Finite Group Databasebeta

← D5×#1479 #12065659

Subgroups — D5×#1479 #12065659

Order 1280.

1282 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
1C2×C4×Q8×D5C211yesmaximal, characteristic
2D5×#431C211yesmaximal, characteristic
3D5×#431C211yesmaximal, characteristic
4C5×#1479C211yesmaximal, characteristic, complemented
5#10602414C211yesmaximal, characteristic, complemented
6#10601560C211yesmaximal, characteristic, complemented
7#10601559C211yesmaximal, characteristic, complemented
8#10599024C214yesmaximal, complemented
9D5×Q8⋊C8C214yesmaximal, complemented
10C22×Q8×D5C411yescharacteristic
11C2×C4×C5×Q8C2211yescharacteristic
12C2×Q8×Dic5C411yescharacteristic
13C4×Q8×D5—21no—
14C4×Q8×D5—21no—
15C4×Q8×D5—21no—
16C4×Q8×D5—21no—
17C4×Q8×D5C412yes—
18C4×Q8×D5C412yes—
19C4×Q8×D5C2212yes—
20C4×Q8×D5C2212yes—
21C2×D5×C4⋊C4—21no—
22C2×D5×C4⋊C4C411yescharacteristic
23C2×#4033—21no—
24C2×#4033C411yescharacteristic
25C2×C42×D5—21no—
26C2×C42×D5C2211yescharacteristic
27C2×C4×Dic10—21no—
28C2×C4×Dic10C2211yescharacteristic
29C5×#431C2211yescharacteristic
30C5×#431C2211yescharacteristic
31#65214C2211yescharacteristic
32#65214C2211yescharacteristic
33#65122—21no—
34#65122C2212yes—
35D5×C4⋊C8—21no—
36D5×C4⋊C8C2212yes—
37D5×C22⋊C8—21no—
38D5×C22⋊C8—21no—
39#65007—21no—
40#65007—21no—
41#64974—21no—
42#64974C2212yes—
43C4×C8×D5—21no—
44C4×C8×D5C2212yes—
45C5×Q8⋊C8C2214yescomplemented
46Q8⋊#168C2214yescomplemented
47#64704C2214yescomplemented
48#64676C2214yescomplemented
49C2×#1479—51nomaximal, Sylow
50C22×C5×Q8C2×C411yescharacteristic
51C2×Q8×D5—21no—
52C2×Q8×D5—21no—
53C2×Q8×D5—24no—
54C2×Q8×D5C818yescomplemented
55C2×Q8×D5C2×C412yes—
56C2×Q8×D5C2×C412yes—
57C22×C4×D5—21no—
58C22×C4×D5—21no—
59C22×C4×D5C2×C411yescharacteristic
60C22×C4×D5D411yescharacteristic
61C22×C4×D5D411yescharacteristic
62C22×Dic10—21no—
63C22×Dic10C2×C411yescharacteristic
64C4×C5×Q8—21no—
65C4×C5×Q8—21no—
66C4×C5×Q8C2×C412yes—
67C4×C5×Q8C2312yes—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4C2×C411yescharacteristic
70C2×C42×C5—21no—
71C2×C42×C5C2311yescharacteristic
72Q8×Dic5—21no—
73Q8×Dic5—21no—
74Q8×Dic5C2×C412yes—
75Q8×Dic5C2×C412yes—
76C2×C4⋊Dic5—21no—
77C2×C4⋊Dic5C2×C411yescharacteristic
78C2×#683—21no—
79C2×#683—21no—
80C2×#683—21no—
81C2×C4×Dic5—21no—
82C2×C4×Dic5—21no—
83C2×C4×Dic5—21no—
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5D411yescharacteristic
86C2×C4×Dic5D411yescharacteristic
87C2×C8×D5—22no—
88C2×C8×D5—22no—
89D5×C4⋊C4—22no—
90D5×C4⋊C4—22no—
91D5×C4⋊C4—21no—
92D5×C4⋊C4—21no—
93D5×C4⋊C4—22no—
94D5×C4⋊C4—22no—
95D5×C4⋊C4C2×C412yes—
96D5×C4⋊C4C2×C412yes—
97#4033—22no—
98#4033—22no—
99#4033—21no—
100#4033—21no—
101#4033—22no—
102#4033—22no—
103#4033C2×C412yes—
104#4033C2×C412yes—
105C42×D5—22no—
106C42×D5—22no—
107C42×D5—22no—
108C42×D5—22no—
109C42×D5C2×C411yescharacteristic
110C42×D5C2×C411yescharacteristic
111C42×D5D411yescharacteristic
112C42×D5D411yescharacteristic
113C42×D5D411yescharacteristic
