Finite Group Databasebeta

← #14439592

Subgroups — #14439592

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
2C2×C5×#932C211yesmaximal, characteristic, complemented
3C22×C3×#686C211yesmaximal, characteristic, complemented
4#11754600C211yesmaximal, characteristic, complemented
5C2×#91312C211yesmaximal, characteristic, complemented
6C2×#91303C211yesmaximal, characteristic, complemented
7#11749096C212yesmaximal, complemented
8#11749095C212yesmaximal, complemented
9#11749073C212yesmaximal, complemented
10#11749072C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615671—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91842—22no—
18#91829C2212yescomplemented
19#91827—22no—
20#91825C2212yescomplemented
21#91815C2211yescharacteristic
22C2×C5×#214C2212yescomplemented
23C5×#932—24no—
24C2×C5×#213C2212yescomplemented
25C2×C5×#208C2211yescharacteristic
26C2×C3×#686—24no—
27C2×C3×#686C2212yes—
28C2×C3×#686C2212yes—
29C22×C3×#168C2211yescharacteristic
30#91563—22no—
31#91463C2212yescomplemented
32#91456—22no—
33#91368C2212yescomplemented
34C2×#6663C2211yescharacteristic, complemented
35C2×#6660C2211yescharacteristic, complemented
36C2×#6659C2211yescharacteristic, complemented
37#91312—24no—
38C2×#6657C2212yescomplemented
39#91303—24no—
40C2×#6654C2211yescharacteristic, complemented
41C2×#6653C2212yescomplemented
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83830—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66164—31no—
47C2×#4096—31no—
48#66139—31no—
49C22×#686D311yescharacteristic, complemented
50C2×#4054—31no—
51#65465—32no—
52#65457—32no—
53#65443—32no—
54#65440—32no—
55#65411—31no—
56C24×C3×C5—21no—
57C23×C3×D5—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×#67—21no—
71C5×#235—22no—
72C5×#235—22no—
73C2×C5×D12C2311yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C5×Dic6C2311yescharacteristic
76C2×C3×D20—22no—
77C2×C3×D20—22no—
78C2×C3×D20—21no—
79C2×C3×D20C2312yes—
80C2×#1201—24no—
81#6719—24no—
82#6719D412yes—
83C4⋊Dic15D412yes—
84C4×Dic15C2312yes—
85C5×#214—24no—
86C5×#213—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×#686—24no—
90C3×#686—24no—
91C2×C3×#168D414yescomplemented
92C2×C3×#168C2311yescharacteristic
93C2×C3×#168C2311yescharacteristic
94#6665—24no—
95#6663—22no—
96#6660—22no—
97#6659—22no—
98#6657—24no—
99#6654—22no—
100#6653—24no—
101C22×C3×D8—51no—
102#5805—51no—
103#5805—51no—
104C2×#932—51no—
105C2×#932D511yescharacteristic, complemented
106C2×#904—51no—
107#5155—52no—
108#5154—52no—
109#5154—52no—
110#5151—52no—
111#5101—51no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C22×D20C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
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—24no—
132C2×#686—31no—
133C2×#686C2×D312yes—
134C2×#686C2×D312yes—
135#4076—62no—
136#4072—31no—
137C22×#168C2×D311yescharacteristic
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
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—21no—
150C22×C3×D5—22no—
151C22×C3×D5—42no—
152C22×C3×D5—82no—
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×#67—42no—
170C2×C5×Dic3—21no—
171C5×D12—21no—
172C5×D12—21no—
173C4×C5×D3—42no—
174C5×Dic6—21no—
175C5×Dic6—21no—
176C3×D20—22no—
177C3×D20—22no—
178C3×D20—42no—
179#1201—84no—
180C3×#168C2×D412yes—
181C3×#168C2×D412yes—
182C5×C3⋊C8C2×D414yes—
183C22×C3×D4—51no—
184C22×C3×D4C2×D511yescharacteristic
185C2×#235—51no—
186C2×#235C2×D511yescharacteristic
187C2×C3×D8—52no—
188C2×C3×D8—52no—
189C2×C3×D8—104no—
190C22×C3×C8—51no—
191#953—102no—
192#953—102no—
193#940—52no—
194#940—52no—
195#938—102no—
196#938—102no—
197#936—52no—
198#936—52no—
199C2×#214—52no—
200C2×#214C2×D512yescomplemented
201#932—24no—
202#932—104no—
203C2×#213—52no—
204C2×#213C2×D512yescomplemented
205#926—51no—
206C2×#208C2×D511yescharacteristic
207C2×Dic12—51no—
208#904—104no—
209C2×D24—51no—
210C2×#204—51no—
