Finite Group Databasebeta

← D5×#4875 #14430114

Subgroups — D5×#4875 #14430114

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#888C211yesmaximal, characteristic
2D5×#887C211yesmaximal, characteristic
3#11750976C211yesmaximal, characteristic, complemented
4C5×#4875C211yesmaximal, characteristic, complemented
5C3×D5×#107C211yesmaximal, characteristic
6#11747882C211yesmaximal, characteristic, complemented
7#11747868C211yesmaximal, characteristic, complemented
8D5×#816C211yesmaximal, characteristic
9D5×Dic3⋊C8C211yesmaximal, characteristic
10D5×#810C211yesmaximal, characteristic
11D5×#807C211yesmaximal, characteristic
12#11747418C211yesmaximal, characteristic, complemented
13#11747300C211yesmaximal, characteristic, complemented
14#11747292C211yesmaximal, characteristic, complemented
15#11747182C211yesmaximal, characteristic, complemented
16D5×#477—31nomaximal, Hall
17C2×D5×Dic6—21no—
18C2×D5×Dic6C2211yescharacteristic
19#91777C2211yescharacteristic
20#91776C2211yescharacteristic
21C5×#888C2211yescharacteristic
22C5×#887C2211yescharacteristic
23C2×C3×C8×D5C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25C3×D5×C4⋊C4C2211yescharacteristic
26#91470C2211yescharacteristic
27#91469C2211yescharacteristic
28D5×C4⋊Dic3C2211yescharacteristic
29D5×Dic3⋊C4—21no—
30D5×Dic3⋊C4—21no—
31C4×D5×Dic3—21no—
32C4×D5×Dic3C2211yescharacteristic
33#91344C2211yescharacteristic
34#91340C2211yescharacteristic
35#91329—21no—
36#91328—21no—
37#91325—21no—
38#91324—21no—
39C2×D5×C3⋊C8C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic
41#91100C2211yescharacteristic
42#91098C2211yescharacteristic
43#91094C2211yescharacteristic
44#91091C2211yescharacteristic
45C5×#816C2211yescharacteristic
46C5×Dic3⋊C8C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C3×#3950C2211yescharacteristic
50C3×#3939C2211yescharacteristic
51C3×#3939C2211yescharacteristic
52#90990C2211yescharacteristic
53#90989C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55#90983C2211yescharacteristic
56#90975C2211yescharacteristic
57#90974C2211yescharacteristic
58#90973C2211yescharacteristic
59#90972C2211yescharacteristic
60C2×#4875—51nomaximal, Hall
61D5×C4⋊Q8—31no—
62C4×Q8×D5—31no—
63C5×#477—31no—
64#65380—31no—
65#65310—31no—
66D5×#107—31no—
67D5×#107D311yescharacteristic
68#65164—31no—
69#65164—31no—
70#65139—31no—
71D5×C4⋊C8—31no—
72D5×#103—31no—
73D5×#103—31no—
74#65083—31no—
75#65083—31no—
76C2×Dic30—21no—
77C2×Dic30C2311yescharacteristic
78C2×C5×Dic6—21no—
79C2×C5×Dic6C2311yescharacteristic
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5C2311yescharacteristic
83C2×#1204—21no—
84C2×#1204—21no—
85C2×#1204—21no—
86C2×D5×Dic3—21no—
87C2×D5×Dic3—21no—
88C2×D5×Dic3D411yescharacteristic
89C2×D5×Dic3D411yescharacteristic
90D5×Dic6—22no—
91D5×Dic6—44no—
92D5×Dic6Q814yescomplemented
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C4⋊Dic15C2311yescharacteristic
