Finite Group Databasebeta

← C4×#65136 #12106908

Subgroups — C4×#65136 #12106908

Order 1280.

948 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65136C211yesmaximal, characteristic
2C4×#4016C211yesmaximal, characteristic, complemented
3C42×D20C211yesmaximal, characteristic
4C4×C5×C4⋊C8C211yesmaximal, characteristic, complemented
5#10601273C211yesmaximal, characteristic
6#10601254C211yesmaximal, characteristic, complemented
7#10601248C211yesmaximal, characteristic, complemented
8C4×#3950C211yesmaximal, characteristic, complemented
9C4×#3949C211yesmaximal, characteristic, complemented
10C4×#3953C211yesmaximal, characteristic
11C4×#3953C211yesmaximal, characteristic
12#10599464C211yesmaximal, characteristic
13#10599463C211yesmaximal, characteristic
14#10599417C211yesmaximal, characteristic, complemented
15#10599415C211yesmaximal, characteristic, complemented
16C2×C4×D20C2211yescharacteristic
17C2×C4×D20C2211yescharacteristic
18C2×C4×D20C2211yescharacteristic
19C2×C42×D5—21no—
20C2×#4016C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C4×C5×C8C2211yescharacteristic
24C2×C4×C5×C8C2211yescharacteristic
25C43×C5C2211yescharacteristic
26C2×#3953C2211yescharacteristic
27C2×#3953C2211yescharacteristic
28C2×#3953C2211yescharacteristic
29C2×#3953C2211yescharacteristic
30C2×#3950C2211yescharacteristic
31C2×#3950C2211yescharacteristic
32C2×#3949C2211yescharacteristic
33C2×#3949C2211yescharacteristic
34C4×#685—21no—
35C4×#685—21no—
36C4×#685—21no—
37#65225C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40C4×C4⋊Dic5C2211yescharacteristic
41C4×C4⋊Dic5C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65222—21no—
44#65222—21no—
45C4×#683—21no—
46C4×#683—21no—
47#65217C2211yescharacteristic
48#65217C2211yescharacteristic
49#65136C418yesdirect product factor
50C5×#336C2211yescharacteristic
51C5×#336C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64771C2211yescharacteristic
59#64771C2211yescharacteristic
60C4×#478—51nomaximal, Sylow
61C22×D20C2311yescharacteristic
62C22×C4×D5—21no—
63C22×C4×D5—21no—
64C22×C4×D5—21no—
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C2×C42×C5D411yescharacteristic
70C2×C42×C5D411yescharacteristic
71C2×C42×C5D411yescharacteristic
72C2×C42×C5D411yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C42×C5C2311yescharacteristic
75C2×C42×C5C2311yescharacteristic
76C2×#685—21no—
77C2×#685—21no—
78C2×#685—21no—
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
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×Dic5—21no—
95C4×D20—22no—
96C4×D20—22no—
97C4×D20—22no—
98C4×D20—22no—
99C4×D20C2×C414yes—
100C4×D20Q814yes—
101C42×D5—44no—
102#4016—22no—
103#4016C2×C414yescomplemented
104C5×C4⋊C8—22no—
105C5×C4⋊C8C2×C414yescomplemented
106C4×C5×C8—22no—
107C4×C5×C8—22no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3963—21no—
117#3953—22no—
118#3953—22no—
119#3953C2×C414yes—
120#3953C2×C414yes—
121#3950—22no—
122#3950C2×C414yescomplemented
123#3949—22no—
124#3949C2×C414yescomplemented
125C2×#478—51no—
126C4×#125—51no—
127C42×D4—51no—
128#1989—51no—
129#1949—51no—
130#1921—51no—
131#1919—51no—
132#1864—51no—
133#1862—51no—
134#1804—51no—
135C4×#107—51no—
136C4×#106—51no—
137C4×C4⋊C8D511yescharacteristic, complemented
138C4×#102—51no—
139C4×#102—51no—
140C23×D5—21no—
141C22×C4×C5C2×D411yescharacteristic
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2411yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20C22×C412yes—
159C2×D20C2×Q812yes—
160C2×D20#4112yes—
161C2×C4×D5—24no—
162C2×C4×D5—24no—
163C2×C4×D5—24no—
164C2×C4×D5—42no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C2×C4×D5—42no—
169C2×C4×D5—42no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8C22×C412yes—
181C2×C5×C8C22×C412yes—
182C42×C5—22no—
183C42×C5—22no—
184C42×C5—22no—
185C42×C5—21no—
186C42×C5—21no—
187C42×C5—41no—
188C42×C5C22×C412yes—
189C42×C5C2×Q812yes—
190C42×C5#4112yes—
