Finite Group Databasebeta

← #12101491

Subgroups — #12101491

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65170C211yesmaximal, characteristic
2#10607699C211yesmaximal, characteristic
3#10605481C211yesmaximal, characteristic
4C5×#1921C211yesmaximal, characteristic, complemented
5#10601402C211yesmaximal, characteristic, complemented
6#10600393C211yesmaximal, characteristic, complemented
7#10600253C211yesmaximal, characteristic, complemented
8#10599660C211yesmaximal, characteristic
9#10599659C211yesmaximal, characteristic
10D5×#340C211yesmaximal, characteristic
11#10599614C211yesmaximal, characteristic, complemented
12#10599611C211yesmaximal, characteristic, complemented
13#10599581C211yesmaximal, characteristic, complemented
14#10599454C211yesmaximal, characteristic
15#10599415C211yesmaximal, characteristic, complemented
16C22×#676C2211yescharacteristic
17C22×C8×D5C2211yescharacteristic
18C2×#4038C2211yescharacteristic
19C2×#4038C2211yescharacteristic
20C2×D5×C4⋊C4C2211yescharacteristic
21C2×D5×C4⋊C4C2211yescharacteristic
22C2×#4018C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C5×#389C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26C2×#3949C2211yescharacteristic
27#65278—21no—
28#65274C2211yescharacteristic
29#65265—21no—
30C4⋊C4×Dic5C2211yescharacteristic
31C4⋊C4×Dic5C2211yescharacteristic
32#65262C2211yescharacteristic
33C2×#3940C2211yescharacteristic
34C2×#3939C2211yescharacteristic
35C4×#685—21no—
36C4×C4⋊Dic5C2211yescharacteristic
37C4×#683—21no—
38#65217C2211yescharacteristic
39#65170C418yescomplemented
40#64957—21no—
41#64955—21no—
42#64939—21no—
43#64938—21no—
44C5×#340C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
47C5×#336C2211yescharacteristic
48#64771C2211yescharacteristic
49#64771C2211yescharacteristic
50#64771C2211yescharacteristic
51#64770C2211yescharacteristic
52#64770C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64744C2211yescharacteristic
60#21035—51nomaximal, Sylow
61C22×C4×D5—21no—
62C22×C4×D5—21no—
63C22×C4×D5C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C42×C5—21no—
72C2×C42×C5C2311yescharacteristic
73C2×#685—21no—
74C2×#685—21no—
75C2×#685D411yescharacteristic
76C2×#685D411yescharacteristic
77C2×C4⋊Dic5—21no—
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
82C2×#683—21no—
83C2×#683—21no—
84C2×#683—21no—
85C2×#683—21no—
86C2×#683D411yescharacteristic
87C2×#683D411yescharacteristic
88C2×C4×Dic5—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C2×#676—22no—
97C2×#676—22no—
98C2×#676C2×C414yes—
99C2×C8×D5—22no—
100C2×C8×D5—22no—
101C2×C8×D5—22no—
102#4038—22no—
103#4038—22no—
104#4038C2×C414yes—
105#4038Q814yes—
106D5×C4⋊C4—22no—
107D5×C4⋊C4—22no—
108D5×C4⋊C4—22no—
109D5×C4⋊C4C2×C414yes—
110#4018—22no—
111#4018—22no—
112C5×#107C2×C414yescomplemented
113C5×#95—21no—
114C5×#95—21no—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119#3963—21no—
120#3963—21no—
121#3949C2×C414yescomplemented
122#3940C2×C414yescomplemented
123#3939C2×C414yescomplemented
124C2×#428—51no—
125#2317—51no—
126#2274—51no—
127#1921—51no—
128#1921D511yescharacteristic, complemented
129#1920—51no—
130#1920—51no—
131#1919—51no—
132#1919—51no—
133#1918—51no—
134#1918—51no—
135#1736—51no—
136#1735—51no—
137C2×#340—51no—
138#1729—51no—
139C23×D5C2×D411yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2411yescharacteristic
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5C2×D411yescharacteristic
152C22×Dic5C2×D411yescharacteristic
153C22×Dic5C2×D411yescharacteristic
154C2×C4×D5—24no—
155C2×C4×D5—42no—
156C2×C4×D5—81no—
157C2×C4×D5—81no—
158C2×C4×D5—81no—
159C2×C4×D5—81no—
160C2×C4×D5C22×C412yes—
161C2×C4×D5C2×Q812yes—
162C2×C4×D5#4112yes—
163C2×C4×D5#4112yes—
164C2×C4×D5#4112yes—
165C2×C4×D5#4112yes—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8C22×C412yes—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—81no—
