Finite Group Databasebeta

← #14412759

Subgroups — #14412759

Order 1920.

1452 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
1C2×#92001C211yesmaximal, characteristic
2C3×#65857C211yesmaximal, characteristic, complemented
3C2×#91283C211yesmaximal, characteristic, complemented
4#11751105C211yesmaximal, characteristic, complemented
5C5×#5002C211yesmaximal, characteristic, complemented
6C2×#90974C211yesmaximal, characteristic, complemented
7#11748384C211yesmaximal, characteristic, complemented
8#11747499C212yesmaximal, complemented
9#11747498C212yesmaximal, complemented
10#11747487C212yesmaximal, complemented
11D5×#810C212yesmaximal, complemented
12#10610563—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C2×#6780—22no—
17C2×#6772C2212yes—
18C2×D3×Dic10—21no—
19#92001—24no—
20#92001C418yescomplemented
21C2×#6765—21no—
22C2×D5×Dic6C2212yes—
23C3×C5×#117C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25C22×C5×C3⋊C8C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C3×#4038C2212yes—
28C3×D5×C4⋊C4C2212yes—
29C3×#4027—22no—
30C3×C4×D20—21no—
31C3×C4×Dic10—21no—
32C2×#6649C2212yes—
33#91283—24no—
34C2×D5×C3⋊C8C2212yes—
35#91094C2212yes—
36#91094C2212yes—
37C5×#810C2211yescharacteristic
38C5×#810C2211yescharacteristic
39C5×#809C2211yescharacteristic
40C5×#809C2211yescharacteristic
41#90974C2212yes—
42#90974C2212yes—
43#90972C2212yes—
44#90966C2212yes—
45#82570—51nomaximal, Hall
46C2×#4150—31no—
47C2×#4047—31no—
48#65857D311yescharacteristic, complemented
49C5×#416—31no—
50#65521—31no—
51C2×#3948—31no—
52#65293—31no—
53#65091—32no—
54D5×#103—32no—
55#65061—32no—
56#65060—32no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15—21no—
59C2×Dic30—21no—
60C2×Dic30—22no—
61C2×Dic30C2×C414yescomplemented
62C2×Dic30C2312yes—
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235C2×C414yescomplemented
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×C22⋊D5D412yes—
70C22×C3×Dic5—21no—
71C3×#709C2×C414yes—
72C3×#709D414yes—
73C2×C3×D20D411yescharacteristic
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2312yes—
76C2×C3×Dic10D411yescharacteristic
77C2×#1204—22no—
78C2×#1201—22no—
79C2×D3×Dic5—22no—
80#6780—216no—
81C2×D5×Dic3—22no—
82#6772—24no—
83#6772C2×C418yescomplemented
84D3×Dic10—28no—
85#6765—28no—
86D5×Dic6—24no—
87D5×Dic6C2×C418yescomplemented
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5—21no—
92#6710—22no—
93C2×C3⋊#168C2312yes—
94C2×C5×C3⋊C8—22no—
95C2×C5×C3⋊C8C2311yescharacteristic
96C2×C5×C3⋊C8C2311yescharacteristic
97C3×#685—22no—
98C3×C4⋊Dic5—21no—
99C3×C4⋊Dic5C2312yes—
100C3×#683—22no—
101C3×C4×Dic5—22no—
102#6649—24no—
103D5×C3⋊C8—24no—
104C2×#1010—51no—
