Finite Group Databasebeta

← #13007817

Subgroups — #13007817

Order 1280.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3500C211yesmaximal, characteristic, complemented
2#10619196C211yesmaximal, characteristic, complemented
3Dic5×2−1+4C211yesmaximal, characteristic, complemented
4#10619186C211yesmaximal, characteristic, complemented
5Dic5×H(5,𝔽2)C211yesmaximal, characteristic, complemented
6#10618625C212yesmaximal, complemented
7#10618620C212yesmaximal, complemented
8#10618613C212yesmaximal, complemented
9#10618612C212yesmaximal, complemented
10#10618544C216yesmaximal, complemented
11#10618537C216yesmaximal, complemented
12#10618529C216yesmaximal, complemented
13#10618528C216yesmaximal, complemented
14#10618258C213yesmaximal, complemented
15#10618240C213yesmaximal, complemented
16#10618233C213yesmaximal, complemented
17#10618215C213yesmaximal, complemented
18#10618128C213yesmaximal, complemented
19#10618120C213yesmaximal, complemented
20#10617966C213yesmaximal, complemented
21C2×#66014C213yesmaximal, complemented
22C4×D5×#41C211yesmaximal, characteristic, complemented
23#10617730C211yesmaximal, characteristic, complemented
24C2×C5×2−1+4C2211yescharacteristic
25C2×C5×H(5,𝔽2)C2211yescharacteristic
26C2×D5×#41C2211yescharacteristic
27C5×#548C2212yescomplemented
28C5×#548C2212yescomplemented
29C5×#546C2216yescomplemented
30C5×#546C2216yescomplemented
31C5×#536C2213yescomplemented
32C5×#535C2213yescomplemented
33C5×#532C2213yescomplemented
34C2×C5×#124C2213yescomplemented
35C4×C5×#41C2211yescharacteristic
36#66168C2212yes—
37#66167C2213yes—
38#66167C2213yescomplemented
39#66165C2212yes—
40#66163C2216yescomplemented
41#66162C2213yes—
42#66162C2213yescomplemented
43#66161C2211yescharacteristic
44#66161C2211yescharacteristic
45#66161C2212yescomplemented
46#66161C2213yescomplemented
47#66161C2213yescomplemented
48#66161C2216yescomplemented
49#41×Dic5C2211yescharacteristic
50#41×Dic5C2213yescomplemented
51#41×Dic5C2213yescomplemented
52#41×Dic5C2212yescomplemented
53#41×Dic5C2216yescomplemented
54#66158C2216yescomplemented
55#66151C2212yescomplemented
56#66150C2213yescomplemented
57Q8×C22⋊D5C2212yescomplemented
58C2×#4092C2213yescomplemented
59#66146C2212yescomplemented
60#66146C2213yescomplemented
61C2×Q8×Dic5C2213yescomplemented
62C2×Q8×Dic5C2212yescomplemented
63#66140C2216yes—
64#66139C2213yes—
65D4×C22⋊D5C2216yes—
66C2×#4084C2213yes—
67#66132C2213yescomplemented
68#66132C2216yescomplemented
69C2×D4×Dic5C2213yescomplemented
70C2×D4×Dic5C2216yescomplemented
71#66065C2216yescomplemented
72#66062C2213yescomplemented
73#66062C2213yescomplemented
74#66053C2216yescomplemented
75#66050C2213yescomplemented
76#66050C2213yescomplemented
77#66016C2216yescomplemented
78#66016C2216yescomplemented
79#66015C2216yescomplemented
80#66015C2216yescomplemented
81#66014C2216yescomplemented
82#66014C2211yescharacteristic, complemented
83#66014C2213yescomplemented
84#66014C2213yescomplemented
85#66014C2213yescomplemented
86#66014C2216yescomplemented
87#66014C2216yescomplemented
88#66014C2216yescomplemented
89#66014C2216yescomplemented
90#66014C2216yescomplemented
91#66014C2216yescomplemented
92#66005C2216yescomplemented
93#66005C2216yescomplemented
94#65999C22112yescomplemented
95#65992C22112yescomplemented
96#65984C22112yescomplemented
97#65983C22112yescomplemented
98#65977C2216yescomplemented
99#65976C2216yescomplemented
100#65975C2216yescomplemented
101#65973C2216yescomplemented
102#65969C2216yescomplemented
103#65959C2216yescomplemented
104#65958C2216yescomplemented
105#65956C2216yescomplemented
106#65953C2216yescomplemented
107#65952C2216yescomplemented
108#65950C2216yescomplemented
109#65948C2216yescomplemented
110#65945C2216yescomplemented
111#65940C2216yescomplemented
112#65940C2216yescomplemented
113#65937C2216yescomplemented
114#65935C22112yescomplemented
115#65935C22112yescomplemented
116#65934C2216yescomplemented
117#65934C2216yescomplemented
118#65934C2216yescomplemented
