Finite Group Databasebeta

← #14427851

Subgroups — #14427851

Order 1920.

1040 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
1#11756550C211yesmaximal, characteristic, complemented
2C23×C5×C3⋊C8C211yesmaximal, characteristic, complemented
3C3×#66125C211yesmaximal, characteristic, complemented
4C2×#91311C211yesmaximal, characteristic, complemented
5#11748560C212yesmaximal, complemented
6#11748541C212yesmaximal, complemented
7#11748539C212yesmaximal, complemented
8#11748518C212yesmaximal, complemented
9#11748451C211yesmaximal, characteristic, complemented
10#11748411C211yesmaximal, characteristic, complemented
11#11748365C211yesmaximal, characteristic, complemented
12#10615473—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16#91842—21no—
17#91819C2212yes—
18#91818—21no—
19C4×#1220—22no—
20#91815C2211yescharacteristic
21#91813C2212yes—
22C22×C5×C3⋊C8—24no—
23C22×C5×C3⋊C8C2211yescharacteristic
24C22×C5×C3⋊C8C2212yes—
25C22×C5×C3⋊C8C2212yes—
26C22×C5×C3⋊C8C2211yescharacteristic
27C3×#4099—21no—
28C3×#4076C2212yes—
29C3×#4075—21no—
30C3×C4×C22⋊D5—22no—
31C3×#4072C2211yescharacteristic
32C3×#4070C2212yes—
33C2×#6662C2211yescharacteristic, complemented
34C2×#6658C2211yescharacteristic, complemented
35#91311—24no—
36C2×#6657C2211yescharacteristic, complemented
37C2×#6653C2211yescharacteristic, complemented
38#90990C2212yescomplemented
39#90987C2212yescomplemented
40#90974C2212yescomplemented
41#90971C2212yescomplemented
42#90968C2212yescomplemented
43#90965C2212yescomplemented
44#82922—51nomaximal, Hall
45C23×C5×C8—31no—
46#66125—31no—
47#66125D311yescharacteristic, complemented
48C2×#4050—31no—
49#65405—32no—
50#65404—32no—
51#65403—32no—
52#65403—32no—
53#65402—31no—
54#65402—31no—
55#65395—31no—
56C24×C3×C5D411yescharacteristic
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5D412yes—
60C22×C3×C4×C5D411yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—22no—
64C2×#1220—21no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C2×C3×C22⋊D5—21no—
71C2×C3×C22⋊D5—22no—
72C3×#709—22no—
73C3×#709—22no—
74C2×C3×D20C2311yescharacteristic
75C2×C3×C4×D5—21no—
76C2×C3×Dic10C2311yescharacteristic
77#6719—22no—
78#6719—21no—
79#6714—22no—
80C4⋊Dic15C2312yes—
81#6712—22no—
82C4×Dic15—21no—
83C2×C5×C3⋊C8—22no—
84C2×C5×C3⋊C8—24no—
85C2×C5×C3⋊C8—24no—
86C2×C5×C3⋊C8D414yescomplemented
87C2×C5×C3⋊C8C2312yes—
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C5×C3⋊C8C2311yescharacteristic
90C3×C22⋊Dic5—22no—
91C3×C22⋊Dic5—21no—
92C3×#685—22no—
93C3×C4⋊Dic5C2312yes—
94C3×#683—22no—
95C3×C4×Dic5—21no—
96#6662—22no—
97#6658—22no—
98#6657—22no—
99#6653—22no—
100C3×#525—51no—
101C2×#950—51no—
102#5791—51no—
103C23×C3⋊C8D511yescharacteristic, complemented
104#5233—51no—
105#5051—52no—
106#5048—52no—
107#5041—52no—
108#5038—52no—
109#5002—51no—
110#4998—51no—
111C23×C4×C5C2×D311yescharacteristic
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×C5×C8—31no—
115C22×C5×C8—31no—
116C22×C5×C8—32no—
117C22×C5×C8—32no—
118C22×C5×C8—64no—
119#4099—21no—
120#4099—61no—
121#4076—32no—
122#4076C2×D312yes—
123#4075—21no—
124#4075—61no—
125C4×C22⋊D5—22no—
126C4×C22⋊D5—62no—
127#4072—31no—
128#4072C2×D311yescharacteristic
129#4070—32no—