191C42×C5#4112yes—
192#685—24no—
193#685—24no—
194#685—24no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5C22×C412yes—
205C4⋊Dic5C22×C412yes—
206C4⋊Dic5C22×C412yes—
207C4⋊Dic5C2×Q812yes—
208C4⋊Dic5#4112yes—
209#683—24no—
210#683—24no—
211#683—42no—
212#683—42no—
213C4×Dic5—42no—
214C4×Dic5—42no—
215C4×Dic5—42no—
216C4×Dic5—42no—
217C4×Dic5—42no—
218C2×#125—51no—
219C2×C4×D4—51no—
220C2×C4×D4—51no—
221C2×C4×D4—51no—
222C22×C42—101no—
223#478—58no—
224C2×#107—51no—
225C2×#107—51no—
226C2×#106—51no—
227C2×#106—51no—
228C2×C4⋊C8C2×D511yescharacteristic
229C2×C4⋊C8C2×D511yescharacteristic
230C2×#102—51no—
231C2×#102—51no—
232C2×#102—51no—
233C2×#102—51no—
234C2×C4×C8C2×D511yescharacteristic
235C2×C4×C8C2×D511yescharacteristic
236#389—51no—
237#389—51no—
238#387—101no—
239#387—101no—
240#382—51no—
241C4×C4⋊C4—51no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—101no—
247C4×C4⋊C4—101no—
248C4×C22⋊C4—101no—
249C4×C22⋊C4—101no—
250C4×C22⋊C4—101no—
251C43C2×D511yescharacteristic
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#336C2×D511yescharacteristic
261#336C2×D511yescharacteristic
262C23×C5C22×D411yescharacteristic
263C22×D5—22no—
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—41no—
267C22×D5—41no—
268C22×D5—41no—
269C22×D5—41no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5C4×D412yes—
282C2×C4×C5C4×D412yes—
283C2×C4×C5C22⋊Q812yes—
284C2×C4×C5C22⋊Q812yes—
285C2×C4×C5#13512yes—
286C2×C4×C5#13512yes—
287C2×C4×C5AGL(1,ℤ/8)12yes—
288C2×C4×C5C23×C411yescharacteristic
289C2×C4×C5C22×Q811yescharacteristic
290C2×C4×C5C2×#4111yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×C4×C5C2×#4111yescharacteristic
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315D20—22no—
316D20—22no—
317D20—22no—
318D20C4×Q814yes—
319C4×D5—48no—
320C4×D5—48no—
321C4×D5—48no—
322C5×C8—22no—
323C5×C8—22no—
324C5×C8—41no—
325C5×C8—41no—
326C22×D4—51no—
327C23×C4—101no—
328C23×C4—101no—
329C23×C4—101no—
330C22×C8C22×D511yescharacteristic
331C22×C8C22×D511yescharacteristic
332C22×C8C22×D511yescharacteristic
333C22×C8C22×D511yescharacteristic
334#125—54no—
335#125—102no—
336C4×D4—54no—
337C4×D4—54no—
338C4×D4—102no—
339C4×D4—102no—
340C4×D4—102no—
341C4×D4—102no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—101no—
350C2×C4⋊C4—101no—
351C2×C4⋊C4—101no—
352C2×C4⋊C4—101no—
353C2×C22⋊C4—101no—
354C2×C22⋊C4—101no—
355C2×C22⋊C4—101no—
356C2×C42—101no—
357C2×C42—101no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42—204no—
362C2×C42D2011yescharacteristic
363C2×C42D2011yescharacteristic
364C2×C42D2011yescharacteristic
365C2×C42D2011yescharacteristic
366C2×C42C22×D511yescharacteristic
367C2×C42C22×D511yescharacteristic
368C2×C42C22×D511yescharacteristic
369#107—54no—
370#107—102no—
371#106—54no—
372#106—102no—
373C4⋊C8—22no—
374C4⋊C8C4×D514yescomplemented
375#102—54no—
376#102—54no—
377#102—102no—
378#102—102no—
379C4×C8—22no—
380C4×C8—22no—
381#95—101no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390C22×C5C2×C4×D411yescharacteristic
391C22×C5C2×C22⋊Q811yescharacteristic
392C22×C5#52511yescharacteristic
393C22×C5C2×#13511yescharacteristic
394C22×C5C2×#13511yescharacteristic
395C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C5#57511yescharacteristic
397C2×D5—24no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C4×C5—22no—
405C4×C5—22no—
406C4×C5—22no—
407C4×C5—22no—
408C4×C5—41no—
409C4×C5#47814yescomplemented
410C4×C5C2×C4×Q811yescharacteristic
411C4×C5C4×#4111yescharacteristic
412C4×C5#52911yescharacteristic
413C4×C5#53311yescharacteristic
414Dic5—42no—
415Dic5—42no—
416Dic5—42no—
417Dic5—42no—
418Dic5—42no—
419Dic5—81no—
420Dic5—81no—
421C24—101no—
422C2×D4—52no—
423C2×D4—52no—
424C2×D4—52no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C22×C4—104no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—104no—
435C22×C4—104no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—202no—