97#6712—21no—
98#6712—21no—
99C4×Dic15—21no—
100C4×Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×C4⋊Dic3C2311yescharacteristic
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C4×C5×Dic3—21no—
106C4×C5×Dic3C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C3×C4⋊Dic5C2311yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×#683—21no—
112C2×C3×#168C2311yescharacteristic
113C3×C8×D5—22no—
114Dic3⋊Dic5—21no—
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6669—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5D411yescharacteristic
122Dic3×Dic5D411yescharacteristic
123D5×C3⋊C8—22no—
124C2×#888—51no—
125C2×#887—51no—
126C2×C3×#107—51no—
127C2×#816—51no—
128C2×Dic3⋊C8—51no—
129C2×#810—51no—
130C2×#807—51no—
131#4875—51no—
132#4875—51no—
133#4875—51no—
134#4875—51no—
135#4875—51no—
136#4875—51no—
137#4875—51no—
138#4875D511yescharacteristic, direct product factor
139C2×Q8×D5—31no—
140C2×Q8×D5—61no—
141C5×C4⋊Q8—31no—
142C4×C5×Q8—31no—
143Q8×Dic5—31no—
144#4090—61no—
145C2×C8×D5—31no—
146C2×C8×D5C2×D311yescharacteristic
147D5×C4⋊C4—31no—
148D5×C4⋊C4—61no—
149D5×C4⋊C4—61no—
150D5×C4⋊C4C2×D311yescharacteristic
151D5×C4⋊C4C2×D311yescharacteristic
152#4034—31no—
153#4034—31no—
154#4034—61no—
155#4033—31no—
156#4033—61no—
157C42×D5—31no—
158C42×D5—61no—
159#4015—31no—
160C4×Dic10—31no—
161C4×Dic10—61no—
162C5×#107—31no—
163C5×#107C2×D311yescharacteristic
164C5×C4⋊C8—31no—
165C5×#103—31no—
166C5×#103—31no—
167#3967—31no—
168#3967—31no—
169#3950—31no—
170#3950C2×D311yescharacteristic
171#3948—31no—
172#3948—31no—
173#3946—31no—
174#3946—31no—
175#3942—31no—
176#3942—31no—
177#3939—31no—
178#3939—31no—
179#3939C2×D311yescharacteristic
180#3939C2×D311yescharacteristic
181C4⋊#168—31no—
182C2×#477—151noSylow
183C22×C3×D5C2×D411yescharacteristic
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15C2×D411yescharacteristic
190C2×Dic15C2×D411yescharacteristic
191Dic30—21no—
192Dic30—42no—
193Dic30C2×Q812yescomplemented
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C5×Dic6—21no—
199C5×Dic6—42no—
200C5×Dic6C2×Q812yescomplemented
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C2×D411yescharacteristic
204C3×C4×D5—42no—
205C3×C4×D5—42no—
206C3×C4×D5C2×Q812yes—
207C3×C4×D5#4112yes—
208#1204—24no—
209#1204—42no—
210#1204—42no—
211D5×Dic3—24no—
212D5×Dic3—22no—
213D5×Dic3—42no—
214D5×Dic3Q1614yes—
215C3×C5×C8—21no—
216C3⋊#168—21no—
217C3×#168—21no—
218C5×C3⋊C8—21no—
219C22×Dic6—51no—
220C22×Dic6—101no—
221C22×C3×C8—51no—
222C2×C3×C4⋊C4—51no—
223C2×C3×C4⋊C4—51no—
224C2×C4⋊Dic3—51no—
225C2×Dic3⋊C4—101no—
226C2×Dic3⋊C4—101no—
227C2×C4×Dic3—51no—
228C2×C4×Dic3—101no—
229C22×C3⋊C8—51no—
230#888—51no—
231#888—51no—
232#888—51no—
233#888—101no—
234#888—101no—
235#888C2×D511yescharacteristic
236#887—51no—
237#887—51no—
238#887—51no—
239#887—101no—
240#887—101no—
241#887C2×D511yescharacteristic
