Finite Group Databasebeta

← #12121384

Subgroups — #12121384

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615514C211yesmaximal, characteristic
2#10610809C211yesmaximal, characteristic, complemented
3#10610553C211yesmaximal, characteristic
4C5×#1866C211yesmaximal, characteristic
5#10602801C211yesmaximal, characteristic
6#10601498C211yesmaximal, characteristic, complemented
7#10601488C211yesmaximal, characteristic, complemented
8#10601330C211yesmaximal, characteristic, complemented
9#10601169C211yesmaximal, characteristic
10#10601147C211yesmaximal, characteristic
11#10601083C211yesmaximal, characteristic
12#10599536C211yesmaximal, characteristic, complemented
13#10599525C211yesmaximal, characteristic, complemented
14#10599438C211yesmaximal, characteristic, complemented
15#10599397C211yesmaximal, characteristic, complemented
16C2×C5×#131C2211yescharacteristic
17#41×Dic5C2211yescharacteristic
18C2×#4094C2211yescharacteristic
19#65851C2211yescharacteristic
20C2×C5×#108C2211yescharacteristic
21C5×#424C2211yescharacteristic
22C2×C5×#104C2211yescharacteristic
23C5×#416C2211yescharacteristic
24C2×#3969C2211yescharacteristic
25#65522C2211yescharacteristic
26C2×#3954C2211yescharacteristic
27#65408—21no—
28#65408C2211yescharacteristic
29#65408C2211yescharacteristic
30#65407—21no—
31#65407C2211yescharacteristic
32M16×Dic5C2211yescharacteristic
33#65395C2211yescharacteristic
34#65391—21no—
35#65391C2211yescharacteristic
36#65390C2211yescharacteristic
37C2×#3947C2211yescharacteristic
38C2×#3946—21no—
39C2×#3946C2211yescharacteristic
40C2×#3946C2211yescharacteristic
41C2×C8×Dic5C2211yescharacteristic
42#65287C2211yescharacteristic
43#65286C2211yescharacteristic
44#65221C2211yescharacteristic
45#65120—21no—
46#65119—21no—
47#65117—21no—
48#65117—21no—
49#65088C411yescharacteristic, complemented
50#65085C411yescharacteristic, complemented
51#65083C411yescharacteristic, complemented
52#65080C411yescharacteristic, complemented
53#65055C411yescharacteristic, complemented
54#65052C411yescharacteristic, complemented
55#65050C411yescharacteristic, complemented
56#65048C411yescharacteristic, complemented
57C5×#339C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#64778C2211yescharacteristic
60#64775C2211yescharacteristic
61#64775C2211yescharacteristic
62#64772C2211yescharacteristic
63#64752C2211yescharacteristic
64#64744C2211yescharacteristic
65#64743C2211yescharacteristic
66#64743C2211yescharacteristic
67#22984—51nomaximal, Sylow
68C2×C5×#41C2311yescharacteristic
69C5×#131—22no—
70C5×#131—41no—
71C2×C5×M16—21no—
72C2×C5×M16C2311yescharacteristic
73C2×C5×M16C2311yescharacteristic
74C22×C5×C8—21no—
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×#117C2311yescharacteristic
78C2×C42×C5C2311yescharacteristic
79#4094—22no—
80#4094—41no—
81Q8×Dic5C2×C411yescharacteristic
82Q8×Dic5C2×C411yescharacteristic
83D4×Dic5—21no—
84D4×Dic5—21no—
85D4×Dic5C2×C411yescharacteristic
86D4×Dic5C2×C411yescharacteristic
87#4072—21no—
88#4072C2311yescharacteristic
89#4072C2311yescharacteristic
90C2×C4×Dic5—21no—
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C2×#681—21no—
94C2×#681C2311yescharacteristic
95C2×#681C2311yescharacteristic
96C22×#168—21no—
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99#4036C2×C411yescharacteristic
100#4036C2×C411yescharacteristic
101#4034C2×C411yescharacteristic
102#4034C2×C411yescharacteristic
103#4024—21no—
104#4024—21no—
105C4×Dic10—21no—
106C4×Dic10—21no—
107C5×#108—41no—
108C5×C4⋊C8—21no—
109C5×C4⋊C8—21no—
110C5×#104—22no—
111C5×#103C2×C411yescharacteristic
