Finite Group Databasebeta

← D5×#1549 #12067643

Subgroups — D5×#1549 #12067643

Order 1280.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2D5×#431C211yesmaximal, characteristic
3D5×#423C211yesmaximal, characteristic
4C5×#1549C211yesmaximal, characteristic, complemented
5#10602568C211yesmaximal, characteristic, complemented
6#10601573C211yesmaximal, characteristic, complemented
7#10601301C211yesmaximal, characteristic, complemented
8#10599215C214yesmaximal, complemented
9D5×#332C214yesmaximal, complemented
10C22×Q8×D5—21no—
11C2×C5×C4⋊Q8C2211yescharacteristic
12C2×#4090—21no—
13C2×D5×M16—21no—
14D5×C4⋊Q8—21no—
15D5×C4⋊Q8—21no—
16D5×C4⋊Q8—21no—
17D5×C4⋊Q8—21no—
18D5×C4⋊Q8C412yes—
19D5×C4⋊Q8C412yes—
20D5×C4⋊Q8C2212yes—
21D5×C4⋊Q8C2212yes—
22C2×D5×C4⋊C4—21no—
23C2×D5×C4⋊C4C412yes—
24C2×#4034—21no—
25C2×#4034C412yes—
26C2×C42×D5C2211yescharacteristic
27C2×#4015C2211yescharacteristic
28C5×#431C2211yescharacteristic
29C5×#423C2211yescharacteristic
30#65407—21no—
31#65214C2211yescharacteristic
32#65213C2211yescharacteristic
33#65126—21no—
34#65126C2212yes—
35#65122C2212yes—
36D5×C4⋊C8—21no—
37D5×C4⋊C8C2212yes—
38D5×C4⋊C8C2212yes—
39D5×C22⋊C8—21no—
40#65007—21no—
41#64974—21no—
42C4×C8×D5—21no—
43C5×#332C2214yescomplemented
44#64767C2214yescomplemented
45#64706C2214yescomplemented
46#64702C2214yescomplemented
47C2×#1549—51nomaximal, Sylow
48C22×C5×Q8—21no—
49C2×Q8×D5—22no—
50C2×Q8×D5—22no—
51C2×Q8×D5—22no—
52C2×Q8×D5—22no—
53C2×Q8×D5—48no—
54C22×C4×D5—22no—
55C22×C4×D5C2×C411yescharacteristic
56C22×C4×D5D411yescharacteristic
57C22×C4×D5D411yescharacteristic
58C22×Dic10—21no—
59C22×Dic10—22no—
60C2×C5×M16—21no—
61C5×C4⋊Q8—21no—
62C5×C4⋊Q8—21no—
63C5×C4⋊Q8C2×C412yes—
64C5×C4⋊Q8C2312yes—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4C2×C412yes—
67C2×C42×C5C2311yescharacteristic
68#4090—22no—
69#4090—22no—
70#4090—22no—
71#4090—22no—
72C2×C4⋊Dic5—21no—
73C2×C4⋊Dic5C2×C412yes—
74C2×#683—22no—
75C2×#683—22no—
76C2×C4×Dic5C2×C411yescharacteristic
77C2×C4×Dic5D411yescharacteristic
78C2×C4×Dic5D411yescharacteristic
79C2×#681—21no—
80D5×M16—44no—
81C2×#676—22no—
82C2×C8×D5—22no—
83C2×C8×D5—22no—
84D5×C4⋊C4—22no—
85D5×C4⋊C4—22no—
86D5×C4⋊C4—22no—
87D5×C4⋊C4—22no—
88D5×C4⋊C4—22no—
89D5×C4⋊C4—22no—
90D5×C4⋊C4C2×C414yes—
91D5×C4⋊C4C2×C414yes—
92#4034—22no—
93#4034—22no—
94#4034—22no—
95#4034—22no—
96#4034—22no—
97#4034—22no—
98#4034C2×C414yes—
99#4034C2×C414yes—
100C42×D5C2×C411yescharacteristic
101C42×D5C2×C411yescharacteristic
102C42×D5D411yescharacteristic
103C42×D5D411yescharacteristic
104C42×D5D411yescharacteristic
105C42×D5D411yescharacteristic
106C42×D5C2311yescharacteristic
107C42×D5C2311yescharacteristic
108#4015—21no—
109#4015—21no—
110#4015C2×C412yes—
111#4015C2312yes—
112C5×C4⋊C8—21no—
113C5×C4⋊C8C2312yes—
114C5×C4⋊C8C2312yes—
115C5×C22⋊C8—21no—
116C4×C5×C8—21no—
117C22⋊#168—21no—
118#3952—22no—
119#3946—22no—
120#3946—22no—
121#3946—22no—
122C8×Dic5—22no—
123C4⋊#168—21no—
124C4⋊#168C2312yes—
125C4⋊#168C2312yes—
126C4×#168—21no—
127C22×C4⋊Q8—51no—
128C2×#431—51no—
129C2×#423—51no—
130#1549—51no—
131#1549—51no—
132#1549—54no—
133#1549—51no—
