Finite Group Databasebeta

← C2×D5×#328 #12066380

Subgroups — C2×D5×#328 #12066380

Order 1280.

1846 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊Q8C211yesmaximal, characteristic
2C2×D5×C22⋊C8C211yesmaximal, characteristic
3C2×D5×#95C211yesmaximal, characteristic
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×#64758C211yesmaximal, characteristic, complemented
6C2×#64687C211yesmaximal, characteristic, complemented
7C2×#64672C211yesmaximal, characteristic, complemented
8D5×#328C218yesmaximal, direct product factor
9C22×Q8×D5C411yescharacteristic, complemented
10C23×C4×D5—21no—
11C23×C4×D5C2211yescharacteristic
12C2×C5×C22⋊Q8C2211yescharacteristic
13C2×#4092C411yescharacteristic, complemented
14C2×#4070C2211yescharacteristic
15C22×C8×D5—21no—
16D5×C22⋊Q8—22no—
17D5×C22⋊Q8—22no—
18D5×C22⋊Q8C414yescomplemented
19D5×C22⋊Q8C2214yes—
20C2×#4043C411yescharacteristic, complemented
21C2×#4042—21no—
22C2×D5×C4⋊C4—21no—
23C2×D5×C4⋊C4C411yescharacteristic, complemented
24C2×D5×C22⋊C4—21no—
25C2×#4024—21no—
26C2×C5×C22⋊C8C2211yescharacteristic
27C2×C5×#95C2211yescharacteristic
28C2×#3963—21no—
29C2×#3963C2211yescharacteristic
30C2×C22⋊#168C2211yescharacteristic
31C2×#3952—21no—
32D5×C22⋊C8—22no—
33D5×C22⋊C8C2214yes—
34D5×#95—22no—
35D5×#95C2214yes—
36C5×#328C2214yescomplemented
37#64758C2214yescomplemented
38#64687C2214yescomplemented
39#64672C2214yescomplemented
40C22×#328—51nomaximal, Sylow
41C24×D5D411yescharacteristic
42C22×C5×Q8C2×C411yescharacteristic, complemented
43C23×C4×C5—21no—
44C23×C4×C5C2311yescharacteristic
45C23×Dic5—21no—
46C23×Dic5D411yescharacteristic
47C2×Q8×D5—22no—
48C2×Q8×D5—44no—
49C2×Q8×D5C2×C414yescomplemented
50C22×C4×D5—28no—
51C22×C4×D5—21no—
52C22×C4×D5—21no—
53C22×C4×D5—24no—
54C22×C4×D5—44no—
55C22×C4×D5—44no—
56C22×C4×D5—44no—
57C22×C4×D5C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2×C412yes—
60C22×C4×D5D411yescharacteristic
61C22×C4×D5D412yes—
62C22×C4×D5D411yescharacteristic
63C22×C4×D5D412yes—
64C22×C4×D5C2312yes—
65C22×Dic10—21no—
66C22×Dic10C2×C411yescharacteristic, complemented
67C22×C5×C8—21no—
68C5×C22⋊Q8—21no—
69C5×C22⋊Q8—21no—
70C5×C22⋊Q8C2×C412yescomplemented
71C5×C22⋊Q8C2312yes—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
74C2×C5×C22⋊C4—21no—
75C2×C22⋊Dic5—21no—
76#4092—22no—
77#4092C2×C414yescomplemented
78C2×#685—21no—
79C2×#685—21no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5C2×C411yescharacteristic, complemented
82#4070—21no—
83#4070—21no—
84#4070C2×C412yescomplemented
85#4070C2312yes—
86C2×#683—21no—
87C2×#683—21no—
88C2×#683—21no—
89C22×#168—21no—
90C2×C8×D5—24no—
91C2×C8×D5—44no—
92#4043—22no—
93#4043C2×C414yescomplemented
94#4042—24no—
95#4042—24no—
96D5×C4⋊C4—24no—
97D5×C4⋊C4—22no—
98D5×C4⋊C4—24no—
99D5×C4⋊C4C2×C414yescomplemented
100D5×C22⋊C4—24no—
101D5×C22⋊C4—24no—
102#4024—24no—
