Finite Group Databasebeta

← D5×#5075 #14426022

Subgroups — D5×#5075 #14426022

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#127C211yesmaximal, characteristic
2C2×D5×#214C212yesmaximal, complemented
3C4×D5×Dic6C211yesmaximal, characteristic, complemented
4#11751176C211yesmaximal, characteristic, complemented
5C5×#5075C211yesmaximal, characteristic, complemented
6#11749000C212yesmaximal, complemented
7#11748999C212yesmaximal, complemented
8D5×#832C212yesmaximal, complemented
9#11747083C211yesmaximal, characteristic, complemented
10#11747068C211yesmaximal, characteristic, complemented
11D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12D5×#460—31nomaximal, Hall
13C2×C3×D4×D5—21no—
14C2×C3×D4×D5—21no—
15C2×C3×D4×D5C2212yes—
16C2×D5×Dic6C2211yescharacteristic
17C3×C5×#127C2211yescharacteristic
18C2×#6716C2212yescomplemented
19C4×Dic30C2211yescharacteristic, complemented
20C2×C5×#214C2212yescomplemented
21C4×C5×Dic6C2211yescharacteristic, complemented
22C3×#4086—21no—
23C3×#4086—21no—
24C3×#4086C2212yes—
25C3×#4020C2211yescharacteristic
26C3×C42×D5C2211yescharacteristic
27D5×#214—28no—
28C4×#1204—21no—
29D5×C4⋊Dic3C2211yescharacteristic
30D5×Dic3⋊C4—21no—
31C4×D5×Dic3—21no—
32#91333C2211yescharacteristic, complemented
33Dic5×Dic6C2211yescharacteristic, complemented
34#91323—21no—
35C2×#6657C2212yescomplemented
36C2×#6655C2212yescomplemented
37C2×D5×C3⋊C8C2212yes—
38#91116C2212yescomplemented
39C4⋊(C3⋊#168)C2211yescharacteristic, complemented
40C5×#832C2212yescomplemented
41C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
42#90982C2212yescomplemented
43#90965C2212yescomplemented
44#90964C2212yescomplemented
45C2×#5075—51nomaximal, Hall
46C2×D5×SD16—32no—
47D5×#127D311yescharacteristic
48C4×Q8×D5—31no—
49C5×#460—31no—
50#65452—32no—
51#65364—31no—
52#65316—31no—
53#65137—31no—
54D5×C4⋊C8—31no—
55D5×#102—32no—
56#65051—32no—
57C23×C3×D5—22no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2312yes—
61C2×Dic30C2311yescharacteristic
62C2×C5×Dic6C2311yescharacteristic
63C2×C3×C22⋊D5—22no—
64C2×C3×C22⋊D5—22no—
65C2×C3×C22⋊D5—22no—
66C3×D4×D5—24no—
67C3×D4×D5—24no—
68C3×D4×D5—44no—
69C3×D4×D5—44no—
70C2×C3×D20—21no—
71C2×C3×D20—21no—
72C2×C3×D20C2312yes—
73C2×C3×C4×D5D411yescharacteristic
74C2×C3×C4×D5D411yescharacteristic
75C2×C3×C4×D5C2311yescharacteristic
76C2×#1204—21no—
77C2×D5×Dic3—21no—
78C2×D5×Dic3—21no—
79D5×Dic6—22no—
80D5×Dic6D414yescomplemented
81C3×C42×C5C2311yescharacteristic
82#6716—24no—
83C4⋊Dic15C2311yescharacteristic
84#6712—21no—
85C4×Dic15—21no—
86C2×C3⋊#168C2312yes—
87C5×#214—24no—
88C5×C4⋊Dic3C2311yescharacteristic
89C5×Dic3⋊C4—21no—
90C4×C5×Dic3—21no—
91C2×C5×C3⋊C8C2312yes—
92C3×C4×Dic5D411yescharacteristic
93C3×C4×Dic5D411yescharacteristic
94C3×C4×Dic5C2311yescharacteristic
95Dic3⋊Dic5—21no—
96#6669—21no—
97#6668—21no—
98Dic3×Dic5—21no—
99Dic3×Dic5—21no—
100#6657—24no—
101#6655—24no—
102D5×C3⋊C8—24no—
103C2×C3×#127—51no—
104C22×#214—52no—
105C2×C4×Dic6—51no—
106C2×#832—52no—