134#1549D511yescharacteristic, direct product factor
135C2×#332—54no—
136C23×D5C22⋊C411yescharacteristic
137C2×C5×Q8—22no—
138C2×C5×Q8—22no—
139C2×C5×Q8—44no—
140C22×C4×C5—22no—
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×Dic5—22no—
145C22×Dic5C22⋊C411yescharacteristic
146C22×Dic5C22⋊C411yescharacteristic
147C22×Dic5C22⋊C411yescharacteristic
148Q8×D5—48no—
149Q8×D5—48no—
150Q8×D5—48no—
151Q8×D5—48no—
152C2×C4×D5—24no—
153C2×C4×D5—24no—
154C2×C4×D5—24no—
155C2×C4×D5—24no—
156C2×C4×D5—48no—
157C2×C4×D5C22⋊C411yescharacteristic
158C2×C4×D5C22⋊C411yescharacteristic
159C2×C4×D5C22⋊C411yescharacteristic
160C2×C4×D5C22⋊C411yescharacteristic
161C2×C4×D5C22⋊C411yescharacteristic
162C2×C4×D5C22⋊C411yescharacteristic
163C2×C4×D5SD1614yes—
164C2×C4×D5Q1614yes—
165C2×C4×D5C22×C411yescharacteristic
166C2×C4×D5C22×C411yescharacteristic
167C2×C4×D5C2×D411yescharacteristic
168C2×C4×D5C2×D411yescharacteristic
169C2×C4×D5C2×D411yescharacteristic
170C2×C4×D5C2×D411yescharacteristic
171C2×Dic10—22no—
172C2×Dic10—22no—
173C2×Dic10—24no—
174C2×Dic10—24no—
175C2×Dic10—48no—
176C2×Dic10—44no—
177C5×M16—42no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4C22×C414yes—
184C42×C5C22×C411yescharacteristic
185C42×C5C2×D411yescharacteristic
186C42×C5C2×D411yescharacteristic
187C42×C5C2411yescharacteristic
188C4⋊Dic5—22no—
189C4⋊Dic5—22no—
190C4⋊Dic5—22no—
191C4⋊Dic5C22×C414yes—
192#683—24no—
193#683—24no—
194#683—24no—
195#683—24no—
196C4×Dic5C22⋊C411yescharacteristic
197C4×Dic5C22⋊C411yescharacteristic
198C4×Dic5C22⋊C411yescharacteristic
199C4×Dic5C22⋊C411yescharacteristic
200C4×Dic5C22⋊C411yescharacteristic
201C4×Dic5C22⋊C411yescharacteristic
202C4×Dic5C22×C411yescharacteristic
203C4×Dic5C22×C411yescharacteristic
204C4×Dic5C2×D411yescharacteristic
205C4×Dic5C2×D411yescharacteristic
206C4×Dic5C2×D411yescharacteristic
207C4×Dic5C2×D411yescharacteristic
208#681—42no—
209C2×#168—22no—
210C2×#168—22no—
211#676—44no—
212C8×D5—44no—
213C8×D5—44no—
214C23×Q8—101no—
215C22×M16—101no—
216C2×C4⋊Q8—52no—
217C2×C4⋊Q8—52no—
218C2×C4⋊Q8—52no—
219C2×C4⋊Q8—52no—
220C2×C4⋊Q8—52no—
221C2×C4⋊Q8—51no—
222C2×C4⋊Q8—101no—
223C2×C4⋊Q8—101no—
224C2×C4⋊Q8—101no—
225C2×C4⋊Q8—101no—
226C2×C4⋊Q8—101no—
227C2×C4⋊Q8—101no—
228C2×C4⋊Q8C2×D511yescharacteristic
229C22×C4⋊C4—52no—
230C22×C4⋊C4—101no—
231C22×C42—51no—
232#431—51no—
233#431—52no—
234#431—101no—
235#431—101no—
236#431C2×D511yescharacteristic
237#423—51no—
238#423—52no—
239#423—101no—
240#423—101no—
241#423C2×D511yescharacteristic
242C2×C4⋊C8—52no—
243C2×C4⋊C8—52no—
244C2×C4⋊C8—101no—
245C2×C22⋊C8—101no—
246C2×C4×C8—101no—
247#332—54no—
248#332—54no—
249#332—54no—
250#332C2×D514yescomplemented
251C23×C5C2×C22⋊C411yescharacteristic
252C22×D5—22no—
253C22×D5—22no—
254C22×D5#10314yes—
255C22×D5C2×C22⋊C411yescharacteristic
256C22×D5C2×C22⋊C411yescharacteristic
257C5×Q8—44no—
258C5×Q8—44no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—24no—
262C2×C4×C5—44no—
263C2×C4×C5C2×C22⋊C411yescharacteristic
264C2×C4×C5C2×C22⋊C411yescharacteristic
265C2×C4×C5C2×C22⋊C411yescharacteristic
266C2×C4×C5C2×SD1612yes—
267C2×C4×C5C2×Q1612yes—
268C2×C4×C5C23×C411yescharacteristic
