Finite Group Databasebeta

← C4×#65298 #12106906

Subgroups — C4×#65298 #12106906

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
1C42×C5×D4C211yesmaximal, characteristic
2C2×#65298C211yesmaximal, characteristic
3C4×#4016C211yesmaximal, characteristic, complemented
4C4×#3964C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic
6#10602400C211yesmaximal, characteristic
7#10602399C211yesmaximal, characteristic
8#10602398C211yesmaximal, characteristic
9#10600284C211yesmaximal, characteristic, complemented
10C4×#3939C211yesmaximal, characteristic, complemented
11C4×#3940C211yesmaximal, characteristic, complemented
12#10600261C211yesmaximal, characteristic, complemented
13#10600254C211yesmaximal, characteristic, complemented
14#10600252C211yesmaximal, characteristic, complemented
15C4×C4⋊#168C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C22×C42×C5—21no—
20C2×#4016C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C4×C5×C4⋊C4C2211yescharacteristic
24C4×C5×C22⋊C4—21no—
25C4×C5×C22⋊C4—21no—
26C4×C5×C22⋊C4—21no—
27C43×C5C2211yescharacteristic
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31C2×#3964C2211yescharacteristic
32#65298C418yesdirect product factor
33C2×#3940C2211yescharacteristic
34C2×#3940C2211yescharacteristic
35C2×#3939C2211yescharacteristic
36C2×#3939C2211yescharacteristic
37#65225C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40#65222—21no—
41#65222—21no—
42C4×#683—21no—
43C4×#683—21no—
44#65217C2211yescharacteristic
45#65217C2211yescharacteristic
46C2×C4⋊#168C2211yescharacteristic
47C2×C4⋊#168C2211yescharacteristic
48C2×C4×#168C2211yescharacteristic
49C2×C4×#168C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64744C2211yescharacteristic
59#64744C2211yescharacteristic
60C4×#478—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C4×C5×D4—22no—
66C4×C5×D4—22no—
67C4×C5×D4—22no—
68C4×C5×D4—22no—
69C4×C5×D4C2×C414yes—
70C4×C5×D4Q814yes—
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C42×C5—21no—
78C2×C42×C5—21no—
79C2×C42×C5—21no—
80C2×C42×C5—44no—
81C2×C42×C5D411yescharacteristic
82C2×C42×C5D411yescharacteristic
83C2×C42×C5D411yescharacteristic
84C2×C42×C5D411yescharacteristic
85C2×C42×C5C2311yescharacteristic
86C2×C42×C5C2311yescharacteristic
87C2×C42×C5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×#683—21no—
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96C2×C4×Dic5—21no—
97C2×C4×Dic5—21no—
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C22×#168C2311yescharacteristic
101C22×#168C2311yescharacteristic
102#4016—22no—
103#4016C2×C414yescomplemented
104C5×#95—21no—
105C5×#95—21no—
106C5×#95—21no—
107#3964—22no—
108#3964—22no—
109#3964C2×C414yes—
110#3964C2×C414yes—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3963—21no—
117#3940—22no—
118#3940C2×C414yescomplemented
119#3939—22no—
120#3939C2×C414yescomplemented
121C4⋊#168—22no—
122C4⋊#168C2×C414yescomplemented
123C4×#168—22no—
124C4×#168—22no—
125C2×#478—51no—
126C4×#125—51no—
127C42×D4D511yescharacteristic
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⋊C8—51no—
138C4×#102—51no—
139C4×#102—51no—
140C24×C5—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4C22×C412yes—
145C2×C5×D4C2×Q812yes—
146C2×C5×D4#4112yes—
147C22×C4×C5—24no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—24no—
152C22×C4×C5—24no—
153C22×C4×C5—42no—
154C22×C4×C5—42no—
155C22×C4×C5—42no—
156C22×C4×C5—42no—
157C22×C4×C5—42no—
158C22×C4×C5—42no—
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2411yescharacteristic
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4C22×C412yes—
174C5×C4⋊C4C2×Q812yes—
175C5×C4⋊C4#4112yes—
176C5×C22⋊C4—24no—
177C5×C22⋊C4—24no—
178C5×C22⋊C4—24no—
179C42×C5—22no—
180C42×C5—22no—
181C42×C5—22no—
182C42×C5—21no—
183C42×C5—21no—
184C42×C5—41no—
185C42×C5—42no—
186C42×C5—42no—
187C42×C5—42no—
