Finite Group Databasebeta

← #12106932

Subgroups — #12106932

Order 1280.

988 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic5C211yesmaximal, characteristic
2C2×#65048C211yesmaximal, characteristic
3C4×#4034C211yesmaximal, characteristic, complemented
4C5×#1762C211yesmaximal, characteristic
5#10602402C211yesmaximal, characteristic
6#10600963C211yesmaximal, characteristic
7#10600962C211yesmaximal, characteristic
8#10600946C211yesmaximal, characteristic
9#10600607C211yesmaximal, characteristic, complemented
10#10600602C211yesmaximal, characteristic, complemented
11#10600274C211yesmaximal, characteristic, complemented
12#10599614C211yesmaximal, characteristic, complemented
13#10599613C211yesmaximal, characteristic, complemented
14#10599593C211yesmaximal, characteristic, complemented
15#10599589C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×D4×Dic5C2211yescharacteristic
18C2×D4×Dic5C2211yescharacteristic
19C22×C4×Dic5—21no—
20C2×#4034C2211yescharacteristic
21C2×C4×Dic10—21no—
22C2×C5×#102C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#97C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26C2×#3964C2211yescharacteristic
27C2×#3964C2211yescharacteristic
28C4×C22⋊Dic5—21no—
29C2×#3950C2211yescharacteristic
30C2×#3949C2211yescharacteristic
31C2×#3946C2211yescharacteristic
32C2×#3946C2211yescharacteristic
33#65274C2211yescharacteristic
34#65265C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37#65262C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C22⋊C4×Dic5—21no—
41C22⋊C4×Dic5—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44C4×#683—21no—
45C42×Dic5C2211yescharacteristic
46C2×#3935C2211yescharacteristic
47#65048C418yescomplemented
48#64936—21no—
49#64935—21no—
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64770C2211yescharacteristic
55#64770C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21613—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×Dic5—21no—
64C23×Dic5—21no—
65C22×Dic10—21no—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C4×C5×D4—22no—
69C4×C5×D4Q814yescomplemented
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C22⋊C4—21no—
74C2×C42×C5—21no—
75C2×C42×C5C2311yescharacteristic
76C2×C22⋊Dic5—21no—
77C2×C22⋊Dic5—21no—
78D4×Dic5—22no—
79D4×Dic5—22no—
80D4×Dic5—22no—
81D4×Dic5C2×C414yes—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×#683—21no—
88C2×#683—21no—
89C2×#683—21no—
90C2×#683—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5—44no—
96C2×C4×Dic5D411yescharacteristic
97C2×C4×Dic5D411yescharacteristic
98C2×C4×Dic5D411yescharacteristic
99C2×C4×Dic5D411yescharacteristic
100C2×C4×Dic5C2311yescharacteristic
101C2×C4×Dic5C2311yescharacteristic
102C22×#168C2311yescharacteristic
103C22×#168C2311yescharacteristic
104#4034—22no—
105#4034C2×C414yescomplemented
106C4×Dic10—44no—
107C5×#102—22no—
108C5×#102C2×C414yes—
109C5×#97—22no—
110C5×#95—21no—
111#3964—22no—
112#3964C2×C414yes—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119#3950C2×C414yescomplemented
120#3949—22no—
121#3946—22no—
122#3946C2×C414yescomplemented
123#3940—22no—
124#3939C2×C414yescomplemented
125#3935—22no—
126C2×#474—51no—
127C4×C4⋊Q8—51no—
128C42×D4—51no—
129#1988—51no—
130#1948—51no—
131#1921—51no—
132#1921—51no—
133#1864—51no—
134#1864—51no—
135#1802—51no—
136#1776—51no—
137#1776—51no—
138#1767—51no—
139#1762—51no—
140#1762D511yescharacteristic
141C24×C5—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4C22×C412yes—
146C2×C5×D4C2×Q812yes—
147C2×C5×D4#4112yes—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—24no—
151C22×C4×C5—21no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2411yescharacteristic
157C22×Dic5—24no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—24no—
162C22×Dic5—21no—
163C22×Dic5—42no—
164C22×Dic5—42no—
165C22×Dic5—42no—
166C22×Dic5—42no—
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169C22×Dic5C2×D411yescharacteristic
170C22×Dic5C2×D411yescharacteristic
171C2×Dic10—24no—
172C2×Dic10—42no—
173C2×Dic10—42no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8C22×C412yes—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C412yes—
185C5×C4⋊C4C2×Q812yes—
186C5×C22⋊C4—24no—
187C42×C5—42no—
