Finite Group Databasebeta

← #14427837

Subgroups — #14427837

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
1C2×C5×#950C211yesmaximal, characteristic, complemented
2C3×#66162C211yesmaximal, characteristic, complemented
3#11754563C211yesmaximal, characteristic, complemented
4C22×D5×C3⋊C8C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749366C212yesmaximal, complemented
7#11749365C212yesmaximal, complemented
8#11749120C212yesmaximal, complemented
9#11749119C212yesmaximal, complemented
10#11748451C211yesmaximal, characteristic, complemented
11#11748382C211yesmaximal, characteristic, complemented
12#10615645—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16#91815C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C5×#950—24no—
19C2×C5×#216C2211yescharacteristic, complemented
20C2×C5×#215C2211yescharacteristic, complemented
21C2×C5×#214C2211yescharacteristic, complemented
22C2×C5×#213C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4092C2212yes—
25C3×#4084C2212yes—
26C3×#4083—21no—
27C3×#4081—21no—
28C3×C4×C22⋊D5—22no—
29C3×#4072C2211yescharacteristic
30#91563—21no—
31#91539—21no—
32#91449C2212yes—
33C4×#1201—22no—
34#91359C2212yes—
35C2×D5×C3⋊C8—24no—
36C2×D5×C3⋊C8C2212yes—
37C2×D5×C3⋊C8C2212yes—
38#91119C2212yescomplemented
39#91116C2212yescomplemented
40#90990C2212yescomplemented
41#90987C2212yescomplemented
42#90972C2212yescomplemented
43#90966C2212yescomplemented
44#82922—51nomaximal, Hall
45C2×C5×#135—31no—
46#66162—31no—
47#66162D311yescharacteristic, complemented
48C22×C8×D5—31no—
49#65522—31no—
50#65522—31no—
51#65477—32no—
52#65460—32no—
53#65460—32no—
54#65446—32no—
55#65395—31no—
56C23×C3×D5D411yescharacteristic
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C2×C3×C22⋊D5—22no—
71C22×C3×Dic5D411yescharacteristic
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5D412yes—
75C2×C3×C4×D5C2312yes—
76C2×#1201—22no—
77#6719—21no—
78C4⋊Dic15C2312yes—
79C4×Dic15—21no—
80C2×C3⋊#168—22no—
81C2×C3⋊#168C2312yes—
82C5×#216—22no—
83C5×#215—22no—
84C5×#214—22no—
85C5×#213—22no—
86C2×C5×C3⋊C8D414yescomplemented
87C2×C5×C3⋊C8C2311yescharacteristic
88C2×C5×C3⋊C8C2311yescharacteristic
89C3×C22⋊Dic5—21no—
90C3×C22⋊Dic5—22no—
91C3×#685—22no—
92C3×C4⋊Dic5C2312yes—
93C3×#683—22no—
94C3×C4×Dic5—21no—
95#6669—22no—
96(C2×D3)⋊Dic5—22no—
97#6665—22no—
98D5×C3⋊C8—24no—
99D5×C3⋊C8—24no—
100C3×#525—51no—
101C2×#950D511yescharacteristic, complemented
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×#41—31no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C4×D5C2×D311yescharacteristic
114C5×#135—64no—
115C2×C5×Q16—31no—
116C2×C5×SD16—31no—
117C2×C5×SD16—31no—
118C2×C5×D8—31no—
119C22×C5×C8—31no—
120#4092—32no—
121#4092C2×D312yes—
122#4084—32no—
123#4084C2×D312yes—
124#4083—21no—
125#4083—61no—
126#4081—21no—
127#4081—61no—
128C4×C22⋊D5—22no—
129C4×C22⋊D5—62no—
130#4072—31no—
131#4072C2×D311yescharacteristic
132C22×#168—31no—
133C2×C8×D5—32no—
134C2×C8×D5—32no—
135C2×C8×D5—64no—
136#3967—32no—
137#3967—32no—
138#3964—32no—
139#3964—32no—
140#3950—32no—
141#3949—32no—
142#3050—151noSylow
143C23×C3×C5—21no—
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—21no—
146C22×C3×D5—22no—
147C22×C3×D5—24no—
148C22×C3×D5C2×D412yes—
149C3×C5×Q8—21no—
150C3×C5×Q8—21no—
151C3×C5×D4—21no—
152C3×C5×D4—21no—
153C3×C5×D4—42no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—42no—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5#4112yes—
159C2×C3×C4×C5C2411yescharacteristic
160C2×Dic15—22no—
161C5×#67—42no—
162C2×C5×Dic3—21no—
163C5×D12—21no—
164C5×D12—21no—
165C4×C5×D3—42no—
166C5×Dic6—21no—
167C5×Dic6—21no—
168C3×C22⋊D5—44no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5C2×D412yes—
172C3×C4×D5—24no—
173C3×C4×D5—22no—
174C3×C4×D5—22no—
175#1201—44no—
176C3⋊#168—22no—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41C2×D511yescharacteristic
180C23×C3×C4—51no—
181C2×#235C2×D511yescharacteristic
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—24no—
190C2×#216C2×D511yescharacteristic, complemented
191C2×#215C2×D511yescharacteristic, complemented