119#65930C2216yescomplemented
120#65927C22112yescomplemented
121#65925C22112yescomplemented
122#65921C22112yescomplemented
123#65920C22112yescomplemented
124C4×#713C2211yescharacteristic, complemented
125C4×#713C2211yescharacteristic, complemented
126C4×Q8×D5C2211yescharacteristic, complemented
127C4×Q8×D5C2211yescharacteristic, complemented
128#65903C2212yescomplemented
129#65903C2212yescomplemented
130#65899C2216yescomplemented
131#65899C2216yescomplemented
132#65891C2216yescomplemented
133#65891C2216yescomplemented
134C4×D4×D5C2213yescomplemented
135C4×D4×D5C2213yescomplemented
136#65875C2216yescomplemented
137#65875C2216yescomplemented
138#65873C2216yescomplemented
139#65873C2216yescomplemented
140C4×#711C2216yescomplemented
141C4×#711C2216yescomplemented
142C4×#711C2213yescomplemented
143C4×#711C2213yescomplemented
144#65856C2213yescomplemented
145D5×#117C2213yescomplemented
146#65853C2213yescomplemented
147#65853C2213yescomplemented
148#65829C22112yescomplemented
149#65829C22112yescomplemented
150C2×#4029C2216yescomplemented
151C2×#4027C2216yescomplemented
152C2×#4025C2216yescomplemented
153C2×#4023C2216yescomplemented
154C4×#709C2213yescomplemented
155C2×C42×D5C2213yescomplemented
156#65804C2213yescomplemented
157C2×#4016C2213yescomplemented
158#62810—51nomaximal, Sylow
159C5×2−1+4—28no—
160C5×H(5,𝔽2)—28no—
161C2×C5×#41C2316yes—
162C2×C5×#41C2313yes—
163C2×C5×#41C2313yes—
164C2×C5×#41C2312yes—
165C2×C5×#41C2311yescharacteristic
166C22×C5×Q8C2313yes—
167C22×C5×Q8C2312yes—
168C22×C5×D4C2313yes—
169C22×C5×D4C2316yes—
170C22×C22⋊D5C2316yes—
171C23×Dic5C2316yes—
172D5×#41—28no—
173C2×#713C2311yescharacteristic
174C2×Q8×D5C2311yescharacteristic
175C2×#711C2313yes—
176C2×#711C2316yes—
177C2×#711C2316yes—
178C2×D4×D5C2313yes—
179C2×#709C2313yes—
180C22×C4×D5C2313yes—
181C22×C4×D5C2313yes—
182C22×C4×D5C2313yes—
183C5×C4⋊Q8C2313yes—
184C5×#127C2313yes—
185C5×#124C2313yes—
186C5×#124C2316yes—
187C5×#124C2316yes—
188C5×#124C2316yes—
189C5×#124C2311yescharacteristic
190C5×#123C23112yes—
191C5×C22⋊Q8C2316yes—
192C5×C22⋊Q8C2316yes—
193C5×#121C2316yes—
194C5×#121C2316yes—
195C5×#121C2316yes—
196C5×#121C2316yes—
197C5×#120C23112yes—
198C4×C5×Q8C2311yescharacteristic
199C4×C5×Q8C2311yescharacteristic
200C4×C5×D4C2313yes—
201C4×C5×D4C2313yes—
202C4×C5×D4C2316yes—
203C4×C5×D4C2316yes—
204C5×#117C2313yes—
205C2×C5×C22⋊C4C2316yes—
206C2×C5×C22⋊C4C2316yes—
207C2×C42×C5C2313yes—
208#4099C23112yes—
209C2×C22⋊Dic5C2316yes—
210C2×C22⋊Dic5C2316yes—
211C2×C22⋊Dic5C23112yes—
212#4093C2316yes—
213#4092C2311yescharacteristic
214#4092C2313yes—
215#4092C2313yes—
216#4092C2313yes—
217#4092C2316yes—
218#4092C2316yes—
219#4092C2316yes—
220Q8×Dic5C2311yescharacteristic
221Q8×Dic5C2313yes—
222Q8×Dic5C2313yes—
223Q8×Dic5C2313yes—
224Q8×Dic5C2316yes—
225Q8×Dic5C2311yescharacteristic
226Q8×Dic5C2316yes—
227Q8×Dic5C2312yes—
228Q8×Dic5C2316yes—
229Q8×Dic5C2316yes—
230Q8×Dic5C2311yescharacteristic
231Q8×Dic5C2316yes—
232Q8×Dic5C2312yes—
233#4090C2316yes—
234#4086C2316yes—
235#4085C23112yes—
236#4085C23112yes—
237#4085C23112yes—
238#4085C23112yes—
239#4084C2311yescharacteristic
240#4084C2313yes—
241#4084C2313yes—
242#4084C2313yes—
243#4084C2316yes—
244#4084C2316yes—
245#4084C2316yes—
246#4084C2316yes—
247#4084C2316yes—
248#4083C2316yes—
249#4083C2316yes—
250#4082C2316yes—
251#4082C2316yes—
252#4082C2316yes—
253#4081C23112yes—
254#4081C23112yes—
255#4081C2316yes—
256#4081C2316yes—
257D4×Dic5C2311yescharacteristic
258D4×Dic5C2313yes—
259D4×Dic5C2316yes—
260D4×Dic5C2316yes—
261D4×Dic5C2313yes—
262D4×Dic5C2313yes—
263D4×Dic5C2316yes—
264D4×Dic5C2313yes—
265D4×Dic5C2313yes—
266D4×Dic5C2316yes—
267D4×Dic5C2316yes—
268D4×Dic5C2316yes—
269D4×Dic5C2316yes—
270D4×Dic5C23112yes—
271D4×Dic5C2316yes—
272D4×Dic5C2316yes—
273D4×Dic5C2316yes—
274D4×Dic5C2316yes—
275D4×Dic5C2316yes—
276D4×Dic5C23112yes—
277D4×Dic5C2316yes—
278#4076C2316yes—
279#4076C2316yes—
280#4075C23112yes—
281C4×C22⋊D5C2316yes—
282C4×C22⋊D5C2316yes—
