Finite Group Databasebeta

← C4×#65063 #12106405

Subgroups — C4×#65063 #12106405

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
1C4×#4084C211yesmaximal, characteristic
2C2×#65063C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C4×C5×#102C211yesmaximal, characteristic, complemented
5C4×#3964C211yesmaximal, characteristic, complemented
6#10600993C211yesmaximal, characteristic
7#10600966C211yesmaximal, characteristic, complemented
8#10600948C211yesmaximal, characteristic, complemented
9C4×#3950C211yesmaximal, characteristic, complemented
10C4×#3952C211yesmaximal, characteristic, complemented
11C4×#3939C211yesmaximal, characteristic, complemented
12#10599667C211yesmaximal, characteristic, complemented
13#10599664C211yesmaximal, characteristic, complemented
14#10599607C211yesmaximal, characteristic, complemented
15#10599580C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×#4084C2211yescharacteristic
18C2×C4×C22⋊D5—21no—
19C2×D5×C4⋊C4C2211yescharacteristic
20C2×D5×C4⋊C4C2211yescharacteristic
21C2×C42×D5—21no—
22C2×C42×D5C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C4×C5×C8C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27#65510C2211yescharacteristic
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C4×C22⋊Dic5—21no—
31C2×#3952C2211yescharacteristic
32C2×#3952C2211yescharacteristic
33C2×#3950C2211yescharacteristic
34C2×#3950C2211yescharacteristic
35#65276C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C4⋊C4×Dic5C2211yescharacteristic
38#65262C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41#65245—21no—
42#65233—21no—
43C4×C4⋊Dic5C2211yescharacteristic
44C4×C4⋊Dic5C2211yescharacteristic
45C4×#683—21no—
46C2×C4×#168C2211yescharacteristic
47#65063C418yesdirect 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×#480—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C22×C22⋊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
71C4×C5×D4—22no—
72C4×C5×D4—22no—
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C22⋊C4—21no—
77C2×C42×C5—21no—
78C2×C42×C5C2311yescharacteristic
79C2×C22⋊Dic5—21no—
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—21no—
82#4084—22no—
83#4084C2×C414yes—
84C4×C22⋊D5—44no—
85C2×#685—21no—
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×#683—21no—
91C2×#683—21no—
92C2×#683—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5—21no—
96C2×C4×Dic5—21no—
97C2×C4×Dic5D411yescharacteristic
98C2×C4×Dic5D411yescharacteristic
99C2×C4×Dic5C2311yescharacteristic
100C22×#168C2311yescharacteristic
101C22×#168C2311yescharacteristic
102D5×C4⋊C4—22no—
103D5×C4⋊C4—22no—
104D5×C4⋊C4—22no—
105D5×C4⋊C4C2×C414yescomplemented
106C42×D5—22no—
107C42×D5—22no—
108C42×D5—44no—
109C5×#102—22no—
110C5×#102C2×C414yescomplemented
111C4×C5×C8—22no—
112C5×#95—21no—
113#3964—22no—
114#3964C2×C414yescomplemented
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119#3963—21no—
120#3963—21no—
121#3952—22no—
122#3952C2×C414yescomplemented
123#3950—22no—
124#3950C2×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×#107—51no—
140C4×#102—51no—
141C4×#102D511yescharacteristic, complemented
142C4×C22⋊C8—51no—
143C24×C5—21no—
144C23×D5C2×D411yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4C22×C412yes—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—42no—
155C22×C4×C5—42no—
156C22×C4×C5—42no—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2411yescharacteristic
160C2×C22⋊D5—24no—
161C2×C22⋊D5—42no—
162C2×C22⋊D5—42no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169C22×Dic5C2×D411yescharacteristic
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—24no—
177C2×C4×D5—24no—
178C2×C4×D5—22no—
179C2×C4×D5—22no—
180C2×C4×D5—41no—
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⋊C4C22×C412yes—
199C5×C4⋊C4#4112yes—
200C5×C22⋊C4—42no—
201C42×C5—42no—
202C42×C5#4112yes—
203C42×C5#4112yes—
204C22⋊Dic5—24no—
205C22⋊Dic5—42no—
206C22⋊Dic5—42no—
207#685—42no—
208C4⋊Dic5—21no—
209C4⋊Dic5—21no—
210C4⋊Dic5—21no—
211C4⋊Dic5—21no—
212C4⋊Dic5—21no—
213C4⋊Dic5C22×C412yes—
214C4⋊Dic5C22×C412yes—