192C2×#214C2×D511yescharacteristic, complemented
193C2×#213C2×D511yescharacteristic, complemented
194#930—52no—
195#929—101no—
196C4×#67—102no—
197#926—51no—
198#924—52no—
199C22×C3⋊C8—51no—
200C22×C3⋊C8—52no—
201C22×C3⋊C8—52no—
202C22×C3⋊C8—104no—
203C22×C3⋊C8C2×D511yescharacteristic
204#835—52no—
205#832—52no—
206#810—52no—
207#809—52no—
208#808—52no—
209#807—52no—
210C23×D5#6711yescharacteristic
211C5×#41—22no—
212C5×#41—22no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—31no—
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4—31no—
219C2×C5×D4—61no—
220C2×C5×D4C22×D311yescharacteristic
221C22×C4×C5—21no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—22no—
225C2×C22⋊D5—62no—
226C22×Dic5#6711yescharacteristic
227C2×C4×D5—22no—
228C2×C4×D5—22no—
229C2×C4×D5#6712yes—
230C2×C4×D5C22×D312yes—
231C5×Q16—62no—
232C5×SD16—62no—
233C5×SD16—62no—
234C5×D8—62no—
235C2×C5×C8—34no—
236C2×C5×C8—31no—
237C2×C5×C8—31no—
238C22⋊Dic5—21no—
239C22⋊Dic5—22no—
240C22⋊Dic5—61no—
241C22⋊Dic5—62no—
242#685—22no—
243#685—62no—
244C4⋊Dic5—32no—
245C4⋊Dic5C22×D312yes—
246#683—22no—
247#683—62no—
248C4×Dic5—21no—
249C4×Dic5—61no—
250C2×#168—32no—
251C2×#168—62no—
252C8×D5—64no—
253C8×D5—64no—
254C2×#135—31no—
255C23×C8—151no—
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—22no—
266C22×C3×C5—41no—
267C22×C3×C5—42no—
268C22×C3×C5#12112yes—
269C22×C3×C5C22×D411yescharacteristic
270C2×C5×D3—41no—
271C2×C5×D3—42no—
272C2×C3×D5—28no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5#13514yescomplemented
276C3×C4×C5—41no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—42no—
281C3×Dic5—22no—
282C3×Dic5—42no—
283C5×Dic3—41no—
284C24×C3—51no—
285C3×#41—22no—
286C3×#41—22no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—102no—
290C2×C3×D4C22×D511yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—51no—
293C22×C3×C4—52no—
294C22×C3×C4—52no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299C2×#67—102no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6C22×D511yescharacteristic
305C3×C4⋊C4—52no—
306C3×C4⋊C4—102no—
307C3×C22⋊C4—102no—
308C3×C22⋊C4—102no—
309C3×C22⋊C4—101no—
310C3×C42—101no—
311#217—102no—
312#217—101no—
313#216—22no—
314#215—22no—
315#214—22no—
316#213—22no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—52no—
319Dic3⋊C4—102no—
320C4×Dic3—101no—
321C2×C3⋊C8—52no—
322C2×C3⋊C8—102no—
323C2×C3⋊C8—104no—
324C2×C3⋊C8—104no—
325C2×C3⋊C8C22⋊D514yescomplemented
326C2×C3⋊C8C22×D511yescharacteristic
327C2×C3⋊C8C22×D511yescharacteristic
328C23×C5—21no—
329C23×C5—61no—
330C23×C5C2×#6711yescharacteristic
331C22×D5—22no—
332C22×D5—24no—
333C22×D5C2×#6712yes—
334C5×Q8—21no—
335C5×Q8—21no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×D4—21no—
339C5×D4—21no—
340C5×D4—42no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—21no—
345C2×C4×C5—42no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5#23712yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—44no—
353C22⋊D5—124no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—62no—
357C2×Dic5C2×#6712yes—
358C4×D5—24no—
359C4×D5—22no—
360C4×D5—22no—
361C5×C8—32no—
362C5×C8—32no—
363#168—62no—
364C2×#41—31no—
365C2×#41D3×D511yescharacteristic
366C23×C4—51no—
367#135—64no—
368C2×Q16—31no—
369C2×SD16—31no—
370C2×SD16—31no—
371C2×D8—31no—
372C22×C8—31no—
373C22×C8—152no—
374C22×C8—152no—
375C22×C8—151no—
376C22×C8—304no—
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—81no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399C3×D5—24no—
400C5×D3—81no—
401C23×C3—21no—
402C23×C3—52no—
403C23×C3—104no—
404C23×C3—102no—
405C23×C3D4×D511yescharacteristic
406C22×D3—21no—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—42no—
412C3×D4—204no—
413C2×C3×C4—21no—
414C2×C3×C4—42no—
415C2×C3×C4—52no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4—102no—
419C2×C3×C4—104no—
420C2×C3×C4—102no—
421C2×C3×C4D4×D511yescharacteristic
422C2×C3×C4#71112yes—
423C2×C3×C4C2×C22⋊D512yes—
424C2×C3×C4C23×D511yescharacteristic
425#67—42no—
426#67—204no—
427C2×Dic3—21no—