112C5×#103C2×C411yescharacteristic
113C5×#102C2×C411yescharacteristic
114C5×#102C2×C411yescharacteristic
115#3969Q814yescomplemented
116#3967C2×C411yescharacteristic
117#3967C2×C411yescharacteristic
118#3964C2×C411yescharacteristic
119#3964C2×C411yescharacteristic
120#3963—21no—
121#3963—21no—
122#3954—41no—
123#3950C2×C411yescharacteristic
124#3950C2×C411yescharacteristic
125#3949C2×C411yescharacteristic
126#3949C2×C411yescharacteristic
127#3947—21no—
128#3947—21no—
129#3947—41no—
130#3946—21no—
131#3946—21no—
132#3946—21no—
133#3946—21no—
134#3946—21no—
135#3946—21no—
136#3946—21no—
137#3946—21no—
138#3946C2×C411yescharacteristic
139#3946C2×C411yescharacteristic
140#3946C2×C411yescharacteristic
141#3946C2×C411yescharacteristic
142#3946D411yescharacteristic
143#3946D411yescharacteristic
144#3946D411yescharacteristic
145#3946D411yescharacteristic
146C8×Dic5—21no—
147C8×Dic5—21no—
148C8×Dic5—41no—
149#3940C2×C411yescharacteristic
150#3940C2×C411yescharacteristic
151#3939C2×C411yescharacteristic
152#3939C2×C411yescharacteristic
153#3935—21no—
154C4×#168—21no—
155#3076—51no—
156#2962—51no—
157#2906—51no—
158#1995—51no—
159#1950—51no—
160#1946—51no—
161#1945—51no—
162#1922—51no—
163#1922—51no—
164#1866—51no—
165#1866D511yescharacteristic
166#1768—51no—
167#1765—51no—
168#1764—51no—
169#1759—51no—
170C5×#41—21no—
171C5×#41—21no—
172C5×#41C2×Q812yes—
173C5×#41#4112yes—
174C2×C5×Q8C22×C411yescharacteristic
175C2×C5×D4—21no—
176C2×C5×D4C22×C411yescharacteristic
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5C2411yescharacteristic
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5#4111yescharacteristic
184C22×Dic5#4111yescharacteristic
185C2×Dic10—21no—
186C2×Dic10—21no—
187C5×M16—21no—
188C5×M16—21no—
189C5×M16—21no—
190C5×M16—21no—
191C5×M16—42no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—42no—
199C2×C5×C8C22×C411yescharacteristic
200C2×C5×C8C22×C411yescharacteristic
201C2×C5×C8C2×D411yescharacteristic
202C2×C5×C8C2×D411yescharacteristic
203C5×C4⋊C4C22×C411yescharacteristic
204C5×C4⋊C4C22×C411yescharacteristic
205C5×C22⋊C4—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C22⋊Dic5—21no—
210C22⋊Dic5—21no—
211C22⋊Dic5—21no—
212C22⋊Dic5—21no—
213C4⋊Dic5—21no—
214C4⋊Dic5—21no—
215C4⋊Dic5—21no—
216C4⋊Dic5—21no—
217C4⋊Dic5C22×C411yescharacteristic
218C4⋊Dic5C22×C411yescharacteristic
219C4⋊Dic5C22×C411yescharacteristic
220C4⋊Dic5C22×C411yescharacteristic
221#683—21no—
222#683—21no—
223#683—21no—
224#683—21no—
225C4×Dic5—21no—
226C4×Dic5—21no—
227C4×Dic5—21no—
228C4×Dic5—21no—
229C4×Dic5—21no—
230C4×Dic5C22×C411yescharacteristic
231C4×Dic5C22×C411yescharacteristic
232C4×Dic5C2×D411yescharacteristic
233C4×Dic5C2×D411yescharacteristic
234C4×Dic5C2×Q812yes—
235#681—21no—
236#681—21no—
237#681—21no—
238#681—42no—
239#681C2×Q812yes—
240C2×#168—21no—
241C2×#168—21no—
242C2×#168—21no—
243C2×#168—21no—
244C2×#168—21no—
245C2×#168—21no—
246C2×#168—42no—
247C2×#168C22×C411yescharacteristic
248C2×#168C22×C411yescharacteristic
249C2×#168C2×D411yescharacteristic
250C2×#168C2×D411yescharacteristic
251C2×#131—51no—
252C2×#131C2×D511yescharacteristic
253#533—51no—
254C4×#41—51no—
255#479—51no—
256#479—51no—
257#478—51no—
258#478—51no—
259#477—51no—
260#476—51no—
261#475—51no—
262#474—51no—
263#446—101no—
264#446—101no—
265#446—101no—
266C8×Q8—101no—
267C2×#108—51no—
268C2×#108C2×D511yescharacteristic
269#427—51no—
270#427—51no—
271#424—51no—
272#424—51no—
273#424—51no—
274#424—101no—
275#424—101no—
276#424C2×D511yescharacteristic
277#423—51no—
278#423—101no—
279C2×C4⋊C8—51no—
280C2×C4⋊C8—51no—
281C2×C4⋊C8—101no—