114C42×D5D411yescharacteristic
115C42×D5C2311yescharacteristic
116C42×D5C2311yescharacteristic
117C4×Dic10—21no—
118C4×Dic10—21no—
119C4×Dic10—22no—
120C4×Dic10—22no—
121C4×Dic10—22no—
122C4×Dic10—22no—
123C4×Dic10C2×C412yes—
124C4×Dic10C2312yes—
125C5×C4⋊C8—21no—
126C5×C4⋊C8C2312yes—
127C5×C22⋊C8—21no—
128C5×C22⋊C8—21no—
129C4×C5×C8—21no—
130C4×C5×C8C2312yes—
131C22⋊#168—21no—
132C22⋊#168—21no—
133#3952—22no—
134#3952—22no—
135#3946—22no—
136#3946—22no—
137C8×Dic5—22no—
138C8×Dic5—22no—
139C4⋊#168—21no—
140C4⋊#168C2312yes—
141C4×#168—21no—
142C4×#168C2312yes—
143C22×C4×Q8—51no—
144C2×#431—51no—
145C2×#431—51no—
146#1479—51no—
147#1479—51no—
148#1479—54no—
149#1479—51no—
150#1479D511yescharacteristic, direct product factor
151C2×Q8⋊C8—54no—
152C23×D5C22⋊C411yescharacteristic
153C2×C5×Q8—21no—
154C2×C5×Q8—22no—
155C2×C5×Q8C2×C814yescomplemented
156C2×C5×Q8C22×C412yes—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5C22×C411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5C22⋊C411yescharacteristic
165C22×Dic5C22⋊C411yescharacteristic
166C22×Dic5C22⋊C411yescharacteristic
167Q8×D5—28no—
168Q8×D5—28no—
169Q8×D5—24no—
170Q8×D5—24no—
171Q8×D5C2×C818yes—
172Q8×D5C2×C818yescomplemented
173C2×C4×D5—28no—
174C2×C4×D5—22no—
175C2×C4×D5—22no—
176C2×C4×D5—24no—
177C2×C4×D5—22no—
178C2×C4×D5—22no—
179C2×C4×D5—42no—
180C2×C4×D5—44no—
181C2×C4×D5C22⋊C411yescharacteristic
182C2×C4×D5C22⋊C411yescharacteristic
183C2×C4×D5C22⋊C411yescharacteristic
184C2×C4×D5C22⋊C411yescharacteristic
185C2×C4×D5C22⋊C411yescharacteristic
186C2×C4×D5C22⋊C411yescharacteristic
187C2×C4×D5C2×C814yes—
188C2×C4×D5M1614yes—
189C2×C4×D5C22×C411yescharacteristic
190C2×C4×D5C22×C411yescharacteristic
191C2×C4×D5C2×D411yescharacteristic
192C2×C4×D5C2×D411yescharacteristic
193C2×C4×D5C2×D411yescharacteristic
194C2×C4×D5C2×D411yescharacteristic
195C2×Dic10—21no—
196C2×Dic10—22no—
197C2×Dic10—28no—
198C2×Dic10—22no—
199C2×Dic10—22no—
200C2×Dic10C2×C814yescomplemented
201C2×Dic10C22×C412yes—
202C2×C5×C8—22no—
203C2×C5×C8—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4C22×C412yes—
208C42×C5—22no—
209C42×C5—22no—
210C42×C5C22×C411yescharacteristic
211C42×C5C2×D411yescharacteristic
212C42×C5C2×D411yescharacteristic
213C42×C5C2411yescharacteristic
214C4⋊Dic5—21no—
215C4⋊Dic5—22no—
216C4⋊Dic5—22no—
217C4⋊Dic5C22×C412yes—
218#683—22no—
219#683—22no—
220#683—22no—
221#683—22no—
222#683—22no—
223#683—22no—
224C4×Dic5—22no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C4×Dic5—22no—
228C4×Dic5—22no—
229C4×Dic5—22no—
230C4×Dic5C22⋊C411yescharacteristic
231C4×Dic5C22⋊C411yescharacteristic
232C4×Dic5C22⋊C411yescharacteristic
233C4×Dic5C22⋊C411yescharacteristic
234C4×Dic5C22⋊C411yescharacteristic
235C4×Dic5C22⋊C411yescharacteristic
236C4×Dic5C22×C411yescharacteristic
237C4×Dic5C22×C411yescharacteristic
238C4×Dic5C2×D411yescharacteristic
239C4×Dic5C2×D411yescharacteristic
240C4×Dic5C2×D411yescharacteristic
