Finite Group Databasebeta

← C2×#10599132 #12066613

Subgroups — C2×#10599132 #12066613

Order 1280.

1522 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
1C2×D5×C22⋊Q8C211yesmaximal, characteristic
2C2×D5×C22⋊C8C211yesmaximal, characteristic
3C2×#64956C211yesmaximal, characteristic
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×#64758C211yesmaximal, characteristic, complemented
6C2×#64687C211yesmaximal, characteristic, complemented
7C2×#64672C211yesmaximal, characteristic, complemented
8#10599132C218yesmaximal, direct product factor
9C22×Q8×D5C411yescharacteristic, complemented
10C23×C4×D5C2211yescharacteristic
11C2×C5×C22⋊Q8C2211yescharacteristic
12C2×#4092C411yescharacteristic, complemented
13C22×#685—21no—
14C2×#4070C2211yescharacteristic
15C22×#683—21no—
16C22×C8×D5—21no—
17D5×C22⋊Q8—22no—
18D5×C22⋊Q8—22no—
19D5×C22⋊Q8C414yescomplemented
20D5×C22⋊Q8C2214yes—
21C2×#4043C411yescharacteristic, complemented
22C2×#4042—21no—
23C2×D5×C4⋊C4—21no—
24C2×D5×C4⋊C4C411yescharacteristic, complemented
25C2×D5×C22⋊C4—21no—
26C2×#4024—21no—
27C2×C5×C22⋊C8C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C2×#3963C2211yescharacteristic
30C2×C22⋊#168C2211yescharacteristic
31C2×#3952—21no—
32D5×C22⋊C8—22no—
33D5×C22⋊C8C2214yes—
34#64956—22no—
35#64956C2214yes—
36C5×#328C2214yescomplemented
37#64758C2214yescomplemented
38#64687C2214yescomplemented
39#64672C2214yescomplemented
40C2×#1520—51nomaximal, Sylow
41C24×D5D411yescharacteristic
42C22×C5×Q8C2×C411yescharacteristic
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—21no—
51C22×C4×D5—21no—
52C22×C4×D5—44no—
53C22×C4×D5C2×C411yescharacteristic
54C22×C4×D5C2×C411yescharacteristic
55C22×C4×D5C2×C412yes—
56C22×C4×D5D411yescharacteristic
57C22×C4×D5D412yes—
58C22×C4×D5D411yescharacteristic
59C22×C4×D5D412yes—
60C22×C4×D5C2312yes—
61C22×Dic10—21no—
62C22×Dic10C2×C411yescharacteristic
63C22×C5×C8—21no—
64C5×C22⋊Q8—21no—
65C5×C22⋊Q8—21no—
66C5×C22⋊Q8C2×C412yes—
67C5×C22⋊Q8C2312yes—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4C2×C411yescharacteristic
70C2×C5×C22⋊C4—21no—
71C2×C22⋊Dic5—21no—
72#4092—22no—
73#4092C2×C414yescomplemented
74C2×#685—21no—
75C2×#685—21no—
76C2×#685—24no—
77C2×#685—44no—
78C2×C4⋊Dic5—21no—
79C2×C4⋊Dic5C2×C411yescharacteristic
80#4070—21no—
81#4070—21no—
82#4070C2×C412yes—
83#4070C2312yes—
84C2×#683—21no—
85C2×#683—21no—
86C2×#683—21no—
87C2×#683—24no—
88C2×#683—44no—
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#3963C2312yes—
110C22⋊#168—21no—
111C22⋊#168C2312yes—
112#3952—24no—
113C22×C22⋊Q8—51no—
114C22×C22⋊C8—51no—
115C2×#380—51no—
116#1520—58no—
117C2×#328—51no—
118C2×#328—51no—
119C2×#328—51no—
120C2×#328D511yescharacteristic, complemented
121C24×C5C2×D411yescharacteristic
122C23×D5—42no—
123C23×D5—42no—
124C23×D5C22⋊C411yescharacteristic
125C23×D5C22⋊C411yescharacteristic
126C23×D5C22⋊C412yes—
127C23×D5SD1614yes—
128C23×D5Q1614yes—
129C23×D5C2×D412yes—
130C2×C5×Q8—21no—
131C2×C5×Q8—42no—
132C2×C5×Q8C22×C412yes—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—42no—
137C22×C4×C5—42no—
138C22×C4×C5—42no—
139C22×C4×C5—42no—