282C2×#104—51no—
283C2×#104C2×D511yescharacteristic
284#416—51no—
285#416C2×D511yescharacteristic
286#405—51no—
287#405—51no—
288C4×M16—51no—
289C2×#97—51no—
290C2×C4×C8—51no—
291#376—51no—
292#341—51no—
293#341—51no—
294#339—51no—
295#339—51no—
296#339—51no—
297#339—51no—
298#339—51no—
299#339C2×D511yescharacteristic
300#336—51no—
301#336C2×D511yescharacteristic
302C23×C5—21no—
303C23×C5C2×#4111yescharacteristic
304C5×Q8—21no—
305C5×Q8C4×Q812yes—
306C5×D4—22no—
307C5×D4—22no—
308C5×D4—21no—
309C5×D4C4×Q812yes—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5C23×C411yescharacteristic
319C2×C4×C5C22×D411yescharacteristic
320C2×C4×C5C22×Q811yescharacteristic
321C2×C4×C5C2×#4111yescharacteristic
322C2×C4×C5H(5,𝔽2)11yescharacteristic
323C2×C4×C52−1+411yescharacteristic
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—22no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—42no—
332C2×Dic5—41no—
333C2×Dic5—41no—
334C2×Dic5—81no—
335C2×Dic5C4×D411yescharacteristic
336C2×Dic5C4×D411yescharacteristic
337C2×Dic5C4×D411yescharacteristic
338C2×Dic5C4×D411yescharacteristic
339Dic10—42no—
340Dic10—81no—
341C5×C8—21no—
342C5×C8—21no—
343C5×C8—21no—
344C5×C8—21no—
345C5×C8—41no—
346C5×C8—41no—
347#168—21no—
348#168—21no—
349#168—21no—
350#168—21no—
351#168—22no—
352#168—41no—
353C2×#41C22×D511yescharacteristic
354#131—22no—
355#131—41no—
356#131—102no—
357#131—201no—
358C2×M16—21no—
359C2×M16—51no—
360C2×M16—51no—
361C2×M16—101no—
362C2×M16C22×D511yescharacteristic
363C2×M16C22×D511yescharacteristic
364C22×C8—21no—
365C22×C8—51no—
366C22×C8—51no—
367C22×C8—101no—
368C22×C8C22×D511yescharacteristic
369C22×C8C22×D511yescharacteristic
370C4⋊Q8—51no—
371C4⋊Q8—51no—
372#125—51no—
373#125—51no—
374C22⋊Q8—101no—
375C22⋊Q8—101no—
376C4×Q8—51no—
377C4×Q8—51no—
378C4×Q8—101no—
379C4×Q8—101no—
380C4×D4—51no—
381C4×D4—51no—
382C4×D4—101no—
383C4×D4—101no—
384#117—51no—
385#117—51no—
386#117—101no—
387#117C22×D511yescharacteristic
388C2×C42—51no—
389C2×C42—51no—
390C2×C42—101no—
391C2×C42C22×D511yescharacteristic
392#108—41no—
393#108—201no—
394#107—51no—
395#107—51no—
396#107—51no—
397#107—51no—
398#106—51no—
399#106—51no—
400#106—51no—
401#106—51no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—51no—
405C4⋊C8—51no—
406C4⋊C8—51no—
407C4⋊C8—51no—
408C4⋊C8—51no—
409C4⋊C8—51no—
410C4⋊C8—51no—
411C4⋊C8—51no—
412C4⋊C8—101no—
413C4⋊C8—101no—
414C4⋊C8—101no—
415C4⋊C8—101no—
416C4⋊C8—101no—
417C4⋊C8—101no—
418C4⋊C8—101no—
419C4⋊C8—101no—
420#104—22no—
421#104—54no—
422#103—51no—
423#103—51no—
424#103C4×D511yescharacteristic
425#103C4×D511yescharacteristic
426#102—51no—
427#102—51no—
428#102C4×D511yescharacteristic
429#102C4×D511yescharacteristic
430#97—101no—
431#97—101no—
432#97—101no—
433#97—201no—
434C4×C8—101no—
435C4×C8—101no—
436C4×C8—101no—
437C4×C8—201no—
438#95—101no—
439#95—101no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5—22no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5C2×C4×D411yescharacteristic
446C22×C5#55211yescharacteristic
447C22×C5#55411yescharacteristic
448C4×C5—22no—
449C4×C5—41no—
450C4×C5—41no—
451C4×C5—81no—
452C4×C5C2×C4×Q811yescharacteristic
453C4×C5#52011yescharacteristic
454C4×C5#54611yescharacteristic
455C4×C5D4×Q811yescharacteristic
456Dic5—21no—
457Dic5—21no—
458Dic5—21no—
459Dic5—21no—
460Dic5—42no—
461Dic5—41no—
462Dic5—41no—
463Dic5—41no—
464Dic5—41no—
465#41—21no—
466#41—21no—
467#41#71112yes—
468#41Q8×D512yes—
469C2×Q8—101no—
470C2×Q8—101no—
471C2×Q8C2×C4×D511yescharacteristic
472C2×D4—21no—
473C2×D4C2×C4×D511yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4C23×D511yescharacteristic
