Finite Group Databasebeta

← #14439480

Subgroups — #14439480

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×#91839C211yesmaximal, characteristic, complemented
2C5×#5830C211yesmaximal, characteristic, complemented
3C2×C3×#4097C211yesmaximal, characteristic, complemented
4#11754278C211yesmaximal, characteristic, complemented
5C22×#6656C211yesmaximal, characteristic, complemented
6C2×#91304C211yesmaximal, characteristic, complemented
7#11749354C212yesmaximal, complemented
8#11749323C212yesmaximal, complemented
9#11749108C212yesmaximal, complemented
10#11749076C212yesmaximal, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10615112—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91839—24no—
18C2×#6718C2211yescharacteristic, complemented
19C2×#6717C2211yescharacteristic, complemented
20C2×#6716C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic, complemented
22C22×C3⋊#168C2211yescharacteristic
23C5×#947C2212yes—
24C5×#940C2212yes—
25C5×#937—22no—
26C5×#930—22no—
27C5×#926C2211yescharacteristic
28C3×#4097—24no—
29C2×C3×#689C2212yescomplemented
30C2×C3×#687C2212yescomplemented
31C2×C3×#681C2211yescharacteristic
32#91546—22no—
33#91390—22no—
34#91389C2212yescomplemented
35#91374C2212yescomplemented
36C2×#6659C2212yes—
37C2×#6656—24no—
38C2×#6656C2212yes—
39C2×#6656C2212yes—
40#91304—24no—
41C2×#6654C2212yes—
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83974—51nomaximal, Hall
45C5×#535—31no—
46C2×#4097D311yescharacteristic, complemented
47C2×#4096—31no—
48C22×#687—31no—
49C2×#4078—31no—
50#65860—31no—
51#65365—32no—
52#65363—32no—
53#65349—32no—
54#65348—32no—
55#65286—31no—
56C23×C5×D3—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—21no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C2×C5×#67—24no—
71C2×C5×D12—22no—
72C2×C5×D12—22no—
73C2×C5×D12—21no—
74C2×C5×D12C2312yes—
75C22×C3×Dic5—21no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—21no—
79C2×C3×Dic10C2312yes—
80#6718—22no—
81#6717—22no—
82#6716—22no—
83#6715—22no—
84C2×C3⋊#168D414yescomplemented
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87C5×#217D412yes—
88C5×(C2×D3)⋊C4—24no—
89C5×C4⋊Dic3D412yes—
90C4×C5×Dic3C2312yes—
91C3×#689—24no—
92C3×#687—24no—
93C3×#681D414yescomplemented
94C2×C3×#168C2312yes—
95Dic3⋊Dic5—24no—
96#6667—24no—
97#6659—24no—
98#6656—24no—
99#6656—24no—
100#6654—24no—
101C2×C3×#137—51no—
102#5830D511yescharacteristic, complemented
103C2×#950—51no—
104#5816—51no—
105C22×#215—51no—
106C2×#908—51no—
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5175—52no—
111#5122—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×D4—31no—
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×#127—32no—
117C5×#124—32no—
118C5×#121—62no—
119C5×#120—62no—
120C5×#117—31no—
121#4097—24no—
122#4096—64no—
123C2×#689—31no—
124C2×#689C2×D312yescomplemented
125C2×#688—31no—
126C2×#687—31no—
127C2×#687—32no—
128C2×#687—32no—
129C2×#687—32no—
130C2×#687—64no—
131C2×#687C2×D312yescomplemented
132#4078—64no—
133C2×#686—31no—
134C2×#686—32no—
135C2×#681C2×D311yescharacteristic
136C22×#168—31no—
137#4043—62no—
138#4032—62no—
139#4021—32no—
140#4015—32no—
141#3935—32no—
142C4×#168—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C5×D3—22no—
148C22×C5×D3—42no—
149C22×C5×D3—82no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—42no—
162C2×Dic15—21no—
163D60—21no—
164D60—21no—
165C4×D15—42no—
166Dic30—21no—
167Dic30—21no—
168C5×#67—84no—
169C2×C5×Dic3C2×D414yes—
170C5×D12—22no—
171C5×D12—22no—
172C5×D12—42no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—42no—
175C3×Dic10—22no—
176C3×Dic10—22no—
177C3×Dic10—42no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C3×#168C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8—51no—
183C2×#235—51no—
184C22×D12C2×D511yescharacteristic
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16—51no—
189#950—104no—
190#947—52no—
191#947C2×D512yes—
