Finite Group Databasebeta

← D5×A4×M16 #14514137

Subgroups — D5×A4×M16 #14514137

Order 1920.

800 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D5×A4C211yesmaximal, characteristic
2C5×A4×M16C211yesmaximal, characteristic, complemented
3A4×#681C211yesmaximal, characteristic, complemented
4A4×#676C212yesmaximal, complemented
5C8×D5×A4C212yesmaximal, complemented
6C22×D5×M16C311yesmaximal, characteristic, complemented, Hall
7C22×D5×A4C411yescharacteristic
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4×Dic5C411yescharacteristic
10C4×D5×A4C411yescharacteristic
11C4×D5×A4C411yescharacteristic
12C4×D5×A4C2211yescharacteristic
13C4×D5×A4C2211yescharacteristic
14C3×D5×M16—41nomaximal
15C5×C8×A4C2212yescomplemented
16A4×#168C2212yescomplemented
17C2×A4×M16—51nomaximal, Hall
18C23×C4×D5C2×C311yescharacteristic
19C22×C5×M16C2×C311yescharacteristic, complemented
20C22×#681C2×C311yescharacteristic, complemented
21C2×D5×M16—31no—
22C2×D5×M16—31no—
23C2×D5×M16—31no—
24C2×D5×M16—32no—
25C2×D5×M16—32no—
26C2×D5×M16—31no—
27C22×#676C2×C312yescomplemented
28C22×C8×D5C2×C312yescomplemented
29C22×C5×A4C2×C411yescharacteristic
30C2×D5×A4—22no—
31C2×D5×A4C2×C411yescharacteristic
32C2×D5×A4C2×C411yescharacteristic
33C2×C3×C4×D5—41no—
34C4×C5×A4C2×C411yescharacteristic
35C4×C5×A4C2311yescharacteristic
36A4×Dic5C2×C411yescharacteristic
37A4×Dic5C2×C411yescharacteristic
38C3×C5×M16—41no—
39C3×#681—41no—
40C3×#676—42no—
41C3×C8×D5—42no—
42C22×C4×A4—51no—
43A4×M16—51no—
44A4×M16—52no—
45A4×M16D511yescharacteristic, direct product factor
46C2×C8×A4—52no—
47C24×D5C3×C411yescharacteristic
48C23×C4×C5C22×C311yescharacteristic
49C23×Dic5C3×C411yescharacteristic
50C22×C4×D5—31no—
51C22×C4×D5—31no—
52C22×C4×D5—31no—
53C22×C4×D5—31no—
54C22×C4×D5—31no—
55C22×C4×D5—31no—
56C22×C4×D5—31no—
57C22×C4×D5—31no—
58C22×C4×D5C3×C411yescharacteristic
59C22×C4×D5C3×C411yescharacteristic
60C22×C4×D5C22×C311yescharacteristic
61C22×C4×D5C22×C311yescharacteristic
62C2×C5×M16—31no—
63C2×C5×M16—32no—
64C2×C5×M16—31no—
65C22×C5×C8C22×C312yescomplemented
66C2×#681—31no—
67C2×#681—32no—
68C2×#681—31no—
69C22×#168C22×C312yescomplemented
70D5×M16—32no—
71D5×M16—32no—
72D5×M16—34no—
73D5×M16—34no—
74D5×M16—32no—
75D5×M16—31no—
76D5×M16—31no—
77D5×M16—31no—
78D5×M16—32no—
79D5×M16—32no—
80D5×M16A411yescharacteristic, direct product factor
81C2×#676—32no—
82C2×#676—32no—
83C2×#676—32no—
84C2×#676—32no—
85C2×C8×D5—32no—
86C2×C8×D5—32no—
87C2×C8×D5—32no—
88C2×C8×D5—32no—
89C23×M16—51noSylow
90C22×C3×D5—41no—
91C2×C5×A4—21no—
92C2×C5×A4C22×C411yescharacteristic
93D5×A4—21no—
94D5×A4M1612yesdirect product factor