283C4×C22⋊D5C2316yes—
284C4×C22⋊D5C2316yes—
285C4×C22⋊D5C2316yes—
286C4×C22⋊D5C2316yes—
287C2×#685C2316yes—
288#4072C2313yes—
289#4072C2313yes—
290#4072C2313yes—
291#4072C23112yes—
292#4072C2316yes—
293#4072C2316yes—
294#4072C2316yes—
295#4072C2316yes—
296C2×C4⋊Dic5C2313yes—
297C2×C4⋊Dic5C2313yes—
298C2×C4⋊Dic5C2316yes—
299C2×C4⋊Dic5C2316yes—
300C2×C4⋊Dic5C2316yes—
301#4070C2316yes—
302#4070C2316yes—
303#4070C2316yes—
304#4070C2316yes—
305C2×#683C2316yes—
306C2×#683C2316yes—
307C2×#683C2316yes—
308C2×C4×Dic5C2313yes—
309C2×C4×Dic5C2313yes—
310C2×C4×Dic5C2313yes—
311C2×C4×Dic5C2316yes—
312C2×C4×Dic5C2316yes—
313C2×C4×Dic5C2316yes—
314#4044C23112yes—
315#4044C23112yes—
316#4043C2316yes—
317#4043C2316yes—
318#4039C2313yes—
319#4039C2313yes—
320#4038C2316yes—
321#4038C2316yes—
322#4038C2313yes—
323#4038C2313yes—
324D5×C4⋊C4C2313yes—
325D5×C4⋊C4C2313yes—
326#4036C2316yes—
327#4036C2316yes—
328#4036C2316yes—
329#4036C2316yes—
330#4035C23112yes—
331#4035C23112yes—
332#4034C2316yes—
333#4034C2316yes—
334#4033C2316yes—
335#4033C2316yes—
336#4033C2313yes—
337#4033C2313yes—
338#4032C23112yes—
339#4032C23112yes—
340#4031C23112yes—
341#4031C23112yes—
342#4029C2316yes—
343#4029C23112yes—
344#4029C23112yes—
345#4029C23112yes—
346#4029C2316yes—
347#4029C2312yes—
348#4029C2316yes—
349#4027C2316yes—
350#4027C23112yes—
351#4027C23112yes—
352#4027C23112yes—
353#4027C2316yes—
354#4027C2316yes—
355#4027C2316yes—
356#4027C2312yes—
357#4027C2316yes—
358D5×C22⋊C4C2316yes—
359#4025C2316yes—
360#4025C23112yes—
361#4025C23112yes—
362#4025C23112yes—
363#4025C2316yes—
364#4025C23112yes—
365#4025C23112yes—
366#4025C2316yes—
367#4025C2312yes—
368#4024C23112yes—
369#4024C23112yes—
370#4024C23112yes—
371#4024C23112yes—
372#4023C2316yes—
373#4023C23112yes—
374#4023C23112yes—
375#4023C23112yes—
376#4023C2316yes—
377#4023C2316yes—
378#4023C2312yes—
379#4023C2316yes—
380C4×D20C2313yes—
381C4×D20C2313yes—
382#4018C2316yes—
383C42×D5C2313yes—
384C42×D5C2313yes—
385C42×D5C2311yescharacteristic
386C42×D5C2313yes—
387C42×D5C2313yes—
388C42×D5C2313yes—
389C42×D5C2313yes—
390C42×D5C2313yes—
391#4016C2316yes—
392#4016C2313yes—
393#4016C2316yes—
394#4016C2316yes—
395#4016C2311yescharacteristic
396#4015C2313yes—
397#4015C2313yes—
398C4×Dic10C2316yes—
399C4×Dic10C2316yes—
400C4×Dic10C2313yes—
401C4×Dic10C2313yes—
402#3524—52no—
403#3521—56no—
404#3516—52no—
405#3513—56no—
406#3512—53no—
407#3510—53no—
408#3504—51no—
409#3500D511yescharacteristic, complemented
410#3495—53no—
411#3494—53no—
412#3489—51no—
413#3488—51no—
414#3482—52no—
415#3481—56no—
416#3480—52no—
417#3475—56no—
418#3461—53no—
419#3460—53no—
420#3444—53no—
421C2×#529—53no—
422C4×2−1+4—51no—
423C4×H(5,𝔽2)—51no—
424C2×C4×#41—51no—
425C24×C5C2416yes—
426C23×D5C2413yes—
427C5×#41—28no—
428C5×#41—224no—
429C5×#41—212no—
430C5×#41—212no—
431C5×#41#4118yescomplemented
432C2×C5×Q8—28no—
433C2×C5×Q8—212no—
434C2×C5×Q8C2416yes—
435C2×C5×Q8C2413yes—
436C2×C5×Q8C2411yescharacteristic
437C2×C5×Q8C2411yescharacteristic
438C2×C5×D4—224no—
439C2×C5×D4—212no—
440C2×C5×D4C2416yes—
441C2×C5×D4C2416yes—
442C2×C5×D4C2416yes—
443C2×C5×D4C2413yes—
444C2×C5×D4C2411yescharacteristic
445C2×C5×D4C2416yes—
446C2×C5×D4C2416yes—
447C2×C5×D4C2413yes—
448C22×C4×C5C2416yes—
449C22×C4×C5C2416yes—
450C22×C4×C5C2416yes—
451C22×C4×C5C2413yes—
452C22×C4×C5C2413yes—
453C22×C4×C5C2413yes—
454C2×C22⋊D5—412no—
455C2×C22⋊D5C2416yes—
456C2×C22⋊D5C2412yes—
457C2×C22⋊D5C2416yes—
458C2×C22⋊D5C2416yes—
459C2×C22⋊D5C24112yes—
460C2×C22⋊D5C2416yes—
461C22×Dic5—412no—
462C22×Dic5C2413yes—
463C22×Dic5C2413yes—
464C22×Dic5C2412yes—
465C22×Dic5C2416yes—
466C22×Dic5C2413yes—
467C22×Dic5C2416yes—
468C22×Dic5C24112yes—
469C22×Dic5C2416yes—
470C22×Dic5C2416yes—
471C22×Dic5C2416yes—
472#713—24no—
473Q8×D5—24no—
474#711—212no—
475#711—412no—
476#711—412no—
477D4×D5—212no—
478#709—212no—
479C2×D20C2413yes—
480C2×C4×D5—212no—
481C2×C4×D5—46no—
482C2×C4×D5—46no—
483C2×C4×D5C2411yescharacteristic
484C2×C4×D5C2411yescharacteristic