192#946—102no—
193#944—52no—
194C2×#216—51no—
195C2×#215—51no—
196C2×#215—52no—
197C2×#215—52no—
198C2×#215—104no—
199#940C2×D512yes—
200#937—22no—
201C2×#214—51no—
202C2×#213—51no—
203#930—22no—
204#929—102no—
205#926C2×D511yescharacteristic
206C22×C3⋊C8—51no—
207#908—104no—
208C2×D24—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C24×C5—61no—
213C5×#41—22no—
214C5×#41—22no—
215C2×C5×Q8C22×D311yescharacteristic
216C2×C5×D4—21no—
217C2×C5×D4—32no—
218C2×C5×D4—64no—
219C2×C5×D4—62no—
220C2×C5×D4—61no—
221C2×C5×D4—62no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—61no—
226C22×Dic5—21no—
227#709—62no—
228#709—62no—
229C2×D20—31no—
230C2×C4×D5—61no—
231C2×Dic10—22no—
232C2×Dic10—22no—
233C2×Dic10—21no—
234C2×Dic10—31no—
235C2×Dic10C22×D312yes—
236C5×C4⋊C4—32no—
237C5×C22⋊C4—32no—
238C5×C22⋊C4—64no—
239C42×C5—32no—
240#689—24no—
241#689—62no—
242#688—62no—
243#687—24no—
244#687—64no—
245#687—64no—
246#687—62no—
247#687—64no—
248#686—62no—
249#686—64no—
250#685—64no—
251C4⋊Dic5—64no—
252#681#6714yescomplemented
253C2×#168—34no—
254C2×#168—31no—
255C2×#168—31no—
256C2×#168C22×D312yes—
257C2×#137—51no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—31no—
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—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—41no—
274C2×D15—42no—
275C2×C5×D3—42no—
276C2×C5×D3—44no—
277C2×C5×D3—84no—
278C3×C4×C5—41no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—42no—
284C5×Dic3—24no—
285C23×D3—21no—
286C3×#41—22no—
287C3×#41—22no—
288C2×C3×Q8—52no—
289C2×C3×Q8—101no—
290C2×C3×Q8—102no—
291C2×C3×Q8—102no—
292C2×C3×Q8C22×D511yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4C22×D511yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—24no—
299C2×#67—101no—
300#235—102no—
301#235—102no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—21no—
305C2×D12—51no—
306C2×D12C22×D512yes—
307C2×C4×D3—101no—
308C2×Dic6—51no—
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16—54no—
312C2×C3×C8—52no—
313#217C22⋊D512yes—
314#216—102no—
315#215—104no—
316#215—104no—
317#215—102no—
318#214—102no—
319#213—102no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—104no—
322C4⋊Dic3C22⋊D512yes—
323Dic3⋊C4—104no—
324C4×Dic3C22×D512yes—
325C2×C3⋊C8—54no—
326C2×C3⋊C8—51no—
327C2×C3⋊C8—51no—
328D24—104no—
329#204—104no—
330C23×C5—21no—
331C23×C5—62no—
332C23×C5—122no—
333C23×C5—242no—
334C23×C5D3×D411yescharacteristic
335C22×D5—61no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×D4—21no—
339C5×D4—21no—
340C5×D4—42no—
341C5×D4—62no—
342C5×D4—62no—
343C5×D4—122no—
344C5×D4—244no—
345C2×C4×C5—21no—
346C2×C4×C5—34no—
347C2×C4×C5—42no—
348C2×C4×C5D3×D411yescharacteristic
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—122no—
353C2×Dic5—22no—
354C2×Dic5—42no—
355C2×Dic5—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—22no—
360Dic10—22no—
361Dic10—42no—
362Dic10—61no—
363Dic10—61no—
364#168—32no—
365#168—32no—
366#168C2×#6714yes—
367C2×#41—151no—
368C2×#41D3×D511yescharacteristic
369C22×Q8—51no—
370C22×D4—31no—
371#137—104no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—52no—
375C2×Q16—151no—
376C2×SD16—52no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—151no—
381C2×SD16—151no—
382C2×SD16—304no—
383C2×D8—152no—
384C2×D8—151no—
385C2×M16—51no—
386C22×C8—151no—
387C4⋊Q8—152no—
388#127—32no—
389#124—32no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—62no—
394#120—62no—
395#117—31no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—81no—
403C5×D3—82no—
404C23×C3—21no—
405C23×C3C2×C22⋊D511yescharacteristic
406C22×D3—22no—
407C22×D3—42no—
408C22×D3—82no—
409C22×D3—101no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—102no—
413C3×Q8—102no—
414C3×Q8—202no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—42no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
420C2×C3×C4—102no—
421C2×C3×C4—202no—
422C2×C3×C4D4×D512yes—