241C4×Dic5C2×D411yescharacteristic
242C2×#168—22no—
243C2×#168—22no—
244C8×D5—44no—
245C8×D5—44no—
246C23×Q8—51no—
247C2×C4×Q8—51no—
248C2×C4×Q8—52no—
249C2×C4×Q8—52no—
250C2×C4×Q8—52no—
251C2×C4×Q8—52no—
252C2×C4×Q8—51no—
253C2×C4×Q8—51no—
254C2×C4×Q8—101no—
255C2×C4×Q8—101no—
256C2×C4×Q8—101no—
257C2×C4×Q8—101no—
258C2×C4×Q8—101no—
259C2×C4×Q8—101no—
260C2×C4×Q8C2×D511yescharacteristic
261C22×C4⋊C4—51no—
262C22×C4⋊C4—101no—
263C22×C42—51no—
264C22×C42—101no—
265#431—51no—
266#431—52no—
267#431—51no—
268#431—52no—
269#431—101no—
270#431—101no—
271#431—101no—
272#431—101no—
273#431C2×D511yescharacteristic
274#431C2×D511yescharacteristic
275C2×C4⋊C8—52no—
276C2×C4⋊C8—101no—
277C2×C22⋊C8—101no—
278C2×C22⋊C8—101no—
279C2×C4×C8—52no—
280C2×C4×C8—101no—
281Q8⋊C8—54no—
282Q8⋊C8—54no—
283Q8⋊C8—54no—
284Q8⋊C8C2×D514yescomplemented
285C23×C5C2×C22⋊C411yescharacteristic
286C22×D5—22no—
287C22×D5—22no—
288C22×D5C22⋊C814yes—
289C22×D5C2×C22⋊C411yescharacteristic
290C22×D5C2×C22⋊C411yescharacteristic
291C5×Q8—22no—
292C5×Q8—24no—
293C5×Q8C22×C814yes—
294C2×C4×C5—22no—
295C2×C4×C5—24no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—41no—
299C2×C4×C5—42no—
300C2×C4×C5C2×C22⋊C411yescharacteristic
301C2×C4×C5C2×C22⋊C411yescharacteristic
302C2×C4×C5C2×C22⋊C411yescharacteristic
303C2×C4×C5C22×C812yes—
304C2×C4×C5C2×M1612yes—
305C2×C4×C5C23×C411yescharacteristic
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5C22×D411yescharacteristic
308C2×Dic5—22no—
309C2×Dic5—24no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—41no—
313C2×Dic5—42no—
314C2×Dic5C22⋊C814yes—
315C2×Dic5C2×C22⋊C411yescharacteristic
316C2×Dic5C2×C22⋊C411yescharacteristic
317C2×Dic5C2×C22⋊C411yescharacteristic
318C2×Dic5C2×C22⋊C411yescharacteristic
319C2×Dic5C2×C22⋊C411yescharacteristic
320C2×Dic5C2×C22⋊C411yescharacteristic
321C4×D5—28no—
322C4×D5—28no—
323C4×D5—22no—
324C4×D5—22no—
325C4×D5—22no—
326C4×D5—22no—
327C4×D5—22no—
328C4×D5—41no—
329C4×D5—41no—
330C4×D5—44no—
331C4×D5—44no—
332C4×D5C22⋊C814yes—
333C4×D5C22⋊C814yes—
334C4×D5C22×C812yes—
335C4×D5C22×C812yes—
336C4×D5C2×M1612yes—
337C4×D5C2×M1612yes—
338C4×D5#13714yes—
339Dic10—22no—
340Dic10—24no—
341Dic10—28no—
342Dic10—28no—
343Dic10C22×C814yes—
344C5×C8—42no—
345C5×C8—42no—
346#168—42no—
347#168—42no—
348C22×Q8—58no—
349C22×Q8—52no—
350C22×Q8—52no—
351C22×Q8—51no—
352C22×Q8—101no—
353C22×Q8—101no—
354C22×Q8—101no—
355C22×Q8—104no—
356C22×Q8C4×D511yescharacteristic
357C23×C4—51no—
358C23×C4—51no—
359C23×C4—51no—
360C23×C4—101no—
361C23×C4—101no—
362C22×C8—102no—
363C22×C8—102no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—52no—
367C4×Q8—52no—
368C4×Q8—52no—
369C4×Q8—52no—
370C4×Q8—52no—
371C4×Q8—52no—
372C4×Q8—102no—
373C4×Q8—102no—
374C4×Q8—102no—
375C4×Q8—102no—
376C4×Q8—102no—
377C4×Q8—102no—
378C4×Q8—102no—
379C4×Q8—102no—
380C4×Q8—101no—
381C4×Q8—101no—
382C4×Q8—101no—
383C4×Q8—101no—
384C4×Q8—101no—
385C4×Q8—101no—
386C4×Q8C4×D512yes—