178C5×C4⋊C4C22×C412yes—
179C5×C4⋊C4C22×C412yes—
180C5×C4⋊C4C2×Q812yes—
181C42×C5—21no—
182C42×C5—21no—
183C42×C5—81no—
184#685—24no—
185#685—24no—
186#685—22no—
187#685—22no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—81no—
194C4⋊Dic5C22×C412yes—
195C4⋊Dic5C22×C412yes—
196C4⋊Dic5C2×Q812yes—
197#683—24no—
198#683—22no—
199#683—22no—
200#683—42no—
201#683—81no—
202#683—81no—
203C4×Dic5—21no—
204C4×Dic5—21no—
205C4×Dic5—24no—
206C4×Dic5—24no—
207C4×Dic5—81no—
208C4×Dic5—81no—
209C4×Dic5—81no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168C22×C412yes—
216#676—28no—
217C8×D5—44no—
218C22×M16—51no—
219C23×C8—51no—
220C2×#117—51no—
221C2×#117—51no—
222C2×#117—51no—
223C22×C4⋊C4—51no—
224C22×C4⋊C4—51no—
225#428—58no—
226C2×#107—51no—
227C2×#107C2×D511yescharacteristic
228C2×#106—51no—
229C2×#106—51no—
230#389—51no—
231#389—51no—
232#389—51no—
233#389C2×D511yescharacteristic
234#385—101no—
235#385—101no—
236#384—101no—
237#382—101no—
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—101no—
242C4×C4⋊C4—101no—
243C4×C4⋊C4C2×D511yescharacteristic
244C4×C22⋊C4—101no—
245C4×C22⋊C4—101no—
246#340—51no—
247#340—51no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340C2×D511yescharacteristic
256#340C2×D511yescharacteristic
257#340C2×D511yescharacteristic
258#336—51no—
259#336—51no—
260#336—51no—
261#336C2×D511yescharacteristic
262C23×C5C22×D411yescharacteristic
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—21no—
267C22×D5C4×D412yes—
268C22×D5C22⋊Q812yes—
269C22×D5#12312yes—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
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—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
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—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
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×Dic5C4×D412yes—
313C2×Dic5C22⋊Q812yes—
314C2×Dic5#12312yes—
315C4×D5—84no—
316C4×D5—84no—
317C4×D5#11714yes—
318C4×D5C4×Q814yes—
319C4×D5#12514yes—
320C4×D5#12614yes—
321C5×C8—22no—
322C5×C8—41no—
323#168—22no—
324#168—41no—
325C23×C4—51no—
326C23×C4—101no—
327C23×C4—101no—
328C2×M16—54no—
329C2×M16—102no—
330C2×M16—102no—
331C22×C8—51no—
332C22×C8—51no—
333C22×C8—102no—
334C22×C8—102no—
335C22×C8—102no—
336C22×C8C22×D511yescharacteristic
337C22×C8C22×D511yescharacteristic
338#117—54no—
339#117—54no—
340#117—102no—
341#117—102no—
342#117—102no—
343#117—102no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—54no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—102no—
353C2×C4⋊C4—102no—
354C2×C4⋊C4—102no—
355C2×C4⋊C4—101no—
356C2×C4⋊C4—101no—
357C2×C4⋊C4—101no—
358C2×C4⋊C4—101no—
359C2×C4⋊C4—101no—
360C2×C4⋊C4C22×D511yescharacteristic
361C2×C4⋊C4C22×D511yescharacteristic
362C2×C4⋊C4C22×D511yescharacteristic
363C2×C4⋊C4C22×D511yescharacteristic
364C2×C22⋊C4—51no—
365C2×C22⋊C4—51no—
366C2×C22⋊C4—101no—
367C2×C22⋊C4—101no—
368C2×C42—21no—
369C2×C42—51no—
370C2×C42—101no—
371C2×C42—101no—
372C2×C42—101no—
373C2×C42—101no—
374C2×C42—101no—
375C2×C42C22×D511yescharacteristic
376#107—54no—
377#107C4×D514yescomplemented
378#106—54no—
379#106—54no—
380#95—21no—
381#95—21no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386#95—101no—
387#95—101no—
388C22×C5C2×C4×D411yescharacteristic
389C22×C5C2×C22⋊Q811yescharacteristic
390C22×C5C2×#12311yescharacteristic
391C22×C5#57611yescharacteristic
392C22×C5#57711yescharacteristic
393C22×C5#57711yescharacteristic
394C22×C5#57811yescharacteristic
395C2×D5—22no—
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—22no—
400C2×D5—22no—
401C2×D5#38714yes—
402C4×C5—42no—
403C4×C5—41no—
404C4×C5—41no—
405C4×C5—42no—
406C4×C5—42no—
407C4×C5—81no—
408C4×C5C2×#11711yescharacteristic
409C4×C5C2×C4×Q811yescharacteristic
410C4×C5C2×#12511yescharacteristic
411C4×C5C2×#12611yescharacteristic
