Finite Group Databasebeta

← C4×#65094 #12106416

Subgroups — C4×#65094 #12106416

Order 1280.

976 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4092C211yesmaximal, characteristic
2C2×#65094C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic
4C4×C5×#103C211yesmaximal, characteristic, complemented
5C4×#3967C211yesmaximal, characteristic, complemented
6#10601061C211yesmaximal, characteristic
7#10601034C211yesmaximal, characteristic, complemented
8#10601016C211yesmaximal, characteristic, complemented
9C4×#3949C211yesmaximal, characteristic, complemented
10C4×#3952C211yesmaximal, characteristic
11C4×#3940C211yesmaximal, characteristic, complemented
12#10599668C211yesmaximal, characteristic
13#10599664C211yesmaximal, characteristic
14#10599611C211yesmaximal, characteristic, complemented
15#10599582C211yesmaximal, characteristic, complemented
16C2×C4×C5×Q8C2211yescharacteristic
17C2×#4092C2211yescharacteristic
18C2×D5×C4⋊C4C2211yescharacteristic
19C2×D5×C4⋊C4C2211yescharacteristic
20C2×C42×D5—21no—
21C2×C42×D5C2211yescharacteristic
22C2×C5×#103C2211yescharacteristic
23C2×C5×#103C2211yescharacteristic
24C2×C4×C5×C8C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26#65519C2211yescharacteristic
27C2×#3967C2211yescharacteristic
28C2×#3967C2211yescharacteristic
29C2×#3952C2211yescharacteristic
30C2×#3952C2211yescharacteristic
31C2×#3949C2211yescharacteristic
32C2×#3949C2211yescharacteristic
33#65278—21no—
34#65276C2211yescharacteristic
35#65267—21no—
36C4⋊C4×Dic5C2211yescharacteristic
37C4⋊C4×Dic5C2211yescharacteristic
38#65262C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40C2×#3940C2211yescharacteristic
41C4×#685—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44C4×#683—21no—
45C4×#683—21no—
46C2×C4×#168C2211yescharacteristic
47#65094C418yesdirect product factor
48D5×#95—21no—
49#64938—21no—
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64770C2211yescharacteristic
55#64770C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60C4×#483—51nomaximal, Sylow
61C22×C5×Q8C2311yescharacteristic
62C22×C4×D5—21no—
63C22×C4×D5—21no—
64C22×C4×D5D411yescharacteristic
65C22×C4×D5D411yescharacteristic
66C22×C4×D5C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C4×C5×Q8—22no—
70C4×C5×Q8—22no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C42×C5—21no—
76C2×C42×C5—21no—
77C2×C42×C5C2311yescharacteristic
78#4092—22no—
79#4092C2×C414yes—
80C2×#685—21no—
81C2×#685—21no—
82C2×C4⋊Dic5C2311yescharacteristic
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×#683—21no—
87C2×#683—21no—
88C2×#683—21no—
89C2×#683—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5D411yescharacteristic
95C2×C4×Dic5D411yescharacteristic
96C2×C4×Dic5C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99D5×C4⋊C4—22no—
100D5×C4⋊C4—22no—
101D5×C4⋊C4—22no—
102D5×C4⋊C4C2×C414yes—
103C42×D5—22no—
104C42×D5—22no—
105C42×D5—44no—
106C5×#103—22no—
107C5×#103C2×C414yescomplemented
108C4×C5×C8—22no—
109C5×#95—21no—
110#3967—22no—
111#3967C2×C414yescomplemented
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119#3963—21no—
120#3952—22no—
121#3952C2×C414yes—
122#3949—22no—
123#3949C2×C414yescomplemented
124#3940—22no—
125#3940C2×C414yescomplemented
126C4×#168—22no—
127C2×#483—51no—
128C4×C22⋊Q8—51no—
129C2×C4×C4⋊C4—51no—
130#1927—51no—
131#1927—51no—
132#1920—51no—
133#1920—51no—
134#1872—51no—
135#1853—51no—
136#1823—51no—
137C4×#106—51no—
138C4×#106—51no—
139C4×#103—51no—
140C4×#103D511yescharacteristic, complemented
141C4×C22⋊C8—51no—
142C23×D5C2×D411yescharacteristic
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8C22×C412yes—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2411yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5C2×D411yescharacteristic
161C22×Dic5C2×D411yescharacteristic
162C22×Dic5C2×D411yescharacteristic
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—21no—
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—24no—
170C2×C4×D5—24no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—41no—
174C2×C4×D5—42no—
175C2×C4×D5—42no—
176C2×C4×D5—42no—
177C2×C4×D5—42no—
178C2×C4×D5SD1614yes—
179C2×C4×D5C22×C412yes—
