Finite Group Databasebeta

← D5×#3517 #13007548

Subgroups — D5×#3517 #13007548

Order 1280.

7854 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3517C211yesmaximal, characteristic, complemented
2D5×#557C211yesmaximal, characteristic, complemented
3#10618924C211yesmaximal, characteristic, complemented
4D5×#553C216yesmaximal, complemented
5#10618787C216yesmaximal, complemented
6D5×#550C212yesmaximal, complemented
7D5×#550C213yesmaximal, complemented
8D5×#550C211yesmaximal, characteristic, complemented
9#10618675C213yesmaximal, complemented
10#10618674C211yesmaximal, characteristic, complemented
11#10618673C212yesmaximal, complemented
12D5×#547C213yesmaximal, complemented
13#10618585C213yesmaximal, complemented
14D5×#540C216yesmaximal, complemented
15#10618371C216yesmaximal, complemented
16D5×#532C213yesmaximal, complemented
17#10618129C213yesmaximal, complemented
18D5×#529C213yesmaximal, complemented
19#10618027C213yesmaximal, complemented
20D5×#520C212yesmaximal, complemented
21#10617797C212yesmaximal, complemented
22#10617754C211yesmaximal, characteristic, complemented
23C4×D5×#41C211yesmaximal, characteristic, complemented
24C2×D5×#41C2211yescharacteristic
25C2×D5×#41C2212yes—
26C2×D5×#41C2216yes—
27C5×#557C2211yescharacteristic, complemented
28C5×#553C2216yescomplemented
29C5×#550C2212yescomplemented
30C5×#550C2211yescharacteristic, complemented
31C5×#550C2213yescomplemented
32C5×#547C2213yescomplemented
33C5×#540C2216yescomplemented
34C5×#532C2213yescomplemented
35C5×#529C2213yescomplemented
36C5×#520C2212yescomplemented
37C4×C5×#41C2211yescharacteristic, complemented
38#66168C2216yescomplemented
39#66168C2212yescomplemented
40#66168C2212yescomplemented
41#66168C2212yescomplemented
42#66166C2216yescomplemented
43#66161C2212yescomplemented
44#41×Dic5C2211yescharacteristic, complemented
45#66158C2216yescomplemented
46#66060C2213yescomplemented
47#66059C2213yescomplemented
48D5×C4⋊Q8C2213yes—
49#66055C2213yescomplemented
50#66053C2216yescomplemented
51#66052C2216yescomplemented
52#66052C2216yescomplemented
53#66052C2213yescomplemented
54#66052C2213yescomplemented
55#66050C2213yescomplemented
56D5×#127C2216yes—
57D5×#127C2213yes—
58#66043C22112yescomplemented
59#66040C2216yescomplemented
60D5×#126C2216yes—
61#66032C2216yescomplemented
62#66029C2216yescomplemented
63#66025C2213yescomplemented
64D5×#125C2216yes—
65D5×#125C2211yescharacteristic
66#66019C2216yescomplemented
67#66014C2213yescomplemented
68D5×#124C2213yes—
69#66002C2216yescomplemented
70#65997C22112yescomplemented
71#65997C22112yescomplemented
72#65995C22112yescomplemented
73#65989C22112yescomplemented
74D5×#123C2216yes—
75D5×#123C22112yes—
76#65983C2216yescomplemented
77#65965C2216yescomplemented
78D5×C22⋊Q8C2213yes—
79#65958C2213yescomplemented