242C3×#107—51no—
243C3×#107—51no—
244C3×#107—51no—
245C3×#107C2×D511yescharacteristic
246#816—51no—
247#816—51no—
248#816—51no—
249#816C2×D511yescharacteristic
250Dic3⋊C8—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8C2×D511yescharacteristic
254#810—51no—
255#810—51no—
256#810—51no—
257#810C2×D511yescharacteristic
258#807—51no—
259#807—51no—
260#807—51no—
261#807C2×D511yescharacteristic
262C2×C5×Q8—31no—
263C2×C5×Q8—61no—
264Q8×D5—34no—
265Q8×D5—62no—
266Q8×D5—124no—
267C2×C4×D5—21no—
268C2×C4×D5—21no—
269C2×C4×D5—31no—
270C2×C4×D5—31no—
271C2×C4×D5—61no—
272C2×C4×D5—61no—
273C2×C4×D5C22×D311yescharacteristic
274C2×Dic10—31no—
275C2×Dic10—61no—
276C2×Dic10—61no—
277C2×Dic10—61no—
278C2×Dic10—61no—
279C2×C5×C8—31no—
280C2×C5×C8C22×D311yescharacteristic
281C5×C4⋊C4—31no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4—61no—
284C5×C4⋊C4C22×D311yescharacteristic
285C5×C4⋊C4C22×D311yescharacteristic
286C42×C5—31no—
287C42×C5—61no—
288C4⋊Dic5—31no—
289C4⋊Dic5—61no—
290C4⋊Dic5—61no—
291C4⋊Dic5C22×D311yescharacteristic
292C4⋊Dic5C22×D311yescharacteristic
293#683—21no—
294#683—21no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300C4×Dic5—31no—
301C4×Dic5—31no—
302C4×Dic5—31no—
303C4×Dic5—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C2×#168—31no—
307C2×#168C22×D311yescharacteristic
308C8×D5—22no—
309C8×D5—62no—
310C2×C4⋊Q8—151no—
311C2×C4×Q8—151no—
312#477—31no—
313#477—151no—
314#477—151no—
315#477—151no—
316#477—151no—
317#477—151no—
318#477—151no—
319#477—151no—
320C2×#107—51no—
321C2×#107—151no—
322C2×C4⋊C8—151no—
323C2×#103—151no—
324C2×#103—151no—
325C22×C3×C5C22×D411yescharacteristic
326C2×C3×D5C22⋊Q812yes—
327C2×C3×D5C2×Q1612yes—
328C2×C3×D5AGL(1,ℤ/8)12yes—
329C3×C4×C5—41no—
330C3×C4×C5—41no—
331C3×C4×C5C22×Q811yescharacteristic
332C3×C4×C5C2×#4111yescharacteristic
333Dic15—22no—
334Dic15—21no—
335Dic15—41no—
336Dic15C2×Q1612yes—
337C3×Dic5—41no—
338C3×Dic5—41no—
339C3×Dic5C22⋊Q812yes—
340C5×Dic3—22no—
341C5×Dic3—21no—
342C5×Dic3—41no—
343C5×Dic3C2×Q1612yes—
344C22×C3×C4—51no—
345C22×C3×C4—101no—
346C22×C3×C4—101no—
347C22×Dic3—51no—
348C22×Dic3—51no—
349C22×Dic3—101no—
350C22×Dic3—101no—
351C2×Dic6—21no—
352C2×Dic6—51no—
353C2×Dic6—54no—
354C2×Dic6—102no—
355C2×Dic6—101no—
356C2×Dic6—101no—
357C2×Dic6—101no—
358C2×Dic6—101no—
359C2×Dic6—204no—
360C2×Dic6C22×D511yescharacteristic
361C2×C3×C8—51no—
362C2×C3×C8—102no—
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4C22×D511yescharacteristic
369C3×C4⋊C4C22×D511yescharacteristic
370C4⋊Dic3—51no—
371C4⋊Dic3—101no—
372C4⋊Dic3C22×D511yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381C4×Dic3—21no—
382C4×Dic3—51no—
383C4×Dic3—51no—
384C4×Dic3—51no—
385C4×Dic3—101no—
386C4×Dic3—101no—
387C4×Dic3—101no—
388C4×Dic3C22×D511yescharacteristic
389C2×C3⋊C8—51no—
390C2×C3⋊C8—102no—
391C2×C3⋊C8C22×D511yescharacteristic
