Finite Group Databasebeta

← #12107147

Subgroups — #12107147

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10610776C211yesmaximal, characteristic, complemented
2#10610756C211yesmaximal, characteristic
3#10610247C211yesmaximal, characteristic
4C5×#1950C211yesmaximal, characteristic, complemented
5#10601515C211yesmaximal, characteristic
6#10601515C211yesmaximal, characteristic
7#10601496C211yesmaximal, characteristic, complemented
8#10601495C211yesmaximal, characteristic, complemented
9#10601322C211yesmaximal, characteristic
10#10601260C211yesmaximal, characteristic, complemented
11#10600661C211yesmaximal, characteristic, complemented
12#10599720C211yesmaximal, characteristic
13#10599719C211yesmaximal, characteristic
14#10599718C211yesmaximal, characteristic, complemented
15#10599718C211yesmaximal, characteristic, complemented
16C2×#4053C2211yescharacteristic
17C2×#4053C2211yescharacteristic
18C4×#709C2211yescharacteristic
19#65804C2211yescharacteristic
20C2×C5×#108C2211yescharacteristic
21C2×C5×#108C2211yescharacteristic
22C5×#423C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C4×C5×M16C2211yescharacteristic
25C2×#3957C2211yescharacteristic
26C2×#3957C2211yescharacteristic
27#65411C2211yescharacteristic
28#65411C2211yescharacteristic
29#65411C2211yescharacteristic
30#65411C2211yescharacteristic
31#65408C2211yescharacteristic
32#65408C2211yescharacteristic
33#65402C2211yescharacteristic
34#65402C2211yescharacteristic
35#65395C2211yescharacteristic
36#65395C2211yescharacteristic
37C2×#3947C2211yescharacteristic
38C2×C8×Dic5C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40C2×#3935C2211yescharacteristic
41#65140C411yescharacteristic, complemented
42#65139C411yescharacteristic, complemented
43#65136C411yescharacteristic, complemented
44#65136C411yescharacteristic, complemented
45#65135C411yescharacteristic, complemented
46#65131C411yescharacteristic, complemented
47#65118C411yescharacteristic, complemented
48#65118C411yescharacteristic, complemented
49#65117—21no—
50#65117—21no—
51#65117—21no—
52#65117—21no—
53#64996—21no—
54D5×#97—21no—
55#64978—21no—
56#64978—21no—
57C5×#341C2211yescharacteristic
58C5×#341C2211yescharacteristic
59#64775C2211yescharacteristic
60#64775C2211yescharacteristic
61#64775C2211yescharacteristic
62#64775C2211yescharacteristic
63#64775C2211yescharacteristic
64#64775C2211yescharacteristic
65#64770C2211yescharacteristic
66#64770C2211yescharacteristic
67#21629—51nomaximal, Sylow
68C2×#709C2311yescharacteristic
69C2×C5×M16C2311yescharacteristic
70C2×C5×M16C2311yescharacteristic
71C2×C5×M16C2311yescharacteristic
72C2×C5×M16C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C2×C42×C5C2311yescharacteristic
76C4×C22⋊D5—21no—
77C4×C22⋊D5—21no—
78#4072C2311yescharacteristic
79#4072C2311yescharacteristic
80#4072C2311yescharacteristic
81C2×C4⋊Dic5—21no—
82#4070—21no—
83#4070—21no—
84C2×C4×Dic5C2311yescharacteristic
85C2×C4×Dic5C2311yescharacteristic
86C22×#168C2311yescharacteristic
87C22×#168C2311yescharacteristic
88#4053—22no—
89#4053—22no—
90#4053—22no—
91#4053Q814yescomplemented
92C2×#676—21no—
93C2×#676—21no—
94C2×C8×D5—21no—
95C2×C8×D5—21no—
96C4×D20C2×C411yescharacteristic
97C4×D20C2×C411yescharacteristic
98#4018—21no—
99C42×D5—21no—
100#4016C2×C411yescharacteristic
101#4016C2×C411yescharacteristic
102#4015C2×C411yescharacteristic
103#4015C2×C411yescharacteristic
104C4×Dic10—21no—
105C4×Dic10—21no—
106C4×Dic10C2×C411yescharacteristic
107C4×Dic10C2×C411yescharacteristic
108C5×#108—22no—
109C5×#108—22no—
110C5×C4⋊C8—21no—
111C5×C4⋊C8—21no—
112C5×C4⋊C8C2×C411yescharacteristic