80#65953C2216yescomplemented
81#65953C2216yescomplemented
82#65952C2216yescomplemented
83#65949C22112yescomplemented
84#65949C22112yescomplemented
85#65948C2216yescomplemented
86#65945C2216yescomplemented
87D5×#121C2216yes—
88D5×#121C22112yes—
89D5×#121C2216yes—
90D5×#121C2216yes—
91D5×#121C2216yes—
92D5×#121C2213yes—
93#65935C22112yescomplemented
94#65934C2213yescomplemented
95#65933C22112yescomplemented
96#65933C2216yescomplemented
97#65933C2216yescomplemented
98#65933C2216yescomplemented
99#65933C2216yescomplemented
100#65930C2216yescomplemented
101#65930C2216yescomplemented
102#65914C2213yescomplemented
103#65911C2211yescharacteristic, complemented
104#65911C2213yescomplemented
105#65911C2212yescomplemented
106#65908C2212yescomplemented
107#65908C2212yescomplemented
108C4×#713C2211yescharacteristic, complemented
109C4×#713C2211yescharacteristic, complemented
110C4×Q8×D5C2211yescharacteristic
111C4×Q8×D5C2213yes—
112C4×Q8×D5C2212yes—
113C4×Q8×D5C2211yescharacteristic
114#65904C2211yescharacteristic, complemented
115#65903C2212yescomplemented
116#65901C2213yescomplemented
117#65899C2216yescomplemented
118#65896C2216yescomplemented
119#65896C2216yescomplemented
120#65892C2216yescomplemented
121#65891C2213yescomplemented
122#65889C2213yescomplemented
123#65887C2213yescomplemented
124#65887C2216yescomplemented
125#65887C2216yescomplemented
126#65887C2213yescomplemented
127#65885C2213yescomplemented
128#65882C2216yescomplemented
129#65882C2216yescomplemented
130#65880C2216yescomplemented
131#65880C2216yescomplemented
132C4×D4×D5C2213yes—
133C4×D4×D5C2216yes—
134C4×D4×D5C2216yes—
135C4×D4×D5C2213yes—
136C4×D4×D5C2216yes—
137C4×D4×D5C2216yes—
138C4×D4×D5C2213yes—
139#65874C22112yescomplemented
140#65872C2216yescomplemented
141C4×#711C2213yescomplemented
142C4×#711C2213yescomplemented
143#65869C2216yescomplemented
144#65864C2216yescomplemented
145#65862C2216yescomplemented
146#65857C2216yescomplemented
147#65856C2213yescomplemented
148D5×#117C2216yes—
149D5×#117C2213yes—
150#65848C2216yescomplemented
151#65841C2216yescomplemented
152#65838C2216yescomplemented
153C2×D5×C4⋊C4C2216yes—
154#65813C2213yescomplemented
155#65811C2213yescomplemented
156C4×#709C2213yescomplemented
157C2×C42×D5C2213yes—
158C2×#3517—51nomaximal, Sylow
159C2×C5×#41C2311yescharacteristic
160C2×C5×#41C2312yes—
161C2×C5×#41C2316yes—
162D5×#41—28no—
163D5×#41—216no—
164D5×#41—424no—
165C2×#713C2311yescharacteristic
166C2×#713C2312yes—
167C2×#713C2316yes—
168C2×Q8×D5C2313yes—
169C2×Q8×D5C2311yescharacteristic
170C2×#711C2313yes—
171C2×#711C2316yes—
172C2×#711C2316yes—
173C2×#711C23112yes—
174C2×D4×D5C2313yes—
175C2×D4×D5C2316yes—
176C2×D4×D5C2313yes—
177C2×D4×D5C2316yes—
178C2×D4×D5C2316yes—
179C2×D4×D5C23112yes—
180C2×#709C2313yes—
181C2×#709C2316yes—