103#4024—24no—
104C5×C22⋊C8—21no—
105C5×C22⋊C8C2312yes—
106C5×#95—21no—
107C5×#95C2312yes—
108#3963—21no—
109#3963—24no—
110#3963C2312yes—
111C22⋊#168—21no—
112C22⋊#168C2312yes—
113#3952—24no—
114C22×C22⋊Q8—51no—
115C22×C22⋊C8—51no—
116C22×#95—51no—
117C2×#328—51no—
118C2×#328—51no—
119C2×#328—58no—
120C2×#328—51no—
121C2×#328D511yescharacteristic, direct product factor
122C24×C5C2×D411yescharacteristic
123C23×D5—24no—
124C23×D5—24no—
125C23×D5C22⋊C412yes—
126C23×D5C22⋊C411yescharacteristic
127C23×D5C22⋊C411yescharacteristic
128C23×D5SD1614yes—
129C23×D5Q1614yes—
130C23×D5C2×D412yes—
131C2×C5×Q8—21no—
132C2×C5×Q8—42no—
133C2×C5×Q8C22×C412yescomplemented
134C22×C4×C5—24no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—42no—
139C22×C4×C5—42no—
140C22×C4×C5—42no—
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2411yescharacteristic
147C22×Dic5—24no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—22no—
151C22×Dic5—42no—
152C22×Dic5—42no—
153C22×Dic5—42no—
154C22×Dic5C22⋊C411yescharacteristic
155C22×Dic5C22⋊C411yescharacteristic
156C22×Dic5C22⋊C412yes—
157C22×Dic5C2×D412yes—
158Q8×D5—48no—
159Q8×D5—48no—
160C2×C4×D5—24no—
161C2×C4×D5—24no—
162C2×C4×D5—216no—
163C2×C4×D5—24no—
164C2×C4×D5—24no—
165C2×C4×D5—44no—
166C2×C4×D5—44no—
167C2×C4×D5—44no—
168C2×C4×D5—44no—
169C2×C4×D5—42no—
170C2×C4×D5—42no—
171C2×C4×D5—432no—
172C2×C4×D5—48no—
173C2×C4×D5—44no—
174C2×C4×D5—44no—
175C2×C4×D5—48no—
176C2×C4×D5C22⋊C412yes—
177C2×C4×D5C22⋊C412yes—
178C2×C4×D5C22⋊C412yes—
179C2×C4×D5C22⋊C412yes—
180C2×C4×D5C22×C412yes—
181C2×C4×D5C22×C412yes—
182C2×C4×D5C2×D412yes—
183C2×C4×D5C2×D412yes—
184C2×Dic10—21no—
185C2×Dic10—24no—
186C2×Dic10—44no—
187C2×Dic10—42no—
188C2×Dic10C22×C412yescomplemented
189C2×C5×C8—22no—
190C2×C5×C8—42no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4C22×C412yescomplemented
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C22⋊Dic5—22no—
198C22⋊Dic5—22no—
199#685—24no—
200#685—24no—
201C4⋊Dic5—21no—
202C4⋊Dic5—24no—
203C4⋊Dic5C22×C412yescomplemented
204#683—22no—
205#683—22no—
206#683—24no—
207#683—24no—
208C2×#168—22no—
209C2×#168—42no—
210C8×D5—48no—
211C23×Q8—51no—
212C24×C4—51no—
213C24×C4—101no—
214C23×C8—101no—
215C2×C22⋊Q8—51no—
216C2×C22⋊Q8—51no—
217C2×C22⋊Q8—54no—
218C2×C22⋊Q8—54no—
219C2×C22⋊Q8—51no—
220C2×C22⋊Q8—101no—
221C2×C22⋊Q8—101no—
222C2×C22⋊Q8—102no—
223C2×C22⋊Q8—102no—
224C2×C22⋊Q8C2×D511yescharacteristic
225C22×C4⋊C4—51no—
226C22×C4⋊C4—101no—
227C22×C22⋊C4—101no—
228C2×C22⋊C8—51no—
229C2×C22⋊C8—54no—
230C2×C22⋊C8—102no—
231C2×C22⋊C8—101no—
232C2×C22⋊C8C2×D511yescharacteristic
233C2×#95—51no—
234C2×#95—54no—
235C2×#95—102no—
236C2×#95—101no—
237C2×#95C2×D511yescharacteristic
238#328—54no—
239#328—54no—
240#328—54no—
241#328C2×D514yesdirect product factor
242C23×C5—22no—
243C23×C5—22no—
244C23×C5C2×C22⋊C411yescharacteristic