95C2×C3×C4×C5—41no—
96C2×C3×Dic5—41no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101C3×C5×C8—42no—
102C3×#168—42no—
103C23×A4—51no—
104C2×C4×A4—51no—
105C2×C4×A4—51no—
106C2×C4×A4—51no—
107C2×C4×A4—51no—
108C2×C4×A4—51no—
109C2×C4×A4C2×D511yescharacteristic
110C2×C3×M16—201no—
111C8×A4—52no—
112C8×A4C2×D512yescomplemented
113C24×C5C2×C3×C411yescharacteristic
114C23×D5—22no—
115C23×D5—31no—
116C23×D5—31no—
117C23×D5—31no—
118C23×D5—31no—
119C23×D5—62no—
120C23×D5C2×C3×C411yescharacteristic
121C23×D5C2×C3×C411yescharacteristic
122C22×C4×C5—31no—
123C22×C4×C5—31no—
124C22×C4×C5—31no—
125C22×C4×C5—31no—
126C22×C4×C5C2×C3×C411yescharacteristic
127C22×C4×C5C23×C311yescharacteristic
128C22×Dic5—31no—
129C22×Dic5—31no—
130C22×Dic5—31no—
131C22×Dic5—31no—
132C22×Dic5C2×C3×C411yescharacteristic
133C22×Dic5C2×C3×C411yescharacteristic
134C2×C4×D5—32no—
135C2×C4×D5—32no—
136C2×C4×D5—32no—
137C2×C4×D5—32no—
138C2×C4×D5—32no—
139C2×C4×D5—32no—
140C2×C4×D5—32no—
141C2×C4×D5—31no—
142C2×C4×D5—31no—
143C2×C4×D5—31no—
144C2×C4×D5—31no—
145C2×C4×D5—31no—
146C2×C4×D5—31no—
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×C4×D5—31no—
151C2×C4×D5—31no—
152C2×C4×D5—31no—
153C2×C4×D5—31no—
154C2×C4×D5—31no—
155C2×C4×D5—31no—
156C2×C4×D5—31no—
157C2×C4×D5—31no—
158C2×C4×D5—31no—
159C2×C4×D5—31no—
160C2×C4×D5—31no—
161C2×C4×D5—31no—
162C2×C4×D5—31no—
163C2×C4×D5—31no—
164C2×C4×D5C2×A411yescharacteristic
165C5×M16—32no—
166C5×M16—31no—
167C5×M16—32no—
168C5×M16C2×A411yescharacteristic, complemented
169C2×C5×C8—32no—
170C2×C5×C8—32no—
171#681—32no—
172#681—31no—
173#681—32no—
174#681C2×A411yescharacteristic, complemented
175C2×#168—32no—
176C2×#168—32no—
177#676—34no—
178#676—32no—
179#676—32no—
180#676—32no—
181#676C2×A412yescomplemented
182C8×D5—34no—
183C8×D5—32no—
184C8×D5—32no—
185C8×D5—32no—
186C8×D5C2×A412yescomplemented
187C24×C4—51no—
188C22×M16—51no—
189C22×M16—52no—
190C22×M16—151no—
191C22×M16—152no—
192C22×M16—151no—
193C22×M16—152no—
194C22×M16—151no—
195C22×M16—151no—
196C22×M16C3×D511yescharacteristic, complemented
197C23×C8—52no—
198C22×C3×C5—41no—
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C2×C3×D5—82no—
202C5×A4C2×M1611yescharacteristic, complemented
203C3×C4×C5—41no—
204C3×C4×C5—41no—
205C3×Dic5—41no—
206C3×Dic5—41no—
207C22×A4—51no—
208C22×A4—51no—
209C22×A4—102no—
210C22×A4C4×D511yescharacteristic
211C22×C3×C4—201no—
212C4×A4—51no—
213C4×A4—51no—
214C4×A4C4×D511yescharacteristic
215C4×A4C22×D511yescharacteristic
216C3×M16—41no—
217C3×M16—202no—
218C3×M16—201no—
219C2×C3×C8—202no—
220C23×C5—21no—
221C23×C5—31no—
222C23×C5—31no—