130#4070C2×D312yes—
131C2×Dic20—31no—
132#4050—64no—
133C2×D40—31no—
134C2×#677—31no—
135C2×#677—31no—
136#3953—32no—
137#3953—32no—
138#3950—32no—
139#3949—32no—
140#3948—32no—
141#3948—32no—
142#3050—151noSylow
143C23×C3×C5—22no—
144C23×C3×C5—24no—
145C23×C3×C5C2×D411yescharacteristic
146C23×C3×C5C2×D412yes—
147C22×D15—21no—
148C22×C3×D5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—24no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—42no—
159#1220—44no—
160C2×Dic15—22no—
161C2×Dic15—21no—
162D60—21no—
163D60—21no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C3×C22⋊D5—42no—
168C3×C22⋊D5—44no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—21no—
171C3×D20—21no—
172C3×D20—21no—
173C3×C4×D5—42no—
174C3×Dic10—21no—
175C3×Dic10—21no—
176C5×C3⋊C8—22no—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41—51no—
180C23×C3×C4C2×D511yescharacteristic
181C2×#235—51no—
182C3×#123—101no—
183C3×C22⋊Q8—52no—
184C3×#121—52no—
185C3×#120—101no—
186C3×C4×D4—102no—
187C3×#117—51no—
188#953—101no—
189#950—104no—
190C2×#216—51no—
191C2×#215—51no—
192C2×#214—51no—
193C2×#213—51no—
194#930—52no—
195#929—101no—
196C4×#67—102no—
197#926—51no—
198#924—52no—
199C22×C3⋊C8—24no—
200C22×C3⋊C8C2×D511yescharacteristic
201C22×C3⋊C8C2×D512yes—
202C22×C3⋊C8C2×D512yes—
203C22×C3⋊C8C2×D511yescharacteristic
204#835—52no—
205#832—52no—
206#810—52no—
207#809—52no—
208#808—52no—
209#807—52no—
210C24×C5#6711yescharacteristic
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5#6712yes—
214C22×C4×C5#6711yescharacteristic
215C22×C4×C5C22×D312yes—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—21no—
218C2×C22⋊D5—22no—
219C2×C22⋊D5—61no—
220C2×C22⋊D5—62no—
221#709—22no—
222#709—22no—
223#709—62no—
224#709—62no—
225C2×D20—31no—
226C2×D20C22×D311yescharacteristic
227C2×C4×D5—21no—
228C2×C4×D5—61no—
229C2×Dic10—31no—
230C2×Dic10C22×D311yescharacteristic
231C2×C5×C8—34no—
232C2×C5×C8—31no—
233C2×C5×C8—31no—
234C2×C5×C8—32no—
235C2×C5×C8—64no—
236C2×C5×C8—64no—
237C2×C5×C8—62no—
238C22⋊Dic5—22no—
239C22⋊Dic5—21no—
240C22⋊Dic5—62no—
241C22⋊Dic5—61no—
242#685—22no—
243#685—62no—
244C4⋊Dic5—32no—
245C4⋊Dic5C22×D312yes—
246#683—22no—
247#683—62no—
248C4×Dic5—21no—
249C4×Dic5—61no—
250Dic20—62no—
251D40—62no—
252#677—62no—
253#677—62no—
254C2×#135—151no—
255C23×C8—31no—
256#525—51no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—151no—
264#416—151no—
265C22×C3×C5—28no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5#12112yes—
270C22×C3×C5#13514yescomplemented
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—41no—
273C2×D15—42no—
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5—22no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—41no—
281Dic15—42no—
282C3×Dic5—41no—
283C3×Dic5—42no—
284C24×C3D2011yescharacteristic
285C3×#41—102no—
286C3×#41—102no—
287C2×C3×Q8—51no—
288C2×C3×D4—51no—
289C2×C3×D4—102no—
290C2×C3×D4—101no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—101no—
294C22×C3×C4D2012yes—
295C22×C3×C4D2011yescharacteristic
296C22×C3×C4C22×D512yes—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—102no—
299C2×#67—101no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—51no—
305C3×C4⋊C4—52no—
306C3×C4⋊C4—102no—