188C42×C5C22×C412yes—
189C42×C5C2×Q812yes—
190C42×C5#4112yes—
191C42×C5#4112yes—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5C22×C412yes—
199C4⋊Dic5C22×C412yes—
200#683—24no—
201#683—24no—
202#683—42no—
203#683—42no—
204C4×Dic5—42no—
205C4×Dic5—42no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168C22×C412yes—
217C2×#168C22×C412yes—
218C2×#125—51no—
219C2×C4×D4C2×D511yescharacteristic
220C2×C4×D4C2×D511yescharacteristic
221C2×C4×D4C2×D511yescharacteristic
222C22×C42—21no—
223#478—58no—
224C2×#107—51no—
225C2×#107—51no—
226C2×#106—51no—
227C2×#106—51no—
228C2×C4⋊C8—51no—
229C2×C4⋊C8—51no—
230C2×#102—51no—
231C2×#102—51no—
232C2×#102—51no—
233C2×#102—51no—
234C2×C4×C8—51no—
235C2×C4×C8—51no—
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—101no—
244C4×C4⋊C4—101no—
245C4×C4⋊C4C2×D511yescharacteristic
246C4×C4⋊C4C2×D511yescharacteristic
247C4×C4⋊C4C2×D511yescharacteristic
248C4×C22⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
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#336—51no—
261#336—51no—
262C23×C5—22no—
263C23×C5—22no—
264C23×C5—22no—
265C23×C5—41no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5C22×D411yescharacteristic
270C5×D4—22no—
271C5×D4—22no—
272C5×D4—22no—
273C5×D4C4×Q814yes—
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×C5—21no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—21no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—48no—
289C2×C4×C5—48no—
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—48no—
297C2×C4×C5C4×D412yes—
298C2×C4×C5C4×D412yes—
299C2×C4×C5C22⋊Q812yes—
300C2×C4×C5C22⋊Q812yes—
301C2×C4×C5#13512yes—
302C2×C4×C5#13512yes—
303C2×C4×C5AGL(1,ℤ/8)12yes—
304C2×C4×C5C23×C411yescharacteristic
305C2×C4×C5C22×Q811yescharacteristic
306C2×C4×C5C2×#4111yescharacteristic
307C2×C4×C5C2×#4111yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C2×C4×C5C2×#4111yescharacteristic
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322#168—22no—
323#168—22no—
324#168—41no—
325#168—41no—
326C22×D4C22×D511yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C22×C8—51no—
331C22×C8—51no—
332C22×C8—51no—
333C22×C8—51no—
334#125—54no—
335#125—102no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4Dic1014yes—
341C4×D4C4×D514yes—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4—101no—
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C4⋊C4C22×D511yescharacteristic
352C2×C4⋊C4C22×D511yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—44no—
360C2×C42—101no—
361C2×C42—101no—
362C2×C42C22⋊D511yescharacteristic
363C2×C42C22⋊D511yescharacteristic
364C2×C42C22⋊D511yescharacteristic
365C2×C42C22⋊D511yescharacteristic
366C2×C42C22×D511yescharacteristic
367C2×C42C22×D511yescharacteristic
368C2×C42C22×D511yescharacteristic
369#107—54no—
370#107—102no—
371#106—54no—
372#106—102no—
373C4⋊C8—54no—
374C4⋊C8—102no—
375#102—54no—
376#102—54no—
377#102—102no—
378#102—102no—
379C4×C8—102no—
380C4×C8—102no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—101no—
385#95—101no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390C22×C5—24no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5—42no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5C2×C4×D411yescharacteristic
398C22×C5C2×C22⋊Q811yescharacteristic
399C22×C5#52511yescharacteristic
400C22×C5C2×#13511yescharacteristic
401C22×C5C2×#13511yescharacteristic
402C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
403C22×C5#57511yescharacteristic
404C4×C5—22no—
405C4×C5—22no—
406C4×C5—22no—
407C4×C5—22no—
408C4×C5—42no—
409C4×C5—41no—
410C4×C5—42no—
411C4×C5—42no—
412C4×C5#47814yescomplemented
413C4×C5C2×C4×Q811yescharacteristic
414C4×C5C4×#4111yescharacteristic
415C4×C5#52911yescharacteristic
416C4×C5#53311yescharacteristic
417Dic5—42no—
418Dic5—42no—
419Dic5—81no—
420Dic5—81no—