211C2×#204—51no—
212#815—52no—
213C8×Dic3—52no—
214C24×C5—21no—
215C23×D5—21no—
216C5×#41—62no—
217C5×#41—62no—
218C2×C5×Q8—31no—
219C2×C5×D4—22no—
220C2×C5×D4—21no—
221C2×C5×D4—22no—
222C2×C5×D4—31no—
223C2×C5×D4—61no—
224C2×C5×D4C22×D312yes—
225C22×C4×C5—61no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—64no—
228C2×C22⋊D5—64no—
229C2×C22⋊D5—61no—
230#709—62no—
231#709—62no—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—21no—
235C2×D20—31no—
236C2×D20C22×D312yes—
237C2×C4×D5—61no—
238C2×Dic10—31no—
239C5×SD16—64no—
240C5×D8—64no—
241C5×M16—34no—
242C2×C5×C8—32no—
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—62no—
246#688—62no—
247#687—62no—
248#686—24no—
249#686—24no—
250#686—62no—
251#685—64no—
252C4⋊Dic5—32no—
253C4×Dic5—32no—
254C2×#168#6714yescomplemented
255C2×#168C22×D311yescharacteristic
256C2×#168C22×D311yescharacteristic
257D40—64no—
258#677—64no—
259C2×AGL(1,ℤ/8)—31no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—151no—
262C22×D8—51no—
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—41no—
279C2×C5×D3—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—
287Dic15—41no—
288C5×Dic3—41no—
289C24×C3—21no—
290C24×C3—101no—
291C2×C3×D4—22no—
292C2×C3×D4—21no—
293C2×C3×D4—22no—
294C2×C3×D4—52no—
295C2×C3×D4—102no—
296C2×C3×D4—101no—
297C2×C3×D4—102no—
298C2×C3×D4C22×D512yes—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—21no—
301C2×#67—104no—
302C2×#67—104no—
303C2×#67—101no—
304#235—22no—
305#235—22no—
306#235—102no—
307#235—102no—
308C2×D12—51no—
309C2×D12C22×D511yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—101no—
312C2×Dic6—51no—
313C2×Dic6C22×D511yescharacteristic
314C3×D8—104no—
315C3×D8—104no—
316C2×C3×C8—54no—
317C2×C3×C8—51no—
318C2×C3×C8—51no—
319#217—52no—
320#217—104no—
321#217—104no—
322#214—24no—
323#214—104no—
324#213—24no—
325#213—104no—
326C4⋊Dic3—52no—
327C4×Dic3—52no—
328#208C22⋊D514yescomplemented
329C2×C3⋊C8C22×D512yes—
330Dic12—102no—
331D24—102no—
332#204—102no—
333#204—102no—
334C23×C5—22no—
335C23×C5—42no—
336C23×C5—61no—
337C23×C5—82no—
338C23×C5D3×D411yescharacteristic
339C22×D5—22no—
340C22×D5—42no—
341C22×D5—61no—
342C22×D5—82no—
343C5×Q8—61no—
344C5×Q8—61no—
345C5×D4—22no—
346C5×D4—22no—
347C5×D4—42no—
348C5×D4—61no—
349C5×D4—61no—
350C5×D4—122no—
351C2×C4×C5—61no—
352C2×C4×C5—122no—
353C2×C4×C5D3×D412yes—
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5C2×#6712yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—122no—
358C22⋊D5—244no—
359C22⋊D5—244no—
360C2×Dic5—34no—
361C2×Dic5—61no—
362D20—22no—
363D20—22no—
364D20—42no—
365D20—61no—
366D20—61no—
367C4×D5—122no—
368Dic10—61no—
369Dic10—61no—
370C5×C8—34no—
371#168C2×#6712yes—
372#168C2×#6712yes—
373C2×#41—31no—
374C2×#41—151no—
375C22×D4—51no—
376C22×D4D3×D511yescharacteristic
377AGL(1,ℤ/8)—64no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—32no—
382C2×SD16—152no—
383C2×SD16—151no—
384C2×SD16—151no—
385C2×D8—32no—
386C2×D8—52no—
387C2×D8—52no—
388C2×D8—104no—
389C2×D8—152no—
390C2×D8—151no—
391C2×M16—31no—
392C22×C8—51no—
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—82no—
410C5×D3—81no—
411C23×C3—22no—
412C23×C3—42no—
413C23×C3—82no—
414C23×C3—102no—
415C23×C3—202no—
416C23×C3—402no—
417C23×C3D4×D511yescharacteristic
418C22×D3—21no—
419C22×D3—101no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—42no—
423C3×D4—102no—
424C3×D4—102no—
425C3×D4—202no—
426C2×C3×C4D4×D512yes—
427C2×C3×C4D4×D511yescharacteristic
428C2×C3×C4C2×C22⋊D512yes—
429C2×C3×C4C23×D511yescharacteristic
430#67—42no—
431#67—202no—
432#67—404no—
433#67—404no—
434C2×Dic3—21no—
435C2×Dic3—54no—
436C2×Dic3—101no—
437D12—21no—
438D12—21no—
439D12—101no—
440D12—101no—
441C4×D3—42no—
442C4×D3—202no—
443Dic6—21no—
444Dic6—21no—
445Dic6—101no—
446Dic6—101no—
447C3×C8—52no—
448C3×C8—52no—
449C3⋊C8C2×C22⋊D514yes—
450C22×C5—22no—