392C22×D5D3×D411yescharacteristic
393C5×Q8—32no—
394C5×Q8—61no—
395C5×Q8—122no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—31no—
399C2×C4×C5—31no—
400C2×C4×C5—61no—
401C2×C4×C5—61no—
402C2×C4×C5C23×D311yescharacteristic
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—31no—
406C2×Dic5—31no—
407C2×Dic5—61no—
408C2×Dic5—61no—
409C2×Dic5D3×D411yescharacteristic
410C4×D5—34no—
411C4×D5—42no—
412C4×D5—42no—
413C4×D5—64no—
414C4×D5—62no—
415C4×D5—122no—
416C4×D5#23512yes—
417C4×D5D3×Q812yes—
418Dic10—32no—
419Dic10—61no—
420Dic10—64no—
421Dic10—122no—
422Dic10—122no—
423Dic10—122no—
424C5×C8—21no—
425C5×C8—61no—
426#168—21no—
427#168—61no—
428C22×Q8—151no—
429C22×Q8—301no—
430C22×C8—51no—
431C22×C8—151no—
432C4⋊Q8—31no—
433C4⋊Q8—151no—
434C4⋊Q8—151no—
435C4⋊Q8—151no—
436C4⋊Q8—301no—
437C4⋊Q8—301no—
438C4×Q8—31no—
439C4×Q8—151no—
440C4×Q8—151no—
441C4×Q8—151no—
442C4×Q8—301no—
443C4×Q8—301no—
444C2×C4⋊C4—51no—
445C2×C4⋊C4—51no—
446C2×C4⋊C4—151no—
447C2×C4⋊C4—301no—
448C2×C4⋊C4—301no—
449C2×C42—151no—
450C2×C42—301no—
451#107—31no—
452#107—51no—
453#107—51no—
454#107—51no—
455#107—151no—
456#107—151no—
457#107—151no—
458#107D3×D511yescharacteristic
459C4⋊C8—31no—
460C4⋊C8—151no—
461C4⋊C8—151no—
462C4⋊C8—151no—
463#103—31no—
464#103—31no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#103—151no—
471C2×C3×C5C2×C22⋊Q811yescharacteristic
472C2×C3×C5C22×Q1611yescharacteristic
473C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
474C3×D5#47714yescomplemented
475C23×C3—51no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—51no—
479C2×C3×C4—52no—
480C2×C3×C4—52no—
481C2×C3×C4—101no—
482C2×C3×C4—101no—
483C2×C3×C4—202no—
484C2×C3×C4—202no—
485C2×C3×C4C23×D511yescharacteristic
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—51no—
489C2×Dic3—54no—
490C2×Dic3—51no—
491C2×Dic3—104no—
492C2×Dic3—102no—
493C2×Dic3—101no—
494C2×Dic3—101no—
495C2×Dic3—202no—
496C2×Dic3D4×D511yescharacteristic
497C2×Dic3D4×D511yescharacteristic
498Dic6—21no—
499Dic6—42no—
500Dic6—52no—
501Dic6—104no—
502Dic6—101no—
503Dic6—202no—
504Dic6—202no—
505Dic6—202no—
506Dic6Q8×D512yescomplemented
507C3×C8—21no—
508C3×C8—101no—
509C3⋊C8—21no—
510C3⋊C8—101no—
511C22×C5C2×D3×D411yescharacteristic
512C2×D5#89612yes—
513C2×D5#91112yes—
514C2×D5D3×Q1612yes—
515C4×C5—32no—
516C4×C5—41no—
517C4×C5—41no—
518C4×C5—61no—
519C4×C5—62no—
520C4×C5—121no—
521C4×C5C2×#23511yescharacteristic
522C4×C5C2×D3×Q811yescharacteristic
523Dic5—32no—
524Dic5—41no—
525Dic5—41no—
526Dic5—61no—
527Dic5—62no—
528Dic5—121no—
529Dic5#89612yes—
530C2×Q8—31no—
531C2×Q8—61no—
532C2×Q8—154no—
533C2×Q8—151no—
534C2×Q8—301no—
535C2×Q8—301no—
536C2×Q8—301no—
537C2×Q8—302no—
538C2×Q8—301no—
539C2×Q8—604no—
540C22×C4—51no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—151no—
544C22×C4—151no—
545C22×C4—301no—
546C22×C4—301no—
547C2×C8—31no—
548C2×C8—51no—