180C2×C4×D5#4112yes—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8C22×C412yes—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—42no—
192C5×C4⋊C4C22×C412yes—
193C5×C4⋊C4#4112yes—
194C42×C5—42no—
195C42×C5—42no—
196C42×C5#4112yes—
197C42×C5#4112yes—
198#685—24no—
199#685—42no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—21no—
205C4⋊Dic5C22×C412yes—
206C4⋊Dic5C22×C412yes—
207C4⋊Dic5#4112yes—
208#683—24no—
209#683—24no—
210#683—24no—
211#683—42no—
212C4×Dic5—22no—
213C4×Dic5—22no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—42no—
217C4×Dic5—42no—
218C4×Dic5—42no—
219C4×Dic5—42no—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—21no—
225C2×#168C22×C412yes—
226C2×C22⋊Q8—51no—
227C2×C4×Q8C2×D511yescharacteristic
228C22×C4⋊C4—51no—
229C22×C4⋊C4—51no—
230C22×C42—51no—
231C22×C42—101no—
232#483—58no—
233C2×#106—51no—
234C2×#106—51no—
235C2×#106—51no—
236C2×#106—51no—
237C2×#103—51no—
238C2×#103—51no—
239C2×#103C2×D511yescharacteristic
240C2×#103C2×D511yescharacteristic
241C2×C22⋊C8—51no—
242C2×C22⋊C8—51no—
243C2×C4×C8—51no—
244C2×C4×C8C2×D511yescharacteristic
245#391—51no—
246#389—51no—
247#387—101no—
248#385—101no—
249#380—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—51no—
252C4×C4⋊C4—51no—
253C4×C4⋊C4—51no—
254C4×C4⋊C4—101no—
255C4×C4⋊C4—101no—
256C4×C4⋊C4—101no—
257C4×C4⋊C4C2×D511yescharacteristic
258C4×C22⋊C4—101no—
259C2×#95—101no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264#340—51no—
265#340—51no—
266#340C2×D511yescharacteristic
267#340C2×D511yescharacteristic
268#336—51no—
269#336—51no—
270C23×C5C22×D411yescharacteristic
271C22×D5—21no—
272C22×D5—21no—
273C22×D5—21no—
274C22×D5—21no—
275C22×D5C4×D412yes—
276C22×D5C2×SD1612yes—
277C22×D5#13512yes—
278C5×Q8—22no—
279C5×Q8—22no—
280C5×Q8—41no—
281C5×Q8—41no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5#12312yes—
297C2×C4×C5#12312yes—
298C2×C4×C5C2×SD1612yes—
299C2×C4×C5#13712yes—
300C2×C4×C5C23×C411yescharacteristic
301C2×C4×C5C2×#4111yescharacteristic
302C2×C4×C5C2×#4111yescharacteristic
303C2×C4×C5C2×#4111yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—21no—
313C2×Dic5—22no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5C4×D412yes—
326C2×Dic5C2×SD1612yes—
327C4×D5—22no—
328C4×D5—22no—
329C4×D5—22no—
330C4×D5—22no—
331C4×D5—28no—
332C4×D5—44no—
333C4×D5—48no—
334C4×D5—48no—
335C5×C8—22no—
336C5×C8—41no—
337#168—22no—
338#168—41no—
339C22×Q8C22×D511yescharacteristic
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—101no—
344C23×C4—101no—
345C22×C8—51no—
346C22×C8—51no—
347C22×C8C22×D511yescharacteristic
348C22×C8C22×D511yescharacteristic
349C22⋊Q8—54no—
350C22⋊Q8—102no—
351C4×Q8—22no—
352C4×Q8—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—54no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4—102no—
360C2×C4⋊C4—102no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4—102no—
365C2×C4⋊C4—101no—
366C2×C4⋊C4C22×D511yescharacteristic
367C2×C4⋊C4C22×D511yescharacteristic
368C2×C4⋊C4C22×D511yescharacteristic
369C2×C22⋊C4—101no—
370C2×C22⋊C4—101no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—51no—
376C2×C42—102no—
377C2×C42—102no—
378C2×C42—101no—
379C2×C42—101no—
380C2×C42—101no—
381C2×C42—101no—
382C2×C42—204no—
383C2×C42C22×D511yescharacteristic
384#106—54no—
385#106—54no—
386#106—102no—
387#106—102no—
388#103—22no—
389#103—54no—
390#103—102no—
391#103C4×D514yescomplemented
392C22⋊C8—54no—
393C22⋊C8—102no—
394C4×C8—22no—
395C4×C8—102no—
396#95—21no—
397#95—101no—
398#95—101no—
399#95—101no—
400#95—101no—
401#95—101no—
402#95—101no—
403#95—101no—
404#95—101no—
405C22×C5C2×C4×D411yescharacteristic
406C22×C5C2×#12311yescharacteristic
407C22×C5#52511yescharacteristic
408C22×C5C22×SD1611yescharacteristic
409C22×C5C2×#13511yescharacteristic
410C22×C5C2×#13711yescharacteristic
411C22×C5#57511yescharacteristic
412C2×D5—22no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5C4×SD1614yes—
419C4×C5—22no—
420C4×C5—42no—
421C4×C5—42no—
422C4×C5—42no—
423C4×C5—81no—
424C4×C5#48314yescomplemented
425C4×C5C4×#4111yescharacteristic
426C4×C5C4×#4111yescharacteristic
427C4×C5#52911yescharacteristic
428C4×C5#52911yescharacteristic