451C22×C5—44no—
452C22×C5—42no—
453C22×C5—84no—
454C22×C5—122no—
455C22×C5—121no—
456C22×C5#94012yes—
457C22×C5C2×D3×D411yescharacteristic
458C2×D5—44no—
459C2×D5—42no—
460C2×D5—84no—
461C2×D5—122no—
462C2×D5—121no—
463C4×C5—121no—
464C4×C5#94012yes—
465C4×C5C2×D3×D411yescharacteristic
466C4×C5C22×#6711yescharacteristic
467Dic5—64no—
468Dic5—121no—
469C24—21no—
470C24—101no—
471#41—62no—
472#41—62no—
473#41—302no—
474#41—302no—
475C2×Q8—31no—
476C2×Q8—151no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—31no—
481C2×D4—52no—
482C2×D4—61no—
483C2×D4—102no—
484C2×D4—102no—
485C2×D4—101no—
486C2×D4—151no—
487C2×D4—304no—
488C2×D4—304no—
489C2×D4—301no—
490C2×D4C2×D3×D512yes—
491C22×C4—61no—
492C22×C4—301no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—64no—
496SD16—304no—
497SD16—302no—
498SD16—302no—
499D8—64no—
500D8—104no—
501D8—104no—
502D8—304no—
503D8—302no—
504M16—34no—
505C2×C8—32no—
506C2×C8—54no—
507C2×C8—51no—
508C2×C8—51no—
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—204no—
520C22×C3—202no—
521C22×C3—404no—
522C22×C3#408612yes—
523C22×C3C2×D4×D511yescharacteristic
524C2×D3—42no—
525C2×D3—41no—
526C2×D3—202no—
527C2×D3—201no—
528C3×C4#408612yes—
529C3×C4C2×D4×D511yescharacteristic
530C3×C4C22×C22⋊D511yescharacteristic
531Dic3—41no—
532Dic3—104no—
533Dic3—201no—
534C2×C5—22no—
535C2×C5—82no—
536C2×C5—241no—
537C2×C5#575712yes—
538C2×C5C2×#94011yescharacteristic
539D5—82no—
540D5—241no—
541C23—22no—
542C23—42no—
543C23—61no—
544C23—82no—
545C23—102no—
546C23—202no—
547C23—301no—
548C23—402no—
549C23#679011yescharacteristic
550Q8—61no—
551Q8—61no—
552Q8—301no—
553Q8—301no—
554D4—22no—
555D4—22no—
556D4—42no—
557D4—61no—
558D4—61no—
559D4—102no—
560D4—102no—
561D4—122no—
562D4—202no—
563D4—301no—
564D4—301no—
565D4—602no—
566D4—1204no—
567D4—1204no—
568C2×C4—61no—
569C2×C4—122no—
570C2×C4—154no—
571C2×C4—301no—
572C2×C4—602no—
573C2×C4D5×#6712yes—
574C2×C4D3×C22⋊D512yes—
575C2×C4#679011yescharacteristic
576C2×C4C22×D3×D511yescharacteristic
577C8—34no—
578C8—52no—
579C8—52no—
580C2×C3—22no—
581C2×C3—82no—
582C2×C3—402no—
583C2×C3#6610812yes—
584C2×C3C2×#408611yescharacteristic
585D3—81no—
586D3—401no—
587C5#8383011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—44no—
591C22—84no—
592C22—121no—
593C22—122no—
594C22—202no—
595C22—204no—
596C22—404no—
597C22—601no—
598C22—602no—
599C22#9156712yes—
600C22C2×#679011yescharacteristic
601C4—121no—
602C4—304no—
603C4—601no—
604C4#9156712yes—
605C4C2×D5×#6711yescharacteristic
606C4C2×D3×C22⋊D511yescharacteristic
607C3#1061567111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—82no—
610C2—241no—
611C2—402no—
612C2—1201no—
613C2#1175470312yes—
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. C2×C5×#932C2semidirect
3. C22×C3×#686C2semidirect
4. #11754600C2semidirect
5. C2×#91312C2semidirect
6. C2×#91303C2semidirect
7. #11749096C2semidirect
8. #11749095C2semidirect
9. #11749073C2semidirect
10. #11749072C2semidirect
11. #11748324C2semidirect
18. #91829C22semidirect
20. #91825C22semidirect
22. C2×C5×#214C22semidirect
24. C2×C5×#213C22semidirect
31. #91463C22semidirect
33. #91368C22semidirect
34. C2×#6663C22semidirect
35. C2×#6660C22semidirect
36. C2×#6659C22semidirect
38. C2×#6657C22semidirect
40. C2×#6654C22semidirect
41. C2×#6653C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
49. C22×#686D3semidirect
87. C5×#208D4semidirect
91. C2×C3×#168D4semidirect
105. C2×#932D5semidirect
200. C2×#214C2×D5semidirect
204. C2×#213C2×D5semidirect
254. C2×#168#67semidirect
328. #208C22⋊D5semidirect
514. C3×C5#3155semidirect
587. C5#83830semidirect
607. C3#10615671semidirect

Maximal subgroups

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

subgroupindex
#117565642
C2×C5×#9322
C22×C3×#6862
#117546002
C2×#913122
C2×#913032
#117490962
#117490952
#117490732
#117490722
#117483242
#106156713
#838305