107#5075—51no—
108#5075—52no—
109#5075—51no—
110#5075—52no—
111#5075—51no—
112#5075D511yescharacteristic, direct product factor
113C2×C4⋊(C3⋊C8)—51no—
114C2×Q8×D5—31no—
115C2×D4×D5—21no—
116C2×D4×D5—21no—
117C2×D4×D5C2×D312yes—
118C2×C5×SD16—32no—
119C5×#127C2×D311yescharacteristic
120C4×C5×Q8—31no—
121Q8×Dic5—31no—
122C2×#688—32no—
123#4086—21no—
124#4086—21no—
125#4086C2×D312yes—
126C2×#687—32no—
127D5×SD16—68no—
128C2×#677—32no—
129C2×C8×D5—32no—
130D5×C4⋊C4—31no—
131D5×C4⋊C4—61no—
132#4033—31no—
133#4033—61no—
134#4020C2×D311yescharacteristic
135C42×D5—61no—
136C42×D5C2×D311yescharacteristic
137C4×Dic10—31no—
138C4×Dic10—61no—
139C5×C4⋊C8—31no—
140C5×#102—32no—
141#3964—32no—
142#3953—32no—
143#3946—32no—
144#3941—32no—
145C4⋊#168—31no—
146C2×#460—151noSylow
147C23×C3×C5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—44no—
150C22×C3×D5—44no—
151C22×C3×D5—44no—
152C22×C3×D5C2×D411yescharacteristic
153C3×C5×D4—22no—
154C3×C5×D4—22no—
155C3×C5×D4—42no—
156C3×C5×D4—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5C2411yescharacteristic
160C2×Dic15—21no—
161C2×Dic15—21no—
162Dic30—21no—
163Dic30C2×D412yescomplemented
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C5×Dic6—21no—
167C5×Dic6C2×D412yescomplemented
168C3×C22⋊D5—44no—
169C3×C22⋊D5—44no—
170C3×C22⋊D5—44no—
171C2×C3×Dic5C2×D411yescharacteristic
172C2×C3×Dic5C2×D411yescharacteristic
173C2×C3×Dic5C2×D411yescharacteristic
174C3×D20—22no—
175C3×D20—22no—
176C3×D20—42no—
177C3×D20—42no—
178C3×C4×D5—22no—
179C3×C4×D5SD1614yescomplemented
180C3×C4×D5C2×D412yes—
181C3×C4×D5#4112yes—
182#1204—24no—
183D5×Dic3—24no—
184D5×Dic3—42no—
185C3⋊#168—22no—
186C5×C3⋊C8—22no—
187C22×C3×D4—52no—
188C22×C3×D4—101no—
189C22×C3×D4—101no—
190C22×Dic6—51no—
191C3×#127—52no—
192C3×#127—51no—
193C3×#127—101no—
194C3×#127—101no—
195C3×#127C2×D511yescharacteristic
196C2×C3×C42—51no—
197C2×#214—52no—
198C2×#214—52no—
199C2×#214—52no—
200C2×#214—108no—
201C2×#214C2×D512yescomplemented
202C2×C4⋊Dic3—51no—
203C2×Dic3⋊C4—101no—
204C2×C4×Dic3—101no—
205C22×C3⋊C8—52no—
206C4×Dic6—51no—
207C4×Dic6—51no—
208C4×Dic6—51no—
209C4×Dic6—101no—
210C4×Dic6—101no—
211C4×Dic6C2×D511yescharacteristic, complemented
212#832—52no—
213#832—52no—
214#832—52no—
215#832C2×D512yescomplemented
216C4⋊(C3⋊C8)—51no—
217C4⋊(C3⋊C8)—52no—
218C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
219C23×D5—22no—
220C2×C5×Q8—31no—
221C2×C5×D4—21no—
222C2×C5×D4—21no—
223C2×C5×D4C22×D312yes—
224C2×C22⋊D5—22no—
225C2×C22⋊D5—22no—
226C2×C22⋊D5—22no—
227Q8×D5—34no—
228Q8×D5—62no—
229D4×D5—24no—
230D4×D5—24no—
231D4×D5—44no—
232D4×D5—44no—
233C2×D20—21no—
234C2×D20—21no—
235C2×D20C22×D312yes—
236C2×C4×D5—61no—
237C2×C4×D5—61no—
238C2×C4×D5#6711yescharacteristic
239C2×C4×D5#6711yescharacteristic
240C2×C4×D5C22×D311yescharacteristic
241C2×Dic10—31no—
242C2×Dic10—61no—
243C5×SD16—64no—
244C2×C5×C8—32no—
245C5×C4⋊C4—31no—
246C5×C4⋊C4—61no—
247C42×C5—61no—
248C42×C5C22×D311yescharacteristic
249#688—64no—
250#687—64no—