182C2×#709C2316yes—
183C2×#709C23112yes—
184C22×C4×D5C2313yes—
185C22×C4×D5C2313yes—
186C22×C4×D5C2316yes—
187C22×C4×D5C2313yes—
188C22×C4×D5C23112yes—
189C5×C4⋊Q8C2313yes—
190C5×#127C2313yes—
191C5×#127C2316yes—
192C5×#126C2316yes—
193C5×#125C2311yescharacteristic
194C5×#125C2316yes—
195C5×#124C2313yes—
196C5×#123C2316yes—
197C5×#123C23112yes—
198C5×C22⋊Q8C2313yes—
199C5×#121C2316yes—
200C5×#121C2316yes—
201C5×#121C2313yes—
202C5×#121C23112yes—
203C5×#121C2316yes—
204C5×#121C2316yes—
205C4×C5×Q8C2313yes—
206C4×C5×Q8C2312yes—
207C4×C5×Q8C2311yescharacteristic
208C4×C5×Q8C2311yescharacteristic
209C4×C5×D4C2313yes—
210C4×C5×D4C2313yes—
211C4×C5×D4C2316yes—
212C4×C5×D4C2316yes—
213C4×C5×D4C2316yes—
214C4×C5×D4C2316yes—
215C4×C5×D4C2313yes—
216C5×#117C2313yes—
217C5×#117C2316yes—
218C2×C5×C4⋊C4C2316yes—
219C2×C42×C5C2313yes—
220#4093C2313yes—
221#4092C2313yes—
222Q8×Dic5C2313yes—
223Q8×Dic5C2311yescharacteristic
224Q8×Dic5C2312yes—
225Q8×Dic5C2311yescharacteristic
226#4090C2316yes—
227#4086C2316yes—
228#4086C2316yes—
229#4086C2316yes—
230#4086C2316yes—
231#4086C23112yes—
232#4086C2316yes—
233#4086C23112yes—
234#4085C2316yes—
235#4085C23112yes—
236#4085C23112yes—
237#4085C23112yes—
238#4085C23112yes—
239#4085C23112yes—
240#4085C23112yes—
241#4084C2316yes—
242#4084C2316yes—
243#4084C2313yes—
244#4084C2316yes—
245#4084C2316yes—
246#4084C23112yes—
247#4082C2313yes—
248#4081C2316yes—
249#4081C23112yes—
250D4×Dic5C2316yes—
251D4×Dic5C2316yes—
252D4×Dic5C2313yes—
253D4×Dic5C2316yes—
254D4×Dic5C2313yes—
255D4×Dic5C2316yes—
256D4×Dic5C2313yes—
257#4076C2316yes—
258#4076C2316yes—
259#4076C2313yes—
260#4076C2316yes—
261#4076C2316yes—
262#4076C23112yes—
263#4075C2316yes—
264#4075C23112yes—
265C4×C22⋊D5C2316yes—
266C4×C22⋊D5C2316yes—
267C4×C22⋊D5C2316yes—
268C4×C22⋊D5C23112yes—
269C4×C22⋊D5C23112yes—
270C4×C22⋊D5C2316yes—
271C4×C22⋊D5C2316yes—
272C4×C22⋊D5C23112yes—
273#4072C2313yes—
274#4072C2316yes—
275C2×C4⋊Dic5C2316yes—
276#4070C2313yes—
277C2×#683C23112yes—
278C2×C4×Dic5C2313yes—
279C2×C4×Dic5C2313yes—
280C2×C4×Dic5C2313yes—
281#4044C2316yes—
282#4044C2316yes—
283#4044C2316yes—
284#4043C2313yes—
285#4042C2316yes—
286#4041C2316yes—
287#4041C2316yes—
288#4041C2316yes—
289#4041C2316yes—
290#4041C2313yes—
291#4041C23112yes—
292#4040C23112yes—
293#4040C23112yes—
294#4040C2316yes—
295#4040C2316yes—
296#4039C2316yes—
297#4039C2316yes—
298#4039C2316yes—
299#4039C2313yes—
300#4039C2313yes—
301#4039C2313yes—
302#4039C2316yes—
303#4038C2316yes—
304#4038C2313yes—
305#4038C2316yes—
306#4038C2313yes—
307D5×C4⋊C4C2316yes—
308D5×C4⋊C4C2316yes—
309D5×C4⋊C4C2316yes—
310D5×C4⋊C4C2313yes—
311D5×C4⋊C4C2316yes—
312D5×C4⋊C4C23112yes—
313D5×C4⋊C4C2316yes—
314D5×C4⋊C4C2312yes—
315D5×C4⋊C4C2313yes—
316D5×C4⋊C4C2311yescharacteristic
317D5×C4⋊C4C2312yes—