113C5×C4⋊C8C2×C411yescharacteristic
114C5×C4⋊C8C2×C411yescharacteristic
115C5×C4⋊C8C2×C411yescharacteristic
116C5×#97—21no—
117C4×C5×C8—21no—
118#3963—21no—
119#3957—22no—
120#3957—22no—
121#3953C2×C411yescharacteristic
122#3953C2×C411yescharacteristic
123#3953C2×C411yescharacteristic
124#3953C2×C411yescharacteristic
125#3950C2×C411yescharacteristic
126#3950C2×C411yescharacteristic
127#3950C2×C411yescharacteristic
128#3950C2×C411yescharacteristic
129#3949C2×C411yescharacteristic
130#3949C2×C411yescharacteristic
131#3949C2×C411yescharacteristic
132#3949C2×C411yescharacteristic
133#3948C2×C411yescharacteristic
134#3948C2×C411yescharacteristic
135#3948C2×C411yescharacteristic
136#3948C2×C411yescharacteristic
137#3947—21no—
138#3947—21no—
139#3947—21no—
140#3947—21no—
141#3947—22no—
142#3946—21no—
143#3946—21no—
144#3946—21no—
145#3946—21no—
146C8×Dic5—21no—
147C8×Dic5—21no—
148C8×Dic5—21no—
149C8×Dic5—21no—
150C8×Dic5—22no—
151#3935D411yescharacteristic
152#3935D411yescharacteristic
153#3935D411yescharacteristic
154#3935D411yescharacteristic
155#3076—51no—
156#2961—51no—
157#2875—51no—
158#1986—51no—
159#1950D511yescharacteristic, complemented
160#1922—51no—
161#1922—51no—
162#1866—51no—
163#1866—51no—
164#1806—51no—
165#1773—51no—
166#1772—51no—
167#1771—51no—
168#1765—51no—
169#1764—51no—
170C22×C4×C5#4111yescharacteristic
171C22×C4×C5#4111yescharacteristic
172C22×C4×C5C2411yescharacteristic
173C2×C22⋊D5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176#709—21no—
177#709—21no—
178#709C2×Q812yes—
179#709#4112yes—
180C2×D20C22×C411yescharacteristic
181C2×C4×D5—21no—
182C2×C4×D5—21no—
183C2×C4×D5—21no—
184C2×Dic10—21no—
185C2×Dic10—21no—
186C2×Dic10C22×C411yescharacteristic
187C5×M16—21no—
188C5×M16—21no—
189C5×M16—21no—
190C5×M16—21no—
191C5×M16—21no—
192C5×M16—21no—
193C5×M16C2×Q812yes—
194C5×M16#4112yes—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8C22×C411yescharacteristic
204C2×C5×C8C22×C411yescharacteristic
205C2×C5×C8C22×C411yescharacteristic
206C2×C5×C8C22×C411yescharacteristic
207C42×C5C22×C411yescharacteristic
208C42×C5C22×C411yescharacteristic
209C42×C5C2×D411yescharacteristic
210C42×C5C2×D411yescharacteristic
211C22⋊Dic5—21no—
212C22⋊Dic5—21no—
213C22⋊Dic5—21no—
214#685—21no—
215#685—21no—
216C4⋊Dic5—21no—
217C4⋊Dic5—21no—
218C4⋊Dic5—42no—
219C4⋊Dic5C22×C411yescharacteristic
220C4⋊Dic5C22×C411yescharacteristic
221C4⋊Dic5C22×C411yescharacteristic
222C4⋊Dic5C22×C411yescharacteristic
223C4⋊Dic5C22×C411yescharacteristic
224C4⋊Dic5C22×C411yescharacteristic
225#683—21no—
226#683—21no—
227#683—21no—
228#683—21no—
229#683—21no—
230#683—21no—
231C4×Dic5—21no—
232C4×Dic5—21no—
233C4×Dic5—21no—
234C4×Dic5—21no—
235C4×Dic5—21no—
236C4×Dic5—21no—
237C4×Dic5—21no—
238C4×Dic5—21no—
239C4×Dic5—21no—
240C2×#168—21no—
241C2×#168—21no—
242C2×#168C2×D411yescharacteristic
243C2×#168C2×D411yescharacteristic
244C2×#168C2×D411yescharacteristic
245C2×#168C2×D411yescharacteristic
246C2×#168C2×Q812yes—
247C2×#168#4112yes—
248#676—24no—
249#676—24no—
250C8×D5—24no—
251C8×D5—24no—
252C2×#131—51no—
253C2×#131—51no—
254#533—51no—
255C4×#41—51no—
256#479—51no—
257#479—51no—
258#478—51no—
259#478—51no—
260#477—51no—
261#476—51no—
262#475—51no—
263#474—51no—
264#446—101no—
265#446—101no—
266#446—101no—
267#446—101no—
268C2×#108C2×D511yescharacteristic
269C2×#108C2×D511yescharacteristic
270#427—51no—
271#427—51no—
272#424—51no—
273#424—51no—
274#423C2×D511yescharacteristic
275C2×C4⋊C8C2×D511yescharacteristic
276C2×#104—51no—
277C2×#104—51no—
278#416—51no—
279#416—51no—
280#405—51no—
281#405—51no—
