Finite Group Databasebeta

← #12109673

Subgroups — #12109673

Order 1280.

818 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊C8C211yesmaximal, characteristic
2#10605878C211yesmaximal, characteristic
3#10605483C211yesmaximal, characteristic
4C5×#1949C211yesmaximal, characteristic, complemented
5#10601423C211yesmaximal, characteristic
6#10601409C211yesmaximal, characteristic, complemented
7#10601370C211yesmaximal, characteristic
8#10601357C211yesmaximal, characteristic, complemented
9#10601248C211yesmaximal, characteristic, complemented
10#10600333C211yesmaximal, characteristic, complemented
11#10600261C211yesmaximal, characteristic, complemented
12#10599662C211yesmaximal, characteristic
13#10599661C211yesmaximal, characteristic
14#10599591C211yesmaximal, characteristic, complemented
15#10599590C211yesmaximal, characteristic, complemented
16C22×C8×D5C2211yescharacteristic
17C22×C8×D5C2211yescharacteristic
18C2×C42×D5C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C5×#382C2211yescharacteristic
23C4×C5×C4⋊C4C2211yescharacteristic
24C2×#3950C2211yescharacteristic
25C2×#3949C2211yescharacteristic
26C2×#3946C2211yescharacteristic
27C2×#3946C2211yescharacteristic
28#65276C2211yescharacteristic
29#65276C2211yescharacteristic
30#65276C2211yescharacteristic
31#65276C2211yescharacteristic
32#65266C2211yescharacteristic
33#65266C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C4×#685—21no—
41#65225C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65221—21no—
44C2×C4⋊#168C2211yescharacteristic
45D5×C4⋊C8C418yescomplemented
46#64955—21no—
47#64953—21no—
48#64953—21no—
49#64940—21no—
50#64940—21no—
51#64937—21no—
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21960—51nomaximal, Sylow
61C22×C4×D5D411yescharacteristic
62C22×C4×D5D411yescharacteristic
63C22×C4×D5C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C2×C5×C4⋊C4C2311yescharacteristic
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C42×C5—21no—
71C2×C42×C5C2311yescharacteristic
72C2×#685—21no—
73C2×#685—21no—
74C2×#685—21no—
75C2×#685—21no—
76C2×C4⋊Dic5C2311yescharacteristic
77C2×C4⋊Dic5C2311yescharacteristic
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4×Dic5—21no—
81C2×C4×Dic5—21no—
82C2×C4×Dic5—21no—
83C2×C4×Dic5D411yescharacteristic
84C2×C4×Dic5D411yescharacteristic
85C2×C4×Dic5C2311yescharacteristic
86C22×#168C2311yescharacteristic
87C22×#168C2311yescharacteristic
88C2×C8×D5—41no—
89C2×C8×D5—41no—
90C2×C8×D5—41no—
91C2×C8×D5—41no—
92C2×C8×D5C2×C414yes—
93C2×C8×D5C2×C414yes—
94C42×D5C2×C414yes—
95C42×D5Q814yes—
96C5×#107—41no—
97C5×#106—41no—
98C5×C4⋊C8C2×C414yes—
99C5×#95—21no—
100C5×#95—21no—
101C5×#95—21no—
102#3963—21no—
103#3963—21no—
104#3963—21no—
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#3963—21no—
114#3963—21no—
115#3950—41no—
116#3949—41no—
117#3946C2×C414yes—
118#3946C2×C414yes—
119#3940—41no—
120#3940—41no—
121#3939—41no—
122#3939—41no—
123C4⋊#168C2×C414yes—
124C22×C4⋊C8—51no—
125#2283—51no—
126#2283—51no—
127#1949—51no—
128#1949—51no—
129#1949—51no—
130#1949—51no—
131#1949—51no—
132#1949—51no—
133#1949—51no—
134#1949D511yescharacteristic, complemented
135#1808—51no—
136#1808—51no—
137#1807—51no—
138#1807—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—22no—
155C2×C4×D5—22no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—41no—
161C2×C4×D5—41no—
162C2×C4×D5C4⋊C414yes—
163C2×C4×D5C4⋊C414yes—
164C2×C4×D5C22×C412yes—
165C2×C4×D5C2×Q812yes—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8C22×C412yes—