318D5×C4⋊C4C2311yescharacteristic
319D5×C4⋊C4C2316yes—
320#4036C2316yes—
321#4036C2316yes—
322#4036C2311yescharacteristic
323#4036C2311yescharacteristic
324#4035C23112yes—
325#4035C2312yes—
326#4035C2312yes—
327#4035C23112yes—
328#4034C2316yes—
329#4034C2316yes—
330#4033C2316yes—
331#4033C2313yes—
332#4033C2313yes—
333#4033C2313yes—
334#4033C2316yes—
335#4032C2316yes—
336#4032C23112yes—
337#4031C2316yes—
338#4031C2316yes—
339#4030C2316yes—
340#4030C23112yes—
341#4030C23112yes—
342#4030C23112yes—
343#4030C23112yes—
344#4030C23112yes—
345#4030C23112yes—
346#4029C2316yes—
347#4029C23112yes—
348#4029C2316yes—
349#4029C23112yes—
350#4027C2316yes—
351#4027C2316yes—
352#4027C23112yes—
353#4027C23112yes—
354#4027C2316yes—
355#4027C23112yes—
356#4027C2316yes—
357#4027C2316yes—
358D5×C22⋊C4C2316yes—
359D5×C22⋊C4C2316yes—
360D5×C22⋊C4C2316yes—
361D5×C22⋊C4C2316yes—
362D5×C22⋊C4C2316yes—
363D5×C22⋊C4C2316yes—
364#4025C2316yes—
365#4025C2316yes—
366#4025C2316yes—
367#4024C2316yes—
368#4023C2316yes—
369#4023C2316yes—
370#4023C2316yes—
371#4022C2316yes—
372#4021C2313yes—
373#4020C2313yes—
374#4020C2316yes—
375C4×D20C2313yes—
376C4×D20C2313yes—
377C4×D20C2316yes—
378C4×D20C2316yes—
379C4×D20C2313yes—
380C4×D20C2316yes—
381C4×D20C2316yes—
382#4018C2316yes—
383#4018C2316yes—
384#4018C2316yes—
385C42×D5C2313yes—
386C42×D5C2316yes—
387C42×D5C2313yes—
388C42×D5C2311yescharacteristic
389C42×D5C2313yes—
390C42×D5C2313yes—
391C42×D5C2313yes—
392C42×D5C2313yes—
393C42×D5C2313yes—
394#4016C2316yes—
395#4016C2311yescharacteristic
396#4015C2313yes—
397C4×Dic10C2313yes—
398C4×Dic10C2313yes—
399C4×Dic10C2316yes—
400C4×Dic10C2316yes—
401C4×Dic10C2313yes—
402#3517—51no—
403#3517—56no—
404#3517—52no—
405#3517—51no—
406#3517—53no—
407#3517—53no—
408#3517—56no—
409#3517—53no—
410#3517—53no—
411#3517—52no—
412#3517—51no—
413#3517D511yescharacteristic, direct product factor
414C2×#557—51no—
415C2×#553—56no—
416C2×#550—53no—
417C2×#550—51no—
418C2×#550—52no—
419C2×#547—53no—
420C2×#540—56no—
421C2×#532—53no—
422C2×#529—53no—
423C2×#520—52no—
424C2×C4×#41—51no—
425C23×D5C2413yes—
426C23×D5C2416yes—
427C5×#41—24no—
428C5×#41—28no—
429C5×#41—412no—
430C2×C5×Q8C2413yes—
431C2×C5×Q8C2411yescharacteristic
432C2×C5×D4C2413yes—
433C2×C5×D4C2416yes—
434C2×C5×D4C2413yes—
435C2×C5×D4C2416yes—
436C2×C5×D4C2416yes—
437C2×C5×D4C24112yes—
438C22×C4×C5C2413yes—
439C22×C4×C5C2413yes—
440C22×C4×C5C2416yes—
441C22×C4×C5C2413yes—
442C22×C4×C5C24112yes—
443C2×C22⋊D5C2416yes—
444C2×C22⋊D5C2416yes—
445C2×C22⋊D5C24112yes—
446C2×C22⋊D5C24112yes—
447C2×C22⋊D5C24112yes—
448C2×C22⋊D5C2416yes—
449C2×C22⋊D5C24112yes—
450C2×C22⋊D5C2416yes—
451C22×Dic5C2413yes—
452C22×Dic5C2413yes—
453C22×Dic5C2416yes—
454C22×Dic5C24112yes—
455C22×Dic5C2413yes—
456#713—24no—
457#713—28no—