251C4⋊Dic5—31no—
252C4⋊Dic5—61no—
253#683—61no—
254#683—61no—
255#683—61no—
256C4×Dic5—61no—
257C4×Dic5—61no—
258C4×Dic5—61no—
259C4×Dic5#6711yescharacteristic
260C4×Dic5#6711yescharacteristic
261C4×Dic5C22×D311yescharacteristic
262C2×#168—32no—
263#677—64no—
264C8×D5—64no—
265C22×SD16—152no—
266C2×#127—51no—
267C2×C4×Q8—151no—
268#460—31no—
269#460—152no—
270#460—151no—
271#460—151no—
272#460—152no—
273#460—151no—
274C2×C4⋊C8—151no—
275C2×#102—152no—
276C22×C3×C5—42no—
277C22×C3×C5—42no—
278C22×C3×C5—42no—
279C22×C3×C5C22×D411yescharacteristic
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—88no—
284C2×C3×D5#12112yes—
285C2×C3×D5C2×SD1612yes—
286C2×C3×D5AGL(1,ℤ/8)12yes—
287C3×C4×C5—21no—
288C3×C4×C5C2×SD1612yescomplemented
289C3×C4×C5C22×D411yescharacteristic
290C3×C4×C5C2×#4111yescharacteristic
291Dic15—22no—
292Dic15—41no—
293C3×Dic5—21no—
294C3×Dic5#12112yes—
295C3×Dic5C2×SD1612yescomplemented
296C5×Dic3—22no—
297C5×Dic3—41no—
298C24×C3—102no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—52no—
302C2×C3×D4—104no—
303C2×C3×D4—104no—
304C2×C3×D4—102no—
305C2×C3×D4—102no—
306C2×C3×D4—102no—
307C2×C3×D4—101no—
308C2×C3×D4—101no—
309C2×C3×D4—204no—
310C2×C3×D4—204no—
311C2×C3×D4C22×D512yes—
312C22×C3×C4—51no—
313C22×C3×C4—51no—
314C22×C3×C4—51no—
315C22×Dic3—101no—
316C22×Dic3—101no—
317C2×Dic6—51no—
318C2×Dic6—54no—
319C2×Dic6—102no—
320C2×Dic6—101no—
321C2×Dic6C22×D511yescharacteristic
322C3×C42—51no—
323C3×C42—51no—
324C3×C42—51no—
325C3×C42C22×D511yescharacteristic
326#214—24no—
327#214—104no—
328#214—104no—
329#214—104no—
330C4⋊Dic3—51no—
331C4⋊Dic3—101no—
332C4⋊Dic3C22×D511yescharacteristic
333Dic3⋊C4—21no—
334Dic3⋊C4—101no—
335Dic3⋊C4—101no—
336Dic3⋊C4—101no—
337C4×Dic3—21no—
338C4×Dic3—101no—
339C4×Dic3—101no—
340C4×Dic3—101no—
341C2×C3⋊C8—52no—
342C2×C3⋊C8—104no—
343C2×C3⋊C8C22×D512yes—
344C23×C5—22no—
345C22×D5—22no—
346C22×D5—44no—
347C22×D5—44no—
348C22×D5—44no—
349C22×D5C2×#6711yescharacteristic
350C5×Q8—32no—
351C5×Q8—61no—
352C5×D4—22no—
353C5×D4—22no—
354C5×D4—42no—
355C5×D4—42no—
356C2×C4×C5—61no—
357C2×C4×C5—61no—
358C2×C4×C5C2×#6711yescharacteristic
359C2×C4×C5C2×#6711yescharacteristic
360C2×C4×C5C23×D311yescharacteristic
361C22⋊D5—44no—
362C22⋊D5—44no—
363C22⋊D5—44no—
364C2×Dic5—61no—
365C2×Dic5—61no—
366C2×Dic5C2×#6711yescharacteristic
367C2×Dic5C2×#6711yescharacteristic
368C2×Dic5C2×#6711yescharacteristic
369D20—22no—
370D20—22no—
371D20—42no—
372D20—42no—
373C4×D5—22no—
374C4×D5—64no—
375C4×D5—122no—
376C4×D5#21414yescomplemented
377C4×D5D3×D412yes—
378C4×D5#23712yes—
379Dic10—32no—
380Dic10—61no—
381Dic10—64no—
382C5×C8—62no—
383#168—62no—
384C22×Q8—151no—
385C22×D4—52no—
386C22×D4—101no—
387C22×D4—101no—
388C2×SD16—32no—
389C2×SD16—152no—
390C2×SD16—152no—
391C2×SD16—152no—
392C2×SD16—308no—
393C22×C8—152no—
394#127—52no—
395#127—51no—
396#127—101no—
397#127—101no—
398#127D3×D511yescharacteristic
399C4×Q8—31no—
400C4×Q8—151no—
401C4×Q8—151no—
402C4×Q8—151no—
403C4×Q8—301no—