223C23×C5—61no—
224C23×C5C22×C3×C411yescharacteristic
225C22×D5—21no—
226C22×D5—31no—
227C22×D5—31no—
228C22×D5—32no—
229C22×D5—32no—
230C22×D5—31no—
231C22×D5—31no—
232C22×D5—31no—
233C22×D5—31no—
234C22×D5—31no—
235C22×D5—62no—
236C22×D5—62no—
237C22×D5—62no—
238C22×D5—62no—
239C22×D5—62no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—61no—
244C22×D5C3×M1612yescomplemented
245C22×D5C4×A411yescharacteristic
246C2×C4×C5—32no—
247C2×C4×C5—31no—
248C2×C4×C5—31no—
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—31no—
252C2×C4×C5—31no—
253C2×C4×C5—31no—
254C2×C4×C5C22×A411yescharacteristic
255C2×Dic5—32no—
256C2×Dic5—31no—
257C2×Dic5—31no—
258C2×Dic5—31no—
259C2×Dic5—31no—
260C2×Dic5—31no—
261C2×Dic5—31no—
262C2×Dic5—31no—
263C2×Dic5C4×A411yescharacteristic
264C4×D5—32no—
265C4×D5—32no—
266C4×D5—32no—
267C4×D5—32no—
268C4×D5—31no—
269C4×D5—31no—
270C4×D5—31no—
271C4×D5—31no—
272C4×D5—31no—
273C4×D5—31no—
274C4×D5—31no—
275C4×D5—31no—
276C4×D5—31no—
277C4×D5—31no—
278C4×D5—31no—
279C4×D5—31no—
280C4×D5C4×A411yescharacteristic
281C4×D5C4×A411yescharacteristic
282C4×D5C22×A411yescharacteristic
283C4×D5C22×A411yescharacteristic
284C5×C8—32no—
285C5×C8C22×A412yescomplemented
286#168—32no—
287#168C22×A412yescomplemented
288C25—51no—
289C23×C4—51no—
290C23×C4—51no—
291C23×C4—51no—
292C23×C4—51no—
293C23×C4—51no—
294C23×C4—151no—
295C23×C4—151no—
296C23×C4—151no—
297C23×C4—151no—
298C23×C4—151no—
299C23×C4—151no—
300C23×C4—151no—
301C23×C4—151no—
302C23×C4C2×C3×D511yescharacteristic
303C2×M16—31no—
304C2×M16—32no—
305C2×M16—31no—
306C2×M16—51no—
307C2×M16—152no—
308C2×M16—152no—
309C2×M16—152no—
310C2×M16—152no—
311C2×M16—152no—
312C2×M16—151no—
313C2×M16—152no—
314C2×M16—151no—
315C2×M16—154no—
316C2×M16—152no—
317C2×M16—152no—
318C2×M16—152no—
319C2×M16—154no—
320C2×M16—151no—
321C2×M16—151no—
322C2×M16—152no—
323C2×M16—151no—
324C22×C8—52no—
325C22×C8—152no—
326C22×C8—152no—
327C22×C8—152no—
328C22×C8—152no—
329C22×C8C2×C3×D512yescomplemented
330C2×C3×C5—41no—
331C2×C3×C5—81no—
332C3×D5—42no—
333C3×D5—81no—
334C23×C3—201no—
335C2×A4—21no—
336C2×A4—52no—
337C2×A4—101no—
338C2×A4C2×C4×D511yescharacteristic
339C2×C3×C4—41no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4—201no—
343C2×C3×C4—201no—
344C2×C3×C4—201no—
345C3×C8—42no—
346C3×C8—202no—
347C22×C5—31no—
348C22×C5—31no—
349C22×C5—31no—
350C22×C5—61no—
351C22×C5—61no—
352C22×C5—61no—
353C22×C5—61no—
354C22×C5C2×C3×M1611yescharacteristic, complemented
355C22×C5C2×C4×A411yescharacteristic
356C2×D5—22no—
357C2×D5—32no—
358C2×D5—31no—
359C2×D5—32no—
360C2×D5—32no—
361C2×D5—32no—
362C2×D5—31no—
