Finite Group Databasebeta

← #12107089

Subgroups — #12107089

Order 1280.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614048C211yesmaximal, characteristic
2C2×#65048C211yesmaximal, characteristic
3#10605358C211yesmaximal, characteristic, complemented
4C5×#1762C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic
6#10600963C211yesmaximal, characteristic
7#10600960C211yesmaximal, characteristic
8#10600947C211yesmaximal, characteristic
9#10600625C211yesmaximal, characteristic, complemented
10#10600607C211yesmaximal, characteristic, complemented
11C4×#3939C211yesmaximal, characteristic, complemented
12#10599613C211yesmaximal, characteristic, complemented
13#10599608C211yesmaximal, characteristic, complemented
14#10599592C211yesmaximal, characteristic, complemented
15#10599590C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×D4×Dic5C2211yescharacteristic
18C2×D4×Dic5C2211yescharacteristic
19C2×#4034C2211yescharacteristic
20C2×C5×#102C2211yescharacteristic
21C2×C5×#102C2211yescharacteristic
22C2×C5×#97C2211yescharacteristic
23C4×C5×C4⋊C4C2211yescharacteristic
24C2×#3964C2211yescharacteristic
25C2×#3964C2211yescharacteristic
26C4×C22⋊Dic5—21no—
27C2×#3963—21no—
28C2×#3950C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31C2×#3946C2211yescharacteristic
32#65274C2211yescharacteristic
33#65266C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36#65262C2211yescharacteristic
37C2×#3939C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C22⋊C4×Dic5—21no—
40C22⋊C4×Dic5—21no—
41C4×C4⋊Dic5C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65222—21no—
44#65221C2211yescharacteristic
45#65218—21no—
46C2×C4×#168C2211yescharacteristic
47#65048C418yescomplemented
48#64944—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#21624—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×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97#4034—22no—
98#4034C2×C414yescomplemented
99C5×#102—22no—
100C5×#102C2×C414yes—
101C5×#97—22no—
102C5×#95—21no—
103#3964—22no—
104#3964C2×C414yes—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963D411yescharacteristic
114#3963D411yescharacteristic
115#3963D411yescharacteristic
116#3963D411yescharacteristic
117#3950C2×C414yescomplemented
118#3949—22no—
119#3946—22no—
120#3946C2×C414yescomplemented
121#3939—22no—
122#3939C2×C414yescomplemented
123C4×#168—22no—
124C2×#474—51no—
125#2331—51no—
126#2275—51no—
127#1987—51no—
128#1949—51no—
129#1921—51no—
130#1918—51no—
131#1864—51no—
132#1862—51no—
133#1804—51no—
134#1776—51no—
135C4×#107—51no—
136#1768—51no—
137#1762D511yescharacteristic
138C4×#102—51no—
139C24×C5—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4C22×C412yes—
144C2×C5×D4C2×Q812yes—
145C2×C5×D4#4112yes—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—24no—
149C22×C4×C5—21no—
150C22×C4×C5—81no—
151C22×C4×C5—81no—
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2411yescharacteristic
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—24no—
159C22×Dic5—24no—
160C22×Dic5—21no—
161C22×Dic5—81no—
162C22×Dic5—81no—
163C22×Dic5—81no—
164C22×Dic5—81no—
165C22×Dic5C2×D411yescharacteristic
166C22×Dic5C2×D411yescharacteristic
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169C2×Dic10—24no—
170C2×Dic10—81no—
171C2×Dic10—81no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8C22×C412yes—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4C22×C412yes—
183C5×C4⋊C4C2×Q812yes—
184C5×C22⋊C4—24no—
185C42×C5—81no—
186C42×C5C2×Q812yes—
187C42×C5#4112yes—