105C3×#520—51no—
106C2×#948—51no—
107#5004—51no—
108#5004—52no—
109#5002—52no—
110#5002D511yescharacteristic, complemented
111C2×#810—51no—
112C2×#810—52no—
113#4966—51no—
114#4966—52no—
115C2×C5×#41—31no—
116#4150—38no—
117#4150—64no—
118C2×Q8×D5—32no—
119C2×#711—32no—
120C2×#711—62no—
121C2×#709—61no—
122C2×#709C2×D311yescharacteristic
123C22×Dic10—31no—
124C22×Dic10—61no—
125C22×C5×C8—31no—
126C5×#117C2×D311yescharacteristic
127C2×C4⋊Dic5C2×D311yescharacteristic
128C2×#681—31no—
129#4047—64no—
130C2×#676—32no—
131C2×C8×D5—32no—
132#4038C2×D312yes—
133D5×C4⋊C4C2×D312yes—
134#4027—22no—
135C4×D20—21no—
136C4×Dic10—21no—
137C5×#103—31no—
138C5×#103—31no—
139C5×#102—31no—
140C5×#102—31no—
141#3967—32no—
142#3964—32no—
143#3948—32no—
144#3948—32no—
145#3942—32no—
146#3942—32no—
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×C5×D3—21no—
150C22×C3×D5C2×D412yes—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—24no—
158C2×Dic15—22no—
159Dic30—24no—
160Dic30—22no—
161Dic30C22×C414yes—
162C5×#67—24no—
163C2×C5×Dic3—21no—
164C5×D12—21no—
165C5×D12C22×C412yes—
166C4×C5×D3—24no—
167C5×Dic6—21no—
168C5×Dic6C22×C412yes—
169C3×C22⋊D5C22⋊C418yes—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—81no—
172C2×C3×Dic5C2×D412yes—
173C3×D20C22⋊C414yes—
174C3×C4×D5—82no—
175C3×C4×D5C22×C414yes—
176C3×C4×D5C2×D414yes—
177C3×Dic10C22⋊C414yes—
178#1204—28no—
179#1201—28no—
180D3×Dic5—28no—
181D5×Dic3—28no—
182C3⋊#168—22no—
183C5×C3⋊C8—21no—
184C5×C3⋊C8—21no—
185C2×C3×#41—51no—
186#1010—58no—
187#1010—104no—
188C2×D3×Q8—101no—
189C2×#237—101no—
190C2×#237—102no—
191C2×#235—52no—
192C2×#235C2×D511yescharacteristic
193C22×Dic6—51no—
194C22×Dic6—52no—
195C3×C4×Q8—101no—
196C3×C4×D4—101no—
197C3×C4×D4—102no—
198C3×#117—52no—
199C3×#117C2×D511yescharacteristic
200C2×C3×C4⋊C4—51no—
201C2×C3×C4⋊C4—52no—
202#948—104no—
203C2×#208—51no—
204C2×#208—52no—
205C22×C3⋊C8—52no—
206C22×C3⋊C8C2×D511yescharacteristic
207#810—52no—
208#810—52no—
209#810—52no—
210#810—52no—
211#810—52no—
212#810C2×D511yescharacteristic
213#810C2×D511yescharacteristic
214#809—52no—
215#809C2×D511yescharacteristic
216#809C2×D511yescharacteristic
217C5×#41—34no—
218C5×#41—62no—
219C2×C5×Q8—31no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—62no—
225C2×C22⋊D5#6712yes—
226C22×Dic5—21no—
227C22×Dic5—61no—
228C22×Dic5—62no—
229Q8×D5—38no—
230Q8×D5—64no—
231#711—38no—
232#711—616no—
233#711—64no—
234#709—68no—
235#709C4×D314yes—
236#709D1214yes—
237C2×D20#6711yescharacteristic
238C2×C4×D5—22no—
239C2×C4×D5—62no—
240C2×C4×D5C22×D312yes—
241C2×Dic10—34no—
242C2×Dic10—32no—
243C2×Dic10—62no—
244C2×Dic10—61no—
245C2×Dic10—62no—
246C2×Dic10—68no—