458#713—412no—
459Q8×D5—212no—
460Q8×D5#4118yescomplemented
461#711—212no—
462#711—224no—
463#711—412no—
464#711—424no—
465D4×D5—212no—
466D4×D5—224no—
467D4×D5—212no—
468D4×D5—412no—
469D4×D5—412no—
470D4×D5—424no—
471#709—212no—
472#709—224no—
473#709—424no—
474#709—412no—
475C2×D20C2413yes—
476C2×D20C2413yes—
477C2×D20C2416yes—
478C2×D20C24112yes—
479C2×D20C2416yes—
480C2×D20C2416yes—
481C2×C4×D5—212no—
482C2×C4×D5—224no—
483C2×C4×D5—212no—
484C2×C4×D5—46no—
485C2×C4×D5—424no—
486C2×C4×D5C2413yes—
487C2×C4×D5C2411yescharacteristic
488C2×C4×D5C2411yescharacteristic
489C2×C4×D5C2412yes—
490C2×C4×D5C2416yes—
491C2×C4×D5C2413yes—
492C2×C4×D5C2413yes—
493C2×C4×D5C2416yes—
494C2×C4×D5C2413yes—
495C2×C4×D5C2413yes—
496C2×C4×D5C2413yes—
497C2×C4×D5C2416yes—
498C2×C4×D5C2412yes—
499C2×C4×D5C24112yes—
500C2×C4×D5C24112yes—
501C2×C4×D5C2413yes—
502C2×C4×D5C2413yes—
503C2×C4×D5C2413yes—
504C2×C4×D5C2411yescharacteristic
505C2×Dic10C2413yes—
506C2×Dic10C2416yes—
507C2×Dic10C2413yes—
508C5×C4⋊C4C2413yes—
509C5×C4⋊C4C2416yes—
510C5×C4⋊C4C2416yes—
511C5×C4⋊C4C2412yes—
512C5×C4⋊C4C2413yes—
513C5×C4⋊C4C2411yescharacteristic
514C5×C4⋊C4C2412yes—
515C5×C4⋊C4C2416yes—
516C5×C4⋊C4C2411yescharacteristic
517C5×C4⋊C4C2416yes—
518C5×C22⋊C4C2416yes—
519C5×C22⋊C4C2416yes—
520C5×C22⋊C4C2416yes—
521C5×C22⋊C4C2416yes—
522C5×C22⋊C4C2416yes—
523C5×C22⋊C4C2416yes—
524C42×C5C2411yescharacteristic
525C42×C5C2413yes—
526C42×C5C2413yes—
527C42×C5C2413yes—
528C42×C5C2416yes—
529C22⋊Dic5C2416yes—
530C22⋊Dic5C2416yes—
531C22⋊Dic5C2416yes—
532C22⋊Dic5C2416yes—
533C22⋊Dic5C2416yes—
534C22⋊Dic5C2416yes—
535#685C2416yes—
536#685C2416yes—
537#685C2416yes—
538#685C2416yes—
539#685C2416yes—
540#685C2416yes—
541#685C2416yes—
542#685C2416yes—
543#685C2416yes—
544#685C2416yes—
545#685C2416yes—
546#685C2416yes—
547C4⋊Dic5C2411yescharacteristic
548C4⋊Dic5C2416yes—
549C4⋊Dic5C2413yes—
550C4⋊Dic5C2413yes—
551C4⋊Dic5C2416yes—
552C4⋊Dic5C2416yes—
553C4⋊Dic5C2411yescharacteristic
554C4⋊Dic5C2412yes—
555C4⋊Dic5C2416yes—
556C4⋊Dic5C2412yes—
557#683C2412yes—
558#683C2416yes—
559#683C2416yes—
560#683C2416yes—
561#683C2416yes—
562#683C24112yes—
563#683C2412yes—
564#683C2412yes—
565#683C24112yes—
566#683C2412yes—
567#683C2416yes—
568#683C2416yes—
569#683C2412yes—
570#683C2412yes—
571C4×Dic5C2413yes—
572C4×Dic5C2413yes—
573C4×Dic5C2413yes—
574C4×Dic5C2416yes—
575C4×Dic5C2416yes—
576C4×Dic5C2411yescharacteristic
577C4×Dic5C2411yescharacteristic
578C4×Dic5C2411yescharacteristic
579C4×Dic5C2413yes—
580C4×Dic5C2413yes—
581C4×Dic5C2413yes—
582C4×Dic5C2413yes—
583C4×Dic5C2413yes—
584C4×Dic5C2413yes—
585C4×Dic5C2416yes—
586C22×#41—51no—
587C22×#41—52no—
588C22×#41—56no—
589#557—53no—
590#557—56no—
591#557—53no—
592#557—52no—
593#557—51no—
594#557C2×D511yescharacteristic, complemented