282#405—51no—
283#405—51no—
284#405—101no—
285#405—101no—
286C4×M16—101no—
287C4×M16C2×D511yescharacteristic
288C2×#97—51no—
289C2×#97—51no—
290C2×#97—101no—
291C2×C4×C8—51no—
292C4×C4⋊C4—51no—
293#341C2×D511yescharacteristic
294#341C2×D511yescharacteristic
295#339—51no—
296#339—51no—
297#339—51no—
298#339—51no—
299#339—51no—
300#339—51no—
301#336—51no—
302#336—51no—
303C23×C5C2×#4111yescharacteristic
304C22×D5—21no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5C4×D411yescharacteristic
308C2×C4×C5C4×D411yescharacteristic
309C2×C4×C5C4×D411yescharacteristic
310C2×C4×C5C4×D411yescharacteristic
311C2×C4×C5C23×C411yescharacteristic
312C2×C4×C5C22×D411yescharacteristic
313C2×C4×C5C22×Q811yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C2×C4×C5C2×#4111yescharacteristic
317C22⋊D5—22no—
318C22⋊D5—22no—
319C2×Dic5—21no—
320C2×Dic5—22no—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—41no—
332D20—21no—
333D20C4×Q812yes—
334C4×D5—22no—
335C4×D5—22no—
336C4×D5—81no—
337C4×D5—81no—
338Dic10—21no—
339Dic10—81no—
340Dic10—81no—
341Dic10C4×Q812yes—
342C5×C8—21no—
343C5×C8—21no—
344C5×C8—21no—
345C5×C8—21no—
346C5×C8—22no—
347C5×C8—22no—
348C5×C8—41no—
349C5×C8—41no—
350#168—21no—
351#168—21no—
352#168C22⋊Q812yes—
353#168C22⋊Q812yes—
354C2×#41—51no—
355#131—54no—
356#131—102no—
357#131—102no—
358#131—102no—
359C2×M16—101no—
360C2×M16—101no—
361C2×M16C22×D511yescharacteristic
362C2×M16C22×D511yescharacteristic
363C2×M16C22×D511yescharacteristic
364C2×M16C22×D511yescharacteristic
365C22×C8—51no—
366C22×C8—51no—
367C22×C8—101no—
368C22×C8—101no—
369C22×C8C22×D511yescharacteristic
370C22×C8C22×D511yescharacteristic
371C4⋊Q8—51no—
372C4⋊Q8—51no—
373#125—51no—
374#125—51no—
375C22⋊Q8—101no—
376C22⋊Q8—101no—
377C4×Q8—51no—
378C4×Q8—51no—
379C4×Q8—101no—
380C4×Q8—101no—
381C4×D4—51no—
382C4×D4—51no—
383C4×D4—101no—
384C4×D4—101no—
385#117—51no—
386#117—51no—
387#117—51no—
388#117—101no—
389C2×C4⋊C4—101no—
390C2×C42—51no—
391C2×C42—51no—
392C2×C42—101no—
393C2×C42C22×D511yescharacteristic
394#108—22no—
395#108—22no—
396#107—51no—
397#107—51no—
398#107—51no—
399#107—51no—
400#106—51no—
401#106—51no—
402#106—51no—
403#106—51no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—101no—
407C4⋊C8—101no—
408C4⋊C8—101no—
409C4⋊C8—101no—
410C4⋊C8C4×D511yescharacteristic
411C4⋊C8C4×D511yescharacteristic
412C4⋊C8C4×D511yescharacteristic
413C4⋊C8C4×D511yescharacteristic
414#104—102no—
415#104—102no—
416#103—51no—
417#103—51no—
418#103—51no—
419#103—51no—
420#102—51no—
421#102—51no—
422#102—51no—
423#102—51no—
424#97—21no—
425#97—51no—
426#97—51no—
427#97—51no—
428#97—51no—
429#97—102no—
430#97—101no—
431#97—101no—
432#97—101no—
433#97—101no—
434C4×C8—21no—
435C4×C8—102no—
436C4×C8—101no—
437C4×C8—101no—
438C4×C8—101no—
439C4×C8—101no—
440#95—101no—
441C22×C5—21no—
442C22×C5—21no—
443C22×C5C2×C4×D411yescharacteristic
444C22×C5#52911yescharacteristic
445C22×C5#53311yescharacteristic
446C2×D5—22no—
447C2×D5—41no—
448C2×D5—41no—
449C4×C5—21no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—21no—
453C4×C5C2×C4×Q811yescharacteristic
454C4×C5C4×#4111yescharacteristic
455C4×C5C2×C22⋊Q811yescharacteristic
456C4×C5#52511yescharacteristic
457Dic5—22no—
458Dic5—42no—
459Dic5—41no—
460Dic5—41no—
461Dic5—41no—
462Dic5—41no—
463Dic5—41no—
464Dic5—41no—
465Dic5—81no—
466#41—52no—
467#41—52no—
468#41—101no—
469#41—101no—
470C2×Q8—51no—
471C2×Q8—101no—
472C2×Q8—101no—
473C2×D4—51no—
474C2×D4—101no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4#71311yescharacteristic
481C22×C4#71311yescharacteristic
482C22×C4C23×D511yescharacteristic