363C2×D5—62no—
364C2×D5—61no—
365C2×D5—61no—
366C2×D5—62no—
367C2×D5—64no—
368C2×D5—62no—
369C2×D5—61no—
370C2×D5—61no—
371C2×D5C2×C4×A411yescharacteristic
372C2×D5C2×C4×A411yescharacteristic
373C4×C5—31no—
374C4×C5—31no—
375C4×C5C2×C4×A411yescharacteristic
376C4×C5C23×A411yescharacteristic
377Dic5—31no—
378Dic5—31no—
379Dic5C2×C4×A411yescharacteristic
380Dic5C2×C4×A411yescharacteristic
381C24—51no—
382C24—51no—
383C24—102no—
384C24—151no—
385C24—151no—
386C24—151no—
387C24—151no—
388C24—302no—
389C24C3×C4×D511yescharacteristic
390C22×C4—31no—
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—51no—
395C22×C4—51no—
396C22×C4—51no—
397C22×C4—151no—
398C22×C4—151no—
399C22×C4—151no—
400C22×C4—151no—
401C22×C4—151no—
402C22×C4—151no—
403C22×C4—151no—
404C22×C4—151no—
405C22×C4—151no—
406C22×C4—151no—
407C22×C4—152no—
408C22×C4—152no—
409C22×C4—152no—
410C22×C4—152no—
411C22×C4—152no—
412C22×C4—152no—
413C22×C4—152no—
414C22×C4—151no—
415C22×C4—151no—
416C22×C4—151no—
417C22×C4—151no—
418C22×C4—151no—
419C22×C4—151no—
420C22×C4—151no—
421C22×C4—151no—
422C22×C4—151no—
423C22×C4—151no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—151no—
428C22×C4—151no—
429C22×C4—151no—
430C22×C4—151no—
431C22×C4C3×C4×D511yescharacteristic
432C22×C4C22×C3×D511yescharacteristic
433M16—32no—
434M16—31no—
435M16—32no—
436M16—51no—
437M16—52no—
438M16—152no—
439M16—152no—
440M16—154no—
441M16—152no—
442M16—152no—
443M16—151no—
444M16—152no—
445M16D5×A411yescharacteristic, direct product factor
446C2×C8—32no—
447C2×C8—32no—
448C2×C8—52no—
449C2×C8—152no—
450C2×C8—152no—
451C2×C8—154no—
452C2×C8—152no—
453C2×C8—152no—
454C2×C8—152no—
455C3×C5—41noHall
456C22×C3—41no—
457C22×C3—201no—
458C22×C3—201no—
459C22×C3—402no—
460A4D5×M1611yescharacteristic, direct product factor
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—201no—
464C3×C4—201no—
465C2×C5—21no—
466C2×C5—31no—
467C2×C5—31no—
468C2×C5—61no—
469C2×C5C22×C4×A411yescharacteristic
470D5—21no—
471D5—32no—
472D5—61no—
473D5A4×M1612yesdirect product factor
474C23—21no—
475C23—31no—
476C23—31no—
477C23—51no—
478C23—52no—
479C23—61no—
480C23—101no—
481C23—151no—
482C23—151no—
483C23—151no—
484C23—151no—
485C23—151no—
486C23—152no—
487C23—152no—
488C23—151no—
489C23—151no—
490C23—301no—
491C23—302no—
492C23—302no—
493C23—302no—
494C23—302no—
495C23—302no—
496C23—302no—
497C23—302no—
498C23—302no—
499C23C2×C3×C4×D511yescharacteristic
500C2×C4—32no—
501C2×C4—31no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—31no—
506C2×C4—31no—
507C2×C4—31no—
508C2×C4—51no—
509C2×C4—51no—
510C2×C4—51no—
511C2×C4—51no—