421C24—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C2×Dic1012yes—
426C2×D4C2×C4×D512yes—
427C2×D4#70912yes—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4C2×C22⋊D511yescharacteristic
445C22×C4C2×C22⋊D511yescharacteristic
446C22×C4C2×C22⋊D511yescharacteristic
447C22×C4C2×C22⋊D511yescharacteristic
448C22×C4C2×C22⋊D511yescharacteristic
449C22×C4C2×C22⋊D511yescharacteristic
450C22×C4C23×D511yescharacteristic
451C2×C8—52no—
452C2×C8—52no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—101no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—52no—
467C4⋊C4—52no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—104no—
471C4⋊C4—104no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—202no—
477C4⋊C4—202no—
478C4⋊C4C2×Dic1012yes—
479C4⋊C4C2×C4×D512yes—
480C4⋊C4#70912yes—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C42—22no—
485C42—22no—
486C42—21no—
487C42—21no—
488C42—22no—
489C42—41no—
490C42—42no—
491C42—42no—
492C42—42no—
493C42—202no—
494C42—202no—
495C42C2×Dic1012yes—
496C42C2×C4×D512yes—
497C42#70912yes—
498C42#70912yes—
499C2×C5—44no—
500C2×C5C4×C22⋊Q811yescharacteristic
501C2×C5C4×#13511yescharacteristic
502C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
503C2×C5C2×#47811yescharacteristic
504C2×C5#307611yescharacteristic
505C2×C5#310211yescharacteristic
506C2×C5#310511yescharacteristic
507C23—22no—
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23C22×C22⋊D511yescharacteristic
515D4—22no—
516D4—22no—
517D4—22no—
518D4C4×Dic1014yes—
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—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—48no—
534C2×C4—48no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—48no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4#407012yes—
555C2×C4#407012yes—
556C2×C4C4×C22⋊D512yes—
557C2×C4C4×C22⋊D512yes—
558C2×C4#407812yes—
559C2×C4#409612yes—
560C2×C4#409612yes—
561C2×C4C22×Dic1011yescharacteristic
562C2×C4C22×C4×D511yescharacteristic
563C2×C4C2×#70911yescharacteristic
564C2×C4C2×#70911yescharacteristic
565C2×C4C2×#70911yescharacteristic
566C2×C4C2×#70911yescharacteristic
567C8—102no—
568C8—102no—
569C8—201no—
570C8—201no—
571C5C4×#47811yescharacteristic, complemented, Sylow
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×#407011yescharacteristic
580C22C2×C4×C22⋊D511yescharacteristic
581C22#6612511yescharacteristic
582C22C2×#407811yescharacteristic
583C22C2×#409611yescharacteristic
584C22C2×#409611yescharacteristic
585C22#6615611yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—202no—
595C4—202no—
596C4—401no—
597C4—401no—
598C4#6529814yesdirect product factor
599C4C2×C4×Dic1011yescharacteristic
600C4#6580411yescharacteristic
601C4C4×#70911yescharacteristic
602C4#6581311yescharacteristic
603C2—44no—
604C2C4×#407011yescharacteristic
605C2C4×#407811yescharacteristic
606C2C2×#6529811yescharacteristic
607C2#1061404011yescharacteristic
608C2C4×#409611yescharacteristic
609C2#1061423811yescharacteristic
610C2#1061425911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC42×C5×D4C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenterC42×D4D5
hypocenterC5C4×#478
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
3. C4×#4016C2semidirect
9. #10600284C2semidirect
10. C4×#3939C2semidirect
11. C4×#3940C2semidirect
12. #10600261C2semidirect
13. #10600254C2semidirect
14. #10600252C2semidirect
15. C4×C4⋊#168C2semidirect
32. #65298C4direct (N × H)
103. #4016C2×C4semidirect
118. #3940C2×C4semidirect
120. #3939C2×C4semidirect
122. C4⋊#168C2×C4semidirect
412. C4×C5#478semidirect
571. C5C4×#478semidirect
598. C4#65298direct (N × H)

Maximal subgroups

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

subgroupindex
C42×C5×D42
C2×#652982
C4×#40162
C4×#39642
#106024002
#106023992
#106023982
#106002842
C4×#39392
C4×#39402
#106002612
#106002542
#106002522
C4×C4⋊#1682
C4×#4785