307C3×C22⋊C4—101no—
308C3×C22⋊C4—102no—
309C3×C22⋊C4—102no—
310C3×C42—101no—
311#217—102no—
312#217—101no—
313#216—102no—
314#215—102no—
315#214—102no—
316#213—102no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—52no—
319Dic3⋊C4—102no—
320C4×Dic3—101no—
321C2×C3⋊C8—22no—
322C2×C3⋊C8—24no—
323C2×C3⋊C8—24no—
324C2×C3⋊C8C22⋊D514yescomplemented
325C2×C3⋊C8C22×D512yes—
326C2×C3⋊C8C22×D511yescharacteristic
327C2×C3⋊C8C22×D511yescharacteristic
328C23×C5—22no—
329C23×C5—24no—
330C23×C5C2×#6711yescharacteristic
331C23×C5C2×#6712yes—
332C22×D5—21no—
333C22×D5—61no—
334C2×C4×C5—22no—
335C2×C4×C5—24no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5D3×D412yes—
339C2×C4×C5#23712yes—
340C2×C4×C5C2×#6712yes—
341C2×C4×C5C2×#6711yescharacteristic
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—42no—
344C22⋊D5—44no—
345C22⋊D5—122no—
346C22⋊D5—124no—
347C2×Dic5—22no—
348C2×Dic5—21no—
349C2×Dic5—62no—
350C2×Dic5—61no—
351D20—21no—
352D20—21no—
353D20—61no—
354D20—61no—
355C4×D5—42no—
356C4×D5—122no—
357Dic10—21no—
358Dic10—21no—
359Dic10—61no—
360Dic10—61no—
361C5×C8—32no—
362C5×C8—32no—
363C5×C8—62no—
364C2×#41—51no—
365C2×#41—151no—
366C23×C4D3×D511yescharacteristic
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—31no—
373C22×C8—31no—
374C22×C8—32no—
375C22×C8—32no—
376C22×C8—64no—
377#123—101no—
378#123—301no—
379C22⋊Q8—52no—
380C22⋊Q8—152no—
381#121—52no—
382#121—152no—
383#120—101no—
384#120—301no—
385C4×D4—102no—
386C4×D4—302no—
387#117—51no—
388#117—151no—
389#107—152no—
390#106—152no—
391#103—152no—
392#103—152no—
393#102—152no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5—24no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399D15—81no—
400C3×D5—81no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3—101no—
404C23×C3C2×D2012yes—
405C23×C3C2×D2011yescharacteristic
406C22×D3—101no—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—101no—
410C3×D4—101no—
411C3×D4—204no—
412C3×D4—202no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—102no—
418C2×C3×C4—101no—
419C2×C3×C4—202no—
420C2×C3×C4C2×D2012yes—
421C2×C3×C4C2×D2011yescharacteristic
422C2×C3×C4#70912yes—
423C2×C3×C4C2×C22⋊D512yes—
424C2×C3×C4C23×D511yescharacteristic
425#67—204no—
426#67—202no—
427C2×Dic3—102no—
428C2×Dic3—101no—
429D12—101no—
430D12—101no—
431C4×D3—202no—
432Dic6—101no—
433Dic6—101no—
434C3⋊C8—22no—
435C3⋊C8C2×C22⋊D512yes—
436C3⋊C8C2×C22⋊D512yes—
437C22×C5—28no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5#93912yes—
442C22×C5#95014yescomplemented
443C22×C5C22×#6711yescharacteristic
444C2×D5—41no—
445C2×D5—42no—
446C2×D5—121no—
447C2×D5—122no—
448C4×C5—22no—
449C4×C5#93912yes—
450C4×C5C2×D3×D411yescharacteristic
451C4×C5C2×#23711yescharacteristic
452Dic5—41no—
453Dic5—42no—
454Dic5—121no—
455Dic5—122no—
456C24#120211yescharacteristic
457#41—102no—
458#41—102no—
459#41—302no—
460#41—302no—
461C2×Q8—51no—
462C2×Q8—151no—
463C2×D4—51no—
464C2×D4—102no—
465C2×D4—101no—
466C2×D4—151no—
467C2×D4—302no—
468C2×D4—301no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—101no—
472C22×C4—301no—
473C22×C4#120211yescharacteristic
474C22×C4#120212yes—
475C22×C4C2×D3×D512yes—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—32no—
