Finite Group Databasebeta

← #14439591

Subgroups — #14439591

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
1C22×#6715C211yesmaximal, characteristic, complemented
2C5×#5805C211yesmaximal, characteristic, complemented
3C2×C3×#4078C211yesmaximal, characteristic, complemented
4#11754609C211yesmaximal, characteristic, complemented
5C2×#91305C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11749098C212yesmaximal, complemented
8#11749097C212yesmaximal, complemented
9#11749078C212yesmaximal, complemented
10#11749076C212yesmaximal, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10615113—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6715—24no—
18C2×#6715C2212yes—
19C2×#6715C2212yes—
20C22×C3⋊#168C2211yescharacteristic
21C5×#953—22no—
22C5×#940C2212yescomplemented
23C5×#938—22no—
24C5×#936C2212yescomplemented
25C5×#926C2211yescharacteristic
26C2×C3×#687C2212yescomplemented
27C3×#4078—24no—
28C2×C3×#686C2212yescomplemented
29C2×C3×#681C2211yescharacteristic
30#91572—22no—
31#91458C2212yescomplemented
32#91450—22no—
33#91374C2212yescomplemented
34C2×#6661C2211yescharacteristic, complemented
35C2×#6660C2212yescomplemented
36C2×#6656C2211yescharacteristic, complemented
37C2×#6655C2211yescharacteristic, complemented
38#91305—24no—
39C2×#6654C2212yescomplemented
40#91297—24no—
41C2×#6652C2211yescharacteristic, complemented
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83940—51nomaximal, Hall
45C5×#535—31no—
46C2×#4096—31no—
47C2×#4095—31no—
48C2×#4078D311yescharacteristic, complemented
49C22×#686—31no—
50#65859—31no—
51#65363—32no—
52#65362—32no—
53#65348—32no—
54#65347—32no—
55#65286—31no—
56C24×C3×C5—21no—
57C23×D15—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×D60—22no—
64C2×D60—22no—
65C2×D60—21no—
66C2×D60C2312yes—
67C2×C5×#67—21no—
68C2×C5×#67—24no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—24no—
81#6715—24no—
82#6715—24no—
83C2×C3⋊#168D414yescomplemented
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86C5×#217—24no—
87C5×#217D412yes—
88C5×C4⋊Dic3D412yes—
89C4×C5×Dic3C2312yes—
90C3×#687—24no—
91C3×#686—24no—
92C3×#681D414yescomplemented
93C2×C3×#168C2312yes—
94#6667—24no—
95#6661—22no—
96#6660—24no—
97#6656—22no—
98#6655—22no—
99#6654—24no—
100#6652—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5830—51no—
103C2×#950—51no—
104#5805D511yescharacteristic, complemented
105C22×#213—51no—
106C2×#908—51no—
107#5176—52no—
108#5168—52no—
109#5154—52no—
110#5151—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709C2×D311yescharacteristic
115C22×D20—31no—
116C5×#127—32no—
117C5×#124—32no—
118C5×#121—62no—
119C5×#120—62no—
120C5×#117—31no—
121#4096—64no—
122#4095—64no—
123C2×#689—31no—
124C2×#688—31no—
125C2×#688—32no—
126C2×#687—31no—
127C2×#687C2×D312yescomplemented
128#4078—24no—
129C2×#686—32no—
130C2×#686—32no—
131C2×#686—31no—
132C2×#686—32no—
133C2×#686—64no—
134C2×#686C2×D312yescomplemented
135C2×#681C2×D311yescharacteristic
136C22×#168—31no—
137#4041—62no—
138#4028—62no—
139#4021—32no—