549C2×C8—102no—
550C2×C8—151no—
551C2×C8—302no—
552C2×C8C2×D3×D511yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C4⋊C4C2×D3×D511yescharacteristic
570C42—31no—
571C42—61no—
572C42—151no—
573C42—151no—
574C42—151no—
575C42—301no—
576C42—301no—
577C42—301no—
578C3×C5C2×#47711yescharacteristic, complemented, Hall
579C22×C3—52no—
580C22×C3—52no—
581C22×C3—52no—
582C22×C3C2×D4×D511yescharacteristic
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—52no—
586C3×C4—201no—
587C3×C4—201no—
588C3×C4C2×Q8×D511yescharacteristic
589C3×C4D5×#4111yescharacteristic
590Dic3—21no—
591Dic3—22no—
592Dic3—41no—
593Dic3—52no—
594Dic3—101no—
595Dic3—102no—
596Dic3—201no—
597Dic3D5×Q1612yes—
598C2×C5C2×#89611yescharacteristic
599C2×C5C2×#91111yescharacteristic
600C2×C5C2×D3×Q1611yescharacteristic
601D5#487514yesdirect product factor
602C23—51no—
603Q8—32no—
604Q8—61no—
605Q8—122no—
606Q8—152no—
607Q8—304no—
608Q8—301no—
609Q8—602no—
610Q8—602no—
611Q8—602no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—51no—
617C2×C4—52no—
618C2×C4—52no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—154no—
624C2×C4—151no—
625C2×C4—151no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—302no—
629C2×C4—304no—
630C2×C4—301no—
631C2×C4—301no—
632C2×C4—602no—
633C2×C4C22×D3×D511yescharacteristic
634C8—21no—
635C8—61no—
636C8—101no—
637C8—301no—
638C2×C3—54no—
639C2×C3D5×C22⋊Q811yescharacteristic
640C2×C3C2×D5×Q1611yescharacteristic
641C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
642C5C2×#487511yescharacteristic, complemented, Sylow
643C22—52no—
644C22—52no—
645C22—52no—
646C22D3×D4×D511yescharacteristic
647C4—32no—
648C4—41no—
649C4—41no—
650C4—52no—
651C4—61no—
652C4—62no—
653C4—121no—
654C4—152no—
655C4—201no—
656C4—201no—
657C4—301no—
658C4—302no—
659C4—601no—
660C4D5×#23511yescharacteristic
661C4D3×Q8×D511yescharacteristic
662C3D5×#47711yescharacteristic, complemented, Sylow
663C2—54no—
664C2D5×#89611yescharacteristic
665C2D5×#91111yescharacteristic
666C2D3×D5×Q1611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenter#107D3×D5
hypocenterC3×C5C2×#477
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #11750976C2semidirect
4. C5×#4875C2semidirect
6. #11747882C2semidirect
7. #11747868C2semidirect
12. #11747418C2semidirect
13. #11747300C2semidirect
14. #11747292C2semidirect
15. #11747182C2semidirect
92. D5×Dic6Q8semidirect
138. #4875D5direct (N × H)
193. Dic30C2×Q8semidirect
200. C5×Dic6C2×Q8semidirect
474. C3×D5#477semidirect
506. Dic6Q8×D5semidirect
578. C3×C5C2×#477semidirect
601. D5#4875direct (N × H)
642. C5C2×#4875semidirect
662. C3D5×#477semidirect

Maximal subgroups

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

subgroupindex
D5×#8882
D5×#8872
#117509762
C5×#48752
C3×D5×#1072
#117478822
#117478682
D5×#8162
D5×Dic3⋊C82
D5×#8102
D5×#8072
#117474182
#117473002
#117472922
#117471822
D5×#4773
C2×#48755