Finite Group Databasebeta

← C4×#65171 #12106411

Subgroups — C4×#65171 #12106411

Order 1280.

1060 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65171C211yesmaximal, characteristic
2C4×#4041C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C4×C5×#107C211yesmaximal, characteristic, complemented
5#10601425C211yesmaximal, characteristic, complemented
6#10601416C211yesmaximal, characteristic, complemented
7#10601402C211yesmaximal, characteristic, complemented
8C4×#3953C211yesmaximal, characteristic, complemented
9C4×#3952C211yesmaximal, characteristic, complemented
10C4×#3939C211yesmaximal, characteristic, complemented
11C4×#3941C211yesmaximal, characteristic, complemented
12#10599673C211yesmaximal, characteristic
13#10599664C211yesmaximal, characteristic, complemented
14#10599608C211yesmaximal, characteristic, complemented
15#10599584C211yesmaximal, characteristic, complemented
16C2×#4041C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×D5×C4⋊C4C2211yescharacteristic
19C2×C4×D20—21no—
20C2×C4×D20C2211yescharacteristic
21C2×C42×D5—21no—
22C2×C42×D5C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#107C2211yescharacteristic
25C2×C4×C5×C8C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C2×#3953C2211yescharacteristic
29C2×#3953C2211yescharacteristic
30C2×#3952C2211yescharacteristic
31C2×#3952C2211yescharacteristic
32#65277C2211yescharacteristic
33#65276C2211yescharacteristic
34#65274C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C2×#3941C2211yescharacteristic
38C2×#3941C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C4×#685—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43C4×#683—21no—
44C2×C4×#168C2211yescharacteristic
45#65171C418yesdirect product factor
46#64959—21no—
47#64954—21no—
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×#480—51nomaximal, Sylow
61C22×D20—21no—
62C22×D20C2311yescharacteristic
63C22×C4×D5—21no—
64C22×C4×D5—21no—
65C22×C4×D5—21no—
66C22×C4×D5D411yescharacteristic
67C22×C4×D5D411yescharacteristic
68C22×C4×D5C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C42×C5—21no—
76C2×C42×C5—21no—
77C2×C42×C5C2311yescharacteristic
78C2×#685—21no—
79C2×#685—21no—
80C2×#685—21no—
81C2×#685—21no—
82C2×#685—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×#683—21no—
88C2×#683—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5D411yescharacteristic
93C2×C4×Dic5D411yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97#4041—22no—
98#4041C2×C414yes—
99D5×C4⋊C4—22no—
100D5×C4⋊C4—22no—
101D5×C4⋊C4—22no—
102D5×C4⋊C4C2×C414yescomplemented
103C4×D20—22no—
104C4×D20—22no—
105C4×D20—44no—
106C42×D5—22no—
107C42×D5—22no—
108C42×D5—44no—
109C5×#107—22no—
110C5×#107C2×C414yescomplemented
111C4×C5×C8—22no—
112C5×#95—21no—
113C5×#95—21no—
114#3963—21no—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119#3953—22no—
120#3953C2×C414yescomplemented
121#3952—22no—
122#3952C2×C414yescomplemented
123#3941—22no—
124#3941C2×C414yescomplemented
125#3939—22no—
126#3939C2×C414yescomplemented
127C4×#168—22no—
128C2×#480—51no—
129C4×#121—51no—
130C2×C4×C4⋊C4—51no—
131#1925—51no—
132#1925—51no—
133#1918—51no—
134#1918—51no—
135#1874—51no—
136#1852—51no—
137#1823—51no—
138C4×#107—51no—
139C4×#107D511yescharacteristic, complemented
140C4×#102—51no—
141C4×#102—51no—
142C4×C22⋊C8—51no—
143C23×D5—21no—
144C23×D5C2×D411yescharacteristic
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2411yescharacteristic