215C4⋊Dic5#4112yes—
216#683—24no—
217#683—24no—
218#683—42no—
219C4×Dic5—22no—
220C4×Dic5—22no—
221C4×Dic5—21no—
222C4×Dic5—21no—
223C4×Dic5—42no—
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—101no—
235C2×C4×D4C2×D511yescharacteristic
236C22×C4⋊C4—51no—
237C22×C4⋊C4—51no—
238C22×C42—51no—
239C22×C42—101no—
240#480—58no—
241C2×#107—51no—
242C2×#107—51no—
243C2×#107—51no—
244C2×#107—51no—
245C2×#102—51no—
246C2×#102—51no—
247C2×#102C2×D511yescharacteristic
248C2×#102C2×D511yescharacteristic
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—51no—
262C4×C4⋊C4—101no—
263C4×C4⋊C4—101no—
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×C5—22no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5C22×D411yescharacteristic
285C22×D5—21no—
286C22×D5—21no—
287C22×D5—21no—
288C22×D5—21no—
289C22×D5C4×D412yes—
290C22×D5C2×D812yes—
291C22×D5#13512yes—
292C5×D4—22no—
293C5×D4—22no—
294C5×D4—41no—
295C5×D4—41no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
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—41no—
307C2×C4×C5—84no—
308C2×C4×C5#12312yes—
309C2×C4×C5#12312yes—
310C2×C4×C5C2×D812yes—
311C2×C4×C5#13712yes—
312C2×C4×C5C23×C411yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C2×C4×C5C2×#4111yescharacteristic
317C2×C4×C5C2×#4111yescharacteristic
318C22⋊D5—48no—
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—21no—
326C2×Dic5—22no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—41no—
332C2×Dic5—41no—
333C2×Dic5—41no—
334C2×Dic5—41no—
335C2×Dic5—41no—
336C2×Dic5—41no—
337C2×Dic5—41no—
338C2×Dic5C4×D412yes—
339C2×Dic5C2×D812yes—
340C4×D5—22no—
341C4×D5—22no—
342C4×D5—22no—
343C4×D5—22no—
344C4×D5—28no—
345C4×D5—44no—
346C4×D5—48no—
347C4×D5—48no—
348C5×C8—22no—
349C5×C8—41no—
350#168—22no—
351#168—41no—
352C22×D4—101no—
353C22×D4C22×D511yescharacteristic
354C23×C4—21no—
355C23×C4—51no—
356C23×C4—51no—
357C23×C4—51no—
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—22no—
367C4×D4—22no—
368C4×D4—204no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—51no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—54no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—102no—
375C2×C4⋊C4—102no—
376C2×C4⋊C4—101no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—102no—
379C2×C4⋊C4—101no—
380C2×C4⋊C4C22×D511yescharacteristic
381C2×C4⋊C4C22×D511yescharacteristic
382C2×C4⋊C4C22×D511yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—101no—
385C2×C22⋊C4—101no—
386C2×C22⋊C4—101no—
387C2×C22⋊C4—101no—
388C2×C42—21no—
389C2×C42—51no—
390C2×C42—51no—
391C2×C42—51no—
392C2×C42—102no—
393C2×C42—102no—
394C2×C42—101no—
395C2×C42—101no—
396C2×C42—101no—
397C2×C42—101no—
398C2×C42—204no—
399C2×C42C22×D511yescharacteristic
400#107—54no—
401#107—54no—
402#107—102no—
403#107—102no—
404#102—22no—
405#102—54no—
406#102—102no—
407#102C4×D514yescomplemented
408C22⋊C8—54no—
409C22⋊C8—102no—
410C4×C8—22no—
411C4×C8—102no—
412#95—21no—
413#95—101no—
414#95—101no—
415#95—101no—
416#95—101no—
417#95—101no—
418#95—101no—
419C22×C5—42no—
420C22×C5—42no—
421C22×C5—42no—
422C22×C5—81no—
423C22×C5—81no—
424C22×C5—81no—
425C22×C5—81no—
426C22×C5C2×C4×D411yescharacteristic
427C22×C5C2×#12311yescharacteristic
428C22×C5#52511yescharacteristic
429C22×C5C22×D811yescharacteristic
430C22×C5C2×#13511yescharacteristic
431C22×C5C2×#13711yescharacteristic
432C22×C5#57511yescharacteristic
433C2×D5—22no—
434C2×D5—22no—
435C2×D5—22no—
436C2×D5—22no—
437C2×D5—22no—
438C2×D5—22no—
439C2×D5C4×D814yes—
440C4×C5—22no—
441C4×C5—42no—
442C4×C5—42no—
443C4×C5—81no—
444C4×C5#48014yescomplemented
445C4×C5C4×#4111yescharacteristic
446C4×C5C4×#4111yescharacteristic
447C4×C5#52911yescharacteristic
448C4×C5#52911yescharacteristic
449Dic5—22no—
450Dic5—22no—
451Dic5—41no—
452Dic5—42no—
453Dic5—42no—
454Dic5—42no—
455Dic5—81no—
456C24—21no—
457C24—51no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—104no—
464C2×D4—202no—
465C2×D4—202no—
466C2×D4C2×C4×D512yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—52no—
476C22×C4—52no—
477C22×C4—54no—
478C22×C4—51no—
479C22×C4—104no—