483M16—21no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—104no—
490M16—104no—
491M16#71112yes—
492M16Q8×D512yes—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—51no—
502C2×C8—51no—
503C2×C8—52no—
504C2×C8—52no—
505C2×C8—51no—
506C2×C8—51no—
507C2×C8—104no—
508C2×C8—104no—
509C2×C8—101no—
510C2×C8—101no—
511C2×C8C2×C4×D511yescharacteristic
512C2×C8C2×C4×D511yescharacteristic
513C2×C8C2×C4×D511yescharacteristic
514C2×C8C2×C4×D511yescharacteristic
515C4⋊C4—51no—
516C4⋊C4—51no—
517C4⋊C4—51no—
518C4⋊C4—51no—
519C4⋊C4—51no—
520C4⋊C4—51no—
521C4⋊C4—101no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4—101no—
525C4⋊C4—101no—
526C4⋊C4—101no—
527C4⋊C4—101no—
528C4⋊C4—101no—
529C4⋊C4—202no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C22⋊C4—101no—
533C22⋊C4—101no—
534C22⋊C4—101no—
535C42—101no—
536C42—101no—
537C42—101no—
538C42—101no—
539C42—101no—
540C42—101no—
541C42—101no—
542C42—101no—
543C42—101no—
544C42C2×C4×D511yescharacteristic
545C42C2×C4×D511yescharacteristic
546C42D4×D511yescharacteristic
547C42D4×D511yescharacteristic
548C2×C5—21no—
549C2×C5—21no—
550C2×C5C4×C22⋊Q811yescharacteristic
551C2×C5#295611yescharacteristic
552C2×C5#295711yescharacteristic
553D5—42no—
554C23—101no—
555C23C2×#71311yescharacteristic
556Q8—52no—
557Q8—101no—
558Q8—401no—
559Q8—401no—
560D4—52no—
561D4—102no—
562D4—102no—
563D4—101no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—101no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—101no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—401no—
582C2×C4—401no—
583C2×C4#403911yescharacteristic
584C2×C4#403911yescharacteristic
585C2×C4#403911yescharacteristic
586C2×C4#403911yescharacteristic
587C2×C4C22×C4×D511yescharacteristic
588C2×C4C2×D4×D511yescharacteristic
589C2×C4C2×#71111yescharacteristic
590C2×C4C2×Q8×D511yescharacteristic
591C2×C4D5×#4111yescharacteristic
592C2×C4D5×#4111yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—22no—
598C8—22no—
599C8—41no—
600C8—41no—
601C8—52no—
602C8—52no—
603C8—101no—
604C8—101no—
605C5#2162911yescharacteristic, complemented, Sylow
606C22—21no—
607C22—21no—
608C22—102no—
609C22—201no—
610C22—201no—
611C22C2×#403911yescharacteristic
612C22#6602511yescharacteristic
613C22#6606211yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—102no—
619C4—202no—
620C4—201no—
621C4—201no—
622C4—201no—
623C4—201no—
624C4—201no—
625C4—201no—
626C4—401no—
627C4C4×#71111yescharacteristic
628C4C4×Q8×D511yescharacteristic
629C4#6594011yescharacteristic
630C4D5×C22⋊Q811yescharacteristic
631C2—21no—
632C2—21no—
633C2—202no—
634C2#1060769611yescharacteristic
635C2#1061098011yescharacteristic
636C2#1061098911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1950C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C23
cosocleC22×C4×C5C24
hypercenter#1950D5
hypocenterC5#21629
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
1. #10610776C2semidirect
4. C5×#1950C2semidirect
7. #10601496C2semidirect
8. #10601495C2semidirect
10. #10601260C2semidirect
11. #10600661C2semidirect
14. #10599718C2semidirect
15. #10599718C2semidirect
41. #65140C4semidirect
42. #65139C4semidirect
43. #65136C4semidirect
44. #65136C4semidirect
45. #65135C4semidirect
46. #65131C4semidirect
47. #65118C4semidirect
48. #65118C4semidirect
91. #4053Q8semidirect
159. #1950D5semidirect
605. C5#21629semidirect

Maximal subgroups

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

subgroupindex
#106107762
#106107562
#106102472
C5×#19502
#106015152
#106014962
#106014952
#106013222
#106012602
#106006612
#105997202
#105997192
#105997182
#216295