387C4×Q8C22×D512yes—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—51no—
390C2×C4⋊C4—52no—
391C2×C4⋊C4—52no—
392C2×C4⋊C4—101no—
393C2×C4⋊C4—101no—
394C2×C4⋊C4—102no—
395C2×C4⋊C4—102no—
396C2×C4⋊C4—102no—
397C2×C4⋊C4—102no—
398C2×C4⋊C4—101no—
399C2×C4⋊C4—101no—
400C2×C4⋊C4—101no—
401C2×C4⋊C4—101no—
402C2×C4⋊C4C4×D511yescharacteristic
403C2×C42—21no—
404C2×C42—51no—
405C2×C42—51no—
406C2×C42—51no—
407C2×C42—51no—
408C2×C42—51no—
409C2×C42—51no—
410C2×C42—51no—
411C2×C42—51no—
412C2×C42—51no—
413C2×C42—51no—
414C2×C42—51no—
415C2×C42—102no—
416C2×C42—102no—
417C2×C42—102no—
418C2×C42—102no—
419C2×C42—101no—
420C2×C42—101no—
421C2×C42—101no—
422C2×C42C22×D511yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—52no—
425C4⋊C8—102no—
426C4⋊C8—102no—
427C4⋊C8—101no—
428C4⋊C8C22×D512yes—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—102no—
432C22⋊C8—102no—
433C22⋊C8—101no—
434C22⋊C8—101no—
435C4×C8—21no—
436C4×C8—52no—
437C4×C8—102no—
438C4×C8—102no—
439C4×C8—101no—
440C4×C8C22×D512yes—
441C22×C5—21no—
442C22×C5—21no—
443C22×C5C2×C22⋊C812yes—
444C22×C5C22×C22⋊C411yescharacteristic
445C2×D5—21no—
446C2×D5—21no—
447C2×D5—28no—
448C2×D5C2×C22⋊C812yes—
449C2×D5C2×C22⋊C812yes—
450C2×D5#41912yes—
451C2×D5#42112yes—
452C4×C5—24no—
453C4×C5—21no—
454C4×C5—21no—
455C4×C5—21no—
456C4×C5—42no—
457C4×C5C2×C22⋊C812yes—
458C4×C5C23×C811yescharacteristic
459C4×C5C22×M1611yescharacteristic
460C4×C5C2×#13712yes—
461Dic5—24no—
462Dic5—21no—
463Dic5—21no—
464Dic5—21no—
465Dic5—42no—
466Dic5C2×C22⋊C812yes—
467Dic5C2×C22⋊C812yes—
468Dic5#41912yes—
469C24—51no—
470C2×Q8—21no—
471C2×Q8—22no—
472C2×Q8—58no—
473C2×Q8—58no—
474C2×Q8—52no—
475C2×Q8—54no—
476C2×Q8—102no—
477C2×Q8—102no—
478C2×Q8—108no—
479C2×Q8—104no—
480C2×Q8—104no—
481C2×Q8—108no—
482C2×Q8—108no—
483C2×Q8—101no—
484C2×Q8—102no—
485C2×Q8C8×D514yescomplemented
486C2×Q8C2×C4×D512yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—51no—
490C22×C4—51no—
491C22×C4—51no—
492C22×C4—51no—
493C22×C4—51no—
494C22×C4—51no—
495C22×C4—54no—
496C22×C4—54no—
497C22×C4—51no—
498C22×C4—51no—
499C22×C4—51no—
500C22×C4—51no—
501C22×C4—51no—
502C22×C4—51no—
503C22×C4—51no—
504C22×C4—51no—
505C22×C4—51no—
506C22×C4—104no—
507C22×C4—102no—
508C22×C4—102no—
509C22×C4—108no—
510C22×C4—102no—
511C22×C4—102no—
512C22×C4—101no—
513C22×C4—101no—
514C22×C4—202no—
515C22×C4—204no—
516C22×C4C2×C4×D511yescharacteristic
517C22×C4D4×D511yescharacteristic
518C22×C4D4×D511yescharacteristic
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—102no—
522C2×C8—102no—
523C2×C8—204no—
524C2×C8—204no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—52no—
529C4⋊C4—102no—
530C4⋊C4—102no—
531C4⋊C4—102no—
532C4⋊C4—102no—
533C4⋊C4—102no—
534C4⋊C4—102no—
535C4⋊C4—102no—
536C4⋊C4—101no—
537C4⋊C4—102no—
538C4⋊C4C2×C4×D512yes—
539C42—22no—
540C42—22no—
541C42—51no—
542C42—51no—
543C42—51no—
544C42—51no—
545C42—51no—
546C42—51no—
547C42—51no—
548C42—51no—
549C42—51no—
550C42—51no—
551C42—51no—
552C42—51no—