485C2×C4×D5C2411yescharacteristic
486C2×C4×D5C2413yes—
487C2×C4×D5C2413yes—
488C2×C4×D5C2413yes—
489C2×C4×D5C2413yes—
490C2×C4×D5C2413yes—
491C2×C4×D5C2413yes—
492C2×C4×D5C2413yes—
493C2×C4×D5C2413yes—
494C2×C4×D5C2413yes—
495C2×Dic10C2413yes—
496C2×Dic10C2416yes—
497C2×Dic10C2416yes—
498C5×C4⋊C4C2413yes—
499C5×C4⋊C4C2413yes—
500C5×C4⋊C4C2416yes—
501C5×C4⋊C4C2416yes—
502C5×C22⋊C4C2416yes—
503C5×C22⋊C4C2416yes—
504C5×C22⋊C4C24112yes—
505C5×C22⋊C4C24112yes—
506C5×C22⋊C4C2416yes—
507C5×C22⋊C4C2412yes—
508C5×C22⋊C4C2412yes—
509C42×C5C2411yescharacteristic
510C42×C5C2413yes—
511C42×C5C2413yes—
512C42×C5C2413yes—
513C22⋊Dic5C2416yes—
514C22⋊Dic5C2416yes—
515C22⋊Dic5C2416yes—
516C22⋊Dic5C2416yes—
517C22⋊Dic5C24112yes—
518C22⋊Dic5C2416yes—
519C22⋊Dic5C24112yes—
520C22⋊Dic5C2416yes—
521C22⋊Dic5C2416yes—
522C22⋊Dic5C2416yes—
523C22⋊Dic5C2412yes—
524C22⋊Dic5C2416yes—
525C22⋊Dic5C2412yes—
526#685C2416yes—
527#685C2416yes—
528#685C2416yes—
529#685C24112yes—
530#685C2416yes—
531#685C2412yes—
532#685C2416yes—
533C4⋊Dic5C2416yes—
534C4⋊Dic5C2416yes—
535C4⋊Dic5C2413yes—
536C4⋊Dic5C2413yes—
537C4⋊Dic5C2411yescharacteristic
538C4⋊Dic5C2411yescharacteristic
539C4⋊Dic5C2413yes—
540C4⋊Dic5C2413yes—
541C4⋊Dic5C2416yes—
542C4⋊Dic5C2416yes—
543C4⋊Dic5C2416yes—
544C4⋊Dic5C24112yes—
545C4⋊Dic5C2416yes—
546C4⋊Dic5C2416yes—
547C4⋊Dic5C2412yes—
548#683C2412yes—
549#683C2412yes—
550#683C2416yes—
551#683C2416yes—
552#683C2416yes—
553#683C2416yes—
554#683C24112yes—
555#683C24112yes—
556#683C2416yes—
557#683C24112yes—
558#683C2416yes—
559#683C2412yes—
560#683C2416yes—
561C4×Dic5C2413yes—
562C4×Dic5C2413yes—
563C4×Dic5C2416yes—
564C4×Dic5C2416yes—
565C4×Dic5C2411yescharacteristic
566C4×Dic5C2411yescharacteristic
567C4×Dic5C2411yescharacteristic
568C4×Dic5C2413yes—
569C4×Dic5C2413yes—
570C4×Dic5C2413yes—
571C4×Dic5C2413yes—
572C4×Dic5C2413yes—
573C4×Dic5C2413yes—
574C4×Dic5C2413yes—
575C4×Dic5C2416yes—
576C4×Dic5C24112yes—
577C4×Dic5C2416yes—
578C4×Dic5C2412yes—
579C4×Dic5C2416yes—
580C2×2−1+4C2×D511yescharacteristic
581C2×H(5,𝔽2)C2×D511yescharacteristic
582C22×#41—51no—
583#559—56no—
584#559—56no—
585#557—52no—
586#557—52no—
587#556—56no—
588#556—56no—
589#556—56no—
590#555—56no—
591#554—56no—
592#554—56no—
593#554—56no—
594#553—512no—
595#553—512no—
596#553—56no—
597#553—56no—
598#553—56no—
599#553—56no—
600#552—512no—
601#552—56no—
602#552—56no—
603#552—56no—
604#552—56no—
605#551—512no—
606#551—512no—
607#551—512no—
608#551—512no—
609#550—52no—
610D4×Q8—52no—
611#548—52no—
612#548—52no—
613#548C2×D512yescomplemented
614#548C2×D512yescomplemented
615#547—56no—
616#547—56no—
617#546—56no—
618#546—56no—
619#546—512no—
620#546C2×D516yescomplemented
621#546C2×D516yescomplemented
622D42—56no—
623#544—53no—
624#544—53no—
625#542—56no—
626#542—56no—
627#542—56no—
628#542—56no—
629#541—56no—
630#541—56no—
631#540—56no—
632#540—56no—
633#539—512no—
634#538—512no—
635#537—53no—
636#537—53no—
637#536—53no—
638#536C2×D513yescomplemented
639#535—53no—
640#535C2×D513yescomplemented
641#533—53no—
642#533—53no—
643#533—56no—
644#533—53no—
645#532—53no—
646#532—53no—
647#532—56no—
648#532C2×D513yescomplemented
649#529—53no—
650#529—56no—
651#529—56no—
652#529—56no—
653#529—56no—
654#529—56no—
655#529—56no—
656#529—56no—
657#529—51no—
658#529—53no—
659#529—53no—
660#529—512no—
661#529—56no—
662#529—56no—
663#529—56no—
664#529—56no—
665#529—56no—
666#529—56no—
667C2×#126—56no—
668C2×#125—53no—
669C2×#124C2×D513yescomplemented
670#525—53no—
671#525—53no—
672#525—56no—
673#525—56no—
674#525—512no—
675C2×#123—56no—
676C2×C22⋊Q8—53no—
677C2×#121—53no—
678#520—51no—
679#520—53no—
680#520—52no—
681#520—51no—
682#520—53no—
683#520—56no—
684#519—53no—
685#519—52no—
686#518—53no—
687#518—56no—
688C4×#41—51no—
689C4×#41—53no—
690C4×#41—52no—
691C4×#41—53no—
692C4×#41—56no—
693C4×#41—51no—
694C4×#41—51no—
695C4×#41—53no—
696C4×#41—53no—
697C4×#41—56no—
698C4×#41—56no—
699C4×#41—53no—
700C4×#41—53no—