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5C2×D411yescharacteristic
156C22×Dic5C2×D411yescharacteristic
157C22×Dic5C2×D411yescharacteristic
158C2×D20—21no—
159C2×D20—21no—
160C2×D20—21no—
161C2×D20—21no—
162C2×D20—24no—
163C2×D20—21no—
164C2×D20—42no—
165C2×D20—42no—
166C2×D20C22×C412yes—
167C2×C4×D5—22no—
168C2×C4×D5—22no—
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5—24no—
174C2×C4×D5—24no—
175C2×C4×D5—22no—
176C2×C4×D5—22no—
177C2×C4×D5—41no—
178C2×C4×D5—42no—
179C2×C4×D5—42no—
180C2×C4×D5—42no—
181C2×C4×D5—42no—
182C2×C4×D5—42no—
183C2×C4×D5—42no—
184C2×C4×D5—42no—
185C2×C4×D5D814yes—
186C2×C4×D5C22×C412yes—
187C2×C4×D5#4112yes—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8C22×C412yes—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4C22×C412yes—
200C5×C4⋊C4C22×C412yes—
201C5×C4⋊C4#4112yes—
202C42×C5—42no—
203C42×C5—42no—
204C42×C5#4112yes—
205C42×C5#4112yes—
206#685—24no—
207#685—42no—
208#685—42no—
209#685—42no—
210#685—42no—
211C4⋊Dic5—21no—
212C4⋊Dic5—21no—
213C4⋊Dic5—21no—
214C4⋊Dic5—21no—
215C4⋊Dic5—42no—
216C4⋊Dic5C22×C412yes—
217C4⋊Dic5#4112yes—
218#683—24no—
219#683—24no—
220C4×Dic5—22no—
221C4×Dic5—22no—
222C4×Dic5—21no—
223C4×Dic5—21no—
224C4×Dic5—42no—
225C4×Dic5—42no—
226C4×Dic5—42no—
227C2×#168—21no—
228C2×#168—21no—
229C2×#168—21no—
230C2×#168—21no—
231C2×#168—21no—
232C2×#168C22×C412yes—
233C2×#121—51no—
234C2×C4×D4—51no—
235C2×C4×D4—101no—
236C22×C4⋊C4—51no—
237C22×C4⋊C4—51no—
238C22×C42—51no—
239C22×C42—101no—
240#480—58no—
241C2×#107—51no—
242C2×#107—51no—
243C2×#107C2×D511yescharacteristic
244C2×#107C2×D511yescharacteristic
245C2×#102—51no—
246C2×#102—51no—
247C2×#102—51no—
248C2×#102—51no—
249C2×C22⋊C8—51no—
250C2×C22⋊C8—51no—
251C2×C4×C8—51no—
252C2×C4×C8C2×D511yescharacteristic
253#390—51no—
254#389—51no—
255#388—101no—
256#386—101no—
257#380—51no—
258C4×C4⋊C4—51no—
259C4×C4⋊C4—51no—
260C4×C4⋊C4—51no—
261C4×C4⋊C4—101no—
262C4×C4⋊C4—101no—
263C4×C4⋊C4C2×D511yescharacteristic
264C4×C4⋊C4C2×D511yescharacteristic
265C4×C22⋊C4—101no—
266C2×#95—101no—
267#340—51no—
268#340—51no—
269#340—51no—
270#340—51no—
271#340—51no—
272#340—51no—
273#340C2×D511yescharacteristic
274#340C2×D511yescharacteristic
275#336—51no—
276#336—51no—
277C23×C5C22×D411yescharacteristic
278C22×D5—21no—
279C22×D5—21no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—22no—
283C22×D5—41no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
287C22×D5—41no—
288C22×D5—41no—
289C22×D5C4×D412yes—
290C22×D5C2×D812yes—
291C22×D5#13512yes—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5#12312yes—
307C2×C4×C5#12312yes—
308C2×C4×C5C2×D812yes—
309C2×C4×C5#13712yes—
310C2×C4×C5C23×C411yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5—22no—
321C2×Dic5—21no—
322C2×Dic5—22no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—41no—
326C2×Dic5—41no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—41no—
332C2×Dic5C4×D412yes—
333C2×Dic5C2×D812yes—
334D20—22no—
335D20—22no—
336D20—48no—
337D20—41no—
338D20—41no—
339C4×D5—22no—
340C4×D5—22no—
341C4×D5—22no—
342C4×D5—22no—
343C4×D5—28no—
344C4×D5—44no—
345C4×D5—48no—
346C4×D5—48no—
347C4×D5—84no—
348C5×C8—22no—
349C5×C8—41no—
350#168—22no—
351#168—41no—
352C22×D4—51no—
353C22×D4—101no—
354C23×C4—51no—
355C23×C4—51no—
356C23×C4—51no—
357C23×C4—101no—
358C23×C4—101no—
359C23×C4—101no—
360C22×C8—51no—
361C22×C8—51no—
362C22×C8C22×D511yescharacteristic