188C42×C5C2×Q812yes—
189C42×C5#4112yes—
190C22⋊Dic5—24no—
191C22⋊Dic5—24no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—42no—
198C4⋊Dic5C22×C412yes—
199C4⋊Dic5C22×C412yes—
200C4⋊Dic5#4112yes—
201#683—24no—
202#683—42no—
203#683—42no—
204#683—42no—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5—22no—
208C4×Dic5—22no—
209C4×Dic5—22no—
210C4×Dic5—41no—
211C4×Dic5—42no—
212C4×Dic5—42no—
213C4×Dic5—42no—
214C4×Dic5—42no—
215C4×Dic5C22×C412yes—
216C4×Dic5#4112yes—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168C22×C412yes—
223C2×C4⋊Q8—51no—
224C2×C4×Q8—101no—
225C2×C4×D4—51no—
226C2×C4×D4—51no—
227C2×C4×D4C2×D511yescharacteristic
228C22×C42—101no—
229#474—58no—
230C2×#107—51no—
231C2×#107—51no—
232C2×#106—51no—
233C2×#106—51no—
234C2×C4⋊C8—51no—
235C2×C4⋊C8—51no—
236C2×#102—51no—
237C2×#102—51no—
238C2×#102C2×D511yescharacteristic
239C2×#102C2×D511yescharacteristic
240C2×#97—51no—
241C2×#97C2×D511yescharacteristic
242#391—101no—
243#389—51no—
244#389—51no—
245#389—101no—
246#384—51no—
247C4×C4⋊C4—51no—
248C4×C4⋊C4—51no—
249C4×C4⋊C4—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—101no—
252C4×C4⋊C4C2×D511yescharacteristic
253C4×C22⋊C4—101no—
254C4×C22⋊C4—101no—
255C4×C22⋊C4—101no—
256C43—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340C2×D511yescharacteristic
264#340C2×D511yescharacteristic
265#336—51no—
266#336—51no—
267C23×C5—22no—
268C23×C5—22no—
269C23×C5—22no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5C22×D411yescharacteristic
275C5×D4—22no—
276C5×D4—22no—
277C5×D4—22no—
278C5×D4C4×Q814yescomplemented
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—48no—
286C2×C4×C5—41no—
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×C5C22⋊Q812yes—
294C2×C4×C5C22⋊Q812yes—
295C2×C4×C5C23×C411yescharacteristic
296C2×C4×C5C22×Q811yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×C4×C5C2×#4111yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C2×C4×C5C2×#4111yescharacteristic
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—21no—
308C2×Dic5—22no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—48no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—48no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5C4×D412yes—
323C2×Dic5C4×D412yes—
324C2×Dic5AGL(1,ℤ/8)12yes—
325C2×Dic5AGL(1,ℤ/8)12yes—
326C2×Dic5#13712yes—
327Dic10—48no—
328C5×C8—22no—
329C5×C8—41no—
330#168—22no—
331#168—41no—
332C22×Q8—101no—
333C22×D4C22×D511yescharacteristic
334C23×C4—21no—
335C23×C4—101no—
336C23×C4—101no—
337C22×C8—51no—
338C22×C8—51no—
339C22×C8C22×D511yescharacteristic
340C22×C8C22×D511yescharacteristic
341C4⋊Q8—54no—
342C4⋊Q8—102no—
343C4×Q8—204no—
344C4×D4—22no—
345C4×D4—54no—
346C4×D4—102no—
347C4×D4—102no—
348C4×D4—102no—
349C4×D4Dic1014yescomplemented
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4—101no—
356C2×C4⋊C4—101no—
357C2×C4⋊C4—101no—
358C2×C4⋊C4—101no—
359C2×C4⋊C4C22×D511yescharacteristic
360C2×C4⋊C4C22×D511yescharacteristic
361C2×C4⋊C4C22×D511yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—101no—
364C2×C22⋊C4—101no—
365C2×C42—21no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42—51no—
370C2×C42—51no—
371C2×C42—51no—
372C2×C42—101no—
373C2×C42—101no—
374C2×C42—101no—
375C2×C42—101no—
376C2×C42—204no—
377C2×C42C22×D511yescharacteristic
378#107—54no—
379#107—54no—
380#106—102no—
381#106—102no—
382C4⋊C8—54no—
383C4⋊C8—102no—
384#102—22no—
385#102—54no—
386#102—102no—
387#102C4×D514yes—
388#97—22no—
389#97—102no—
390#95—21no—
391#95—101no—
392#95—101no—
393#95—101no—
394#95—101no—
395#95—101no—
396#95—101no—
397C22×C5—24no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5—42no—
401C22×C5—42no—
402C22×C5—42no—
403C22×C5—42no—
404C22×C5C2×C4×D411yescharacteristic
405C22×C5C2×C22⋊Q811yescharacteristic
406C22×C5#52511yescharacteristic
407C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C5C2×#13711yescharacteristic
410C22×C5#57511yescharacteristic
411C4×C5—22no—
412C4×C5—22no—
413C4×C5—42no—
414C4×C5—42no—
415C4×C5—81no—
416C4×C5C2×C4×Q811yescharacteristic
417C4×C5C4×#4111yescharacteristic
418C4×C5#52911yescharacteristic
419C4×C5#53311yescharacteristic
420Dic5—22no—
421Dic5—22no—
422Dic5—42no—
423Dic5—41no—