269C2×C4×C5C22×D411yescharacteristic
270C2×C4×C5C22×D411yescharacteristic
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—24no—
274C2×Dic5—44no—
275C2×Dic5#10314yes—
276C2×Dic5C2×C22⋊C411yescharacteristic
277C2×Dic5C2×C22⋊C411yescharacteristic
278C2×Dic5C2×C22⋊C411yescharacteristic
279C2×Dic5C2×C22⋊C411yescharacteristic
280C2×Dic5C2×C22⋊C411yescharacteristic
281C2×Dic5C2×C22⋊C411yescharacteristic
282C4×D5—22no—
283C4×D5—22no—
284C4×D5—22no—
285C4×D5—22no—
286C4×D5—22no—
287C4×D5—22no—
288C4×D5—48no—
289C4×D5—48no—
290C4×D5#10114yes—
291C4×D5#10314yes—
292C4×D5#10314yes—
293C4×D5C2×SD1612yes—
294C4×D5C2×SD1612yes—
295C4×D5C2×Q1612yes—
296C4×D5C2×Q1612yes—
297C4×D5AGL(1,ℤ/8)14yes—
298Dic10—48no—
299Dic10—44no—
300Dic10—44no—
301Dic10—48no—
302C5×C8—42no—
303C5×C8—42no—
304#168—42no—
305#168—42no—
306C22×Q8—21no—
307C22×Q8—102no—
308C22×Q8—102no—
309C22×Q8—102no—
310C22×Q8—102no—
311C22×Q8—102no—
312C22×Q8—101no—
313C22×Q8—208no—
314C23×C4—51no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—102no—
318C2×M16—21no—
319C2×M16—102no—
320C2×M16—101no—
321C2×M16—204no—
322C22×C8—102no—
323C22×C8—102no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—54no—
327C4⋊Q8—54no—
328C4⋊Q8—52no—
329C4⋊Q8—52no—
330C4⋊Q8—102no—
331C4⋊Q8—102no—
332C4⋊Q8—102no—
333C4⋊Q8—102no—
334C4⋊Q8—102no—
335C4⋊Q8—102no—
336C4⋊Q8—102no—
337C4⋊Q8—102no—
338C4⋊Q8—102no—
339C4⋊Q8—102no—
340C4⋊Q8—101no—
341C4⋊Q8—101no—
342C4⋊Q8C4×D512yes—
343C4⋊Q8C22×D512yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—52no—
346C2×C4⋊C4—54no—
347C2×C4⋊C4—54no—
348C2×C4⋊C4—102no—
349C2×C4⋊C4—102no—
350C2×C4⋊C4—102no—
351C2×C4⋊C4—102no—
352C2×C4⋊C4—102no—
353C2×C4⋊C4—102no—
354C2×C4⋊C4—102no—
355C2×C4⋊C4—102no—
356C2×C4⋊C4—101no—
357C2×C4⋊C4C4×D512yes—
358C2×C42—51no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42C22×D511yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—52no—
372C4⋊C8—52no—
373C4⋊C8—102no—
374C4⋊C8—102no—
375C4⋊C8—102no—
376C4⋊C8—101no—
377C4⋊C8C22×D512yes—
378C4⋊C8C22×D512yes—
379C22⋊C8—21no—
380C22⋊C8—102no—
381C22⋊C8—101no—
382C4×C8—21no—
383C4×C8—102no—
384C4×C8—101no—
385C22×C5—21no—
386C22×C5—21no—
387C22×C5C2×#10312yes—
388C22×C5C22×C22⋊C411yescharacteristic
389C2×D5—21no—
390C2×D5—21no—
391C2×D5—28no—
392C2×D5C2×#10112yes—
393C2×D5C2×#10312yes—
394C2×D5C2×#10312yes—
395C2×D5#41812yes—
396C4×C5—21no—
397C4×C5—21no—
398C4×C5—44no—
399C4×C5C2×#10112yes—
400C4×C5C2×#10312yes—
401C4×C5C22×SD1611yescharacteristic
402C4×C5C22×Q1611yescharacteristic
403C4×C5C2×AGL(1,ℤ/8)12yes—
404Dic5—21no—
405Dic5—21no—
406Dic5—44no—
407Dic5C2×#10112yes—
408Dic5C2×#10312yes—
409Dic5C2×#10312yes—
410Dic5#41812yes—
411C24—51no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—44no—
415C2×Q8—104no—
416C2×Q8—104no—
417C2×Q8—102no—
418C2×Q8—102no—
419C2×Q8—204no—
420C2×Q8—208no—
421C2×Q8—208no—
422C2×Q8—208no—
423C2×Q8—208no—
424C2×Q8—208no—
425C22×C4—22no—
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—54no—
434C22×C4—54no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—51no—
438C22×C4—51no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—104no—
444C22×C4—104no—
445C22×C4—104no—