247C2×Dic10#6711yescharacteristic
248C2×C5×C8—31no—
249C2×C5×C8—31no—
250C2×C5×C8—62no—
251C5×C4⋊C4C22×D311yescharacteristic
252C5×C4⋊C4C22×D311yescharacteristic
253C5×C22⋊C4—21no—
254C42×C5—21no—
255#685—22no—
256C4⋊Dic5—21no—
257C4⋊Dic5C22×D312yes—
258#683—22no—
259C4×Dic5—22no—
260#681—62no—
261C2×#168—32no—
262#676—64no—
263C8×D5—64no—
264C2×2−1+4—151no—
265C2×#131—151no—
266#520—51no—
267#419—152no—
268#419—151no—
269#417—152no—
270#417—151no—
271#416—31no—
272#416—152no—
273C2×#103—152no—
274C2×#103—151no—
275C22×C3×C5—21no—
276C22×C3×C5—21no—
277C22×C3×C5C2×C22⋊C412yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×C5×D3—22no—
280C2×C5×D3—41no—
281C2×C5×D3—41no—
282C2×C3×D5—22no—
283C2×C3×D5—22no—
284C2×C3×D5C2×C22⋊C414yes—
285C3×C4×C5—41no—
286C3×C4×C5—41no—
287C3×C4×C5C2×C22⋊C412yes—
288C3×C4×C5C23×C411yescharacteristic
289C3×C4×C5C22×D411yescharacteristic
290Dic15—24no—
291C3×Dic5—42no—
292C3×Dic5C2×C22⋊C414yes—
293C5×Dic3—22no—
294C3×#41—54no—
295C3×#41—54no—
296C2×C3×Q8—51no—
297C2×C3×D4—52no—
298C2×C3×D4—51no—
299C22×C3×C4—52no—
300C22×C3×C4—102no—
301C22×C3×C4—101no—
302C22×C3×C4C22×D511yescharacteristic
303C2×#67—21no—
304C2×#67—102no—
305C22×Dic3—102no—
306C22×Dic3—101no—
307D3×Q8—108no—
308#237—108no—
309#237—1016no—
310#235—22no—
311#235—58no—
312#235—104no—
313#235C4×D514yescomplemented
314C2×D12C22×D511yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—102no—
317C2×Dic6—54no—
318C2×Dic6—52no—
319C2×Dic6—58no—
320C2×Dic6—104no—
321C2×Dic6—102no—
322C2×Dic6—101no—
323C2×Dic6—102no—
324C2×Dic6C22×D511yescharacteristic
325C3×C4⋊C4—52no—
326C3×C4⋊C4—102no—
327C3×C4⋊C4—101no—
328C3×C4⋊C4C22×D511yescharacteristic
329C3×C4⋊C4C22×D511yescharacteristic
330C3×C22⋊C4—21no—
331C3×C22⋊C4—102no—
332C3×C42—21no—
333C3×C42—102no—
334#208—104no—
335#208—102no—
336C2×C3⋊C8—22no—
337C2×C3⋊C8—52no—
338C2×C3⋊C8—104no—
339C2×C3⋊C8C22×D511yescharacteristic
340C2×C3⋊C8C22×D511yescharacteristic
341C23×C5—61no—
342C23×C5C2×#6711yescharacteristic
343C22×D5C2×#6712yes—
344C5×Q8—32no—
345C5×Q8—61no—
346C5×D4—32no—
347C5×D4—64no—
348C5×D4—61no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—61no—
352C2×C4×C5—64no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5C2×D1212yes—
355C2×C4×C5C2×#6711yescharacteristic
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—68no—
358C22⋊D5(C2×D3)⋊C418yes—
359C2×Dic5—22no—
360C2×Dic5—64no—
361C2×Dic5—62no—
362C2×Dic5—68no—
363C2×Dic5—81no—
364C2×Dic5C2×#6712yes—
365D20(C2×D3)⋊C414yes—
366C4×D5—68no—
367C4×D5—82no—
368C4×D5C2×C4×D314yes—
369C4×D5C2×D1214yes—
370Dic10—34no—
371Dic10—64no—
372Dic10—62no—
373Dic10—68no—
374Dic10(C2×D3)⋊C414yes—
375C5×C8—61no—
376C5×C8—61no—