482M16—21no—
483M16—21no—
484M16—21no—
485M16—21no—
486M16—42no—
487M16—52no—
488M16—101no—
489M16—101no—
490M16—101no—
491M16—202no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8—51no—
500C2×C8—51no—
501C2×C8—51no—
502C2×C8—51no—
503C2×C8—101no—
504C2×C8—101no—
505C2×C8—101no—
506C2×C8—101no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—202no—
510C2×C8C2×C4×D511yescharacteristic
511C2×C8C2×C4×D511yescharacteristic
512C2×C8D4×D511yescharacteristic
513C2×C8D4×D511yescharacteristic
514C4⋊C4—51no—
515C4⋊C4—51no—
516C4⋊C4—51no—
517C4⋊C4—51no—
518C4⋊C4—101no—
519C4⋊C4—101no—
520C4⋊C4—101no—
521C4⋊C4—101no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4—101no—
525C4⋊C4—101no—
526C4⋊C4C2×C4×D511yescharacteristic
527C4⋊C4C2×C4×D511yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—101no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C22⋊C4—101no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—51no—
537C42—51no—
538C42—51no—
539C42—51no—
540C42—52no—
541C42—101no—
542C42—101no—
543C42—101no—
544C42—101no—
545C42—101no—
546C2×C5—21no—
547C2×C5—21no—
548C2×C5—42no—
549C2×C5#236011yescharacteristic
550C2×C5#295511yescharacteristic
551C2×C5#295711yescharacteristic
552C23—21no—
553C23D5×#4111yescharacteristic
554Q8—21no—
555Q8—202no—
556Q8—401no—
557Q8#403312yes—
558D4—22no—
559D4—22no—
560D4—21no—
561D4#403312yes—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—51no—
571C2×C4—51no—
572C2×C4—51no—
573C2×C4—51no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—102no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—202no—
582C2×C4—201no—
583C2×C4—201no—
584C2×C4—401no—
585C2×C4C22×C4×D511yescharacteristic
586C2×C4C2×D4×D511yescharacteristic
587C2×C4C2×#71111yescharacteristic
588C2×C4#414411yescharacteristic
589C2×C4C2×Q8×D511yescharacteristic
590C2×C4#415011yescharacteristic
591C8—21no—
592C8—21no—
593C8—21no—
594C8—21no—
595C8—41no—
596C8—41no—
597C8—101no—
598C8—101no—
599C8—101no—
600C8—101no—
601C8—102no—
602C8—201no—
603C5#2298411yescharacteristic, complemented, Sylow
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C4×D4×D511yescharacteristic
610C22#6597011yescharacteristic
611C22#6598411yescharacteristic
612C4—22no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—101no—
617C4—101no—
618C4—101no—
619C4—101no—
620C4—202no—
621C4—201no—
622C4—201no—
623C4—201no—
624C4—201no—
625C4C2×#403311yescharacteristic
626C4#6588011yescharacteristic
627C4#6592511yescharacteristic
628C4#6596611yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1060612711yescharacteristic
633C2#1061161911yescharacteristic
634C2#1061163011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1866C2
socleC22×C5C2×C4×D4
prime radicalC2×C5×#41C23
cosocleC22×C4×C5C24
hypercenter#1866D5
hypocenterC5#22984
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #10610809C2semidirect
6. #10601498C2semidirect
7. #10601488C2semidirect
8. #10601330C2semidirect
12. #10599536C2semidirect
13. #10599525C2semidirect
14. #10599438C2semidirect
15. #10599397C2semidirect
49. #65088C4semidirect
50. #65085C4semidirect
51. #65083C4semidirect
52. #65080C4semidirect
53. #65055C4semidirect
54. #65052C4semidirect
55. #65050C4semidirect
56. #65048C4semidirect
115. #3969Q8semidirect
603. C5#22984semidirect

Maximal subgroups

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

subgroupindex
#106155142
#106108092
#106105532
C5×#18662
#106028012
#106014982
#106014882
#106013302
#106011692
#106011472
#106010832
#105995362
#105995252
#105994382
#105993972
#229845