439C22×C4—202no—
440C22×C4—202no—
441C22×C4—202no—
442C22×C4—202no—
443C22×C4—202no—
444C22×C4C2×D2011yescharacteristic
445C22×C4C2×D2011yescharacteristic
446C22×C4C2×D2011yescharacteristic
447C22×C4C2×D2011yescharacteristic
448C22×C4C2×D2011yescharacteristic
449C22×C4C2×D2011yescharacteristic
450C22×C4C23×D511yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8C2×C4×D512yes—
462C2×C8C2×C4×D512yes—
463C4⋊C4—52no—
464C4⋊C4—52no—
465C4⋊C4—52no—
466C4⋊C4—52no—
467C4⋊C4—52no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—104no—
474C4⋊C4—104no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—202no—
480C4⋊C4—202no—
481C22⋊C4—104no—
482C22⋊C4—104no—
483C22⋊C4—104no—
484C42—21no—
485C42—21no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—41no—
490C42—202no—
491C42—202no—
492C42—202no—
493C42—202no—
494C42—202no—
495C42C2×C4×D512yes—
496C42#70912yes—
497C42#71112yes—
498C42Q8×D512yes—
499C2×C5C4×C22⋊Q811yescharacteristic
500C2×C5C4×#13511yescharacteristic
501C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
502C2×C5C2×#47811yescharacteristic
503C2×C5#307611yescharacteristic
504C2×C5#310211yescharacteristic
505C2×C5#310511yescharacteristic
506D5—44no—
507C23—102no—
508C23—102no—
509C23—102no—
510C23—201no—
511C23—201no—
512C23—201no—
513C23—201no—
514C23C22×D2011yescharacteristic
515D4—54no—
516D4—102no—
517D4—102no—
518D4—102no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—102no—
535C2×C4—208no—
536C2×C4—208no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—201no—
540C2×C4—201no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—208no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4C4×D2012yes—
555C2×C4C4×D2012yes—
556C2×C4#404312yes—
557C2×C4#404312yes—
558C2×C4#405012yes—
559C2×C4#405012yes—
560C2×C4#405412yes—
561C2×C4C22×C4×D511yescharacteristic
562C2×C4C2×#70911yescharacteristic
563C2×C4C2×#71111yescharacteristic
564C2×C4C2×Q8×D511yescharacteristic
565C2×C4D5×#4111yescharacteristic
566C2×C4D5×#4111yescharacteristic
567C8—22no—
568C8—22no—
569C8—41no—
570C8—41no—
571C5C4×#47811yescharacteristic, complemented, Sylow
572C22—104no—
573C22—202no—
574C22—202no—
575C22—202no—
576C22—202no—
577C22—202no—
578C22—202no—
579C22C2×C4×D2011yescharacteristic
580C22C2×#404311yescharacteristic
581C22#6585811yescharacteristic
582C22C2×#405011yescharacteristic
583C22C2×#405011yescharacteristic
584C22C2×#405411yescharacteristic
585C22#6608211yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—41no—
591C4—202no—
592C4—202no—
593C4—202no—
594C4—202no—
595C4—202no—
596C4—401no—
597C4—401no—
598C4#6513614yesdirect product factor
599C4C4×#71111yescharacteristic
600C4#6589111yescharacteristic
601C4C4×Q8×D511yescharacteristic
602C4#6591211yescharacteristic
603C2—204no—
604C2C4×#404311yescharacteristic
605C2C4×#405011yescharacteristic
606C2C4×#405411yescharacteristic
607C2C2×#6513611yescharacteristic
608C2#1061075611yescharacteristic
609C2#1061103011yescharacteristic
610C2#1061103111yescharacteristic
subgroupG/H
centerC22×C4C2×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×C4⋊C8C2
socleC23×C5C22×D4
prime radicalC22×D20C23
cosocleC22×C4×C5C24
hypercenterC4×C4⋊C8D5
hypocenterC5C4×#478
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#4016C2semidirect
4. C4×C5×C4⋊C8C2semidirect
6. #10601254C2semidirect
7. #10601248C2semidirect
8. C4×#3950C2semidirect
9. C4×#3949C2semidirect
14. #10599417C2semidirect
15. #10599415C2semidirect
49. #65136C4direct (N × H)
103. #4016C2×C4semidirect
105. C5×C4⋊C8C2×C4semidirect
122. #3950C2×C4semidirect
124. #3949C2×C4semidirect
137. C4×C4⋊C8D5semidirect
374. C4⋊C8C4×D5semidirect
409. C4×C5#478semidirect
571. C5C4×#478semidirect
598. C4#65136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#651362
C4×#40162
C42×D202
C4×C5×C4⋊C82
#106012732
#106012542
#106012482
C4×#39502
C4×#39492
C4×#39532
#105994642
#105994632
#105994172
#105994152
C4×#4785