428C2×Dic3—102no—
429D12—21no—
430D12—21no—
431C4×D3—42no—
432Dic6—21no—
433Dic6—21no—
434C3⋊C8—102no—
435C3⋊C8C2×C22⋊D512yes—
436C3⋊C8C2×C22⋊D512yes—
437C22×C5—22no—
438C22×C5—41no—
439C22×C5—42no—
440C22×C5—121no—
441C22×C5—122no—
442C22×C5#93912yes—
443C22×C5C22×#6711yescharacteristic
444C2×D5—28no—
445C2×D5—22no—
446C2×D5—22no—
447C2×D5#95014yescomplemented
448C4×C5—41no—
449C4×C5—121no—
450C4×C5#93912yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C2×#23711yescharacteristic
453Dic5—22no—
454Dic5—42no—
455Dic5—122no—
456C24—51no—
457#41—22no—
458#41—22no—
459#41—62no—
460#41—62no—
461C2×Q8—31no—
462C2×Q8C2×D3×D511yescharacteristic
463C2×D4—21no—
464C2×D4—31no—
465C2×D4—61no—
466C2×D4—102no—
467C2×D4—302no—
468C2×D4C2×D3×D511yescharacteristic
469C22×C4—21no—
470C22×C4—51no—
471C22×C4—52no—
472C22×C4—52no—
473C22×C4—61no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—62no—
478SD16—62no—
479SD16—62no—
480D8—62no—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—152no—
485C2×C8—304no—
486C2×C8—304no—
487C2×C8—302no—
488C4⋊C4—52no—
489C4⋊C4—102no—
490C4⋊C4—152no—
491C4⋊C4—302no—
492C22⋊C4—102no—
493C22⋊C4—102no—
494C22⋊C4—101no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—101no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3—54no—
505C22×C3—108no—
506C22×C3—102no—
507C22×C3—102no—
508C22×C3#408412yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—42no—
511C2×D3—41no—
512C3×C4—41no—
513C3×C4—102no—
514C3×C4—202no—
515C3×C4#408412yes—
516C3×C4C2×#71111yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—41no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—81no—
522C2×C5—241no—
523C2×C5C2×#93911yescharacteristic
524C2×C5C2×#95012yes—
525D5—24no—
526C23—21no—
527C23—52no—
528C23—61no—
529C23—104no—
530C23—102no—
531C23D5×#6711yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—61no—
535Q8—61no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—61no—
540D4—61no—
541D4—122no—
542D4—204no—
543D4—604no—
544C2×C4—21no—
545C2×C4—42no—
546C2×C4—52no—
547C2×C4—61no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—104no—
552C2×C4—102no—
553C2×C4—122no—
554C2×C4—302no—
555C2×C4#678012yes—
556C2×C4D5×#6711yescharacteristic
557C2×C4D3×C22⋊D512yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—32no—
560C8—32no—
561C8—302no—
562C2×C3—22no—
563C2×C3—81no—
564C2×C3—104no—
565C2×C3D5×#13512yes—
566C2×C3C2×#408411yescharacteristic
567D3—81no—
568C5#8292211yescharacteristic, complemented, Sylow
569C22—22no—
570C22—42no—
571C22—41no—
572C22—54no—
573C22—108no—
574C22—102no—
575C22—102no—
576C22—122no—
577C22—121no—
578C22#9154912yes—
579C22C2×D5×#6711yescharacteristic
580C4—41no—
581C4—102no—
582C4—121no—
583C4—202no—
584C4—602no—
585C4#9154912yes—
586C4C2×#678011yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061564511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—104no—
592C2—241no—
593C2D5×#95012yes—
594C2C2×#9154911yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#950C2semidirect
2. C3×#66162C2semidirect
3. #11754563C2semidirect
4. C22×D5×C3⋊C8C2semidirect
5. #11751334C2semidirect
6. #11749366C2semidirect
7. #11749365C2semidirect
8. #11749120C2semidirect
9. #11749119C2semidirect
10. #11748451C2semidirect
11. #11748382C2semidirect
19. C2×C5×#216C22semidirect
20. C2×C5×#215C22semidirect
21. C2×C5×#214C22semidirect
22. C2×C5×#213C22semidirect
38. #91119C22semidirect
39. #91116C22semidirect
40. #90990C22semidirect
41. #90987C22semidirect
42. #90972C22semidirect
43. #90966C22semidirect
47. #66162D3semidirect
86. C2×C5×C3⋊C8D4semidirect
101. C2×#950D5semidirect
190. C2×#216C2×D5semidirect
191. C2×#215C2×D5semidirect
192. C2×#214C2×D5semidirect
193. C2×#213C2×D5semidirect
275. C2×C3×D5#135semidirect
325. C2×C3⋊C8C22⋊D5semidirect
447. C2×D5#950semidirect
500. C3×C5#3050semidirect
568. C5#82922semidirect
588. C3#10615645semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9502
C3×#661622
#117545632
C22×D5×C3⋊C82
#117513342
#117493662
#117493652
#117491202
#117491192
#117484512
#117483822
#106156453
#829225