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2411yescharacteristic
146C22×Dic5—24no—
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5—22no—
150C22×Dic5—42no—
151C22×Dic5—42no—
152C22×Dic5—42no—
153C22×Dic5C22⋊C412yes—
154C22×Dic5C22⋊C411yescharacteristic
155C22×Dic5C22⋊C411yescharacteristic
156C22×Dic5C2×D412yes—
157Q8×D5—48no—
158Q8×D5—48no—
159C2×C4×D5—24no—
160C2×C4×D5—24no—
161C2×C4×D5—24no—
162C2×C4×D5—24no—
163C2×C4×D5—44no—
164C2×C4×D5—44no—
165C2×C4×D5—44no—
166C2×C4×D5—44no—
167C2×C4×D5—42no—
168C2×C4×D5—42no—
169C2×C4×D5—44no—
170C2×C4×D5—44no—
171C2×C4×D5C22⋊C412yes—
172C2×C4×D5C22⋊C412yes—
173C2×C4×D5C22⋊C412yes—
174C2×C4×D5C22⋊C412yes—
175C2×C4×D5C22×C412yes—
176C2×C4×D5C22×C412yes—
177C2×C4×D5C2×D412yes—
178C2×C4×D5C2×D412yes—
179C2×Dic10—21no—
180C2×Dic10—24no—
181C2×Dic10—44no—
182C2×Dic10—42no—
183C2×Dic10C22×C412yes—
184C2×C5×C8—22no—
185C2×C5×C8—42no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4C22×C412yes—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C22⋊Dic5—22no—
193C22⋊Dic5—22no—
194#685—24no—
195#685—24no—
196#685—48no—
197C4⋊Dic5—21no—
198C4⋊Dic5—24no—
199C4⋊Dic5C22×C412yes—
200#683—22no—
201#683—22no—
202#683—24no—
203#683—24no—
204#683—48no—
205C2×#168—22no—
206C2×#168—42no—
207C8×D5—48no—
208C23×Q8—51no—
209C24×C4—51no—
210C23×C8—101no—
211C2×C22⋊Q8—51no—
212C2×C22⋊Q8—51no—
213C2×C22⋊Q8—54no—
214C2×C22⋊Q8—54no—
215C2×C22⋊Q8—51no—
216C2×C22⋊Q8—101no—
217C2×C22⋊Q8—101no—
218C2×C22⋊Q8—102no—
219C2×C22⋊Q8—102no—
220C2×C22⋊Q8C2×D511yescharacteristic
221C22×C4⋊C4—51no—
222C22×C4⋊C4—101no—
223C22×C4⋊C4—101no—
224C22×C22⋊C4—101no—
225C22×C22⋊C4—101no—
226C2×C22⋊C8—51no—
227C2×C22⋊C8—54no—
228C2×C22⋊C8—102no—
229C2×C22⋊C8—101no—
230C2×C22⋊C8C2×D511yescharacteristic
231#380—54no—
232#380—102no—
233C2×#95—51no—
234C2×#95C2×D511yescharacteristic
235#328—54no—
236#328—54no—
237#328—54no—
238#328C2×D514yescomplemented
239C23×C5—22no—
240C23×C5—22no—
241C23×C5C2×C22⋊C411yescharacteristic
242C23×C5C2×C22⋊C411yescharacteristic
243C23×C5C2×SD1612yes—
244C23×C5C2×Q1612yes—
245C23×C5C22×D411yescharacteristic
246C22×D5—22no—
247C22×D5—22no—
248C22×D5—22no—
249C22×D5—22no—
250C22×D5—42no—
251C22×D5—42no—
252C22×D5—42no—
253C22×D5—48no—
254C22×D5—48no—
255C22×D5—42no—
256C22×D5#10314yes—
257C22×D5#10314yes—
258C22×D5#10318yes—
259C22×D5C2×C22⋊C412yes—
260C22×D5C2×C22⋊C412yes—
261C22×D5C2×SD1614yes—
262C22×D5C2×Q1614yes—
263C5×Q8—42no—
264C5×Q8—42no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—84no—
279C2×C4×C5C2×C22⋊C411yescharacteristic
280C2×C4×C5C2×C22⋊C411yescharacteristic
281C2×C4×C5C23×C411yescharacteristic
282C2×C4×C5C22×D411yescharacteristic
283C2×Dic5—22no—
284C2×Dic5—24no—
285C2×Dic5—24no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—84no—
294C2×Dic5#9914yes—
295C2×Dic5C2×C22⋊C412yes—
296C2×Dic5C2×C22⋊C412yes—
297C4×D5—24no—
298C4×D5—24no—
299C4×D5—24no—
300C4×D5—24no—
301C4×D5—42no—
302C4×D5—42no—
303C4×D5—42no—
304C4×D5—42no—
305C4×D5—48no—
306C4×D5—48no—
307Dic10—42no—
308Dic10—48no—
309Dic10—42no—
310C5×C8—42no—
311#168—42no—
312C25—51no—
313C22×Q8—54no—
314C22×Q8—51no—
315C22×Q8—101no—
316C22×Q8—102no—
