Finite Group Databasebeta

← #14427794

Subgroups — #14427794

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
1C3×C5×#525C211yesmaximal, characteristic, complemented
2C2×#91839C211yesmaximal, characteristic, complemented
3#11756550C211yesmaximal, characteristic, complemented
4C23×C3⋊#168C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11751152C212yesmaximal, complemented
7#11751149C212yesmaximal, complemented
8#11751142C212yesmaximal, complemented
9#11751139C212yesmaximal, complemented
10#11751103C211yesmaximal, characteristic, complemented
11#11751099C211yesmaximal, characteristic, complemented
12#10614653—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C3×C5×#123—21no—
17C3×C5×C22⋊Q8C2212yes—
18C3×C5×#121C2212yes—
19C3×C5×#120—21no—
20C3×C4×C5×D4—22no—
21C3×C5×#117C2211yescharacteristic
22#91842—21no—
23#91839—24no—
24C2×#6718C2211yescharacteristic, complemented
25C2×#6717C2211yescharacteristic, complemented
26C2×#6716C2211yescharacteristic, complemented
27C2×#6715C2211yescharacteristic, complemented
28#91819C2212yes—
29#91818—21no—
30C4×#1220—22no—
31#91815C2211yescharacteristic
32#91813C2212yes—
33C22×C3⋊#168—24no—
34C22×C3⋊#168C2211yescharacteristic
35C22×C3⋊#168C2212yes—
36C22×C3⋊#168C2212yes—
37C22×C3⋊#168C2211yescharacteristic
38#91119C2212yescomplemented
39#91116C2212yescomplemented
40#91094C2212yescomplemented
41#91093C2212yescomplemented
42#91092C2212yescomplemented
43#91091C2212yescomplemented
44#82922—51nomaximal, Hall
45C5×#525D311yescharacteristic, complemented
46C2×#4096—31no—
47#66125—31no—
48C23×#168—31no—
49#65522—31no—
50#65340—32no—
51#65337—32no—
52#65330—32no—
53#65327—32no—
54#65291—31no—
55#65287—31no—
56C24×C3×C5D411yescharacteristic
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5D412yes—
67C22×C3×C4×C5D411yescharacteristic
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2311yescharacteristic
70C2×#1220—22no—
71C2×#1220—21no—
72#6817—22no—
73#6817—22no—
74C2×D60C2311yescharacteristic
75C2×C4×D15—21no—
76C2×Dic30C2311yescharacteristic
77C3×C5×C4⋊C4—22no—
78C3×C5×C4⋊C4C2312yes—
79C3×C5×C22⋊C4—21no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—22no—
82C3×C42×C5—21no—
83#6719—22no—
84#6719—21no—
85#6718—22no—
86#6717—22no—
87#6716—22no—
88#6715—22no—
89#6714—22no—
90C4⋊Dic15C2312yes—
91#6712—22no—
92C4×Dic15—21no—
93C2×C3⋊#168—22no—
94C2×C3⋊#168—24no—
95C2×C3⋊#168—24no—
96C2×C3⋊#168D414yescomplemented
97C2×C3⋊#168C2312yes—
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C3×#525D511yescharacteristic, complemented
101C2×#950—51no—
102#5791—51no—
103C23×C3⋊C8—51no—
104#5233—51no—
105#5051—52no—
106#5048—52no—
107#5041—52no—
108#5038—52no—
109#5002—51no—
110#4998—51no—
111C2×C5×#41C2×D311yescharacteristic
112C23×C4×C5C2×D311yescharacteristic
113C2×#709—31no—
114C5×#123—21no—
115C5×C22⋊Q8C2×D312yes—
116C5×#121C2×D312yes—
117C5×#120—21no—
118C4×C5×D4—22no—
119C5×#117C2×D311yescharacteristic
120#4099—61no—
121#4096—64no—
122C2×#689—31no—
123C2×#688—31no—
124C2×#687—31no—
125C2×#686—31no—
126#4076—32no—
127#4075—61no—
128C4×C22⋊D5—62no—
129#4072—31no—
130#4070—32no—
131C22×#168—31no—
132C22×#168—31no—
133C22×#168—32no—
134C22×#168—32no—
135C22×#168—64no—
136#3967—32no—
137#3964—32no—
138#3942—32no—
139#3941—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5—22no—
144C23×C3×C5—24no—
145C23×C3×C5—21no—
146C23×C3×C5C2×D411yescharacteristic
147C23×C3×C5C2×D412yes—
148C22×D15—21no—
149C3×C5×Q8—21no—
150C3×C5×Q8—21no—
151C3×C5×D4—21no—
152C3×C5×D4—21no—
153C3×C5×D4—42no—
154C3×C5×D4—44no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—42no—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D411yescharacteristic
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5#4112yes—
166C2×C3×C4×C5C2411yescharacteristic
167#1220—42no—
168#1220—44no—
169C2×Dic15—22no—
170C2×Dic15—21no—
171D60—21no—
172D60—21no—
173C4×D15—42no—
174Dic30—21no—
175Dic30—21no—
176C3⋊#168—22no—
177C3⋊#168C2×D412yes—
178C3⋊#168C2×D412yes—
179C2×C3×#41C2×D511yescharacteristic
180C23×C3×C4C2×D511yescharacteristic