140#4020—32no—
141#3935—32no—
142C4×#168—32no—
143#3155—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—22no—
149C22×D15—42no—
150C22×D15—82no—
151C22×C5×D3—21no—
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
160D60—22no—
161D60—22no—
162D60—42no—
163C5×#67—42no—
164C5×#67—84no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3C2×D414yes—
167C5×D12—21no—
168C5×D12—21no—
169C4×C5×D3—42no—
170C5×Dic6—21no—
171C5×Dic6—21no—
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#1202—84no—
180C3⋊#168C2×D412yes—
181C3⋊#168C2×D412yes—
182C3×#168C2×D414yes—
183C2×C3×#41—51no—
184C22×C3×D4C2×D511yescharacteristic
185C2×#235C2×D511yescharacteristic
186C22×D12—51no—
187C3×AGL(1,ℤ/8)—104no—
188C2×C3×SD16—52no—
189C2×C3×D8—52no—
190C2×C3×M16—51no—
191#953—22no—
192#950—104no—
193#947—52no—
194C2×#216—51no—
195C2×#215—51no—
196#940—52no—
197#940C2×D512yescomplemented
198#938—22no—
199#937—102no—
200#936C2×D512yescomplemented
201C2×#214—51no—
202C2×#213—52no—
203C2×#213—52no—
204C2×#213—51no—
205C2×#213—104no—
206#930—102no—
207#926C2×D511yescharacteristic
208C22×C3⋊C8—51no—
209#908—104no—
210C2×D24—52no—
211C2×#204—52no—
212#815—52no—
213C8×Dic3—52no—
214C24×C5—21no—
215C23×D5—61no—
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—64no—
224C2×C5×D4—61no—
225C2×C5×D4C22×D312yes—
226C22×C4×C5—61no—
227C22×C4×C5C22×D311yescharacteristic
228C2×C22⋊D5—21no—
229#709—22no—
230#709—22no—
231C2×D20—32no—
232C2×D20—62no—
233C2×D20—62no—
234C2×D20—61no—
235C2×D20—64no—
236C2×D20C22×D311yescharacteristic
237C2×C4×D5—21no—
238C2×Dic10C22×D311yescharacteristic
239C5×C4⋊C4—32no—
240C5×C22⋊C4—32no—
241C5×C22⋊C4—64no—
242C42×C5—32no—
243#689—62no—
244#688—62no—
245#688—64no—
246#687—24no—
247#687—62no—
248#686—24no—
249#686—62no—
250#686—64no—
251#686—64no—
252#686—64no—
253#685—64no—
254#681#6714yescomplemented
255C2×#168—34no—
256C2×#168—31no—
257C2×#168—31no—
258C2×#168C22×D312yes—
259C2×AGL(1,ℤ/8)—51no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—151no—
262C22×D8—151no—
263#535—31no—
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—42no—
277C2×D15—44no—
278C2×D15—84no—
279C2×C5×D3—41no—
280C2×C5×D3—42no—
281C2×C3×D5—41no—
282C2×C3×D5—42no—
283C3×C4×C5#12712yes—
284C3×C4×C5C22×D411yescharacteristic
285C3×C4×C5C22×D411yescharacteristic
286C3×Dic5—41no—
287C5×Dic3—24no—
288C5×Dic3—41no—
289C24×C3—21no—
290C23×D3—101no—
291C3×#41—102no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—22no—
295C2×C3×D4—22no—
296C2×C3×D4—21no—
297C2×C3×D4—51no—
298C2×C3×D4—101no—
299C2×C3×D4C22×D512yes—
300C22×C3×C4—101no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—21no—
303C2×#67—24no—
304C2×#67—104no—
305#235—22no—
306#235—22no—
307C2×D12—52no—
308C2×D12—102no—
309C2×D12—102no—
310C2×D12—101no—
311C2×D12C22×D511yescharacteristic
312C2×C4×D3—21no—
313C2×Dic6C22×D511yescharacteristic
314C3×SD16—104no—
315C3×D8—104no—
316C3×M16—54no—
317C2×C3×C8—52no—
318#217—24no—
319#217C22⋊D512yes—
320#216—102no—
321#215—102no—
322#214—102no—
323#213—102no—