188C22⋊Dic5—24no—
189C22⋊Dic5—24no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—81no—
196C4⋊Dic5C22×C412yes—
197C4⋊Dic5C22×C412yes—
198C4⋊Dic5#4112yes—
199#683—24no—
200#683—81no—
201C4×Dic5—21no—
202C4×Dic5—21no—
203C4×Dic5—81no—
204C4×Dic5—81no—
205C4×Dic5—81no—
206C4×Dic5—81no—
207C4×Dic5C22×C412yes—
208C4×Dic5#4112yes—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168C22×C412yes—
215C2×C4⋊Q8—51no—
216C2×C4×D4—51no—
217C2×C4×D4—51no—
218C2×C4×D4C2×D511yescharacteristic
219#474—58no—
220C2×#107—51no—
221C2×#107—51no—
222C2×#107—51no—
223C2×#106—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×#102—51no—
227C2×#102—51no—
228C2×#102C2×D511yescharacteristic
229C2×#102C2×D511yescharacteristic
230C2×#97C2×D511yescharacteristic
231C2×C4×C8—51no—
232#391—101no—
233#391—101no—
234#389—51no—
235#389—51no—
236#387—101no—
237#387—101no—
238#382—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—51no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4C2×D511yescharacteristic
244C4×C22⋊C4—101no—
245C4×C22⋊C4—101no—
246C4×C22⋊C4—101no—
247#376—51no—
248C2×#95—101no—
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#336—51no—
258#336—51no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5C22×D411yescharacteristic
267C5×D4—22no—
268C5×D4—22no—
269C5×D4—22no—
270C5×D4C4×Q814yes—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—84no—
285C2×C4×C5C22⋊Q812yes—
286C2×C4×C5C22⋊Q812yes—
287C2×C4×C5C23×C411yescharacteristic
288C2×C4×C5C22×Q811yescharacteristic
289C2×C4×C5C2×#4111yescharacteristic
290C2×C4×C5C2×#4111yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—84no—
316C2×Dic5—84no—
317C2×Dic5C4×D412yes—
318C2×Dic5C4×D412yes—
319Dic10—84no—
320C5×C8—22no—
321C5×C8—41no—
322#168—22no—
323#168—41no—
324C22×Q8—101no—
325C22×D4C22×D511yescharacteristic
326C23×C4—21no—
327C23×C4—101no—
328C23×C4—101no—
329C22×C8—51no—
330C22×C8—51no—
331C22×C8C22×D511yescharacteristic
332C22×C8C22×D511yescharacteristic
333C4⋊Q8—54no—
334C4⋊Q8—102no—
335C4×D4—22no—
336C4×D4—54no—
337C4×D4—102no—
338C4×D4—102no—
339C4×D4—102no—
340C4×D4Dic1014yescomplemented
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4C22×D511yescharacteristic
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—101no—
353C2×C22⋊C4—101no—
354C2×C42—21no—
355C2×C42—51no—
356C2×C42—51no—
357C2×C42—101no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42C22×D511yescharacteristic
362#107—54no—
363#107—54no—
364#107—102no—
365#106—102no—
366C4⋊C8—54no—
367C4⋊C8—102no—
368#102—22no—
369#102—54no—
370#102—102no—
371#102C4×D514yes—
372#97—22no—
373C4×C8—102no—
374#95—21no—
375#95—51no—
376#95—51no—
377#95—51no—
378#95—51no—
379#95—101no—
380#95—101no—
381#95—101no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386#95—101no—
387C22×C5—24no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5—42no—
394C22×C5C2×C4×D411yescharacteristic
395C22×C5C2×C22⋊Q811yescharacteristic
396C22×C5#52511yescharacteristic
397C22×C5#57611yescharacteristic
398C22×C5#57611yescharacteristic
399C22×C5#57711yescharacteristic
400C22×C5#57811yescharacteristic
401C4×C5—22no—
402C4×C5—22no—
403C4×C5—42no—
404C4×C5—42no—
405C4×C5—81no—
406C4×C5C2×C4×Q811yescharacteristic
407C4×C5C4×#4111yescharacteristic
408C4×C5#52911yescharacteristic
409C4×C5#53311yescharacteristic
410Dic5—22no—
411Dic5—22no—
412Dic5—41no—
413Dic5—42no—
414Dic5—41no—
415Dic5—42no—
416Dic5—42no—
417Dic5—81no—
418C24—21no—
419C2×Q8—104no—
420C2×Q8—401no—
421C2×Q8—401no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C2×Dic1012yes—