595#553—512no—
596#553—56no—
597#553—512no—
598#553—512no—
599#553—56no—
600#553—56no—
601#553—512no—
602#553—56no—
603#553—56no—
604#553—56no—
605#553—56no—
606#553C2×D516yescomplemented
607#550—56no—
608#550—52no—
609#550—52no—
610#550—52no—
611#550—56no—
612#550—53no—
613#550—53no—
614#550—56no—
615#550—56no—
616#550—512no—
617#550—56no—
618#550—56no—
619#550—56no—
620#550—53no—
621#550—51no—
622#550—52no—
623#550—56no—
624#550—53no—
625#550—53no—
626#550—56no—
627#550C2×D513yescomplemented
628#550C2×D511yescharacteristic, complemented
629#550C2×D512yescomplemented
630#547—56no—
631#547—53no—
632#547—512no—
633#547—56no—
634#547—56no—
635#547—53no—
636#547—53no—
637#547—56no—
638#547C2×D513yescomplemented
639#540—56no—
640#540—56no—
641#540—512no—
642#540—512no—
643#540—512no—
644#540—512no—
645#540—56no—
646#540—56no—
647#540—56no—
648#540—56no—
649#540—56no—
650#540C2×D516yescomplemented
651#532—56no—
652#532—53no—
653#532—53no—
654#532—56no—
655#532—56no—
656#532—56no—
657#532—56no—
658#532—56no—
659#532—53no—
660#532C2×D513yescomplemented
661C2×C4⋊Q8—53no—
662C2×#127—53no—
663C2×#127—56no—
664#529—56no—
665#529—53no—
666#529—53no—
667#529—56no—
668#529—53no—
669#529—53no—
670#529—53no—
671#529—56no—
672#529—53no—
673#529—56no—
674#529—53no—
675#529C2×D513yescomplemented
676C2×#126—56no—
677C2×#125—51no—
678C2×#125—56no—
679C2×#124—53no—
680C2×#123—56no—
681C2×#123—512no—
682C2×C22⋊Q8—53no—
683C2×#121—53no—
684C2×#121—56no—
685C2×#121—56no—
686C2×#121—56no—
687C2×#121—512no—
688C2×#121—56no—
689#520—52no—
690#520—52no—
691#520—52no—
692#520—56no—
693#520—56no—
694#520—56no—
695#520—56no—
696#520C2×D512yescomplemented
697C4×#41—51no—
698C4×#41—51no—
699C4×#41—51no—
700C4×#41—53no—
701C4×#41—53no—
702C4×#41—53no—
703C4×#41—53no—
704C4×#41C2×D511yescharacteristic, complemented
705C2×C4×Q8—51no—
706C2×C4×Q8—51no—
707C2×C4×Q8—52no—
708C2×C4×Q8—53no—
709C2×C4×D4—53no—
710C2×C4×D4—53no—
711C2×C4×D4—56no—
712C2×C4×D4—56no—
713C2×C4×D4—53no—
714C2×C4×D4—56no—
715C2×C4×D4—56no—
716C2×#117—53no—
717C2×#117—56no—
718C22×C4⋊C4—56no—
719C22×C42—53no—
720C23×C5C2513yes—
721C23×C5C2516yes—
722C22×D5—26no—
723C22×D5—212no—
724C22×D5—26no—
725C22×D5—212no—
726C22×D5—26no—
727C22×D5—212no—
728C22×D5C2513yes—
729C22×D5C2516yes—
730C22×D5C2511yescharacteristic
731C5×Q8—26no—
732C5×Q8C2×#4114yescomplemented
733C5×D4—26no—
734C5×D4—212no—
735C5×D4—26no—
736C5×D4—412no—
737C5×D4—46no—
738C5×D4—46no—
739C2×C4×C5—26no—
740C2×C4×C5—212no—
741C2×C4×C5—26no—
742C2×C4×C5—412no—
743C2×C4×C5—43no—
744C2×C4×C5C2511yescharacteristic
745C2×C4×C5C2511yescharacteristic
746C2×C4×C5C2512yes—
747C2×C4×C5C2513yes—
748C2×C4×C5C2513yes—
749C2×C4×C5C2516yes—
750C2×C4×C5C2512yes—
751C2×C4×C5C2513yes—
752C2×C4×C5C2511yescharacteristic
753C22⋊D5—212no—