701C4×#41C2×D511yescharacteristic
702C2×C4×Q8—53no—
703C2×C4×Q8—52no—
704C2×C4×Q8—51no—
705C2×C4×Q8—51no—
706C2×C4×D4—53no—
707C2×C4×D4—56no—
708C2×C4×D4—53no—
709C2×C4×D4—53no—
710C2×C4×D4—56no—
711C2×#117—53no—
712C2×#117—56no—
713C22×C42—53no—
714C23×C5—212no—
715C23×C5—46no—
716C23×C5—46no—
717C23×C5C2516yes—
718C23×C5C2512yes—
719C23×C5C2513yes—
720C22×D5—26no—
721C22×D5—26no—
722C22×D5—43no—
723C22×D5C2513yes—
724C22×D5C2511yescharacteristic
725C5×Q8—212no—
726C5×Q8—26no—
727C5×Q8—22no—
728C5×Q8C2×#4114yes—
729C5×D4—212no—
730C5×D4—212no—
731C5×D4—212no—
732C5×D4—26no—
733C5×D4—22no—
734C5×D4—46no—
735C5×D4—46no—
736C5×D4C2×#41112yes—
737C2×C4×C5—212no—
738C2×C4×C5—212no—
739C2×C4×C5—212no—
740C2×C4×C5—43no—
741C2×C4×C5—43no—
742C2×C4×C5C2×#41112yes—
743C2×C4×C5C2511yescharacteristic
744C2×C4×C5C2511yescharacteristic
745C2×C4×C5C2516yes—
746C2×C4×C5C2512yes—
747C2×C4×C5C2513yes—
748C2×C4×C5C2513yes—
749C2×C4×C5C2513yes—
750C2×C4×C5C2511yescharacteristic
751C22⋊D5—212no—
752C22⋊D5—24no—
753C22⋊D5—212no—
754C22⋊D5—46no—
755C22⋊D5—46no—
756C22⋊D5—412no—
757C2×Dic5—26no—
758C2×Dic5—26no—
759C2×Dic5—24no—
760C2×Dic5—212no—
761C2×Dic5—43no—
762C2×Dic5—46no—
763C2×Dic5—46no—
764C2×Dic5—46no—
765C2×Dic5—412no—
766C2×Dic5—46no—
767C2×Dic5C2511yescharacteristic
768C2×Dic5C2513yes—
769C2×Dic5C2513yes—
770C2×Dic5C2511yescharacteristic
771C2×Dic5C2512yes—
772C2×Dic5C2513yes—
773C2×Dic5C2516yes—
774C2×Dic5C2512yes—
775C2×Dic5C2516yes—
776C2×Dic5C2511yescharacteristic
777D20—26no—
778C4×D5—22no—
779C4×D5—26no—
780C4×D5—22no—
781C4×D5—26no—
782C4×D5—26no—
783C4×D5—26no—
784C4×D5—22no—
785C4×D5—26no—
786C4×D5—43no—
787C4×D5—43no—
788C4×D5—43no—
789C4×D5—43no—
790Dic10—26no—
791Dic10—46no—
792Dic10—46no—
7932−1+4—28no—
794H(5,𝔽2)—28no—
795C2×#41—51no—
796C2×#41—53no—
797C2×#41—56no—
798C2×#41—56no—
799C2×#41—53no—
800C2×#41—108no—
801C2×#41C22×D513yes—
802C2×#41C22×D513yes—
803C2×#41C22×D516yes—
804C2×#41C22×D512yes—
805C2×#41C22×D511yescharacteristic
806C22×Q8—51no—
807C22×Q8C22×D513yes—
808C22×Q8C22×D512yes—
809C22×D4—56no—
810C22×D4—53no—
811C22×D4C22×D513yes—
812C22×D4C22×D516yes—
813C23×C4—56no—
814C23×C4—53no—
815C23×C4—53no—
816C23×C4—53no—
817C4⋊Q8—56no—
818C4⋊Q8—56no—
819C4⋊Q8—56no—
820C4⋊Q8—53no—
821C4⋊Q8—53no—
822C4⋊Q8C22×D513yes—
823#127—56no—
824#127C22×D513yes—
825#126—512no—
826#126—512no—
827#126—56no—
828#126—512no—
829#126—512no—
830#126—512no—
831#126—52no—
832#126—56no—
833#126—56no—
834#126—512no—
835#126—512no—
836#125—56no—
837#125—56no—
838#125—56no—
839#125—512no—
840#125—56no—
841#125—512no—
842#125—53no—
843#125—56no—
844#125—56no—
845#125—56no—
846#125—51no—
847#124—56no—
848#124—56no—
849#124—56no—
850#124—56no—
851#124—512no—
852#124—512no—
853#124C22×D513yes—
854#124C22×D516yes—
855#124C22×D516yes—
856#124C22×D516yes—
857#124C22×D511yescharacteristic
858#123—56no—
859#123—56no—
860#123—512no—
861#123—512no—
862#123—512no—
863#123—56no—
864#123—512no—
865#123—512no—
866#123—512no—
867#123—52no—
868#123—56no—
869#123—56no—
870#123—512no—
871#123—512no—
872#123C22×D5112yes—
873C22⋊Q8—53no—
874C22⋊Q8—56no—
875C22⋊Q8—56no—
876C22⋊Q8—56no—
877C22⋊Q8—51no—
878C22⋊Q8—53no—
879C22⋊Q8—53no—
880C22⋊Q8—56no—
881C22⋊Q8—56no—
882C22⋊Q8—56no—
883C22⋊Q8—56no—
884C22⋊Q8—56no—
885C22⋊Q8—56no—
886C22⋊Q8—512no—
887C22⋊Q8—512no—
888C22⋊Q8—512no—
889C22⋊Q8—512no—
890C22⋊Q8C22×D516yes—
891C22⋊Q8C22×D516yes—
892#121—53no—
893#121—56no—
894#121—56no—
895#121—56no—
896#121—51no—
897#121—53no—
898#121—53no—
899#121—56no—
900#121—56no—
901#121—512no—
902#121—512no—
903#121—512no—
904#121—512no—
905#121—56no—
906#121—56no—
907#121C22×D516yes—
908#121C22×D516yes—
909#121C22×D516yes—
910#121C22×D516yes—
911#120—512no—
912#120—56no—
913#120—56no—
914#120C22×D5112yes—
915C4×Q8—51no—
916C4×Q8—53no—
917C4×Q8—56no—
918C4×Q8—51no—
919C4×Q8—56no—
920C4×Q8—56no—
921C4×Q8—52no—
922C4×Q8—56no—
923C4×Q8—51no—
924C4×Q8—53no—
925C4×Q8—56no—
926C4×Q8—53no—
927C4×Q8—52no—
928C4×Q8—53no—
929C4×Q8—53no—
930C4×Q8—56no—