363C22×C8C22×D511yescharacteristic
364#121—54no—
365#121—102no—
366C4×D4—102no—
367C4×D4—102no—
368C4×D4—204no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—51no—
371C2×C4⋊C4—54no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—102no—
374C2×C4⋊C4—102no—
375C2×C4⋊C4—101no—
376C2×C4⋊C4—101no—
377C2×C4⋊C4—102no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4C22×D511yescharacteristic
380C2×C4⋊C4C22×D511yescharacteristic
381C2×C4⋊C4C22×D511yescharacteristic
382C2×C4⋊C4C22×D511yescharacteristic
383C2×C22⋊C4—101no—
384C2×C22⋊C4—101no—
385C2×C22⋊C4—101no—
386C2×C22⋊C4—101no—
387C2×C22⋊C4—101no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—51no—
391C2×C42—51no—
392C2×C42—51no—
393C2×C42—102no—
394C2×C42—102no—
395C2×C42—101no—
396C2×C42—101no—
397C2×C42—101no—
398C2×C42—204no—
399C2×C42C22×D511yescharacteristic
400#107—22no—
401#107—54no—
402#107—102no—
403#107C4×D514yescomplemented
404#102—54no—
405#102—54no—
406#102—102no—
407#102—102no—
408C22⋊C8—54no—
409C22⋊C8—102no—
410C4×C8—22no—
411C4×C8—102no—
412#95—21no—
413#95—21no—
414#95—101no—
415#95—101no—
416#95—101no—
417#95—101no—
418#95—101no—
419C22×C5C2×C4×D411yescharacteristic
420C22×C5C2×#12311yescharacteristic
421C22×C5#52511yescharacteristic
422C22×C5C22×D811yescharacteristic
423C22×C5C2×#13511yescharacteristic
424C22×C5C2×#13711yescharacteristic
425C22×C5#57511yescharacteristic
426C2×D5—22no—
427C2×D5—22no—
428C2×D5—22no—
429C2×D5—22no—
430C2×D5—22no—
431C2×D5—22no—
432C2×D5—42no—
433C2×D5—42no—
434C2×D5—42no—
435C2×D5—81no—
436C2×D5—81no—
437C2×D5—81no—
438C2×D5—81no—
439C2×D5C4×D814yes—
440C4×C5—22no—
441C4×C5—42no—
442C4×C5—42no—
443C4×C5—42no—
444C4×C5—81no—
445C4×C5#48014yescomplemented
446C4×C5C4×#4111yescharacteristic
447C4×C5C4×#4111yescharacteristic
448C4×C5#52911yescharacteristic
449C4×C5#52911yescharacteristic
450Dic5—22no—
451Dic5—22no—
452Dic5—41no—
453Dic5—42no—
454Dic5—42no—
455Dic5—81no—
456C24—51no—
457C24—101no—
458C2×D4—52no—
459C2×D4—104no—
460C2×D4—101no—
461C2×D4—101no—
462C2×D4—101no—
463C2×D4—101no—
464C2×D4—101no—
465C2×D4—202no—
466C2×D4—202no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—51no—
472C22×C4—51no—
473C22×C4—52no—
474C22×C4—52no—
475C22×C4—54no—
476C22×C4—51no—
477C22×C4—104no—
478C22×C4—102no—
479C22×C4—104no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—102no—
485C22×C4—102no—
486C22×C4—101no—
487C22×C4—101no—
488C22×C4—102no—
489C22×C4—101no—
490C22×C4—201no—
491C22×C4—202no—
492C22×C4—202no—
493C22×C4—202no—
494C22×C4—202no—
495C22×C4—202no—
496C22×C4—202no—
497C22×C4—202no—
498C22×C4D4×D511yescharacteristic
499C22×C4D4×D511yescharacteristic
500C22×C4C23×D511yescharacteristic
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—52no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—101no—
510C2×C8—101no—
511C2×C8—101no—
512C2×C8C2×C4×D512yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—52no—
519C4⋊C4—52no—
520C4⋊C4—104no—
521C4⋊C4—104no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4—101no—
525C4⋊C4—101no—
526C4⋊C4—202no—
527C4⋊C4C2×C4×D512yes—
528C4⋊C4C2×C4×D512yes—
529C4⋊C4#70912yes—
530C22⋊C4—104no—
531C22⋊C4—202no—
532C22⋊C4—202no—
533C22⋊C4—202no—
534C22⋊C4—202no—
535C42—42no—
536C42—42no—
537C42—101no—
538C42—101no—
539C42—102no—
540C42—102no—
541C42—202no—
542C42—202no—
543C42—202no—
544C42#70912yes—
545C42#71312yes—
546C2×C5C4×#12311yescharacteristic
547C2×C5C2×C4×D811yescharacteristic