480C22×C4—102no—
481C22×C4—104no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—101no—
489C22×C4—101no—
490C22×C4—101no—
491C22×C4—102no—
492C22×C4—101no—
493C22×C4—201no—
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—52no—
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—101no—
527C4⋊C4—202no—
528C4⋊C4C2×C4×D512yes—
529C4⋊C4#70912yes—
530C22⋊C4—42no—
531C22⋊C4—104no—
532C22⋊C4—202no—
533C22⋊C4—202no—
534C22⋊C4—202no—
535C42—42no—
536C42—101no—
537C42—101no—
538C42—102no—
539C42—102no—
540C42—202no—
541C42—202no—
542C42—202no—
543C42—202no—
544C42#70912yes—
545C42#71112yes—
546C2×C5—82no—
547C2×C5C4×#12311yescharacteristic
548C2×C5C2×C4×D811yescharacteristic
549C2×C5C4×#13711yescharacteristic
550C2×C5C2×#48011yescharacteristic
551C2×C5#309111yescharacteristic
552C2×C5#310011yescharacteristic
553C2×C5#310811yescharacteristic
554D5—24no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—52no—
563C23—52no—
564C23—52no—
565C23—101no—
566C23—101no—
567C23—101no—
568C23—101no—
569C23C2×D4×D511yescharacteristic
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4—208no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—52no—
587C2×C4—52no—
588C2×C4—84no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—101no—
592C2×C4—101no—
593C2×C4—102no—
594C2×C4—108no—
595C2×C4—102no—
596C2×C4—102no—
597C2×C4—102no—
598C2×C4—101no—
599C2×C4—101no—
600C2×C4—101no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—204no—
605C2×C4—208no—
606C2×C4—208no—
607C2×C4—201no—
608C2×C4—201no—
609C2×C4—201no—
610C2×C4—201no—
611C2×C4—201no—
612C2×C4—201no—
613C2×C4—201no—
614C2×C4—201no—
615C2×C4—201no—
616C2×C4#402912yes—
617C2×C4#402912yes—
618C2×C4D5×D812yes—
619C2×C4#406112yes—
620C2×C4C22×C4×D511yescharacteristic
621C2×C4C2×#70911yescharacteristic
622C2×C4C2×#70911yescharacteristic
623C2×C4C2×#71111yescharacteristic
624C2×C4D5×#4111yescharacteristic
625C2×C4D5×#4111yescharacteristic
626C8—22no—
627C8—41no—
628C8—102no—
629C8—201no—
630C5C4×#48011yescharacteristic, complemented, Sylow
631C22—42no—
632C22—42no—
633C22—42no—
634C22—54no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—102no—
640C22—102no—
641C22—102no—
642C22—102no—
643C22—102no—
644C22—102no—
645C22C2×#402911yescharacteristic
646C22C4×D4×D511yescharacteristic
647C22#6588111yescharacteristic
648C22C2×D5×D811yescharacteristic
649C22C2×#406111yescharacteristic
650C22D5×#13511yescharacteristic
651C22#6610211yescharacteristic
652C4—22no—
653C4—42no—
654C4—42no—
655C4—81no—
656C4—102no—
657C4—102no—
658C4—202no—
659C4—202no—
660C4—202no—
661C4—201no—
662C4—401no—
663C4#6506314yesdirect product factor
664C4C4×#70911yescharacteristic
665C4#6586211yescharacteristic
666C4C4×#71111yescharacteristic
667C4#6589111yescharacteristic
668C2—82no—
669C2—104no—
670C2C4×#402911yescharacteristic
671C2C2×#6506311yescharacteristic
672C2#1061057311yescharacteristic
673C2C4×D5×D811yescharacteristic
674C2#1061132111yescharacteristic
675C2C4×#406111yescharacteristic
676C2#1061138711yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×#102C2
socleC23×C5C22×D4
prime radicalC2×#4084C22
cosocleC22×C4×C5C24
hypercenterC4×#102D5
hypocenterC5C4×#480
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C4×D5×C4⋊C4C2semidirect
4. C4×C5×#102C2semidirect
5. C4×#3964C2semidirect
7. #10600966C2semidirect
8. #10600948C2semidirect
9. C4×#3950C2semidirect
10. C4×#3952C2semidirect
11. C4×#3939C2semidirect
12. #10599667C2semidirect
13. #10599664C2semidirect
14. #10599607C2semidirect
15. #10599580C2semidirect
47. #65063C4direct (N × H)
105. D5×C4⋊C4C2×C4semidirect
110. C5×#102C2×C4semidirect
114. #3964C2×C4semidirect
122. #3952C2×C4semidirect
124. #3950C2×C4semidirect
126. #3939C2×C4semidirect
141. C4×#102D5semidirect
407. #102C4×D5semidirect
444. C4×C5#480semidirect
630. C5C4×#480semidirect
663. C4#65063direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#40842
C2×#650632
C4×D5×C4⋊C42
C4×C5×#1022
C4×#39642
#106009932
#106009662
#106009482
C4×#39502
C4×#39522
C4×#39392
#105996672
#105996642
#105996072
#105995802
C4×#4805