485C2×C8—64no—
486C2×C8—64no—
487C2×C8—62no—
488C4⋊C4—52no—
489C4⋊C4—102no—
490C4⋊C4—152no—
491C4⋊C4—302no—
492C22⋊C4—101no—
493C22⋊C4—102no—
494C22⋊C4—102no—
495C22⋊C4—301no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—101no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—28no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—202no—
506C22×C3—201no—
507C22×C3#405014yescomplemented
508C22×C3#407612yes—
509C22×C3C22×D2011yescharacteristic
510C2×D3—202no—
511C2×D3—201no—
512C3×C4—22no—
513C3×C4—202no—
514C3×C4—201no—
515C3×C4#407612yes—
516C3×C4C2×#70911yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—202no—
519Dic3—201no—
520C2×C5—22no—
521C2×C5—24no—
522C2×C5C2×#93911yescharacteristic
523C2×C5C2×#95012yes—
524D5—81no—
525D5—241no—
526C23—24no—
527C23—22no—
528C23—101no—
529C23—301no—
530C23C2×#120212yes—
531C23C2×#120211yescharacteristic
532Q8—101no—
533Q8—101no—
534Q8—301no—
535Q8—301no—
536D4—101no—
537D4—101no—
538D4—204no—
539D4—202no—
540D4—301no—
541D4—301no—
542D4—604no—
543D4—602no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—102no—
549C2×C4—101no—
550C2×C4—202no—
551C2×C4—302no—
552C2×C4—301no—
553C2×C4—602no—
554C2×C4#677912yes—
555C2×C4C2×#120212yes—
556C2×C4C2×#120211yescharacteristic
557C2×C4D3×C22⋊D512yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—32no—
560C8—32no—
561C8—62no—
562C2×C3—24no—
563C2×C3—22no—
564C2×C3—401no—
565C2×C3C2×#405012yes—
566C2×C3C2×#407611yescharacteristic
567D3—401no—
568C5#8292211yescharacteristic, complemented, Sylow
569C22—28no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—201no—
574C22—202no—
575C22—601no—
576C22—602no—
577C22#9131114yescomplemented
578C22#9156912yes—
579C22C22×#120211yescharacteristic
580C4—22no—
581C4—201no—
582C4—202no—
583C4—601no—
584C4—602no—
585C4#9156912yes—
586C4C2×#677911yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061547311yescharacteristic, complemented, Sylow
589C2—24no—
590C2—22no—
591C2—401no—
592C2—1201no—
593C2C2×#9131112yes—
594C2C2×#9156911yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C22×D4
hypercenterC23×C4D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #11756550C2semidirect
2. C23×C5×C3⋊C8C2semidirect
3. C3×#66125C2semidirect
4. C2×#91311C2semidirect
5. #11748560C2semidirect
6. #11748541C2semidirect
7. #11748539C2semidirect
8. #11748518C2semidirect
9. #11748451C2semidirect
10. #11748411C2semidirect
11. #11748365C2semidirect
33. C2×#6662C22semidirect
34. C2×#6658C22semidirect
36. C2×#6657C22semidirect
37. C2×#6653C22semidirect
38. #90990C22semidirect
39. #90987C22semidirect
40. #90974C22semidirect
41. #90971C22semidirect
42. #90968C22semidirect
43. #90965C22semidirect
47. #66125D3semidirect
86. C2×C5×C3⋊C8D4semidirect
103. C23×C3⋊C8D5semidirect
270. C22×C3×C5#135semidirect
324. C2×C3⋊C8C22⋊D5semidirect
442. C22×C5#950semidirect
500. C3×C5#3050semidirect
507. C22×C3#4050semidirect
568. C5#82922semidirect
577. C22#91311semidirect
588. C3#10615473semidirect

Maximal subgroups

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

subgroupindex
#117565502
C23×C5×C3⋊C82
C3×#661252
C2×#913112
#117485602
#117485412
#117485392
#117485182
#117484512
#117484112
#117483652
#106154733
#829225