245C23×C5C2×C22⋊C411yescharacteristic
246C23×C5C2×SD1612yes—
247C23×C5C2×Q1612yes—
248C23×C5C22×D411yescharacteristic
249C22×D5—22no—
250C22×D5—22no—
251C22×D5—216no—
252C22×D5—216no—
253C22×D5—24no—
254C22×D5—24no—
255C22×D5—24no—
256C22×D5—24no—
257C22×D5#9914yes—
258C22×D5#10314yes—
259C22×D5#10318yes—
260C22×D5#10314yes—
261C22×D5#10414yes—
262C22×D5C2×C22⋊C412yes—
263C22×D5C2×C22⋊C412yes—
264C22×D5C2×SD1614yes—
265C22×D5C2×Q1614yes—
266C5×Q8—42no—
267C5×Q8—42no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—24no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—42no—
278C2×C4×C5—48no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5C2×C22⋊C411yescharacteristic
283C2×C4×C5C2×C22⋊C411yescharacteristic
284C2×C4×C5C23×C411yescharacteristic
285C2×C4×C5C22×D411yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—24no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—48no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5C2×C22⋊C412yes—
299C2×Dic5C2×C22⋊C412yes—
300C4×D5—24no—
301C4×D5—24no—
302C4×D5—24no—
303C4×D5—24no—
304C4×D5—42no—
305C4×D5—42no—
306C4×D5—42no—
307C4×D5—42no—
308C4×D5—432no—
309C4×D5—48no—
310C4×D5—48no—
311Dic10—48no—
312Dic10—42no—
313Dic10—42no—
314C5×C8—42no—
315#168—42no—
316C25—51no—
317C22×Q8—54no—
318C22×Q8—51no—
319C22×Q8—101no—
320C22×Q8—102no—
321C22×Q8—204no—
322C22×Q8C4×D511yescharacteristic, complemented
323C23×C4—21no—
324C23×C4—51no—
325C23×C4—51no—
326C23×C4—51no—
327C23×C4—51no—
328C23×C4—52no—
329C23×C4—52no—
330C23×C4—51no—
331C23×C4—52no—
332C23×C4—52no—
333C23×C4—101no—
334C23×C4—101no—
335C23×C4—104no—
336C23×C4—108no—
337C23×C4—101no—
338C23×C4—204no—
339C23×C4—204no—
340C23×C4—204no—
341C23×C4C22×D511yescharacteristic
342C22×C8—21no—
343C22×C8—104no—
344C22×C8—101no—
345C22×C8—204no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—54no—
349C22⋊Q8—52no—
350C22⋊Q8—52no—
351C22⋊Q8—54no—
352C22⋊Q8—104no—
353C22⋊Q8—104no—
354C22⋊Q8—104no—
355C22⋊Q8—104no—
356C22⋊Q8—102no—
357C22⋊Q8—102no—
358C22⋊Q8—101no—
359C22⋊Q8—101no—
360C22⋊Q8C4×D512yescomplemented
361C22⋊Q8C22×D512yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—54no—
365C2×C4⋊C4—102no—
366C2×C4⋊C4—104no—
367C2×C4⋊C4—104no—
368C2×C4⋊C4—101no—
369C2×C4⋊C4—101no—
370C2×C4⋊C4—101no—
371C2×C4⋊C4—101no—
372C2×C4⋊C4C4×D511yescharacteristic, complemented
373C2×C22⋊C4—21no—
374C2×C22⋊C4—104no—
375C2×C22⋊C4—104no—
376C2×C22⋊C4—101no—
377C2×C22⋊C4—101no—
378C2×C22⋊C4—101no—
379C22⋊C8—21no—
380C22⋊C8—52no—
381C22⋊C8—104no—
382C22⋊C8—101no—
383C22⋊C8C22×D512yes—
384#95—21no—
385#95—52no—
386#95—104no—
387#95—101no—
388#95C22×D512yes—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—21no—
393C22×C5—24no—
394C22×C5—24no—
395C22×C5C2×#9912yes—
396C22×C5C2×#10312yes—
397C22×C5C2×#10312yes—
398C22×C5C2×#10412yes—