181C2×#235—51no—
182C3×#123—21no—
183C3×C22⋊Q8C2×D512yes—
184C3×#121C2×D512yes—
185C3×#120—21no—
186C3×C4×D4—22no—
187C3×#117C2×D511yescharacteristic
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—51no—
200C22×C3⋊C8—51no—
201C22×C3⋊C8—52no—
202C22×C3⋊C8—52no—
203C22×C3⋊C8—104no—
204#835—52no—
205#832—52no—
206#810—52no—
207#809—52no—
208#808—52no—
209#807—52no—
210C24×C5#6711yescharacteristic
211C5×#41—22no—
212C5×#41—22no—
213C2×C5×Q8C22×D311yescharacteristic
214C2×C5×D4—22no—
215C2×C5×D4—21no—
216C2×C5×D4C22×D311yescharacteristic
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—21no—
220C22×C4×C5#6712yes—
221C22×C4×C5#6711yescharacteristic
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—61no—
225C2×C22⋊D5—62no—
226#709—62no—
227#709—62no—
228C2×D20—31no—
229C2×C4×D5—61no—
230C2×Dic10—31no—
231C5×C4⋊C4—22no—
232C5×C4⋊C4C22×D312yes—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—22no—
235C5×C22⋊C4—22no—
236C42×C5—21no—
237C22⋊Dic5—62no—
238C22⋊Dic5—61no—
239#689—62no—
240#688—62no—
241#687—62no—
242#686—62no—
243#685—62no—
244C4⋊Dic5—32no—
245#683—62no—
246C4×Dic5—61no—
247C2×#168—34no—
248C2×#168—31no—
249C2×#168—31no—
250C2×#168—32no—
251C2×#168—64no—
252C2×#168—64no—
253C2×#168—62no—
254C2×#135—151no—
255C23×C8—151no—
256#525—151no—
257#525D1511yescharacteristic, complemented
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—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12112yes—
272C22×C3×C5#13514yescomplemented
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—41no—
275C2×D15—42no—
276C3×C4×C5—22no—
277C3×C4×C5—41no—
278C3×C4×C5—42no—
279C3×C4×C5#12112yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—41no—
283Dic15—42no—
284C24×C3C22⋊D511yescharacteristic
285C3×#41—22no—
286C3×#41—22no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—22no—
289C2×C3×D4—21no—
290C2×C3×D4C22×D511yescharacteristic
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—21no—
294C22×C3×C4C22⋊D512yes—
295C22×C3×C4C22⋊D511yescharacteristic
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—22no—
306C3×C4⋊C4C22×D512yes—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—22no—
310C3×C42—21no—
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—54no—
322C2×C3⋊C8—51no—
323C2×C3⋊C8—51no—
324C2×C3⋊C8—52no—
325C2×C3⋊C8—104no—
326C2×C3⋊C8—104no—
327C2×C3⋊C8—102no—
328C23×C5—22no—
329C23×C5—24no—
330C23×C5—21no—
331C23×C5C2×#6711yescharacteristic
332C23×C5C2×#6712yes—
333C22×D5—61no—
334C5×Q8—21no—
335C5×Q8—21no—
336C5×D4—21no—
337C5×D4—21no—
338C5×D4—42no—
339C5×D4—44no—
340C2×C4×C5—22no—
341C2×C4×C5—24no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—21no—
346C2×C4×C5—42no—
347C2×C4×C5D3×D412yes—
348C2×C4×C5#23712yes—
349C2×C4×C5C2×#6712yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—122no—
353C22⋊D5—124no—
354C2×Dic5—62no—
355C2×Dic5—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—61no—
360Dic10—61no—
361#168—32no—
362#168—32no—
363#168—62no—
364C2×#41—151no—
365C2×#41C2×D1511yescharacteristic
366C23×C4C2×D1511yescharacteristic
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—151no—
373C22×C8—151no—
374C22×C8—152no—
375C22×C8—152no—
376C22×C8—304no—
377#123—21no—
378#123—301no—
379C22⋊Q8—152no—
380C22⋊Q8C2×D1512yes—
381#121—152no—
382#121C2×D1512yes—
383#120—21no—
384#120—301no—
385C4×D4—22no—
386C4×D4—302no—
387#117—151no—
388#117C2×D1511yescharacteristic
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×C5—81no—
398C2×C3×C5C2×#12111yescharacteristic
399C2×C3×C5C2×#13512yes—
400D15—81no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3—21no—
404C23×C3C2×C22⋊D512yes—
405C23×C3C2×C22⋊D511yescharacteristic
406C22×D3—101no—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—44no—
412C3×D4—42no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
420C2×C3×C4D4×D512yes—
421C2×C3×C4#71112yes—
422C2×C3×C4C2×C22⋊D512yes—
423C2×C3×C4C2×C22⋊D511yescharacteristic
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—52no—
435C3⋊C8—52no—
436C3⋊C8—102no—