404C4×Q8—301no—
405C2×C4⋊C4—151no—
406C2×C4⋊C4—301no—
407C2×C42—51no—
408C2×C42—301no—
409C4⋊C8—31no—
410C4⋊C8—152no—
411C4⋊C8—151no—
412#102—32no—
413#102—152no—
414#102—152no—
415#102—152no—
416C2×C3×C5—82no—
417C2×C3×C5C2×#12111yescharacteristic
418C2×C3×C5C22×SD1611yescharacteristic
419C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
420C3×D5—82no—
421C3×D5#46014yescomplemented
422C23×C3—22no—
423C23×C3—51no—
424C23×C3—102no—
425C23×C3—204no—
426C23×C3—204no—
427C23×C3—204no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—42no—
431C3×D4—42no—
432C3×D4—102no—
433C3×D4—102no—
434C3×D4—202no—
435C3×D4—204no—
436C3×D4—204no—
437C3×D4—204no—
438C3×D4—202no—
439C2×C3×C4—51no—
440C2×C3×C4—51no—
441C2×C3×C4—52no—
442C2×C3×C4—52no—
443C2×C3×C4—54no—
444C2×C3×C4—51no—
445C2×C3×C4—102no—
446C2×C3×C4D4×D511yescharacteristic
447C2×C3×C4D4×D511yescharacteristic
448C2×C3×C4C23×D511yescharacteristic
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—104no—
452C2×Dic3—101no—
453C2×Dic3—101no—
454C2×Dic3—202no—
455Dic6—21no—
456Dic6—52no—
457Dic6—104no—
458Dic6—101no—
459Dic6D4×D512yescomplemented
460C3⋊C8—22no—
461C3⋊C8—102no—
462C22×C5—42no—
463C22×C5—42no—
464C22×C5—42no—
465C22×C5C22×#6711yescharacteristic
466C2×D5—42no—
467C2×D5—42no—
468C2×D5—42no—
469C2×D5—88no—
470C2×D5#93212yes—
471C2×D5C2×#21412yes—
472C2×D5#93812yes—
473C4×C5—21no—
474C4×C5—62no—
475C4×C5—121no—
476C4×C5C2×#21412yescomplemented
477C4×C5C2×D3×D411yescharacteristic
478C4×C5C2×#23711yescharacteristic
479Dic5—21no—
480Dic5—62no—
481Dic5—121no—
482Dic5C2×#21412yescomplemented
483Dic5#93812yes—
484C24—102no—
485C2×Q8—31no—
486C2×Q8—154no—
487C2×Q8—151no—
488C2×Q8—301no—
489C2×Q8—302no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—52no—
493C2×D4—104no—
494C2×D4—104no—
495C2×D4—102no—
496C2×D4—102no—
497C2×D4—102no—
498C2×D4—101no—
499C2×D4—101no—
500C2×D4—204no—
501C2×D4—204no—
502C2×D4C2×D3×D512yes—
503C22×C4—51no—
504C22×C4—51no—
505C22×C4—51no—
506C22×C4—301no—
507C22×C4—301no—
508SD16—64no—
509SD16—304no—
510SD16—304no—
511SD16—304no—
512C2×C8—32no—
513C2×C8—152no—
514C2×C8—304no—
515C4⋊C4—31no—
516C4⋊C4—61no—
517C4⋊C4—151no—
518C4⋊C4—301no—
519C4⋊C4—301no—
520C4⋊C4—301no—
521C4⋊C4—301no—
522C42—51no—
523C42—51no—
524C42—51no—
525C42—61no—
526C42—301no—
527C42—301no—
528C42—301no—
529C42C2×D3×D511yescharacteristic
530C3×C5C2×#46011yescharacteristic, complemented, Hall
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—52no—
535C22×C3—52no—
536C22×C3—52no—
537C22×C3—202no—
538C22×C3—202no—
539C22×C3—202no—
540C22×C3—408no—
541C22×C3C2×D4×D511yescharacteristic
542C3×C4—21no—
543C3×C4—52no—
544C3×C4—52no—
545C3×C4—101no—
546C3×C4D5×SD1612yescomplemented
547C3×C4C2×D4×D511yescharacteristic
548C3×C4D5×#4111yescharacteristic
549Dic3—22no—
550Dic3—41no—
551Dic3—102no—
552Dic3—201no—
553C2×C5—82no—
554C2×C5C2×#93211yescharacteristic
555C2×C5C22×#21411yescharacteristic
556C2×C5C2×#93811yescharacteristic
557D5—82no—
558D5#507514yesdirect product factor