399C22×C5C22×C22⋊C411yescharacteristic
400C22×C5C22×SD1611yescharacteristic
401C22×C5C22×Q1611yescharacteristic
402C2×D5—22no—
403C2×D5—22no—
404C2×D5—28no—
405C2×D5—28no—
406C2×D5—216no—
407C2×D5—28no—
408C2×D5#328116yesdirect product factor
409C2×D5C2×#9914yes—
410C2×D5C2×#10314yes—
411C2×D5C2×#10314yes—
412C2×D5C2×#10414yes—
413C4×C5—21no—
414C4×C5—21no—
415C4×C5—21no—
416C4×C5—21no—
417C4×C5—44no—
418C4×C5—42no—
419C4×C5—42no—
420Dic5—22no—
421Dic5—22no—
422Dic5—44no—
423Dic5—42no—
424Dic5—42no—
425C24—51no—
426C24—52no—
427C24—52no—
428C24—51no—
429C24—54no—
430C24—54no—
431C24—104no—
432C24—104no—
433C24D4×D511yescharacteristic
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8—52no—
437C2×Q8—104no—
438C2×Q8—101no—
439C2×Q8—202no—
440C2×Q8—204no—
441C2×Q8—208no—
442C2×Q8—208no—
443C2×Q8C2×C4×D512yescomplemented
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—52no—
454C22×C4—52no—
455C22×C4—52no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—52no—
459C22×C4—52no—
460C22×C4—52no—
461C22×C4—52no—
462C22×C4—52no—
463C22×C4—104no—
464C22×C4—104no—
465C22×C4—104no—
466C22×C4—104no—
467C22×C4—1016no—
468C22×C4—104no—
469C22×C4—102no—
470C22×C4—101no—
471C22×C4—101no—
472C22×C4—202no—
473C22×C4—202no—
474C22×C4—204no—
475C22×C4—204no—
476C22×C4—204no—
477C22×C4—204no—
478C22×C4—208no—
479C22×C4—204no—
480C22×C4—204no—
481C22×C4—208no—
482C22×C4—2032no—
483C22×C4—202no—
484C22×C4—202no—
485C22×C4—202no—
486C22×C4C2×C4×D511yescharacteristic
487C22×C4C2×C4×D511yescharacteristic
488C22×C4D4×D511yescharacteristic
489C22×C4D4×D511yescharacteristic
490C22×C4D4×D511yescharacteristic
491C22×C4C23×D511yescharacteristic
492C2×C8—22no—
493C2×C8—42no—
494C2×C8—102no—
495C2×C8—208no—
496C2×C8—202no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—52no—
501C4⋊C4—104no—
502C4⋊C4—104no—
503C4⋊C4—104no—
504C4⋊C4—102no—
505C4⋊C4—101no—
506C4⋊C4—102no—
507C4⋊C4C2×C4×D512yescomplemented
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—104no—
511C22⋊C4—104no—
512C22⋊C4—102no—
513C22⋊C4—102no—
514C2×C5—21no—
515C2×C5—21no—
516C2×C5—22no—
517C2×C5C2×#32814yescomplemented
518C2×C5C22×#9911yescharacteristic
519C2×C5C22×#10311yescharacteristic
520C2×C5C22×#10411yescharacteristic
521D5—24no—
522D5C2×#32818yesdirect product factor
523C23—22no—
524C23—22no—
525C23—54no—
526C23—52no—
527C23—54no—
528C23—54no—
529C23—52no—
530C23—54no—
531C23—54no—
532C23—58no—
533C23—54no—
534C23—104no—
535C23—104no—
536C23—1016no—
537C23—104no—
538C23—104no—
539C23—1016no—
540C23—102no—
541C23—102no—
542C23D5×C22⋊C411yescharacteristic
543C23D5×C22⋊C411yescharacteristic
544C23D5×SD1612yes—
545C23D5×Q1612yes—
546C23C2×D4×D511yescharacteristic
547Q8—42no—
548Q8—42no—
549Q8—202no—
550Q8—202no—
551Q8—208no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—48no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—52no—