429Dic5—22no—
430Dic5—22no—
431Dic5—41no—
432Dic5—42no—
433Dic5—42no—
434Dic5—42no—
435Dic5—81no—
436C24—51no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D512yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—52no—
450C22×C4—52no—
451C22×C4—54no—
452C22×C4—51no—
453C22×C4—104no—
454C22×C4—102no—
455C22×C4—104no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—101no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—102no—
466C22×C4—101no—
467C22×C4—201no—
468C22×C4—202no—
469C22×C4—202no—
470C22×C4—202no—
471C22×C4—202no—
472C22×C4D4×D511yescharacteristic
473C22×C4D4×D511yescharacteristic
474C22×C4C23×D511yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—52no—
481C2×C8—101no—
482C2×C8—101no—
483C2×C8—101no—
484C2×C8—101no—
485C2×C8—101no—
486C2×C8C2×C4×D512yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—52no—
493C4⋊C4—52no—
494C4⋊C4—52no—
495C4⋊C4—104no—
496C4⋊C4—104no—
497C4⋊C4—104no—
498C4⋊C4—101no—
499C4⋊C4—101no—
500C4⋊C4—101no—
501C4⋊C4—101no—
502C4⋊C4—101no—
503C4⋊C4—202no—
504C4⋊C4C2×C4×D512yes—
505C4⋊C4#70912yes—
506C22⋊C4—104no—
507C22⋊C4—202no—
508C42—42no—
509C42—42no—
510C42—101no—
511C42—101no—
512C42—102no—
513C42—102no—
514C42—202no—
515C42—202no—
516C42—202no—
517C42—202no—
518C42#70912yes—
519C42#71112yes—
520C2×C5C4×#12311yescharacteristic
521C2×C5C2×C4×SD1611yescharacteristic
522C2×C5C4×#13711yescharacteristic
523C2×C5C2×#48311yescharacteristic
524C2×C5#309111yescharacteristic
525C2×C5#310111yescharacteristic
526C2×C5#310811yescharacteristic
527D5—24no—
528C23—52no—
529C23—52no—
530C23—52no—
531C23—101no—
532C23—101no—
533C23—101no—
534C23—101no—
535C23C2×D4×D511yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—52no—
555C2×C4—52no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—108no—
563C2×C4—102no—
564C2×C4—102no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—204no—
572C2×C4—208no—
573C2×C4—208no—
574C2×C4—201no—
575C2×C4—201no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4#402912yes—
584C2×C4#402912yes—
585C2×C4D5×SD1612yes—
586C2×C4#406412yes—
587C2×C4C22×C4×D511yescharacteristic
588C2×C4C2×#70911yescharacteristic
589C2×C4C2×#70911yescharacteristic
590C2×C4C2×#71111yescharacteristic
591C2×C4D5×#4111yescharacteristic
592C2×C4D5×#4111yescharacteristic
593C8—22no—
594C8—41no—
595C8—102no—
596C8—201no—
597C5C4×#48311yescharacteristic, complemented, Sylow
598C22—54no—
599C22—102no—
600C22—102no—
601C22—102no—
602C22—102no—
603C22—102no—
604C22—102no—
605C22C2×#402911yescharacteristic
606C22C4×D4×D511yescharacteristic
607C22#6588111yescharacteristic
608C22C2×D5×SD1611yescharacteristic
609C22C2×#406411yescharacteristic
610C22D5×#13511yescharacteristic
611C22#6610211yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—81no—
617C4—102no—
618C4—102no—
619C4—201no—
620C4—202no—
621C4—202no—
622C4—202no—
623C4—401no—
624C4#6509414yesdirect product factor
625C4C4×#70911yescharacteristic
626C4#6586211yescharacteristic
627C4C4×#71111yescharacteristic
628C4#6589111yescharacteristic
629C2—104no—
630C2C4×#402911yescharacteristic
631C2C2×#6509411yescharacteristic
632C2#1061057311yescharacteristic
633C2C4×D5×SD1611yescharacteristic
634C2#1061138211yescharacteristic
635C2C4×#406411yescharacteristic
636C2#1061145411yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×#103C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenterC4×#103D5
hypocenterC5C4×#483
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. C4×C5×#103C2semidirect
5. C4×#3967C2semidirect
7. #10601034C2semidirect
8. #10601016C2semidirect
9. C4×#3949C2semidirect
11. C4×#3940C2semidirect
14. #10599611C2semidirect
15. #10599582C2semidirect
47. #65094C4direct (N × H)
107. C5×#103C2×C4semidirect
111. #3967C2×C4semidirect
123. #3949C2×C4semidirect
125. #3940C2×C4semidirect
140. C4×#103D5semidirect
391. #103C4×D5semidirect
424. C4×C5#483semidirect
597. C5C4×#483semidirect
624. C4#65094direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#40922
C2×#650942
C4×D5×C4⋊C42
C4×C5×#1032
C4×#39672
#106010612
#106010342
#106010162
C4×#39492
C4×#39522
C4×#39402
#105996682
#105996642
#105996112
#105995822
C4×#4835