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—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C42×C5—42no—
181C42×C5C22×C412yes—
182C42×C5C2×Q812yes—
183#685—42no—
184#685—42no—
185#685—42no—
186#685—42no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4×Dic5—42no—
196C4×Dic5—42no—
197C4×Dic5—42no—
198C4×Dic5C4⋊C414yes—
199C4×Dic5C4⋊C414yes—
200C4×Dic5C22×C412yes—
201C4×Dic5C2×Q812yes—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168C22×C412yes—
207C2×#168C22×C412yes—
208C8×D5—44no—
209C8×D5—44no—
210C23×C8—51no—
211C23×C8—51no—
212C22×C42—51no—
213C2×#107—51no—
214C2×#107—51no—
215C2×#107—51no—
216C2×#107C2×D511yescharacteristic
217C2×#106—51no—
218C2×#106—51no—
219C2×#106—51no—
220C2×#106C2×D511yescharacteristic
221C2×C4⋊C8—51no—
222C2×C4⋊C8—51no—
223C2×C4⋊C8—51no—
224C2×C4⋊C8—58no—
225C2×C4⋊C8C2×D511yescharacteristic
226#383—101no—
227#383—101no—
228#382—51no—
229#382—51no—
230#382—51no—
231#382C2×D511yescharacteristic
232#381—101no—
233#381—101no—
234#380—51no—
235#380—51no—
236#380—51no—
237#380—51no—
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4C2×D511yescharacteristic
242C4×C22⋊C4—101no—
243C4×C22⋊C4—101no—
244#376—101no—
245#376—101no—
246#340—51no—
247#340—51no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340C2×D511yescharacteristic
253#340C2×D511yescharacteristic
254C23×C5C22×D411yescharacteristic
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5—21no—
259C22×D5C2×C4⋊C412yes—
260C22×D5#13512yes—
261C22×D5#13512yes—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5C2×C4⋊C412yes—
279C2×C4×C5C2×C4⋊C412yes—
280C2×C4×C5C23×C411yescharacteristic
281C2×C4×C5C22×Q811yescharacteristic
282C2×C4×C5H(5,𝔽2)11yescharacteristic
283C2×C4×C5H(5,𝔽2)11yescharacteristic
284C2×C4×C52−1+411yescharacteristic
285C2×C4×C52−1+411yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5C2×C4⋊C412yes—
305C2×Dic5C2×C4⋊C412yes—
306C2×Dic5C2×C4⋊C412yes—
307C4×D5—28no—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—22no—
312C4×D5—44no—
313C5×C8—22no—
314C5×C8—22no—
315#168—22no—
316#168—22no—
317C23×C4—51no—
318C23×C4—51no—
319C23×C4—51no—
320C22×C8—51no—
321C22×C8—51no—
322C22×C8—54no—
323C22×C8—54no—
324C22×C8—201no—
325C22×C8—201no—
326C22×C8—201no—
327C22×C8—201no—
328C22×C8C22×D511yescharacteristic
329C22×C8C22×D511yescharacteristic
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4C22×D511yescharacteristic
335C2×C4⋊C4C22×D511yescharacteristic
336C2×C4⋊C4C22×D511yescharacteristic
337C2×C4⋊C4C22×D511yescharacteristic
338C2×C22⋊C4—101no—
339C2×C22⋊C4—101no—
340C2×C22⋊C4—101no—
341C2×C22⋊C4—101no—
342C2×C42—21no—
343C2×C42—51no—
344C2×C42—51no—
345C2×C42—51no—
346C2×C42—54no—
347C2×C42—54no—
348C2×C42—101no—
349C2×C42—101no—
350C2×C42—101no—
351C2×C42C22×D511yescharacteristic
352#107—41no—
353#107—201no—
354#107—201no—
355#107—201no—
356#106—41no—
357#106—201no—
358#106—201no—
359#106—201no—
360C4⋊C8—54no—
361C4⋊C8—54no—
362C4⋊C8—54no—
363C4⋊C8C4×D514yes—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—101no—
368#95—101no—
369#95—101no—
370#95—101no—
371#95—101no—
372#95—101no—
373#95—101no—
374#95—101no—
375#95—101no—
376#95—101no—
377#95—101no—
378#95—101no—
379#95—101no—
380C22×C5C22×C4⋊C411yescharacteristic
381C22×C5#53711yescharacteristic
382C22×C5#53711yescharacteristic
383C22×C5C2×#13511yescharacteristic
384C22×C5C2×#13511yescharacteristic
385C22×C5#57511yescharacteristic
386C22×C5#57511yescharacteristic
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—22no—
392C2×D5—22no—
393C2×D5#42714yes—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—81no—