424Dic5—42no—
425Dic5—42no—
426Dic5—81no—
427Dic5#44214yes—
428C24—21no—
429C2×Q8—104no—
430C2×Q8—202no—
431C2×Q8—202no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4C2×Dic1012yes—
436C2×D4C2×C4×D512yes—
437C2×D4#70912yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—104no—
449C22×C4—104no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4—202no—
455C22×C4—202no—
456C22×C4—202no—
457C22×C4—202no—
458C22×C4D4×D511yescharacteristic
459C22×C4D4×D511yescharacteristic
460C22×C4C23×D511yescharacteristic
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—52no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8C2×C4×D512yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—52no—
478C4⋊C4—52no—
479C4⋊C4—52no—
480C4⋊C4—104no—
481C4⋊C4—101no—
482C4⋊C4—101no—
483C4⋊C4—101no—
484C4⋊C4—101no—
485C4⋊C4—101no—
486C4⋊C4—202no—
487C4⋊C4—202no—
488C4⋊C4—202no—
489C4⋊C4—202no—
490C4⋊C4C2×Dic1012yes—
491C4⋊C4C2×C4×D512yes—
492C22⋊C4—24no—
493C22⋊C4—104no—
494C22⋊C4—104no—
495C42—42no—
496C42—52no—
497C42—52no—
498C42—102no—
499C42—102no—
500C42—102no—
501C42—101no—
502C42—101no—
503C42—201no—
504C42—202no—
505C42—202no—
506C42—202no—
507C42—202no—
508C42C2×Dic1012yes—
509C42#71112yes—
510C2×C5—44no—
511C2×C5C4×C22⋊Q811yescharacteristic
512C2×C5C2×#44211yescharacteristic
513C2×C5C4×#13711yescharacteristic
514C2×C5#307711yescharacteristic
515C2×C5#307911yescharacteristic
516C2×C5#311011yescharacteristic
517C2×C5#311511yescharacteristic
518C23—22no—
519C23—22no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C2×D4×D511yescharacteristic
526Q8—208no—
527D4—22no—
528D4—22no—
529D4—22no—
530D4C4×Dic1014yescomplemented
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—48no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—52no—
549C2×C4—52no—
550C2×C4—101no—
551C2×C4—101no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—101no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—101no—
559C2×C4—102no—
560C2×C4—208no—
561C2×C4—208no—
562C2×C4—201no—
563C2×C4—201no—
564C2×C4—201no—
565C2×C4—201no—
566C2×C4—201no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—201no—
570C2×C4—201no—
571C2×C4#402412yes—
572C2×C4#402412yes—
573C2×C4C22×Dic1011yescharacteristic
574C2×C4C22×C4×D511yescharacteristic
575C2×C4C2×#70911yescharacteristic
576C2×C4C2×#71111yescharacteristic
577C2×C4D5×#4111yescharacteristic
578C2×C4D5×#4111yescharacteristic
579C8—22no—
580C8—41no—
581C8—102no—
582C8—201no—
583C5#2161311yescharacteristic, complemented, Sylow
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22C2×#402411yescharacteristic
592C22C4×D4×D511yescharacteristic
593C22#6588111yescharacteristic
594C22D5×AGL(1,ℤ/8)11yescharacteristic
595C22D5×AGL(1,ℤ/8)11yescharacteristic
596C22#6610711yescharacteristic
597C22D5×#13711yescharacteristic
598C4—22no—
599C4—22no—
600C4—42no—
601C4—42no—
602C4—54no—
603C4—81no—
604C4—102no—
605C4—102no—
606C4—202no—
607C4—202no—
608C4—202no—
609C4—201no—
610C4—401no—
611C4C2×C4×Dic1011yescharacteristic
612C4#6585111yescharacteristic
613C4C4×#71111yescharacteristic
614C4#6587211yescharacteristic
615C2—44no—
616C2C4×#402411yescharacteristic
617C2#1061060111yescharacteristic
618C2#1061064811yescharacteristic
619C2#1061150511yescharacteristic
620C2#1061151011yescharacteristic
621C2D5×#44211yescharacteristic
622C2#1061160311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1762C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenter#1762D5
hypocenterC5#21613
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C4×#4034C2semidirect
9. #10600607C2semidirect
10. #10600602C2semidirect
11. #10600274C2semidirect
12. #10599614C2semidirect
13. #10599613C2semidirect
14. #10599593C2semidirect
15. #10599589C2semidirect
47. #65048C4semidirect
69. C4×C5×D4Q8semidirect
105. #4034C2×C4semidirect
119. #3950C2×C4semidirect
122. #3946C2×C4semidirect
124. #3939C2×C4semidirect
278. C5×D4C4×Q8semidirect
349. C4×D4Dic10semidirect
530. D4C4×Dic10semidirect
583. C5#21613semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic52
C2×#650482
C4×#40342
C5×#17622
#106024022
#106009632
#106009622
#106009462
#106006072
#106006022
#106002742
#105996142
#105996132
#105995932
#105995892
#216135