446C22×C4—104no—
447C22×C4—102no—
448C22×C4—208no—
449C22×C4C2×C4×D511yescharacteristic
450C22×C4D4×D511yescharacteristic
451C22×C4D4×D511yescharacteristic
452M16—42no—
453M16—204no—
454M16—202no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—102no—
458C2×C8—102no—
459C2×C8—204no—
460C2×C8—204no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—54no—
465C4⋊C4—104no—
466C4⋊C4—104no—
467C4⋊C4—104no—
468C4⋊C4—104no—
469C4⋊C4—102no—
470C4⋊C4—102no—
471C4⋊C4—102no—
472C4⋊C4C2×C4×D514yes—
473C42—51no—
474C42—51no—
475C42—51no—
476C42—51no—
477C42—51no—
478C42—51no—
479C42—51no—
480C42—51no—
481C42—51no—
482C42—51no—
483C42—51no—
484C42—51no—
485C42C2×C4×D511yescharacteristic
486C42D4×D511yescharacteristic
487C42D4×D511yescharacteristic
488C42C23×D511yescharacteristic
489C2×C5—22no—
490C2×C5C22×#10111yescharacteristic
491C2×C5C22×#10311yescharacteristic
492C2×C5C2×#41811yescharacteristic
493D5—22no—
494D5#154914yesdirect product factor
495C23—51no—
496C23—51no—
497C23—54no—
498C23—102no—
499C23—102no—
500C23D5×C22⋊C411yescharacteristic
501Q8—44no—
502Q8—44no—
503Q8—204no—
504Q8—208no—
505Q8—208no—
506Q8—204no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—44no—
511C2×C4—51no—
512C2×C4—51no—
513C2×C4—51no—
514C2×C4—51no—
515C2×C4—54no—
516C2×C4—54no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—54no—
522C2×C4—54no—
523C2×C4—54no—
524C2×C4—51no—
525C2×C4—51no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—104no—
535C2×C4—208no—
536C2×C4—208no—
537C2×C4—204no—
538C2×C4D5×C22⋊C411yescharacteristic
539C2×C4D5×C22⋊C411yescharacteristic
540C2×C4D5×C22⋊C411yescharacteristic
541C2×C4D5×SD1612yes—
542C2×C4D5×Q1612yes—
543C2×C4C22×C4×D511yescharacteristic
544C2×C4C2×D4×D511yescharacteristic
545C2×C4C2×D4×D511yescharacteristic
546C8—42no—
547C8—42no—
548C8—202no—
549C8—202no—
550C5C2×#154911yescharacteristic, complemented, Sylow
551C22—21no—
552C22—21no—
553C22—52no—
554C22—52no—
555C22—52no—
556C22—52no—
557C22—108no—
558C22—101no—
559C22—101no—
560C22D5×#10312yes—
561C22C2×D5×C22⋊C411yescharacteristic
562C4—21no—
563C4—21no—
564C4—44no—
565C4—52no—
566C4—52no—
567C4—52no—
568C4—52no—
569C4—101no—
570C4—101no—
571C4—204no—
572C4D5×#10112yes—
573C4D5×#10312yes—
574C4C2×D5×SD1611yescharacteristic
575C4C2×D5×Q1611yescharacteristic
576C4D5×AGL(1,ℤ/8)12yes—
577C2—22no—
578C2—54no—
579C2—102no—
580C2C2×D5×#10111yescharacteristic
581C2C2×D5×#10311yescharacteristic
582C2D5×#41811yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1549C2
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC42×C5C24
hypercenter#1549D5
hypocenterC5C2×#1549
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. C5×#1549C2semidirect
5. #10602568C2semidirect
6. #10601573C2semidirect
7. #10601301C2semidirect
8. #10599215C2semidirect
9. D5×#332C2semidirect
43. C5×#332C22semidirect
44. #64767C22semidirect
45. #64706C22semidirect
46. #64702C22semidirect
134. #1549D5direct (N × H)
250. #332C2×D5semidirect
494. D5#1549direct (N × H)
550. C5C2×#1549semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
D5×#4312
D5×#4232
C5×#15492
#106025682
#106015732
#106013012
#105992152
D5×#3322
C2×#15495