426C2×D4C2×C4×D512yes—
427C2×D4#70912yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—104no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—104no—
443C22×C4—101no—
444C22×C4—401no—
445C22×C4—401no—
446C22×C4—401no—
447C22×C4—401no—
448C22×C4D4×D511yescharacteristic
449C22×C4D4×D511yescharacteristic
450C22×C4C23×D511yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—52no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8C2×C4×D512yes—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—52no—
468C4⋊C4—52no—
469C4⋊C4—52no—
470C4⋊C4—104no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—401no—
477C4⋊C4—401no—
478C4⋊C4C2×Dic1012yes—
479C4⋊C4C2×C4×D512yes—
480C22⋊C4—24no—
481C22⋊C4—104no—
482C22⋊C4—104no—
483C42—52no—
484C42—52no—
485C42—81no—
486C42—101no—
487C42—101no—
488C42—401no—
489C42—401no—
490C42—401no—
491C42—401no—
492C42C2×Dic1012yes—
493C42#71112yes—
494C2×C5—44no—
495C2×C5C4×C22⋊Q811yescharacteristic
496C2×C5#294711yescharacteristic
497C2×C5#294811yescharacteristic
498C2×C5#308111yescharacteristic
499C2×C5#308311yescharacteristic
500C2×C5#311811yescharacteristic
501C2×C5#312411yescharacteristic
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C2×D4×D511yescharacteristic
510Q8—404no—
511D4—22no—
512D4—22no—
513D4—22no—
514D4C4×Dic1014yes—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—52no—
529C2×C4—52no—
530C2×C4—84no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—101no—
542C2×C4—101no—
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—404no—
554C2×C4—404no—
555C2×C4#402412yes—
556C2×C4#402412yes—
557C2×C4C22×Dic1011yescharacteristic
558C2×C4C22×C4×D511yescharacteristic
559C2×C4C2×#70911yescharacteristic
560C2×C4C2×#71111yescharacteristic
561C2×C4D5×#4111yescharacteristic
562C2×C4D5×#4111yescharacteristic
563C8—22no—
564C8—41no—
565C8—102no—
566C8—201no—
567C5#2162411yescharacteristic, complemented, Sylow
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22C2×#402411yescharacteristic
576C22C4×D4×D511yescharacteristic
577C22#6588111yescharacteristic
578C22#6610811yescharacteristic
579C22#6610811yescharacteristic
580C22#6610911yescharacteristic
581C22#6611311yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—81no—
587C4—102no—
588C4—102no—
589C4—201no—
590C4—202no—
591C4—202no—
592C4—201no—
593C4—202no—
594C4—401no—
595C4C2×C4×Dic1011yescharacteristic
596C4#6585111yescharacteristic
597C4C4×#71111yescharacteristic
598C4#6587211yescharacteristic
599C2—44no—
600C2C4×#402411yescharacteristic
601C2#1061060311yescharacteristic
602C2#1061064911yescharacteristic
603C2#1061150711yescharacteristic
604C2#1061151911yescharacteristic
605C2#1061159811yescharacteristic
606C2#1061161711yescharacteristic
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#21624
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. #10605358C2semidirect
9. #10600625C2semidirect
10. #10600607C2semidirect
11. C4×#3939C2semidirect
12. #10599613C2semidirect
13. #10599608C2semidirect
14. #10599592C2semidirect
15. #10599590C2semidirect
47. #65048C4semidirect
69. C4×C5×D4Q8semidirect
98. #4034C2×C4semidirect
117. #3950C2×C4semidirect
120. #3946C2×C4semidirect
122. #3939C2×C4semidirect
340. C4×D4Dic10semidirect
567. C5#21624semidirect

Maximal subgroups

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

subgroupindex
#106140482
C2×#650482
#106053582
C5×#17622
C4×#39642
#106009632
#106009602
#106009472
#106006252
#106006072
C4×#39392
#105996132
#105996082
#105995922
#105995902
#216245