Finite Group Databasebeta

← D5×#5063 #14430141

Subgroups — D5×#5063 #14430141

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#125C211yesmaximal, characteristic
2C4×D5×Dic6C211yesmaximal, characteristic
3#11751164C211yesmaximal, characteristic, complemented
4C5×#5063C211yesmaximal, characteristic, complemented
5D5×#810C211yesmaximal, characteristic
6D5×#810C211yesmaximal, characteristic
7D5×#808C211yesmaximal, characteristic
8D5×#807C211yesmaximal, characteristic
9#11747289C211yesmaximal, characteristic, complemented
10#11747288C211yesmaximal, characteristic, complemented
11#11747287C211yesmaximal, characteristic, complemented
12#11747286C211yesmaximal, characteristic, complemented
13D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
14#11746934C211yesmaximal, characteristic, complemented
15#11746926C211yesmaximal, characteristic, complemented
16D5×#479—31nomaximal, Hall
17C2×D5×Dic6C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C4×C5×Dic6C2211yescharacteristic
21C3×D5×C4⋊C4—21no—
22C3×D5×C4⋊C4—21no—
23C3×D5×C4⋊C4C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25C3×#4036C2211yescharacteristic
26C3×#4036C2211yescharacteristic
27C3×#4035—21no—
28C3×#4035—21no—
29C3×C42×D5C2211yescharacteristic
30C3×#4016C2211yescharacteristic
31C4×#1204—21no—
32D5×C4⋊Dic3C2211yescharacteristic
33D5×Dic3⋊C4—21no—
34C4×D5×Dic3—21no—
35#91333C2211yescharacteristic
36Dic5×Dic6C2211yescharacteristic
37#91323—21no—
38C2×D5×C3⋊C8C2211yescharacteristic
39C2×D5×C3⋊C8C2211yescharacteristic
40#91094C2211yescharacteristic
41#91094C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#810C2211yescharacteristic
46C5×#810C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90990C2211yescharacteristic
51#90989C2211yescharacteristic
52#90987C2211yescharacteristic
53#90986C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90974C2211yescharacteristic
57#90974C2211yescharacteristic
58#90972C2211yescharacteristic
59#90972C2211yescharacteristic
60C2×#5063—51nomaximal, Hall
61D5×#125D311yescharacteristic
62C4×Q8×D5—31no—
63C5×#479—31no—
64#65352—31no—
65#65311—31no—
66D5×#107—31no—
67#65166—31no—
68D5×#106—31no—
69#65146—31no—
70D5×C4⋊C8—31no—
71#65118—31no—
72D5×#103—31no—
73D5×#103—31no—
74#65088—31no—
75#65085—31no—
76C2×Dic30C2311yescharacteristic
77C2×C5×Dic6C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×C4×D5—21no—
80C2×C3×C4×D5D411yescharacteristic
81C2×C3×C4×D5D411yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83C2×#1204—21no—
84C2×D5×Dic3—21no—
85C2×D5×Dic3—21no—
86D5×Dic6—22no—
87D5×Dic6Q814yes—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95C4×Dic15—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×C4⋊Dic3C2311yescharacteristic
99C5×Dic3⋊C4—21no—
100C4×C5×Dic3—21no—
101C2×C5×C3⋊C8C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×C4×Dic5D411yescharacteristic
114C3×C4×Dic5D411yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121D5×C3⋊C8—22no—
122D5×C3⋊C8—22no—
123C2×C3×#125—51no—
124C2×C4×Dic6—51no—
125#5063—51no—
126#5063—51no—
127#5063—51no—
128#5063—51no—
129#5063—51no—
130#5063—51no—
131#5063—51no—
132#5063D511yescharacteristic, direct product factor
133C2×#810—51no—
134C2×#810—51no—
135C2×#808—51no—
136C2×#807—51no—
137C2×C4⋊(C3⋊C8)—51no—
138C2×Q8×D5—31no—
139C5×#125C2×D311yescharacteristic
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142C2×C8×D5—31no—