324#213—104no—
325#213—104no—
326(C2×D3)⋊C4—104no—
327C4⋊Dic3C22⋊D512yes—
328C4×Dic3C22×D512yes—
329C2×C3⋊C8—54no—
330C2×C3⋊C8—51no—
331C2×C3⋊C8—51no—
332D24—104no—
333#204—104no—
334C23×C5—22no—
335C23×C5—42no—
336C23×C5—61no—
337C23×C5—82no—
338C23×C5D3×D411yescharacteristic
339C22×D5—21no—
340C22×D5—62no—
341C22×D5—122no—
342C22×D5—242no—
343C5×Q8—61no—
344C5×Q8—61no—
345C5×D4—22no—
346C5×D4—22no—
347C5×D4—42no—
348C5×D4—61no—
349C5×D4—61no—
350C5×D4—122no—
351C5×D4—244no—
352C2×C4×C5—34no—
353C2×C4×C5—61no—
354C2×C4×C5—122no—
355C2×C4×C5D3×D411yescharacteristic
356C2×C4×C5D3×D412yes—
357C2×C4×C5C2×#6712yes—
358C2×C4×C5C23×D311yescharacteristic
359C22⋊D5—42no—
360C2×Dic5—21no—
361D20—21no—
362D20—21no—
363D20—62no—
364D20—62no—
365D20—122no—
366D20—244no—
367C4×D5—42no—
368Dic10—21no—
369Dic10—21no—
370#168—32no—
371#168—32no—
372#168C2×#6714yes—
373C2×#41—31no—
374C2×#41—51no—
375C22×D4—151no—
376C22×D4D3×D511yescharacteristic
377AGL(1,ℤ/8)—104no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—52no—
382C2×SD16—152no—
383C2×SD16—151no—
384C2×SD16—151no—
385C2×D8—52no—
386C2×D8—152no—
387C2×D8—151no—
388C2×D8—152no—
389C2×D8—152no—
390C2×D8—304no—
391C2×M16—51no—
392C22×C8—151no—
393#127—32no—
394#127—152no—
395#124—32no—
396#124—152no—
397#121—62no—
398#121—302no—
399#120—62no—
400#120—302no—
401#117—31no—
402#97—152no—
403C4×C8—152no—
404C2×C3×C5—22no—
405C2×C3×C5—82no—
406C2×C3×C5C2×#12711yescharacteristic
407C2×C3×C5#57612yes—
408D15—82no—
409C3×D5—81no—
410C5×D3—81no—
411C23×C3—22no—
412C23×C3—42no—
413C23×C3—82no—
414C23×C3—101no—
415C23×C3C2×C22⋊D511yescharacteristic
416C22×D3—21no—
417C22×D3—102no—
418C22×D3—202no—
419C22×D3—402no—
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×D512yes—
432C2×C3×C4C2×C22⋊D511yescharacteristic
433C2×C3×C4C23×D511yescharacteristic
434#67—42no—
435#67—84no—
436#67—404no—
437C2×Dic3—21no—
438C2×Dic3C2×C22⋊D514yes—
439D12—21no—
440D12—21no—
441D12—102no—
442D12—102no—
443D12—202no—
444C4×D3—42no—
445Dic6—21no—
446Dic6—21no—
447C3×C8—54no—
448C3⋊C8—52no—
449C3⋊C8—52no—
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—42no—
459C2×D5—41no—
460C2×D5—124no—
461C2×D5—122no—
462C2×D5—244no—
463C4×C5—64no—
464C4×C5—121no—
465C4×C5#94012yes—
466C4×C5C2×D3×D411yescharacteristic
467C4×C5C22×#6711yescharacteristic
468Dic5—41no—
469C24—21no—
470C24—301no—
471#41—62no—
472#41—62no—
473#41—102no—
474#41—102no—
475C2×Q8—31no—
476C2×Q8—51no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—31no—
481C2×D4—51no—
482C2×D4—64no—
483C2×D4—61no—
484C2×D4—101no—
485C2×D4—152no—
486C2×D4—304no—
487C2×D4—302no—
488C2×D4—301no—
489C2×D4—302no—
490C2×D4C2×D3×D512yes—
491C22×C4—61no—
492C22×C4—101no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—104no—
496SD16—304no—
497SD16—302no—
498SD16—302no—
499D8—104no—
500D8—304no—
501D8—304no—
502D8—304no—
503D8—302no—
504M16—54no—
505C2×C8—52no—
506C2×C8—154no—
507C2×C8—151no—
508C2×C8—151no—
509C4⋊C4—32no—
510C22⋊C4—32no—
511C22⋊C4—64no—
512C22⋊C4—304no—