931C4×Q8—56no—
932C4×Q8—53no—
933C4×Q8—53no—
934C4×Q8—56no—
935C4×Q8—56no—
936C4×Q8C22×D511yescharacteristic
937C4×Q8C22×D511yescharacteristic
938C4×D4—53no—
939C4×D4—56no—
940C4×D4—53no—
941C4×D4—56no—
942C4×D4—53no—
943C4×D4—56no—
944C4×D4—56no—
945C4×D4—56no—
946C4×D4—512no—
947C4×D4—56no—
948C4×D4—56no—
949C4×D4—51no—
950C4×D4—56no—
951C4×D4—53no—
952C4×D4—56no—
953C4×D4—56no—
954C4×D4—53no—
955C4×D4—56no—
956C4×D4—512no—
957C4×D4—56no—
958C4×D4—56no—
959C4×D4—56no—
960C4×D4—56no—
961C4×D4—56no—
962C4×D4—56no—
963C4×D4—56no—
964C4×D4—56no—
965C4×D4—53no—
966C4×D4—53no—
967C4×D4—56no—
968C4×D4—56no—
969C4×D4—56no—
970C4×D4—512no—
971C4×D4—512no—
972C4×D4—512no—
973C4×D4—52no—
974C4×D4—56no—
975C4×D4—56no—
976C4×D4—53no—
977C4×D4—53no—
978C4×D4C22×D513yes—
979C4×D4C22×D513yes—
980C4×D4C22×D516yes—
981C4×D4C22×D516yes—
982#117—53no—
983#117—53no—
984#117—56no—
985#117—56no—
986#117—53no—
987#117—56no—
988#117—512no—
989#117—56no—
990#117—53no—
991#117—53no—
992#117—56no—
993#117—56no—
994#117—56no—
995#117—56no—
996#117—512no—
997#117—512no—
998#117—512no—
999#117—52no—
1000#117—56no—
1001#117—56no—
1002#117—56no—
1003#117C22×D513yes—
1004C2×C4⋊C4—56no—
1005C2×C4⋊C4—56no—
1006C2×C4⋊C4—53no—
1007C2×C4⋊C4—56no—
1008C2×C4⋊C4—56no—
1009C2×C4⋊C4—53no—
1010C2×C4⋊C4—56no—
1011C2×C4⋊C4—56no—
1012C2×C4⋊C4—53no—
1013C2×C4⋊C4—53no—
1014C2×C22⋊C4—56no—
1015C2×C22⋊C4—56no—
1016C2×C22⋊C4—512no—
1017C2×C22⋊C4—56no—
1018C2×C22⋊C4—56no—
1019C2×C22⋊C4C22×D516yes—
1020C2×C22⋊C4C22×D516yes—
1021C2×C42—53no—
1022C2×C42—56no—
1023C2×C42—53no—
1024C2×C42—56no—
1025C2×C42—56no—
1026C2×C42—53no—
1027C2×C42—53no—
1028C2×C42—53no—
1029C2×C42—53no—
1030C2×C42—53no—
1031C2×C42—53no—
1032C2×C42—53no—
1033C2×C42—53no—
1034C2×C42—51no—
1035C2×C42C22×D513yes—
1036C22×C5—23no—
1037C22×C5—23no—
1038C22×C5—22no—
1039C22×C5—26no—
1040C22×C5—26no—
1041C22×C5—22no—
1042C22×C5—22no—
1043C22×C5—26no—
1044C22×C5—812no—
1045C22×C5C22×#4116yes—
1046C22×C5C2611yescharacteristic
1047C2×D5—21no—
1048C2×D5—21no—
1049C2×D5—23no—
1050C2×D5—23no—
1051C2×D5—23no—
1052C2×D5—412no—
1053C2×D5#58512yes—
1054C4×C5—22no—
1055C4×C5—26no—
1056C4×C5—23no—
1057C4×C5—23no—
1058C4×C5—21no—
1059C4×C5—21no—
1060C4×C5C22×#4116yes—
1061C4×C5C22×#4112yes—
1062Dic5—23no—
1063Dic5—21no—
1064Dic5—22no—
1065Dic5—22no—
1066Dic5—26no—
1067Dic5—26no—
1068Dic5—21no—
1069Dic5—23no—
1070Dic5—23no—
1071Dic5#58512yes—
1072C24—53no—
1073C24C23×D516yes—
1074#41—28no—
1075#41—224no—
1076#41—212no—
1077#41—212no—
1078#41—104no—
1079#41—1012no—
1080#41—1012no—
1081#41—2012no—
1082#41—2012no—
1083#41#71118yescomplemented
1084C2×Q8—28no—
1085C2×Q8—212no—
1086C2×Q8—53no—
1087C2×Q8—56no—
1088C2×Q8—56no—
1089C2×Q8—104no—
1090C2×Q8C23×D513yes—
1091C2×Q8C23×D511yescharacteristic
1092C2×Q8C23×D516yes—
1093C2×Q8C23×D511yescharacteristic
1094C2×D4—224no—
1095C2×D4—212no—
1096C2×D4—52no—
1097C2×D4—56no—
1098C2×D4—56no—
1099C2×D4—56no—
1100C2×D4—56no—
1101C2×D4—512no—
1102C2×D4—53no—
1103C2×D4—1012no—
1104C2×D4—2012no—
1105C2×D4C23×D516yes—
1106C2×D4C23×D516yes—
1107C2×D4C23×D513yes—
1108C2×D4C23×D511yescharacteristic
1109C2×D4C23×D516yes—
1110C2×D4C23×D516yes—
1111C2×D4C23×D516yes—
1112C2×D4C23×D513yes—
1113C22×C4—53no—
1114C22×C4—52no—
1115C22×C4—53no—
1116C22×C4—56no—
1117C22×C4—53no—
1118C22×C4—56no—
1119C22×C4—56no—
1120C22×C4—56no—
1121C22×C4—56no—
1122C22×C4—512no—
1123C22×C4—51no—
1124C22×C4—51no—
1125C22×C4—51no—
1126C22×C4—53no—
1127C22×C4—53no—
1128C22×C4—53no—
1129C22×C4—53no—
1130C22×C4—53no—
1131C22×C4—53no—
1132C22×C4—53no—
1133C22×C4—53no—
1134C22×C4—53no—
1135C22×C4—1012no—
1136C22×C4—206no—
1137C22×C4—206no—
1138C22×C4—2012no—
1139C22×C4C23×D516yes—
1140C22×C4C23×D516yes—
1141C22×C4C23×D516yes—
1142C22×C4C23×D513yes—
1143C22×C4C23×D513yes—
1144C22×C4C23×D513yes—
1145C4⋊C4—53no—
1146C4⋊C4—53no—
1147C4⋊C4—56no—
1148C4⋊C4—56no—
1149C4⋊C4—56no—
1150C4⋊C4—53no—
1151C4⋊C4—56no—
1152C4⋊C4—56no—
1153C4⋊C4—56no—
1154C4⋊C4—53no—
1155C4⋊C4—56no—