567C2×C4—52no—
568C2×C4—104no—
569C2×C4—104no—
570C2×C4—104no—
571C2×C4—104no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—104no—
575C2×C4—102no—
576C2×C4—102no—
577C2×C4—202no—
578C2×C4—202no—
579C2×C4—202no—
580C2×C4—202no—
581C2×C4—208no—
582C2×C4—208no—
583C2×C4—2032no—
584C2×C4—202no—
585C2×C4—202no—
586C2×C4—208no—
587C2×C4—202no—
588C2×C4—202no—
589C2×C4—202no—
590C2×C4—202no—
591C2×C4D5×C22⋊C411yescharacteristic
592C2×C4D5×C22⋊C411yescharacteristic
593C2×C4C22×C4×D511yescharacteristic
594C2×C4C2×D4×D511yescharacteristic
595C8—42no—
596C8—202no—
597C5C22×#32811yescharacteristic, complemented, Sylow
598C22—21no—
599C22—21no—
600C22—24no—
601C22—24no—
602C22—21no—
603C22—21no—
604C22—54no—
605C22—54no—
606C22—516no—
607C22—54no—
608C22—54no—
609C22—108no—
610C22—108no—
611C22—1016no—
612C22—102no—
613C22—108no—
614C22—102no—
615C22D5×#9912yes—
616C22D5×#10312yes—
617C22D5×#10312yes—
618C22D5×#10412yes—
619C22C2×D5×C22⋊C411yescharacteristic
620C22C2×D5×SD1611yescharacteristic
621C22C2×D5×Q1611yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—44no—
627C4—42no—
628C4—42no—
629C4—102no—
630C4—102no—
631C4—204no—
632C4—202no—
633C4—202no—
634C2—21no—
635C2—21no—
636C2—22no—
637C2—58no—
638C2—104no—
639C2D5×#32814yesdirect product factor
640C2C2×D5×#9911yescharacteristic
641C2C2×D5×#10311yescharacteristic
642C2C2×D5×#10411yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#328C2
socleC23×C5C2×C22⋊C4
prime radicalC24×D5D4
cosocleC22×C4×C5C24
hypercenterC2×#328D5
hypocenterC5C22×#328
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. C2×C5×#328C2semidirect
5. C2×#64758C2semidirect
6. C2×#64687C2semidirect
7. C2×#64672C2semidirect
8. D5×#328C2direct (N × H)
9. C22×Q8×D5C4semidirect
13. C2×#4092C4semidirect
18. D5×C22⋊Q8C4semidirect
20. C2×#4043C4semidirect
23. C2×D5×C4⋊C4C4semidirect
36. C5×#328C22semidirect
37. #64758C22semidirect
38. #64687C22semidirect
39. #64672C22semidirect
42. C22×C5×Q8C2×C4semidirect
49. C2×Q8×D5C2×C4semidirect
66. C22×Dic10C2×C4semidirect
70. C5×C22⋊Q8C2×C4semidirect
73. C2×C5×C4⋊C4C2×C4semidirect
77. #4092C2×C4semidirect
81. C2×C4⋊Dic5C2×C4semidirect
84. #4070C2×C4semidirect
93. #4043C2×C4semidirect
99. D5×C4⋊C4C2×C4semidirect
121. C2×#328D5direct (N × H)
133. C2×C5×Q8C22×C4semidirect
188. C2×Dic10C22×C4semidirect
194. C5×C4⋊C4C22×C4semidirect
203. C4⋊Dic5C22×C4semidirect
241. #328C2×D5direct (N × H)
322. C22×Q8C4×D5semidirect
360. C22⋊Q8C4×D5semidirect
372. C2×C4⋊C4C4×D5semidirect
408. C2×D5#328direct (N × H)
443. C2×Q8C2×C4×D5semidirect
507. C4⋊C4C2×C4×D5semidirect
517. C2×C5C2×#328semidirect
522. D5C2×#328direct (N × H)
597. C5C22×#328semidirect
639. C2D5×#328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊Q82
C2×D5×C22⋊C82
C2×D5×#952
C2×C5×#3282
C2×#647582
C2×#646872
C2×#646722
D5×#3282
C22×#3285