437C22×C5—28no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—41no—
442C22×C5—42no—
443C22×C5#93912yes—
444C22×C5#95014yescomplemented
445C22×C5C22×#6711yescharacteristic
446C2×D5—121no—
447C2×D5—122no—
448C4×C5—22no—
449C4×C5—41no—
450C4×C5—42no—
451C4×C5#93912yes—
452C4×C5C2×D3×D411yescharacteristic
453C4×C5C2×#23711yescharacteristic
454Dic5—121no—
455Dic5—122no—
456C24#122011yescharacteristic
457#41—22no—
458#41—22no—
459#41—302no—
460#41—302no—
461C2×Q8—151no—
462C2×Q8C22×D1511yescharacteristic
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—151no—
466C2×D4—302no—
467C2×D4—301no—
468C2×D4C22×D1511yescharacteristic
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—301no—
473C22×C4#122011yescharacteristic
474C22×C4#122012yes—
475C22×C4C22×D1512yes—
476C22×C4C22×D1511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—154no—
482C2×C8—151no—
483C2×C8—151no—
484C2×C8—152no—
485C2×C8—304no—
486C2×C8—304no—
487C2×C8—302no—
488C4⋊C4—22no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4C22×D1512yes—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—301no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—21no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—28no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—42no—
507C22×C3#408512yes—
508C22×C3#409614yescomplemented
509C22×C3C22×C22⋊D511yescharacteristic
510C2×D3—201no—
511C2×D3—202no—
512C3×C4—22no—
513C3×C4—41no—
514C3×C4—42no—
515C3×C4#408512yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C2×#71111yescharacteristic
518Dic3—201no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—24no—
522C2×C5—81no—
523C2×C5C2×#93911yescharacteristic
524C2×C5C2×#95012yes—
525D5—241no—
526C23—22no—
527C23—24no—
528C23—21no—
529C23—301no—
530C23C2×#122011yescharacteristic
531C23C2×#122012yes—
532Q8—21no—
533Q8—21no—
534Q8—301no—
535Q8—301no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—44no—
540D4—301no—
541D4—301no—
542D4—602no—
543D4—604no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—42no—
551C2×C4—302no—
552C2×C4—301no—
553C2×C4—602no—
554C2×C4D4×D1512yes—
555C2×C4#681912yes—
556C2×C4C2×#122012yes—
557C2×C4C2×#122011yescharacteristic
558C2×C4C23×D1511yescharacteristic
559C8—152no—
560C8—152no—
561C8—302no—
562C2×C3—24no—
563C2×C3—22no—
564C2×C3—81no—
565C2×C3C2×#408511yescharacteristic
566C2×C3C2×#409612yes—
567D3—401no—
568C5#8292211yescharacteristic, complemented, Sylow
569C22—28no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—42no—
575C22—601no—
576C22—602no—
577C22#9182812yes—
578C22#9183914yescomplemented
579C22C22×#122011yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—601no—
584C4—602no—
585C4#9182812yes—
586C4C2×D4×D1511yescharacteristic
587C4C2×#681911yescharacteristic
588C3#1061465311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—24no—
591C2—81no—
592C2—1201no—
593C2C2×#9182811yescharacteristic
594C2C2×#9183912yes—
subgroupG/H
centerC2×C4C2×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#525C2
socleC22×C3×C5C22×D4
hypercenter#525D15
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C3×C5×#525C2semidirect
2. C2×#91839C2semidirect
3. #11756550C2semidirect
4. C23×C3⋊#168C2semidirect
5. #11751334C2semidirect
6. #11751152C2semidirect
7. #11751149C2semidirect
8. #11751142C2semidirect
9. #11751139C2semidirect
10. #11751103C2semidirect
11. #11751099C2semidirect
24. C2×#6718C22semidirect
25. C2×#6717C22semidirect
26. C2×#6716C22semidirect
27. C2×#6715C22semidirect
38. #91119C22semidirect
39. #91116C22semidirect
40. #91094C22semidirect
41. #91093C22semidirect
42. #91092C22semidirect
43. #91091C22semidirect
45. C5×#525D3semidirect
96. C2×C3⋊#168D4semidirect
100. C3×#525D5semidirect
257. #525D15semidirect
272. C22×C3×C5#135semidirect
444. C22×C5#950semidirect
500. C3×C5#3050semidirect
508. C22×C3#4096semidirect
568. C5#82922semidirect
578. C22#91839semidirect
588. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5252
C2×#918392
#117565502
C23×C3⋊#1682
#117513342
#117511522
#117511492
#117511422
#117511392
#117511032
#117510992
#106146533
#829225