754C22⋊D5—224no—
755C22⋊D5—212no—
756C22⋊D5—412no—
757C22⋊D5—412no—
758C22⋊D5—412no—
759C22⋊D5—46no—
760C22⋊D5—46no—
761C2×Dic5—26no—
762C2×Dic5—212no—
763C2×Dic5—26no—
764C2×Dic5—412no—
765C2×Dic5—43no—
766C2×Dic5C2511yescharacteristic
767C2×Dic5C2511yescharacteristic
768C2×Dic5C2512yes—
769C2×Dic5C2513yes—
770C2×Dic5C2513yes—
771C2×Dic5C2516yes—
772C2×Dic5C2512yes—
773C2×Dic5C2513yes—
774C2×Dic5C2511yescharacteristic
775D20—26no—
776D20—212no—
777D20—26no—
778D20—412no—
779D20—46no—
780D20—46no—
781C4×D5—22no—
782C4×D5—24no—
783C4×D5—26no—
784C4×D5—212no—
785C4×D5—22no—
786C4×D5—26no—
787C4×D5—24no—
788C4×D5—26no—
789C4×D5—212no—
790C4×D5—26no—
791C4×D5—26no—
792C4×D5—212no—
793C4×D5—26no—
794C4×D5—43no—
795C4×D5—43no—
796C4×D5—412no—
797C4×D5—412no—
798C4×D5C2×#41112yes—
799C4×D5H(5,𝔽2)14yes—
800Dic10—26no—
801Dic10—212no—
802Dic10C2×#41112yescomplemented
803C2×#41—51no—
804C2×#41—52no—
805C2×#41—56no—
806C2×#41—53no—
807C2×#41—56no—
808C2×#41—512no—
809C2×#41—56no—
810C2×#41—53no—
811C2×#41—56no—
812C2×#41—512no—
813C2×#41—56no—
814C2×#41—108no—
815C2×#41—1016no—
816C2×#41—2024no—
817C2×#41C22×D511yescharacteristic
818C2×#41C22×D512yes—
819C2×#41C22×D516yes—
820C22×Q8—51no—
821C22×Q8—53no—
822C22×D4—53no—
823C22×D4—56no—
824C22×D4—53no—
825C22×D4—56no—
826C22×D4—56no—
827C22×D4—512no—
828C23×C4—56no—
829C23×C4—53no—
830C23×C4—53no—
831C23×C4—512no—
832C23×C4—53no—
833C4⋊Q8—56no—
834C4⋊Q8—56no—
835C4⋊Q8—56no—
836C4⋊Q8—53no—
837C4⋊Q8C22×D513yes—
838#127—56no—
839#127—56no—
840#127—56no—
841#127—512no—
842#127—512no—
843#127—56no—
844#127—56no—
845#127—53no—
846#127—56no—
847#127C22×D513yes—
848#127C22×D516yes—
849#126—56no—
850#126—56no—
851#126—56no—
852#126—56no—
853#126—56no—
854#126—56no—
855#126—56no—
856#126C22×D516yes—
857#125—52no—
858#125—52no—
859#125—51no—
860#125—51no—
861#125—512no—
862#125—512no—
863#125—56no—
864#125—56no—
865#125—51no—
866#125—56no—
867#125C22×D511yescharacteristic
868#125C22×D516yes—
869#124—53no—
870#124—53no—
871#124—56no—
872#124—56no—
873#124—53no—
874#124C22×D513yes—
875#123—56no—
876#123—512no—
877#123—56no—
878#123—512no—
879#123—56no—
880#123—56no—
881#123—512no—
882#123—512no—
883#123—56no—
884#123—56no—
885#123—56no—
886#123—512no—
887#123—512no—
888#123—512no—
889#123C22×D516yes—
890#123C22×D5112yes—
891C22⋊Q8—53no—
892C22⋊Q8—53no—
893C22⋊Q8—56no—
894C22⋊Q8—53no—
895C22⋊Q8—56no—
896C22⋊Q8C22×D513yes—
897#121—53no—
898#121—56no—
899#121—56no—
900#121—512no—
901#121—56no—
902#121—512no—
903#121—56no—
904#121—512no—
905#121—512no—
906#121—56no—
907#121—512no—
908#121—512no—
909#121—512no—
910#121—53no—
911#121—56no—
912#121—56no—
913#121—56no—
914#121—512no—
915#121—56no—
916#121—53no—
917#121—56no—
918#121—56no—
919#121—56no—
920#121—512no—
921#121—56no—
922#121—56no—