412Dic5—42no—
413Dic5—41no—
414Dic5—41no—
415Dic5—42no—
416Dic5—42no—
417Dic5—81no—
418Dic5#38714yes—
419C24—51no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—51no—
425C22×C4—52no—
426C22×C4—52no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—52no—
430C22×C4—52no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—104no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—202no—
439C22×C4—401no—
440C22×C4—401no—
441C22×C4—401no—
442C22×C4—401no—
443C22×C4D4×D511yescharacteristic
444C22×C4D4×D511yescharacteristic
445C22×C4C23×D511yescharacteristic
446M16—108no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—52no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—204no—
459C2×C8C2×C4×D512yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—52no—
466C4⋊C4—52no—
467C4⋊C4—52no—
468C4⋊C4—81no—
469C4⋊C4—104no—
470C4⋊C4—102no—
471C4⋊C4—102no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—202no—
478C4⋊C4—401no—
479C4⋊C4—401no—
480C4⋊C4—401no—
481C4⋊C4C2×C4×D512yes—
482C4⋊C4C2×C4×D512yes—
483C4⋊C4Q8×D512yes—
484C22⋊C4—102no—
485C22⋊C4—102no—
486C22⋊C4—104no—
487C22⋊C4—104no—
488C42—21no—
489C42—21no—
490C42—81no—
491C42—104no—
492C42—104no—
493C42—101no—
494C42—101no—
495C42—401no—
496C42—401no—
497C42—401no—
498C2×C5C2×#38711yescharacteristic
499C2×C5#294611yescharacteristic
500C2×C5#294711yescharacteristic
501C2×C5#308311yescharacteristic
502C2×C5#308411yescharacteristic
503C2×C5#309611yescharacteristic
504C2×C5#309711yescharacteristic
505D5—24no—
506C23—52no—
507C23—52no—
508C23—52no—
509C23—101no—
510C23—101no—
511C23—101no—
512C23—101no—
513C23C2×D4×D511yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—52no—
535C2×C4—54no—
536C2×C4—54no—
537C2×C4—54no—
538C2×C4—54no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—404no—
558C2×C4—404no—
559C2×C4C22×C4×D511yescharacteristic
560C2×C4C2×Q8×D511yescharacteristic
561C2×C4D5×#4111yescharacteristic
562C2×C4D5×#4111yescharacteristic
563C2×C4D5×#4111yescharacteristic
564C2×C4D5×#4111yescharacteristic
565C8—22no—
566C8—41no—
567C8—102no—
568C8—201no—
569C5#2103511yescharacteristic, complemented, Sylow
570C22—54no—
571C22—102no—
572C22—102no—
573C22—102no—
574C22—102no—
575C22—102no—
576C22—102no—
577C22C4×D4×D511yescharacteristic
578C22D5×C22⋊Q811yescharacteristic
579C22D5×#12311yescharacteristic
580C22#6610011yescharacteristic
581C22#6610411yescharacteristic
582C22#6610811yescharacteristic
583C22#6610911yescharacteristic
584C4—41no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—54no—
590C4—81no—
591C4—202no—
592C4—201no—
593C4—202no—
594C4—201no—
595C4—202no—
596C4—401no—
597C4D5×#11711yescharacteristic
598C4C4×Q8×D511yescharacteristic
599C4D5×#12511yescharacteristic
600C4D5×#12611yescharacteristic
601C2—104no—
602C2D5×#38711yescharacteristic
603C2#1061145011yescharacteristic
604C2#1061159711yescharacteristic
605C2#1061284211yescharacteristic
606C2#1061290211yescharacteristic
607C2#1061310611yescharacteristic
608C2#1061320111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1921C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1921D5
hypocenterC5#21035
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. C5×#1921C2semidirect
5. #10601402C2semidirect
6. #10600393C2semidirect
7. #10600253C2semidirect
11. #10599614C2semidirect
12. #10599611C2semidirect
13. #10599581C2semidirect
15. #10599415C2semidirect
39. #65170C4semidirect
112. C5×#107C2×C4semidirect
121. #3949C2×C4semidirect
122. #3940C2×C4semidirect
123. #3939C2×C4semidirect
128. #1921D5semidirect
377. #107C4×D5semidirect
569. C5#21035semidirect

Maximal subgroups

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

subgroupindex
C2×#651702
#106076992
#106054812
C5×#19212
#106014022
#106003932
#106002532
#105996602
#105996592
D5×#3402
#105996142
#105996112
#105995812
#105994542
#105994152
#210355