143C2×C8×D5—31no—
144D5×C4⋊C4—21no—
145D5×C4⋊C4—21no—
146D5×C4⋊C4—31no—
147D5×C4⋊C4—61no—
148D5×C4⋊C4C2×D311yescharacteristic
149D5×C4⋊C4C2×D311yescharacteristic
150#4036C2×D311yescharacteristic
151#4036C2×D311yescharacteristic
152#4035—21no—
153#4035—21no—
154#4033—31no—
155#4033—61no—
156C42×D5—61no—
157C42×D5C2×D311yescharacteristic
158#4016C2×D311yescharacteristic
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181C2×#479—151noSylow
182C22×C3×D5C2×D411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190Dic30—21no—
191Dic30C2×Q812yes—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C5×Dic6—21no—
195C5×Dic6C2×Q812yes—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5C2×D411yescharacteristic
199C2×C3×Dic5C2×D411yescharacteristic
200C2×C3×Dic5C2×D411yescharacteristic
201C3×C4×D5—22no—
202C3×C4×D5—22no—
203C3×C4×D5—42no—
204C3×C4×D5—42no—
205C3×C4×D5C2×Q812yes—
206C3×C4×D5#4112yes—
207#1204—24no—
208D5×Dic3—24no—
209D5×Dic3—42no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C5×C3⋊C8—21no—
213C5×C3⋊C8—21no—
214C22×Dic6—51no—
215C3×#125—51no—
216C3×#125—51no—
217C3×#125—51no—
218C3×#125—101no—
219C3×#125—101no—
220C3×#125C2×D511yescharacteristic
221C2×C3×C4⋊C4—51no—
222C2×C3×C4⋊C4—51no—
223C2×C3×C4⋊C4—101no—
224C2×C3×C4⋊C4—101no—
225C2×C3×C42—51no—
226C2×C4⋊Dic3—51no—
227C2×Dic3⋊C4—101no—
228C2×C4×Dic3—101no—
229C22×C3⋊C8—51no—
230C22×C3⋊C8—51no—
231C4×Dic6—51no—
232C4×Dic6—51no—
233C4×Dic6—51no—
234C4×Dic6—101no—
235C4×Dic6—101no—
236C4×Dic6C2×D511yescharacteristic
237#810—51no—
238#810—51no—
239#810—51no—
240#810—51no—
241#810—51no—
242#810—51no—
243#810C2×D511yescharacteristic
244#810C2×D511yescharacteristic
245#808—51no—
246#808—51no—
247#808—51no—
248#808C2×D511yescharacteristic
249#807—51no—
250#807—51no—
251#807—51no—
252#807C2×D511yescharacteristic
253C4⋊(C3⋊C8)—51no—
254C4⋊(C3⋊C8)—51no—
255C4⋊(C3⋊C8)—51no—
256C4⋊(C3⋊C8)C2×D511yescharacteristic
257C2×C5×Q8—31no—
258Q8×D5—34no—
259Q8×D5—62no—
260C2×C4×D5—21no—
261C2×C4×D5—21no—
262C2×C4×D5—61no—
263C2×C4×D5—61no—
264C2×C4×D5#6711yescharacteristic
265C2×C4×D5#6711yescharacteristic
266C2×C4×D5C22×D311yescharacteristic
267C2×Dic10—31no—
268C2×Dic10—61no—
269C2×C5×C8—31no—
270C2×C5×C8—31no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4C22×D311yescharacteristic
276C5×C4⋊C4C22×D311yescharacteristic
277C42×C5—61no—
278C42×C5C22×D311yescharacteristic
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—31no—
282C4⋊Dic5—61no—
283C4⋊Dic5C22×D311yescharacteristic
284C4⋊Dic5C22×D311yescharacteristic
285#683—21no—
286#683—21no—
287#683—21no—
288#683—21no—
289#683—21no—
290#683—21no—
291#683—61no—
292#683—61no—
293#683—61no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5#6711yescharacteristic
298C4×Dic5#6711yescharacteristic
299C4×Dic5C22×D311yescharacteristic
300C2×#168—31no—
301C2×#168—31no—
302C8×D5—62no—
303C8×D5—62no—
304C2×#125—51no—
305C2×C4×Q8—151no—
306#479—31no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#479—151no—
312#479—151no—
313#479—151no—
314C2×#107—151no—
315C2×#106—151no—
316C2×C4⋊C8—151no—
317C2×#103—151no—
318C2×#103—151no—
319C22×C3×C5C22×D411yescharacteristic
320C2×C3×D5C22⋊Q812yes—
321C2×C3×D5#13512yes—
322C2×C3×D5#13712yes—
323C3×C4×C5—21no—
324C3×C4×C5—21no—
325C3×C4×C5—41no—
326C3×C4×C5—41no—
327C3×C4×C5C22×Q811yescharacteristic
328C3×C4×C5C2×#4111yescharacteristic