553C42—102no—
554C42—102no—
555C42—102no—
556C42—102no—
557C42—102no—
558C42—102no—
559C42C2×C4×D511yescharacteristic
560C42D4×D511yescharacteristic
561C42D4×D511yescharacteristic
562C42C23×D511yescharacteristic
563C2×C5—22no—
564C2×C5C22×C22⋊C811yescharacteristic
565C2×C5C2×#41911yescharacteristic
566C2×C5C2×#42111yescharacteristic
567D5—22no—
568D5#147914yesdirect product factor
569C23—51no—
570C23—51no—
571C23—54no—
572C23—102no—
573C23—102no—
574C23D5×C22⋊C411yescharacteristic
575Q8—22no—
576Q8—24no—
577Q8—54no—
578Q8—108no—
579Q8—108no—
580Q8—102no—
581Q8—104no—
582Q8C2×C8×D514yes—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—51no—
590C2×C4—51no—
591C2×C4—51no—
592C2×C4—54no—
593C2×C4—52no—
594C2×C4—52no—
595C2×C4—52no—
596C2×C4—52no—
597C2×C4—54no—
598C2×C4—54no—
599C2×C4—54no—
600C2×C4—51no—
601C2×C4—51no—
602C2×C4—51no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—102no—
607C2×C4—108no—
608C2×C4—108no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—104no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—201no—
615C2×C4—201no—
616C2×C4—204no—
617C2×C4—204no—
618C2×C4—201no—
619C2×C4—202no—
620C2×C4D5×C22⋊C411yescharacteristic
621C2×C4D5×C22⋊C411yescharacteristic
622C2×C4D5×C22⋊C411yescharacteristic
623C2×C4C2×C8×D512yes—
624C2×C4D5×M1612yes—
625C2×C4C22×C4×D511yescharacteristic
626C2×C4C2×D4×D511yescharacteristic
627C2×C4C2×D4×D511yescharacteristic
628C8—42no—
629C8—42no—
630C8—202no—
631C8—202no—
632C5C2×#147911yescharacteristic, complemented, Sylow
633C22—21no—
634C22—21no—
635C22—52no—
636C22—52no—
637C22—52no—
638C22—52no—
639C22—108no—
640C22—101no—
641C22—101no—
642C22D5×C22⋊C812yes—
643C22C2×D5×C22⋊C411yescharacteristic
644C4—21no—
645C4—21no—
646C4—24no—
647C4—21no—
648C4—42no—
649C4—52no—
650C4—52no—
651C4—52no—
652C4—101no—
653C4—101no—
654C4—104no—
655C4—101no—
656C4—202no—
657C4D5×C22⋊C812yes—
658C4C22×C8×D511yescharacteristic
659C4C2×D5×M1611yescharacteristic
660C4D5×#13712yes—
661C2—22no—
662C2—54no—
663C2—102no—
664C2C2×D5×C22⋊C811yescharacteristic
665C2D5×#41911yescharacteristic
666C2D5×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC4×C5C23×C8
FrattiniC42C23×D5
FittingC5×#1479C2
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC42×C5C24
hypercenter#1479D5
hypocenterC5C2×#1479
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. C5×#1479C2semidirect
5. #10602414C2semidirect
6. #10601560C2semidirect
7. #10601559C2semidirect
8. #10599024C2semidirect
9. D5×Q8⋊C8C2semidirect
45. C5×Q8⋊C8C22semidirect
46. Q8⋊#168C22semidirect
47. #64704C22semidirect
48. #64676C22semidirect
54. C2×Q8×D5C8semidirect
150. #1479D5direct (N × H)
155. C2×C5×Q8C2×C8semidirect
172. Q8×D5C2×C8semidirect
200. C2×Dic10C2×C8semidirect
284. Q8⋊C8C2×D5semidirect
485. C2×Q8C8×D5semidirect
568. D5#1479direct (N × H)
632. C5C2×#1479semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D52
D5×#4312
C5×#14792
#106024142
#106015602
#106015592
#105990242
D5×Q8⋊C82
C2×#14795