397C4×C5—81no—
398C4×C5—81no—
399C4×C5—81no—
400C4×C5#51811yescharacteristic
401C4×C5#51911yescharacteristic
402C4×C5#54411yescharacteristic
403C4×C5#54411yescharacteristic
404Dic5—22no—
405Dic5—22no—
406Dic5—22no—
407Dic5—81no—
408Dic5—81no—
409Dic5—81no—
410Dic5—81no—
411C24—51no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—52no—
420C22×C4—52no—
421C22×C4—54no—
422C22×C4—54no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4—201no—
434C22×C4—201no—
435C22×C4D4×D511yescharacteristic
436C22×C4D4×D511yescharacteristic
437C22×C4C23×D511yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—52no—
443C2×C8—52no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—204no—
449C2×C8—204no—
450C2×C8C2×C4×D512yes—
451C2×C8C2×C4×D512yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C22⋊C4—202no—
469C22⋊C4—202no—
470C22⋊C4—202no—
471C22⋊C4—202no—
472C42—42no—
473C42—52no—
474C42—52no—
475C42—54no—
476C42—54no—
477C42—202no—
478C42—202no—
479C42—202no—
480C42C2×C4×D512yes—
481C42Q8×D512yes—
482C2×C5#231611yescharacteristic
483C2×C5C2×#42711yescharacteristic
484C2×C5#291111yescharacteristic
485C2×C5#325011yescharacteristic
486C2×C5#325011yescharacteristic
487C2×C5#325011yescharacteristic
488C2×C5#325011yescharacteristic
489D5—24no—
490C23—52no—
491C23—52no—
492C23—52no—
493C23—101no—
494C23—101no—
495C23—101no—
496C23—101no—
497C23C2×D4×D511yescharacteristic
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—52no—
515C2×C4—52no—
516C2×C4—52no—
517C2×C4—108no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—204no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—201no—
540C2×C4—201no—
541C2×C4D5×C4⋊C412yes—
542C2×C4D5×C4⋊C412yes—
543C2×C4C22×C4×D511yescharacteristic
544C2×C4#414411yescharacteristic
545C2×C4C2×Q8×D511yescharacteristic
546C2×C4#414711yescharacteristic
547C2×C4#414911yescharacteristic
548C2×C4#415011yescharacteristic
549C8—22no—
550C8—22no—
551C8—102no—
552C8—102no—
553C5#2196011yescharacteristic, complemented, Sylow
554C22—54no—
555C22—102no—
556C22—102no—
557C22—102no—
558C22—102no—
559C22—102no—
560C22—102no—
561C22C2×D5×C4⋊C411yescharacteristic
562C22#6594211yescharacteristic
563C22#6596311yescharacteristic
564C22D5×#13511yescharacteristic
565C22D5×#13511yescharacteristic
566C22#6610711yescharacteristic
567C22#6611111yescharacteristic
568C4—22no—
569C4—22no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—102no—
575C4—102no—
576C4—102no—
577C4—401no—
578C4—401no—
579C4—401no—
580C4—401no—
581C4#6587911yescharacteristic
582C4#6590611yescharacteristic
583C4#6602311yescharacteristic
584C4#6606311yescharacteristic
585C2—104no—
586C2#1060792611yescharacteristic
587C2D5×#42711yescharacteristic
588C2#1061093911yescharacteristic
589C2#1061227911yescharacteristic
590C2#1061235411yescharacteristic
591C2#1061291111yescharacteristic
592C2#1061299211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1949C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1949D5
hypocenterC5#21960
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. C5×#1949C2semidirect
6. #10601409C2semidirect
8. #10601357C2semidirect
9. #10601248C2semidirect
10. #10600333C2semidirect
11. #10600261C2semidirect
14. #10599591C2semidirect
15. #10599590C2semidirect
45. D5×C4⋊C8C4semidirect
134. #1949D5semidirect
553. C5#21960semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊C82
#106058782
#106054832
C5×#19492
#106014232
#106014092
#106013702
#106013572
#106012482
#106003332
#106002612
#105996622
#105996612
#105995912
#105995902
#219605