329Dic15—22no—
330Dic15—41no—
331C3×Dic5—21no—
332C3×Dic5—21no—
333C3×Dic5—41no—
334C3×Dic5—41no—
335C3×Dic5C22⋊Q812yes—
336C5×Dic3—22no—
337C5×Dic3—41no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—101no—
342C22×C3×C4—101no—
343C22×Dic3—101no—
344C22×Dic3—101no—
345C2×Dic6—51no—
346C2×Dic6—54no—
347C2×Dic6—102no—
348C2×Dic6—101no—
349C2×Dic6C22×D511yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—51no—
353C3×C4⋊C4—51no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4—101no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4C22×D511yescharacteristic
363C3×C4⋊C4C22×D511yescharacteristic
364C3×C42—51no—
365C3×C42—51no—
366C3×C42—51no—
367C3×C42C22×D511yescharacteristic
368C4⋊Dic3—51no—
369C4⋊Dic3—101no—
370C4⋊Dic3C22×D511yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375C4×Dic3—21no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3—101no—
379C2×C3⋊C8—51no—
380C2×C3⋊C8—51no—
381C2×C3⋊C8—102no—
382C2×C3⋊C8—102no—
383C2×C3⋊C8C22×D511yescharacteristic
384C2×C3⋊C8C22×D511yescharacteristic
385C22×D5C2×#6711yescharacteristic
386C5×Q8—32no—
387C5×Q8—61no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—61no—
391C2×C4×C5—61no—
392C2×C4×C5C2×#6711yescharacteristic
393C2×C4×C5C2×#6711yescharacteristic
394C2×C4×C5C23×D311yescharacteristic
395C2×Dic5—21no—
396C2×Dic5—21no—
397C2×Dic5—61no—
398C2×Dic5—61no—
399C2×Dic5C2×#6711yescharacteristic
400C2×Dic5C2×#6711yescharacteristic
401C2×Dic5C2×#6711yescharacteristic
402C4×D5—22no—
403C4×D5—22no—
404C4×D5—42no—
405C4×D5—42no—
406C4×D5—64no—
407C4×D5—122no—
408C4×D5D3×Q812yes—
409C4×D5#23912yes—
410Dic10—32no—
411Dic10—61no—
412Dic10—64no—
413C5×C8—61no—
414C5×C8—61no—
415#168—61no—
416#168—61no—
417C22×Q8—151no—
418C22×C8—151no—
419C22×C8—151no—
420#125—51no—
421#125—51no—
422#125—51no—
423#125—101no—
424#125—101no—
425#125D3×D511yescharacteristic
426C4×Q8—31no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—301no—
431C4×Q8—301no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—101no—
435C2×C4⋊C4—101no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—301no—
438C2×C42—51no—
439C2×C42—301no—
440#107—31no—
441#107—151no—
442#107—151no—
443#107—151no—
444#106—31no—
445#106—151no—
446#106—151no—
447#106—151no—
448C4⋊C8—31no—
449C4⋊C8—151no—
450C4⋊C8—151no—
451C4⋊C8—151no—
452#103—31no—
453#103—31no—
454#103—151no—
455#103—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460C2×C3×C5C2×C22⋊Q811yescharacteristic
461C2×C3×C5C2×#13511yescharacteristic
462C2×C3×C5C2×#13711yescharacteristic
463C3×D5#47914yescomplemented
464C23×C3—51no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—51no—
468C2×C3×C4—52no—
469C2×C3×C4—52no—
470C2×C3×C4—51no—
471C2×C3×C4—51no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—101no—
475C2×C3×C4—101no—
476C2×C3×C4—202no—
477C2×C3×C4—202no—
478C2×C3×C4D4×D511yescharacteristic
479C2×C3×C4D4×D511yescharacteristic
480C2×C3×C4C23×D511yescharacteristic
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—104no—
484C2×Dic3—101no—
485C2×Dic3—101no—
486C2×Dic3—202no—
487Dic6—21no—
488Dic6—52no—
489Dic6—104no—
490Dic6—101no—
491Dic6Q8×D512yes—
492C3⋊C8—21no—
493C3⋊C8—21no—
494C3⋊C8—101no—
495C3⋊C8—101no—
496C22×C5C22×#6711yescharacteristic
497C2×D5#94612yes—
498C2×D5#95012yes—
499C2×D5#95112yes—
500C4×C5—21no—
501C4×C5—21no—
502C4×C5—41no—
503C4×C5—41no—
504C4×C5—62no—