377#168—62no—
3782−1+4—158no—
3792−1+4—304no—
380C2×#41—31no—
381C2×#41—51no—
382C2×#41—152no—
383C2×#41—301no—
384C2×#41—302no—
385C22×Q8—152no—
386C22×Q8—151no—
387C22×Q8—301no—
388#131—304no—
389C2×M16—152no—
390C2×M16—151no—
391C22×C8—31no—
392C22×C8—152no—
393C4×Q8—101no—
394C4×D4—101no—
395C4×D4—102no—
396#117—52no—
397#117D3×D511yescharacteristic
398C2×C4⋊C4—51no—
399C2×C4⋊C4—52no—
400#103—31no—
401#103—31no—
402#103—152no—
403#103—152no—
404#103—152no—
405#103—152no—
406#103—152no—
407#102—31no—
408#102—31no—
409#102—152no—
410C2×C3×C5—22no—
411C2×C3×C5C22×C22⋊C411yescharacteristic
412C2×C3×C5#57711yescharacteristic
413C2×C3×C5#57811yescharacteristic
414C3×D5—24no—
415C5×D3—42no—
416C23×C3—52no—
417C23×C3D4×D511yescharacteristic
418C22×D3—21no—
419C3×Q8—54no—
420C3×D4—58no—
421C3×D4—54no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—52no—
425C2×C3×C4—54no—
426C2×C3×C4—54no—
427C2×C3×C4—102no—
428C2×C3×C4—402no—
429C2×C3×C4—401no—
430C2×C3×C4C2×C4×D512yes—
431C2×C3×C4D4×D512yes—
432C2×C3×C4D4×D511yescharacteristic
433C2×C3×C4C23×D511yescharacteristic
434#67—24no—
435#67—108no—
436C2×Dic3—21no—
437C2×Dic3—108no—
438C2×Dic3—102no—
439C2×Dic3—104no—
440D12—21no—
441D12C2×C4×D512yes—
442C4×D3—24no—
443C4×D3—108no—
444Dic6—21no—
445Dic6—54no—
446Dic6—108no—
447Dic6—102no—
448Dic6—104no—
449Dic6C2×C4×D512yes—
450C3⋊C8—21no—
451C3⋊C8—21no—
452C3⋊C8—102no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5—62no—
456C22×C5—121no—
457C22×C5—121no—
458C22×C5C2×(C2×D3)⋊C412yes—
459C22×C5C22×#6711yescharacteristic
460C2×D5—22no—
461C2×D5—22no—
462C2×D5C2×(C2×D3)⋊C414yes—
463C4×C5—41no—
464C4×C5—41no—
465C4×C5—62no—
466C4×C5C2×(C2×D3)⋊C412yes—
467C4×C5C22×C4×D311yescharacteristic
468C4×C5C22×D1211yescharacteristic
469Dic5—42no—
470Dic5—64no—
471Dic5C2×(C2×D3)⋊C414yes—
472#41—34no—
473#41—54no—
474#41—54no—
475#41—62no—
476#41—158no—
477#41—304no—
478#41—308no—
479#41—3016no—
480C2×Q8—31no—
481C2×Q8—51no—
482C2×Q8—158no—
483C2×Q8—154no—
484C2×Q8—152no—
485C2×Q8—302no—
486C2×Q8—304no—
487C2×Q8—308no—
488C2×Q8—302no—
489C2×Q8—301no—
490C2×D4—31no—
491C2×D4—52no—
492C2×D4—51no—
493C2×D4—61no—
494C2×D4—302no—
495C22×C4—52no—
496C22×C4—61no—
497C22×C4—102no—
498C22×C4—101no—
499C22×C4—302no—
500C22×C4—302no—
501C22×C4—301no—
502C22×C4C2×D3×D511yescharacteristic
503M16—304no—
504M16—302no—
505C2×C8—31no—
506C2×C8—31no—
507C2×C8—62no—
508C2×C8—152no—
509C2×C8—304no—
510C4⋊C4—52no—
511C4⋊C4—102no—
512C4⋊C4—101no—
513C4⋊C4C2×D3×D511yescharacteristic
514C4⋊C4C2×D3×D511yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—102no—
517C42—21no—
518C42—102no—
519C3×C5#289811yescharacteristic, complemented, Hall