317C22×Q8—204no—
318C22×Q8C4×D511yescharacteristic
319C23×C4—21no—
320C23×C4—51no—
321C23×C4—51no—
322C23×C4—51no—
323C23×C4—52no—
324C23×C4—51no—
325C23×C4—51no—
326C23×C4—52no—
327C23×C4—52no—
328C23×C4—52no—
329C23×C4—101no—
330C23×C4—101no—
331C23×C4—101no—
332C23×C4—204no—
333C23×C4C22×D511yescharacteristic
334C22×C8—21no—
335C22×C8—104no—
336C22×C8—101no—
337C22×C8—204no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—54no—
341C22⋊Q8—52no—
342C22⋊Q8—52no—
343C22⋊Q8—54no—
344C22⋊Q8—104no—
345C22⋊Q8—104no—
346C22⋊Q8—104no—
347C22⋊Q8—104no—
348C22⋊Q8—102no—
349C22⋊Q8—102no—
350C22⋊Q8—101no—
351C22⋊Q8—101no—
352C22⋊Q8C4×D512yes—
353C22⋊Q8C22×D512yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—54no—
357C2×C4⋊C4—102no—
358C2×C4⋊C4—104no—
359C2×C4⋊C4—104no—
360C2×C4⋊C4—101no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4—104no—
365C2×C4⋊C4—204no—
366C2×C4⋊C4C4×D511yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—104no—
369C2×C22⋊C4—104no—
370C2×C22⋊C4—101no—
371C2×C22⋊C4—101no—
372C2×C22⋊C4—101no—
373C2×C22⋊C4—104no—
374C2×C22⋊C4—204no—
375C22⋊C8—21no—
376C22⋊C8—52no—
377C22⋊C8—104no—
378C22⋊C8—101no—
379C22⋊C8C22×D512yes—
380#95—21no—
381#95—52no—
382#95—101no—
383#95C22×D512yes—
384C22×C5—21no—
385C22×C5—21no—
386C22×C5—21no—
387C22×C5—21no—
388C22×C5—24no—
389C22×C5—24no—
390C22×C5C2×#9912yes—
391C22×C5C2×#10312yes—
392C22×C5C2×#10312yes—
393C22×C5#42112yes—
394C22×C5C22×C22⋊C411yescharacteristic
395C22×C5C22×SD1611yescharacteristic
396C22×C5C22×Q1611yescharacteristic
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—28no—
402C2×D5—28no—
403C2×D5—48no—
404C2×D5—44no—
405C2×D5—44no—
406C2×D5C2×#10314yes—
407C2×D5C2×#10314yes—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5—21no—
412C4×C5—42no—
413C4×C5—42no—
414C4×C5—82no—
415Dic5—22no—
416Dic5—42no—
417Dic5—42no—
418Dic5—82no—
419Dic5C2×#9914yes—
420C24—51no—
421C24—51no—
422C24—52no—
423C24—52no—
424C24—54no—
425C24—54no—
426C24—202no—
427C24—202no—
428C24D4×D511yescharacteristic
429C2×Q8—21no—
430C2×Q8—42no—
431C2×Q8—52no—
432C2×Q8—104no—
433C2×Q8—101no—
434C2×Q8—202no—
435C2×Q8—204no—
436C2×Q8—208no—
437C2×Q8—208no—
438C2×Q8C2×C4×D512yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—51no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—51no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—52no—
453C22×C4—52no—
454C22×C4—52no—
455C22×C4—52no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—104no—
459C22×C4—104no—
460C22×C4—104no—
461C22×C4—104no—
462C22×C4—104no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—102no—
466C22×C4—202no—
467C22×C4—202no—
468C22×C4—204no—
469C22×C4—204no—
470C22×C4—204no—
471C22×C4—204no—
472C22×C4—204no—
473C22×C4—204no—
474C22×C4—202no—
475C22×C4—202no—
476C22×C4—202no—
477C22×C4C2×C4×D511yescharacteristic
478C22×C4C2×C4×D511yescharacteristic
479C22×C4D4×D511yescharacteristic
480C22×C4D4×D511yescharacteristic
481C22×C4D4×D511yescharacteristic
482C22×C4C23×D511yescharacteristic
483C2×C8—22no—
484C2×C8—42no—
485C2×C8—102no—
486C2×C8—208no—
487C2×C8—202no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—52no—