513C42—32no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—84no—
519C22×C3—201no—
520C22×C3—202no—
521C22×C3#408612yes—
522C22×C3C22×C22⋊D511yescharacteristic
523C2×D3—41no—
524C2×D3—42no—
525C2×D3—202no—
526C2×D3—204no—
527C2×D3—404no—
528C3×C4—201no—
529C3×C4#408612yes—
530C3×C4C2×D4×D511yescharacteristic
531C3×C4C2×D4×D511yescharacteristic
532Dic3—24no—
533Dic3—41no—
534C2×C5—22no—
535C2×C5—82no—
536C2×C5—241no—
537C2×C5#577412yes—
538C2×C5C2×#94011yescharacteristic
539D5—81no—
540D5—242no—
541C23—22no—
542C23—42no—
543C23—61no—
544C23—82no—
545C23—101no—
546C23—302no—
547C23—602no—
548C23—1202no—
549C23D3×C22⋊D511yescharacteristic
550Q8—61no—
551Q8—61no—
552Q8—101no—
553Q8—101no—
554D4—22no—
555D4—22no—
556D4—42no—
557D4—61no—
558D4—61no—
559D4—101no—
560D4—101no—
561D4—122no—
562D4—202no—
563D4—244no—
564D4—302no—
565D4—302no—
566D4—602no—
567D4—1204no—
568C2×C4—34no—
569C2×C4—61no—
570C2×C4—101no—
571C2×C4—122no—
572C2×C4—202no—
573C2×C4D5×#6712yes—
574C2×C4D3×C22⋊D511yescharacteristic
575C2×C4#679012yes—
576C2×C4C22×D3×D511yescharacteristic
577C8—54no—
578C8—152no—
579C8—152no—
580C2×C3—22no—
581C2×C3—82no—
582C2×C3—401no—
583C2×C3C2×#408611yescharacteristic
584C2×C3#6616912yes—
585D3—81no—
586D3—402no—
587C5#8394011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—44no—
591C22—84no—
592C22—121no—
593C22—122no—
594C22—201no—
595C22—202no—
596C22—602no—
597C22—604no—
598C22—1204no—
599C22#9156712yes—
600C22C2×D3×C22⋊D511yescharacteristic
601C4—64no—
602C4—121no—
603C4—201no—
604C4#9156712yes—
605C4C2×D5×#6711yescharacteristic
606C4C2×#679011yescharacteristic
607C3#1061511311yescharacteristic, complemented, Sylow
608C2—22no—
609C2—82no—
610C2—241no—
611C2—401no—
612C2—1202no—
613C2#1175469812yes—
614C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
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. C22×#6715C2semidirect
2. C5×#5805C2semidirect
3. C2×C3×#4078C2semidirect
4. #11754609C2semidirect
5. C2×#91305C2semidirect
6. C2×#91297C2semidirect
7. #11749098C2semidirect
8. #11749097C2semidirect
9. #11749078C2semidirect
10. #11749076C2semidirect
11. #11748327C2semidirect
22. C5×#940C22semidirect
24. C5×#936C22semidirect
26. C2×C3×#687C22semidirect
28. C2×C3×#686C22semidirect
31. #91458C22semidirect
33. #91374C22semidirect
34. C2×#6661C22semidirect
35. C2×#6660C22semidirect
36. C2×#6656C22semidirect
37. C2×#6655C22semidirect
39. C2×#6654C22semidirect
41. C2×#6652C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
48. C2×#4078D3semidirect
83. C2×C3⋊#168D4semidirect
92. C3×#681D4semidirect
104. #5805D5semidirect
127. C2×#687C2×D3semidirect
134. C2×#686C2×D3semidirect
197. #940C2×D5semidirect
200. #936C2×D5semidirect
254. #681#67semidirect
514. C3×C5#3155semidirect
587. C5#83940semidirect
607. C3#10615113semidirect

Maximal subgroups

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

subgroupindex
C22×#67152
C5×#58052
C2×C3×#40782
#117546092
C2×#913052
C2×#912972
#117490982
#117490972
#117490782
#117490762
#117483272
#106151133
#839405