1156C4⋊C4—512no—
1157C4⋊C4—56no—
1158C4⋊C4—56no—
1159C4⋊C4—512no—
1160C4⋊C4—512no—
1161C4⋊C4—512no—
1162C4⋊C4—51no—
1163C4⋊C4—52no—
1164C4⋊C4—51no—
1165C4⋊C4—52no—
1166C4⋊C4—56no—
1167C4⋊C4—52no—
1168C4⋊C4—52no—
1169C4⋊C4—56no—
1170C4⋊C4—56no—
1171C4⋊C4—56no—
1172C4⋊C4—56no—
1173C4⋊C4C23×D513yes—
1174C4⋊C4C23×D513yes—
1175C4⋊C4C23×D516yes—
1176C4⋊C4C23×D516yes—
1177C22⋊C4—56no—
1178C22⋊C4—56no—
1179C22⋊C4—56no—
1180C22⋊C4—56no—
1181C22⋊C4—512no—
1182C22⋊C4—56no—
1183C22⋊C4—512no—
1184C22⋊C4—56no—
1185C22⋊C4—56no—
1186C22⋊C4—52no—
1187C22⋊C4—52no—
1188C22⋊C4—56no—
1189C22⋊C4—56no—
1190C22⋊C4—56no—
1191C22⋊C4—56no—
1192C22⋊C4—56no—
1193C22⋊C4—512no—
1194C22⋊C4—52no—
1195C22⋊C4—56no—
1196C22⋊C4—56no—
1197C22⋊C4C23×D516yes—
1198C22⋊C4C23×D516yes—
1199C22⋊C4C23×D516yes—
1200C22⋊C4C23×D5112yes—
1201C22⋊C4C23×D5112yes—
1202C22⋊C4C23×D512yes—
1203C22⋊C4C23×D512yes—
1204C42—51no—
1205C42—53no—
1206C42—51no—
1207C42—51no—
1208C42—53no—
1209C42—52no—
1210C42—53no—
1211C42—56no—
1212C42—53no—
1213C42—53no—
1214C42—53no—
1215C42—53no—
1216C42—53no—
1217C42—53no—
1218C42—56no—
1219C42—512no—
1220C42—56no—
1221C42—56no—
1222C42—56no—
1223C42C23×D511yescharacteristic
1224C42C23×D513yes—
1225C42C23×D513yes—
1226C42C23×D513yes—
1227C2×C5—26no—
1228C2×C5—42no—
1229C2×C5—46no—
1230C2×C5C23×#4111yescharacteristic
1231C2×C5C2×#58511yescharacteristic
1232C2×C5C2×#58511yescharacteristic
1233D5—22no—
1234D5—43no—
1235C23—212no—
1236C23—46no—
1237C23—46no—
1238C23—51no—
1239C23—53no—
1240C23—106no—
1241C23—106no—
1242C23—203no—
1243C23C24×D516yes—
1244C23C24×D512yes—
1245C23C24×D513yes—
1246Q8—212no—
1247Q8—26no—
1248Q8—22no—
1249Q8—106no—
1250Q8—206no—
1251Q8—206no—
1252Q8C2×#71114yes—
1253D4—212no—
1254D4—212no—
1255D4—212no—
1256D4—26no—
1257D4—22no—
1258D4—46no—
1259D4—46no—
1260D4—1012no—
1261D4—104no—
1262D4—1012no—
1263D4—106no—
1264D4—2012no—
1265D4—206no—
1266D4—206no—
1267D4C2×#711112yes—
1268C2×C4—212no—
1269C2×C4—212no—
1270C2×C4—212no—
1271C2×C4—43no—
1272C2×C4—43no—
1273C2×C4—51no—
1274C2×C4—51no—
1275C2×C4—51no—
1276C2×C4—53no—
1277C2×C4—53no—
1278C2×C4—52no—
1279C2×C4—52no—
1280C2×C4—53no—
1281C2×C4—56no—
1282C2×C4—56no—
1283C2×C4—102no—
1284C2×C4—106no—
1285C2×C4—102no—
1286C2×C4—106no—
1287C2×C4—106no—
1288C2×C4—1012no—
1289C2×C4—104no—
1290C2×C4—106no—
1291C2×C4—102no—
1292C2×C4—106no—
1293C2×C4—106no—
1294C2×C4—106no—
1295C2×C4—203no—
1296C2×C4—203no—
1297C2×C4—203no—
1298C2×C4—203no—
1299C2×C4—203no—
1300C2×C4—2012no—
1301C2×C4—206no—
1302C2×C4—206no—
1303C2×C4—206no—
1304C2×C4—206no—
1305C2×C4C2×#711112yes—
1306C2×C4C24×D511yescharacteristic
1307C2×C4C24×D511yescharacteristic
1308C2×C4C24×D516yes—
1309C2×C4C24×D512yes—
1310C2×C4C24×D513yes—
1311C2×C4C24×D513yes—
1312C2×C4C24×D513yes—
1313C2×C4C24×D511yescharacteristic
1314C5#6281011yescharacteristic, complemented, Sylow
1315C22—23no—
1316C22—23no—
1317C22—22no—
1318C22—26no—
1319C22—26no—
1320C22—22no—
1321C22—22no—
1322C22—26no—
1323C22—52no—
1324C22—812no—
1325C22—101no—
1326C22—101no—
1327C22—103no—
1328C22—103no—
1329C22—103no—
1330C22—2012no—
1331C22C22×#71116yes—
1332C22C25×D511yescharacteristic
1333C4—22no—
1334C4—26no—
1335C4—21no—
1336C4—21no—
1337C4—23no—
1338C4—23no—
1339C4—52no—
1340C4—101no—
1341C4—103no—
1342C4—103no—
1343C4—101no—
1344C4—103no—
1345C4—106no—
1346C4—102no—
1347C4—106no—
1348C4—102no—
1349C4C22×#71116yes—
1350C4C22×#71112yes—
1351C2—26no—
1352C2—46no—
1353C2—42no—
1354C2—102no—
1355C2—203no—
1356C2C23×#71111yescharacteristic
1357C2D5×#58511yescharacteristic
1358C2D5×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3500C2
hypercenter#3500D5
hypocenterC5#62810
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C5×#3500C2semidirect
2. #10619196C2semidirect
3. Dic5×2−1+4C2semidirect
4. #10619186C2semidirect
5. Dic5×H(5,𝔽2)C2semidirect
6. #10618625C2semidirect
7. #10618620C2semidirect
8. #10618613C2semidirect
9. #10618612C2semidirect
10. #10618544C2semidirect
11. #10618537C2semidirect