492C4⋊C4—104no—
493C4⋊C4—104no—
494C4⋊C4—104no—
495C4⋊C4—102no—
496C4⋊C4—101no—
497C4⋊C4—102no—
498C4⋊C4—208no—
499C4⋊C4C2×C4×D512yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—104no—
503C22⋊C4—104no—
504C22⋊C4—102no—
505C22⋊C4—102no—
506C22⋊C4—208no—
507C2×C5—21no—
508C2×C5—21no—
509C2×C5—22no—
510C2×C5#152014yescomplemented
511C2×C5C22×#9911yescharacteristic
512C2×C5C22×#10311yescharacteristic
513C2×C5C2×#42111yescharacteristic
514D5—24no—
515D5—24no—
516C23—22no—
517C23—22no—
518C23—52no—
519C23—52no—
520C23—54no—
521C23—54no—
522C23—54no—
523C23—54no—
524C23—58no—
525C23—102no—
526C23—102no—
527C23—102no—
528C23—102no—
529C23—202no—
530C23—202no—
531C23—202no—
532C23—202no—
533C23—208no—
534C23—208no—
535C23D5×C22⋊C411yescharacteristic
536C23D5×C22⋊C411yescharacteristic
537C23D5×SD1612yes—
538C23D5×Q1612yes—
539C23C2×D4×D511yescharacteristic
540Q8—42no—
541Q8—42no—
542Q8—202no—
543Q8—202no—
544Q8—208no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—54no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—84no—
562C2×C4—104no—
563C2×C4—104no—
564C2×C4—104no—
565C2×C4—104no—
566C2×C4—104no—
567C2×C4—104no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—202no—
572C2×C4—202no—
573C2×C4—202no—
574C2×C4—202no—
575C2×C4—208no—
576C2×C4—208no—
577C2×C4—202no—
578C2×C4—202no—
579C2×C4—202no—
580C2×C4—202no—
581C2×C4—202no—
582C2×C4—404no—
583C2×C4D5×C22⋊C411yescharacteristic
584C2×C4D5×C22⋊C411yescharacteristic
585C2×C4C22×C4×D511yescharacteristic
586C2×C4C2×D4×D511yescharacteristic
587C8—42no—
588C8—202no—
589C5C2×#152011yescharacteristic, complemented, Sylow
590C22—21no—
591C22—21no—
592C22—24no—
593C22—24no—
594C22—21no—
595C22—21no—
596C22—54no—
597C22—54no—
598C22—102no—
599C22—102no—
600C22—108no—
601C22—108no—
602C22—102no—
603C22—102no—
604C22—204no—
605C22—204no—
606C22—208no—
607C22D5×#9912yes—
608C22D5×#10312yes—
609C22D5×#10312yes—
610C22#6511012yes—
611C22C2×D5×C22⋊C411yescharacteristic
612C22C2×D5×SD1611yescharacteristic
613C22C2×D5×Q1611yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—42no—
620C4—54no—
621C4—82no—
622C4—102no—
623C4—202no—
624C4—202no—
625C4—402no—
626C2—21no—
627C2—21no—
628C2—22no—
629C2—104no—
630C2—104no—
631C2#1059913214yesdirect product factor
632C2C2×D5×#9911yescharacteristic
633C2C2×D5×#10311yescharacteristic
634C2C2×#6511011yescharacteristic
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
hypocenterC5C2×#1520
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. #10599132C2direct (N × H)
9. C22×Q8×D5C4semidirect
12. C2×#4092C4semidirect
19. D5×C22⋊Q8C4semidirect
21. C2×#4043C4semidirect
24. C2×D5×C4⋊C4C4semidirect
36. C5×#328C22semidirect
37. #64758C22semidirect
38. #64687C22semidirect
39. #64672C22semidirect
49. C2×Q8×D5C2×C4semidirect
73. #4092C2×C4semidirect
93. #4043C2×C4semidirect
99. D5×C4⋊C4C2×C4semidirect
120. C2×#328D5semidirect
238. #328C2×D5semidirect
510. C2×C5#1520semidirect
589. C5C2×#1520semidirect
631. C2#10599132direct (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×#649562
C2×C5×#3282
C2×#647582
C2×#646872
C2×#646722
#105991322
C2×#15205