559C23—22no—
560C23—51no—
561C23—102no—
562C23—204no—
563C23—204no—
564C23—204no—
565Q8—32no—
566Q8—61no—
567Q8—152no—
568Q8—304no—
569Q8—301no—
570D4—22no—
571D4—22no—
572D4—42no—
573D4—42no—
574D4—102no—
575D4—102no—
576D4—202no—
577D4—204no—
578D4—204no—
579D4—204no—
580D4—202no—
581C2×C4—51no—
582C2×C4—51no—
583C2×C4—54no—
584C2×C4—52no—
585C2×C4—52no—
586C2×C4—51no—
587C2×C4—61no—
588C2×C4—61no—
589C2×C4—102no—
590C2×C4—304no—
591C2×C4—301no—
592C2×C4—301no—
593C2×C4—602no—
594C2×C4D5×#6711yescharacteristic
595C2×C4D5×#6711yescharacteristic
596C2×C4C22×D3×D511yescharacteristic
597C8—62no—
598C8—302no—
599C2×C3—54no—
600C2×C3—82no—
601C2×C3—402no—
602C2×C3D5×#12111yescharacteristic
603C2×C3C2×D5×SD1611yescharacteristic
604C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
605C5C2×#507511yescharacteristic, complemented, Sylow
606C22—42no—
607C22—42no—
608C22—42no—
609C22—52no—
610C22—52no—
611C22—52no—
612C22—202no—
613C22—202no—
614C22—202no—
615C22—408no—
616C22C2×D5×#6711yescharacteristic
617C4—21no—
618C4—52no—
619C4—52no—
620C4—62no—
621C4—101no—
622C4—121no—
623C4—302no—
624C4—601no—
625C4D5×#21412yescomplemented
626C4D3×D4×D511yescharacteristic
627C4D5×#23711yescharacteristic
628C3D5×#46011yescharacteristic, complemented, Sylow
629C2—54no—
630C2—82no—
631C2—402no—
632C2D5×#93211yescharacteristic
633C2C2×D5×#21411yescharacteristic
634C2D5×#93811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC3×D5×#127C2
hypercenter#127D3×D5
hypocenterC3×C5C2×#460
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C2×D5×#214C2semidirect
3. C4×D5×Dic6C2semidirect
4. #11751176C2semidirect
5. C5×#5075C2semidirect
6. #11749000C2semidirect
7. #11748999C2semidirect
8. D5×#832C2semidirect
9. #11747083C2semidirect
10. #11747068C2semidirect
11. D5×C4⋊(C3⋊C8)C2semidirect
18. C2×#6716C22semidirect
19. C4×Dic30C22semidirect
20. C2×C5×#214C22semidirect
21. C4×C5×Dic6C22semidirect
32. #91333C22semidirect
33. Dic5×Dic6C22semidirect
35. C2×#6657C22semidirect
36. C2×#6655C22semidirect
38. #91116C22semidirect
39. C4⋊(C3⋊#168)C22semidirect
40. C5×#832C22semidirect
41. C5×C4⋊(C3⋊C8)C22semidirect
42. #90982C22semidirect
43. #90965C22semidirect
44. #90964C22semidirect
80. D5×Dic6D4semidirect
112. #5075D5direct (N × H)
163. Dic30C2×D4semidirect
167. C5×Dic6C2×D4semidirect
179. C3×C4×D5SD16semidirect
201. C2×#214C2×D5semidirect
211. C4×Dic6C2×D5semidirect
215. #832C2×D5semidirect
218. C4⋊(C3⋊C8)C2×D5semidirect
288. C3×C4×C5C2×SD16semidirect
295. C3×Dic5C2×SD16semidirect
376. C4×D5#214semidirect
421. C3×D5#460semidirect
459. Dic6D4×D5semidirect
476. C4×C5C2×#214semidirect
482. Dic5C2×#214semidirect
530. C3×C5C2×#460semidirect
546. C3×C4D5×SD16semidirect
558. D5#5075direct (N × H)
605. C5C2×#5075semidirect
625. C4D5×#214semidirect
628. C3D5×#460semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1272
C2×D5×#2142
C4×D5×Dic62
#117511762
C5×#50752
#117490002
#117489992
D5×#8322
#117470832
#117470682
D5×C4⋊(C3⋊C8)2
D5×#4603
C2×#50755