423C2×C3×C4D4×D512yes—
424C2×C3×C4C2×C22⋊D511yescharacteristic
425C2×C3×C4C23×D511yescharacteristic
426#67—84no—
427#67—202no—
428C2×Dic3—101no—
429C2×Dic3C2×C22⋊D514yes—
430D12—22no—
431D12—22no—
432D12—42no—
433D12—101no—
434D12—101no—
435C4×D3—202no—
436Dic6—101no—
437Dic6—101no—
438C3×C8—54no—
439C3⋊C8—52no—
440C3⋊C8—52no—
441C22×C5—22no—
442C22×C5—42no—
443C22×C5—41no—
444C22×C5—124no—
445C22×C5—122no—
446C22×C5—244no—
447C22×C5#94012yes—
448C22×C5C2×D3×D411yescharacteristic
449C2×D5—122no—
450C2×D5—121no—
451C4×C5—41no—
452C4×C5—64no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—42no—
457Dic5—121no—
458C24—61no—
459#41—22no—
460#41—22no—
461#41—302no—
462#41—302no—
463C2×Q8—52no—
464C2×Q8—101no—
465C2×Q8—102no—
466C2×Q8—102no—
467C2×Q8—151no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—32no—
471C2×D4—64no—
472C2×D4—62no—
473C2×D4—61no—
474C2×D4—62no—
475C2×D4—151no—
476C2×D4—301no—
477C2×D4C2×D3×D511yescharacteristic
478C22×C4—21no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—104no—
483Q16—302no—
484SD16—104no—
485SD16—304no—
486SD16—302no—
487SD16—304no—
488SD16—304no—
489SD16—302no—
490D8—304no—
491D8—302no—
492M16—54no—
493C2×C8—52no—
494C2×C8—154no—
495C2×C8—151no—
496C2×C8—151no—
497C4⋊C4—32no—
498C4⋊C4—304no—
499C22⋊C4—32no—
500C22⋊C4—64no—
501C22⋊C4—304no—
502C42—32no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—42no—
507C22×C3#408612yes—
508C22×C3C22×C22⋊D511yescharacteristic
509C2×D3—42no—
510C2×D3—44no—
511C2×D3—84no—
512C2×D3—201no—
513C2×D3—202no—
514C3×C4—41no—
515C3×C4—202no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C2×D4×D511yescharacteristic
519Dic3—24no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5—242no—
524C2×C5#577812yes—
525C2×C5C2×#94011yescharacteristic
526D5—241no—
527C23—21no—
528C23—62no—
529C23—122no—
530C23—242no—
531C23—301no—
532C23D3×C22⋊D511yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—102no—
536Q8—102no—
537Q8—202no—
538Q8—301no—
539Q8—301no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—62no—
544D4—62no—
545D4—122no—
546D4—244no—
547D4—301no—
548D4—301no—
549D4—602no—
550C2×C4—21no—
551C2×C4—34no—
552C2×C4—42no—
553C2×C4—102no—
554C2×C4—202no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D511yescharacteristic
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—54no—
562C8—152no—
563C8—152no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3C2×#408611yescharacteristic
567C2×C3#6617012yes—
568D3—82no—
569D3—401no—
570C5#8397411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—41no—
574C22—124no—
575C22—122no—
576C22—244no—
577C22—602no—
578C22—601no—
579C22#9156712yes—
580C22C2×D3×C22⋊D511yescharacteristic
581C4—41no—
582C4—64no—
583C4—202no—
584C4—601no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061511211yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—242no—
592C2—1201no—
593C2#1175534012yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91839C2semidirect
2. C5×#5830C2semidirect
3. C2×C3×#4097C2semidirect
4. #11754278C2semidirect
5. C22×#6656C2semidirect
6. C2×#91304C2semidirect
7. #11749354C2semidirect
8. #11749323C2semidirect
9. #11749108C2semidirect
10. #11749076C2semidirect
11. #11748327C2semidirect
18. C2×#6718C22semidirect
19. C2×#6717C22semidirect
20. C2×#6716C22semidirect
21. C2×#6715C22semidirect
29. C2×C3×#689C22semidirect
30. C2×C3×#687C22semidirect
34. #91389C22semidirect
35. #91374C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
46. C2×#4097D3semidirect
84. C2×C3⋊#168D4semidirect
93. C3×#681D4semidirect
102. #5830D5semidirect
124. C2×#689C2×D3semidirect
131. C2×#687C2×D3semidirect
252. #681#67semidirect
503. C3×C5#3154semidirect
570. C5#83974semidirect
588. C3#10615112semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C5×#58302
C2×C3×#40972
#117542782
C22×#66562
C2×#913042
#117493542
#117493232
#117491082
#117490762
#117483272
#106151123
#839745