12. #10618529C2semidirect
13. #10618528C2semidirect
14. #10618258C2semidirect
15. #10618240C2semidirect
16. #10618233C2semidirect
17. #10618215C2semidirect
18. #10618128C2semidirect
19. #10618120C2semidirect
20. #10617966C2semidirect
21. C2×#66014C2semidirect
22. C4×D5×#41C2semidirect
23. #10617730C2semidirect
27. C5×#548C22semidirect
28. C5×#548C22semidirect
29. C5×#546C22semidirect
30. C5×#546C22semidirect
31. C5×#536C22semidirect
32. C5×#535C22semidirect
33. C5×#532C22semidirect
34. C2×C5×#124C22semidirect
38. #66167C22semidirect
40. #66163C22semidirect
42. #66162C22semidirect
45. #66161C22semidirect
46. #66161C22semidirect
47. #66161C22semidirect
48. #66161C22semidirect
50. #41×Dic5C22semidirect
51. #41×Dic5C22semidirect
52. #41×Dic5C22semidirect
53. #41×Dic5C22semidirect
54. #66158C22semidirect
55. #66151C22semidirect
56. #66150C22semidirect
57. Q8×C22⋊D5C22semidirect
58. C2×#4092C22semidirect
59. #66146C22semidirect
60. #66146C22semidirect
61. C2×Q8×Dic5C22semidirect
62. C2×Q8×Dic5C22semidirect
67. #66132C22semidirect
68. #66132C22semidirect
69. C2×D4×Dic5C22semidirect
70. C2×D4×Dic5C22semidirect
71. #66065C22semidirect
72. #66062C22semidirect
73. #66062C22semidirect
74. #66053C22semidirect
75. #66050C22semidirect
76. #66050C22semidirect
77. #66016C22semidirect
78. #66016C22semidirect
79. #66015C22semidirect
80. #66015C22semidirect
81. #66014C22semidirect
82. #66014C22semidirect
83. #66014C22semidirect
84. #66014C22semidirect
85. #66014C22semidirect
86. #66014C22semidirect
87. #66014C22semidirect
88. #66014C22semidirect
89. #66014C22semidirect
90. #66014C22semidirect
91. #66014C22semidirect
92. #66005C22semidirect
93. #66005C22semidirect
94. #65999C22semidirect
95. #65992C22semidirect
96. #65984C22semidirect
97. #65983C22semidirect
98. #65977C22semidirect
99. #65976C22semidirect
100. #65975C22semidirect
101. #65973C22semidirect
102. #65969C22semidirect
103. #65959C22semidirect
104. #65958C22semidirect
105. #65956C22semidirect
106. #65953C22semidirect
107. #65952C22semidirect
108. #65950C22semidirect
109. #65948C22semidirect
110. #65945C22semidirect
111. #65940C22semidirect
112. #65940C22semidirect
113. #65937C22semidirect
114. #65935C22semidirect
115. #65935C22semidirect
116. #65934C22semidirect
117. #65934C22semidirect
118. #65934C22semidirect
119. #65930C22semidirect
120. #65927C22semidirect
121. #65925C22semidirect
122. #65921C22semidirect
123. #65920C22semidirect
124. C4×#713C22semidirect
125. C4×#713C22semidirect
126. C4×Q8×D5C22semidirect
127. C4×Q8×D5C22semidirect
128. #65903C22semidirect
129. #65903C22semidirect
130. #65899C22semidirect
131. #65899C22semidirect
132. #65891C22semidirect
133. #65891C22semidirect
134. C4×D4×D5C22semidirect
135. C4×D4×D5C22semidirect
136. #65875C22semidirect
137. #65875C22semidirect
138. #65873C22semidirect
139. #65873C22semidirect
140. C4×#711C22semidirect
141. C4×#711C22semidirect
142. C4×#711C22semidirect
143. C4×#711C22semidirect
144. #65856C22semidirect
145. D5×#117C22semidirect
146. #65853C22semidirect
147. #65853C22semidirect
148. #65829C22semidirect
149. #65829C22semidirect
150. C2×#4029C22semidirect
151. C2×#4027C22semidirect
152. C2×#4025C22semidirect
153. C2×#4023C22semidirect
154. C4×#709C22semidirect
155. C2×C42×D5C22semidirect
156. #65804C22semidirect
157. C2×#4016C22semidirect
409. #3500D5semidirect
431. C5×#41#41semidirect
613. #548C2×D5semidirect
614. #548C2×D5semidirect
620. #546C2×D5semidirect
621. #546C2×D5semidirect
638. #536C2×D5semidirect
640. #535C2×D5semidirect
648. #532C2×D5semidirect
669. C2×#124C2×D5semidirect
1083. #41#711semidirect
1314. C5#62810semidirect

Maximal subgroups

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

subgroupindex
C5×#35002
#106191962
Dic5×2−1+42
#106191862
Dic5×H(5,𝔽2)2
#106186252
#106186202
#106186132
#106186122
#106185442
#106185372
#106185292
#106185282
#106182582
#106182402
#106182332
#106182152
#106181282
#106181202
#106179662
C2×#660142
C4×D5×#412
#106177302
#628105