505C4×C5—121no—
506C4×C5C2×D3×Q811yescharacteristic
507C4×C5C2×#23911yescharacteristic
508Dic5—21no—
509Dic5—21no—
510Dic5—41no—
511Dic5—41no—
512Dic5—62no—
513Dic5—121no—
514Dic5#94612yes—
515C2×Q8—31no—
516C2×Q8—154no—
517C2×Q8—151no—
518C2×Q8—301no—
519C2×Q8—302no—
520C22×C4—51no—
521C22×C4—51no—
522C22×C4—51no—
523C22×C4—101no—
524C22×C4—101no—
525C22×C4—301no—
526C22×C4—301no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8—151no—
530C2×C8—151no—
531C2×C8—302no—
532C2×C8—302no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—31no—
536C4⋊C4—51no—
537C4⋊C4—51no—
538C4⋊C4—61no—
539C4⋊C4—101no—
540C4⋊C4—101no—
541C4⋊C4—101no—
542C4⋊C4—101no—
543C4⋊C4—101no—
544C4⋊C4—101no—
545C4⋊C4—101no—
546C4⋊C4—101no—
547C4⋊C4—151no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C4⋊C4C2×D3×D511yescharacteristic
554C42—51no—
555C42—51no—
556C42—51no—
557C42—61no—
558C42—301no—
559C42—301no—
560C42—301no—
561C42C2×D3×D511yescharacteristic
562C3×C5C2×#47911yescharacteristic, complemented, Hall
563C22×C3—52no—
564C22×C3—52no—
565C22×C3—52no—
566C22×C3C2×D4×D511yescharacteristic
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—52no—
572C3×C4—101no—
573C3×C4—101no—
574C3×C4—201no—
575C3×C4—201no—
576C3×C4C2×Q8×D511yescharacteristic
577C3×C4D5×#4111yescharacteristic
578Dic3—22no—
579Dic3—41no—
580Dic3—102no—
581Dic3—201no—
582C2×C5C2×#94611yescharacteristic
583C2×C5C2×#95011yescharacteristic
584C2×C5C2×#95111yescharacteristic
585D5#506314yesdirect product factor
586C23—51no—
587Q8—32no—
588Q8—61no—
589Q8—152no—
590Q8—304no—
591Q8—301no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—51no—
595C2×C4—52no—
596C2×C4—52no—
597C2×C4—51no—
598C2×C4—51no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—101no—
604C2×C4—101no—
605C2×C4—202no—
606C2×C4—202no—
607C2×C4—304no—
608C2×C4—301no—
609C2×C4—301no—
610C2×C4—602no—
611C2×C4D5×#6711yescharacteristic
612C2×C4D5×#6711yescharacteristic
613C2×C4C22×D3×D511yescharacteristic
614C8—61no—
615C8—61no—
616C8—301no—
617C8—301no—
618C2×C3—54no—
619C2×C3D5×C22⋊Q811yescharacteristic
620C2×C3D5×#13511yescharacteristic
621C2×C3D5×#13711yescharacteristic
622C5C2×#506311yescharacteristic, complemented, Sylow
623C22—52no—
624C22—52no—
625C22—52no—
626C22C2×D5×#6711yescharacteristic
627C4—21no—
628C4—21no—
629C4—41no—
630C4—41no—
631C4—52no—
632C4—62no—
633C4—101no—
634C4—101no—
635C4—121no—
636C4—201no—
637C4—201no—
638C4—302no—
639C4—601no—
640C4D3×Q8×D511yescharacteristic
641C4D5×#23911yescharacteristic
642C3D5×#47911yescharacteristic, complemented, Sylow
643C2—54no—
644C2D5×#94611yescharacteristic
645C2D5×#95011yescharacteristic
646C2D5×#95111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenter#125D3×D5
hypocenterC3×C5C2×#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11751164C2semidirect
4. C5×#5063C2semidirect
9. #11747289C2semidirect
10. #11747288C2semidirect
11. #11747287C2semidirect
12. #11747286C2semidirect
14. #11746934C2semidirect
15. #11746926C2semidirect
132. #5063D5direct (N × H)
463. C3×D5#479semidirect
562. C3×C5C2×#479semidirect
585. D5#5063direct (N × H)
622. C5C2×#5063semidirect
642. C3D5×#479semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1252
C4×D5×Dic62
#117511642
C5×#50632
D5×#8102
D5×#8082
D5×#8072
#117472892
#117472882
#117472872
#117472862
D5×C4⋊(C3⋊C8)2
#117469342
#117469262
D5×#4793
C2×#50635