548C2×C5C4×#13711yescharacteristic
549C2×C5C2×#48011yescharacteristic
550C2×C5#309111yescharacteristic
551C2×C5#310011yescharacteristic
552C2×C5#310811yescharacteristic
553D5—24no—
554D5—82no—
555C23—52no—
556C23—52no—
557C23—52no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23—101no—
562C23—102no—
563C23—201no—
564C23—201no—
565C23—201no—
566C23—201no—
567C23—201no—
568C23—201no—
569C23C2×D4×D511yescharacteristic
570D4—102no—
571D4—102no—
572D4—208no—
573D4—201no—
574D4—201no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—52no—
590C2×C4—52no—
591C2×C4—101no—
592C2×C4—101no—
593C2×C4—101no—
594C2×C4—101no—
595C2×C4—102no—
596C2×C4—102no—
597C2×C4—102no—
598C2×C4—102no—
599C2×C4—108no—
600C2×C4—101no—
601C2×C4—101no—
602C2×C4—101no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—204no—
606C2×C4—208no—
607C2×C4—208no—
608C2×C4—201no—
609C2×C4—201no—
610C2×C4—201no—
611C2×C4—201no—
612C2×C4—201no—
613C2×C4—201no—
614C2×C4—201no—
615C2×C4—404no—
616C2×C4#404012yes—
617C2×C4#404012yes—
618C2×C4D5×D812yes—
619C2×C4#406412yes—
620C2×C4C22×C4×D511yescharacteristic
621C2×C4C2×#70911yescharacteristic
622C2×C4C2×#70911yescharacteristic
623C2×C4C2×#71311yescharacteristic
624C2×C4D5×#4111yescharacteristic
625C2×C4D5×#4111yescharacteristic
626C8—22no—
627C8—41no—
628C8—102no—
629C8—201no—
630C5C4×#48011yescharacteristic, complemented, Sylow
631C22—54no—
632C22—102no—
633C22—102no—
634C22—102no—
635C22—102no—
636C22—102no—
637C22—102no—
638C22—202no—
639C22—202no—
640C22—202no—
641C22—401no—
642C22—401no—
643C22—401no—
644C22—401no—
645C22C2×#404011yescharacteristic
646C22C4×D4×D511yescharacteristic
647C22#6588111yescharacteristic
648C22C2×D5×D811yescharacteristic
649C22C2×#406411yescharacteristic
650C22D5×#13511yescharacteristic
651C22#6610211yescharacteristic
652C4—22no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—102no—
658C4—102no—
659C4—202no—
660C4—202no—
661C4—201no—
662C4—401no—
663C4#6517114yesdirect product factor
664C4C4×#70911yescharacteristic
665C4#6586211yescharacteristic
666C4C4×#71311yescharacteristic
667C4#6591411yescharacteristic
668C2—104no—
669C2—402no—
670C2C4×#404011yescharacteristic
671C2C2×#6517111yescharacteristic
672C2#1061091611yescharacteristic
673C2C4×D5×D811yescharacteristic
674C2#1061132111yescharacteristic
675C2C4×#406411yescharacteristic
676C2#1061145411yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×#107C2
socleC23×C5C22×D4
prime radicalC2×#4041C22
cosocleC22×C4×C5C24
hypercenterC4×#107D5
hypocenterC5C4×#480
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. C4×D5×C4⋊C4C2semidirect
4. C4×C5×#107C2semidirect
5. #10601425C2semidirect
6. #10601416C2semidirect
7. #10601402C2semidirect
8. C4×#3953C2semidirect
9. C4×#3952C2semidirect
10. C4×#3939C2semidirect
11. C4×#3941C2semidirect
13. #10599664C2semidirect
14. #10599608C2semidirect
15. #10599584C2semidirect
45. #65171C4direct (N × H)
102. D5×C4⋊C4C2×C4semidirect
110. C5×#107C2×C4semidirect
120. #3953C2×C4semidirect
122. #3952C2×C4semidirect
124. #3941C2×C4semidirect
126. #3939C2×C4semidirect
139. C4×#107D5semidirect
403. #107C4×D5semidirect
445. C4×C5#480semidirect
630. C5C4×#480semidirect
663. C4#65171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#651712
C4×#40412
C4×D5×C4⋊C42
C4×C5×#1072
#106014252
#106014162
#106014022
C4×#39532
C4×#39522
C4×#39392
C4×#39412
#105996732
#105996642
#105996082
#105995842
C4×#4805