512C2×C4—51no—
513C2×C4—151no—
514C2×C4—151no—
515C2×C4—151no—
516C2×C4—151no—
517C2×C4—151no—
518C2×C4—151no—
519C2×C4—151no—
520C2×C4—151no—
521C2×C4—152no—
522C2×C4—152no—
523C2×C4—152no—
524C2×C4—152no—
525C2×C4—151no—
526C2×C4—151no—
527C2×C4—151no—
528C2×C4—151no—
529C2×C4—152no—
530C2×C4—151no—
531C2×C4—151no—
532C2×C4—151no—
533C2×C4—151no—
534C2×C4—151no—
535C2×C4—151no—
536C2×C4—151no—
537C2×C4C2×D5×A411yescharacteristic
538C8—32no—
539C8—52no—
540C8—152no—
541C8C2×D5×A412yescomplemented
542C2×C3—41no—
543C2×C3—81no—
544C2×C3—202no—
545C2×C3—401no—
546C5C2×A4×M1611yescharacteristic, complemented, Sylow
547C22—31no—
548C22—31no—
549C22—31no—
550C22—51no—
551C22—51no—
552C22—61no—
553C22—61no—
554C22—61no—
555C22—61no—
556C22—102no—
557C22—152no—
558C22—152no—
559C22—152no—
560C22—152no—
561C22—151no—
562C22—151no—
563C22—302no—
564C22—301no—
565C22—301no—
566C22—301no—
567C22—301no—
568C22—302no—
569C22—302no—
570C22—304no—
571C22C3×D5×M1611yescharacteristic, complemented
572C22C4×D5×A411yescharacteristic
573C4—31no—
574C4—31no—
575C4—51no—
576C4—51no—
577C4—151no—
578C4—151no—
579C4C4×D5×A411yescharacteristic
580C4C22×D5×A411yescharacteristic
581C3—41noSylow
582C2—21no—
583C2—31no—
584C2—31no—
585C2—52no—
586C2—61no—
587C2—101no—
588C2—152no—
589C2—301no—
590C2C2×C4×D5×A411yescharacteristic
subgroupG/H
center, FrattiniC4C22×D5×A4
commutator, socleC23×C5C22×C3×C4
FittingC22×C5×M16C2×C3
prime radicalC22×D5×A4C4
cosocleC22×C4×C5C23×C3
hypercenterM16D5×A4
hypocenterC22×C5C2×C3×M16
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C5×A4×M16C2semidirect
3. A4×#681C2semidirect
4. A4×#676C2semidirect
5. C8×D5×A4C2semidirect
6. C22×D5×M16C3semidirect
15. C5×C8×A4C22semidirect
16. A4×#168C22semidirect
19. C22×C5×M16C2×C3semidirect
20. C22×#681C2×C3semidirect
27. C22×#676C2×C3semidirect
28. C22×C8×D5C2×C3semidirect
45. A4×M16D5direct (N × H)
65. C22×C5×C8C22×C3semidirect
69. C22×#168C22×C3semidirect
80. D5×M16A4direct (N × H)
94. D5×A4M16direct (N × H)
112. C8×A4C2×D5semidirect
168. C5×M16C2×A4semidirect
174. #681C2×A4semidirect
181. #676C2×A4semidirect
186. C8×D5C2×A4semidirect
196. C22×M16C3×D5semidirect
202. C5×A4C2×M16semidirect
244. C22×D5C3×M16semidirect
285. C5×C8C22×A4semidirect
287. #168C22×A4semidirect
329. C22×C8C2×C3×D5semidirect
354. C22×C5C2×C3×M16semidirect
445. M16D5×A4direct (N × H)
460. A4D5×M16direct (N × H)
473. D5A4×M16direct (N × H)
541. C8C2×D5×A4semidirect
546. C5C2×A4×M16semidirect
571. C22C3×D5×M16semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C5×A4×M162
A4×#6812
A4×#6762
C8×D5×A42
C22×D5×M163
C3×D5×M164
C2×A4×M165