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—54no—
523C22×C3—102no—
524C22×C3—102no—
525C22×C3D5×C22⋊C412yes—
526C22×C3C2×D4×D511yescharacteristic
527C2×D3—22no—
528C2×D3—41no—
529C2×D3—41no—
530C3×C4—41no—
531C3×C4—41no—
532C3×C4—54no—
533C3×C4—202no—
534C3×C4D5×C22⋊C412yes—
535C3×C4C22×C4×D511yescharacteristic
536C3×C4C2×D4×D511yescharacteristic
537Dic3—22no—
538Dic3—104no—
539C2×C5—22no—
540C2×C5—122no—
541C2×C5C22×(C2×D3)⋊C411yescharacteristic
542C2×C5#583611yescharacteristic
543C2×C5#583811yescharacteristic
544D5—24no—
545C23—52no—
546C23—61no—
547C23D5×#6711yescharacteristic
548Q8—32no—
549Q8—54no—
550Q8—61no—
551Q8—154no—
552Q8—308no—
553Q8—304no—
554Q8—302no—
555D4—32no—
556D4—58no—
557D4—54no—
558D4—64no—
559D4—61no—
560D4—308no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—52no—
564C2×C4—54no—
565C2×C4—54no—
566C2×C4—61no—
567C2×C4—64no—
568C2×C4—102no—
569C2×C4—308no—
570C2×C4—308no—
571C2×C4—304no—
572C2×C4—302no—
573C2×C4—402no—
574C2×C4—401no—
575C2×C4C4×D3×D512yes—
576C2×C4D5×D1212yes—
577C2×C4D5×#6711yescharacteristic
578C2×C4C22×D3×D511yescharacteristic
579C8—61no—
580C8—61no—
581C8—302no—
582C2×C3—22no—
583C2×C3—104no—
584C2×C3C2×D5×C22⋊C411yescharacteristic
585C2×C3#6610411yescharacteristic
586C2×C3#6610511yescharacteristic
587D3—42no—
588C5#8257011yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—54no—
592C22—62no—
593C22—102no—
594C22—102no—
595C22—121no—
596C22—121no—
597C22D5×(C2×D3)⋊C412yes—
598C22C2×D5×#6711yescharacteristic
599C4—41no—
600C4—41no—
601C4—54no—
602C4—62no—
603C4—202no—
604C4—304no—
605C4D5×(C2×D3)⋊C412yes—
606C4C2×C4×D3×D511yescharacteristic
607C4C2×D5×D1211yescharacteristic
608C3#1061056311yescharacteristic, complemented, Sylow
609C2—22no—
610C2—104no—
611C2—122no—
612C2C2×D5×(C2×D3)⋊C411yescharacteristic
613C2#1175533711yescharacteristic
614C2#1175533811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#92001C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65857C2semidirect
3. C2×#91283C2semidirect
4. #11751105C2semidirect
5. C5×#5002C2semidirect
6. C2×#90974C2semidirect
7. #11748384C2semidirect
8. #11747499C2semidirect
9. #11747498C2semidirect
10. #11747487C2semidirect
11. D5×#810C2semidirect
20. #92001C4semidirect
48. #65857D3semidirect
61. C2×Dic30C2×C4semidirect
65. C5×#235C2×C4semidirect
83. #6772C2×C4semidirect
87. D5×Dic6C2×C4semidirect
110. #5002D5semidirect
313. #235C4×D5semidirect
519. C3×C5#2898semidirect
588. C5#82570semidirect
608. C3#10610563semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C3×#658572
C2×#912832
#117511052
C5×#50022
C2×#909742
#117483842
#117474992
#117474982
#117474872
D5×#8102
#106105633
#825705