D20—61no—
363D20—61no—
364C4×D5—42no—
365C4×D5—122no—
366Dic10—21no—
367Dic10—21no—
368Dic10—61no—
369Dic10—61no—
370C5×C8—32no—
371C5×C8—32no—
372#168C2×#6714yes—
373C2×#41—51no—
374C2×#41—151no—
375C22×D4—31no—
376C22×D4D3×D511yescharacteristic
377AGL(1,ℤ/8)—104no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—52no—
382C2×SD16—151no—
383C2×SD16—151no—
384C2×SD16—152no—
385C2×D8—32no—
386C2×D8—32no—
387C2×D8—52no—
388C2×D8—64no—
389C2×D8—151no—
390C2×D8—152no—
391C2×M16—51no—
392C22×C8—31no—
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×C5—82no—
406C2×C3×C5C2×#12711yescharacteristic
407C2×C3×C5#57612yes—
408D15—81no—
409C3×D5—81no—
410C5×D3—82no—
411C23×C3—22no—
412C23×C3—42no—
413C23×C3—82no—
414C23×C3—101no—
415C23×C3D4×D511yescharacteristic
416C22×D3—22no—
417C22×D3—42no—
418C22×D3—82no—
419C22×D3—101no—
420C3×Q8—101no—
421C3×Q8—101no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—42no—
425C3×D4—101no—
426C3×D4—101no—
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—202no—
435#67—404no—
436#67—404no—
437C2×Dic3—54no—
438C2×Dic3—101no—
439D12—22no—
440D12—22no—
441D12—42no—
442D12—101no—
443D12—101no—
444C4×D3—202no—
445Dic6—101no—
446Dic6—101no—
447C3×C8—54no—
448C3⋊C8C2×C22⋊D512yes—
449C3⋊C8C2×C22⋊D512yes—
450C22×C5—22no—
451C22×C5—44no—
452C22×C5—42no—
453C22×C5—84no—
454C22×C5—124no—
455C22×C5—122no—
456C22×C5—244no—
457C22×C5#94012yes—
458C22×C5C2×D3×D411yescharacteristic
459C2×D5—42no—
460C2×D5—41no—
461C2×D5—122no—
462C2×D5—121no—
463C4×C5#94012yes—
464C4×C5C2×D3×D411yescharacteristic
465C4×C5C22×#6711yescharacteristic
466Dic5—41no—
467Dic5—64no—
468Dic5—121no—
469C24—21no—
470C24—61no—
471#41—102no—
472#41—102no—
473#41—302no—
474#41—302no—
475C2×Q8—51no—
476C2×Q8—151no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—32no—
481C2×D4—51no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—61no—
485C2×D4—101no—
486C2×D4—151no—
487C2×D4—304no—
488C2×D4—304no—
489C2×D4—301no—
490C2×D4C2×D3×D512yes—
491C22×C4—101no—
492C22×C4—301no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—104no—
496SD16—302no—
497SD16—302no—
498SD16—304no—
499D8—64no—
500D8—64no—
501D8—104no—
502D8—302no—
503D8—304no—
504M16—54no—
505C2×C8—34no—
506C2×C8—31no—
507C2×C8—31no—
508C2×C8—52no—
509C4⋊C4—152no—
510C22⋊C4—152no—
511C22⋊C4—304no—
512C22⋊C4—304no—
513C42—152no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—84no—
519C22×C3—202no—
520C22×C3—201no—
521C22×C3#408612yes—
522C22×C3C2×D4×D511yescharacteristic
523C2×D3—44no—
524C2×D3—42no—
525C2×D3—84no—
526C2×D3—202no—
527C2×D3—201no—
528C3×C4—201no—
529C3×C4#408612yes—
530C3×C4C2×D4×D511yescharacteristic
531C3×C4C22×C22⋊D511yescharacteristic
532Dic3—104no—
533Dic3—201no—
534C2×C5—22no—
535C2×C5—82no—
536C2×C5—242no—
537C2×C5#577412yes—
538C2×C5C2×#94011yescharacteristic
539D5—81no—
540D5—241no—
541C23—22no—
542C23—42no—
543C23—62no—
544C23—82no—
545C23—101no—
546C23—122no—
547C23—242no—
548C23—301no—
549C23#679011yescharacteristic
550Q8—101no—
551Q8—101no—
552Q8—301no—
553Q8—301no—
554D4—22no—
555D4—22no—
556D4—42no—
557D4—62no—
558D4—62no—
559D4—101no—
560D4—101no—
561D4—122no—
562D4—202no—
563D4—301no—
564D4—301no—
565D4—602no—
566D4—1204no—
567D4—1204no—
568C2×C4—101no—
569C2×C4—154no—
570C2×C4—202no—
571C2×C4—301no—
572C2×C4—602no—
573C2×C4D5×#6712yes—
574C2×C4D3×C22⋊D512yes—
575C2×C4#679011yescharacteristic
576C2×C4C22×D3×D511yescharacteristic
577C8—32no—
578C8—32no—
579C8—54no—
580C2×C3—22no—
581C2×C3—82no—
582C2×C3—401no—
583C2×C3#6609112yes—
584C2×C3C2×#408611yescharacteristic
585D3—82no—
586D3—401no—
587C5#8394011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—44no—
591C22—84no—
592C22—122no—
593C22—124no—
594C22—201no—
595C22—202no—
596C22—244no—
597C22—601no—
598C22—602no—
599C22#9156712yes—
600C22C2×#679011yescharacteristic
601C4—201no—
602C4—304no—
603C4—601no—
604C4#9156712yes—
605C4C2×D5×#6711yescharacteristic
606C4C2×D3×C22⋊D511yescharacteristic
607C3#1061556111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—82no—
610C2—242no—
611C2—401no—
612C2—1201no—
613C2#1175470412yes—
614C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3155
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #11756564C2semidirect
2. C22×C5×#213C2semidirect
3. C2×C3×#4078C2semidirect
4. #11754604C2semidirect
5. C2×#91311C2semidirect
6. C2×#91304C2semidirect
7. #11749096C2semidirect
8. #11749095C2semidirect
9. #11749077C2semidirect
10. #11749075C2semidirect
11. #11748326C2semidirect
18. #91829C22semidirect
20. #91825C22semidirect
26. C2×C3×#687C22semidirect
28. C2×C3×#686C22semidirect
31. #91463C22semidirect
33. #91370C22semidirect
34. C2×#6662C22semidirect
35. C2×#6659C22semidirect
36. C2×#6658C22semidirect
38. C2×#6657C22semidirect
40. C2×#6654C22semidirect
41. C2×#6653C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
49. C2×#4078D3semidirect
87. C2×C5×C3⋊C8D4semidirect
92. C3×#681D4semidirect
105. C22×#213D5semidirect
129. C2×#687C2×D3semidirect
133. C2×#686C2×D3semidirect
253. #681#67semidirect
329. C2×C3⋊C8C22⋊D5semidirect
514. C3×C5#3155semidirect
587. C5#83940semidirect
607. C3#10615561semidirect

Maximal subgroups

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

subgroupindex
#117565642
C22×C5×#2132
C2×C3×#40782
#117546042
C2×#913112
C2×#913042
#117490962
#117490952
#117490772
#117490752
#117483262
#106155613
#839405