923#121—512no—
924#121—512no—
925#121—512no—
926#121—512no—
927#121—512no—
928#121—512no—
929#121C22×D513yes—
930#121C22×D516yes—
931#121C22×D516yes—
932#121C22×D516yes—
933#121C22×D5112yes—
934#121C22×D516yes—
935C4×Q8—51no—
936C4×Q8—51no—
937C4×Q8—52no—
938C4×Q8—53no—
939C4×Q8—53no—
940C4×Q8—53no—
941C4×Q8—56no—
942C4×Q8—56no—
943C4×Q8—53no—
944C4×Q8—53no—
945C4×Q8—53no—
946C4×Q8—56no—
947C4×Q8—56no—
948C4×Q8—53no—
949C4×Q8C22×D511yescharacteristic
950C4×Q8C22×D511yescharacteristic
951C4×Q8C22×D512yes—
952C4×Q8C22×D513yes—
953C4×D4—53no—
954C4×D4—53no—
955C4×D4—56no—
956C4×D4—56no—
957C4×D4—53no—
958C4×D4—56no—
959C4×D4—56no—
960C4×D4—56no—
961C4×D4—56no—
962C4×D4—512no—
963C4×D4—512no—
964C4×D4—56no—
965C4×D4—56no—
966C4×D4—56no—
967C4×D4—512no—
968C4×D4—53no—
969C4×D4—53no—
970C4×D4—56no—
971C4×D4—56no—
972C4×D4—53no—
973C4×D4—56no—
974C4×D4—56no—
975C4×D4—56no—
976C4×D4—56no—
977C4×D4—512no—
978C4×D4—512no—
979C4×D4—56no—
980C4×D4—56no—
981C4×D4—56no—
982C4×D4—512no—
983C4×D4—53no—
984C4×D4—53no—
985C4×D4—56no—
986C4×D4—56no—
987C4×D4—53no—
988C4×D4—56no—
989C4×D4—56no—
990C4×D4C22×D513yes—
991C4×D4C22×D513yes—
992C4×D4C22×D516yes—
993C4×D4C22×D516yes—
994C4×D4C22×D513yes—
995C4×D4C22×D516yes—
996C4×D4C22×D516yes—
997#117—53no—
998#117—56no—
999#117—53no—
1000#117—53no—
1001#117—56no—
1002#117—56no—
1003#117—56no—
1004#117—56no—
1005#117—56no—
1006#117—56no—
1007#117—56no—
1008#117—56no—
1009#117C22×D513yes—
1010#117C22×D516yes—
1011C2×C4⋊C4—512no—
1012C2×C4⋊C4—56no—
1013C2×C4⋊C4—53no—
1014C2×C4⋊C4—56no—
1015C2×C4⋊C4—56no—
1016C2×C4⋊C4—512no—
1017C2×C4⋊C4—56no—
1018C2×C4⋊C4—56no—
1019C2×C4⋊C4—52no—
1020C2×C4⋊C4—53no—
1021C2×C4⋊C4—51no—
1022C2×C4⋊C4—52no—
1023C2×C4⋊C4—56no—
1024C2×C4⋊C4—51no—
1025C2×C4⋊C4—56no—
1026C2×C4⋊C4C22×D516yes—
1027C2×C22⋊C4—56no—
1028C2×C22⋊C4—56no—
1029C2×C22⋊C4—56no—
1030C2×C22⋊C4—56no—
1031C2×C22⋊C4—56no—
1032C2×C22⋊C4—56no—
1033C2×C42—53no—
1034C2×C42—53no—
1035C2×C42—53no—
1036C2×C42—53no—
1037C2×C42—53no—
1038C2×C42—56no—
1039C2×C42—53no—
1040C2×C42—53no—
1041C2×C42—53no—
1042C2×C42—53no—
1043C2×C42—53no—
1044C2×C42—51no—
1045C2×C42C22×D513yes—
1046C22×C5—23no—
1047C22×C5—26no—
1048C22×C5—23no—
1049C22×C5—26no—
1050C22×C5—23no—
1051C22×C5—26no—
1052C22×C5C2611yescharacteristic
1053C2×D5—23no—
1054C2×D5—26no—
1055C2×D5—23no—
1056C2×D5—26no—
1057C2×D5—23no—
1058C2×D5—26no—
1059C2×D5—412no—
1060C2×D5—424no—
1061C2×D5C22×#4112yes—
1062C2×D5C2×H(5,𝔽2)12yes—
1063C2×D5#58512yes—
1064C4×C5—21no—
1065C4×C5—22no—
1066C4×C5—26no—
1067C4×C5—23no—
1068C4×C5—21no—
1069C4×C5—23no—
1070C4×C5—22no—
1071C4×C5C22×#4116yes—
1072C4×C5C2×H(5,𝔽2)12yes—
1073Dic5—21no—
1074Dic5—22no—
1075Dic5—26no—
1076Dic5—23no—
1077Dic5—21no—
1078Dic5—23no—
1079Dic5—22no—
1080Dic5C22×#4116yes—
1081Dic5C2×H(5,𝔽2)12yes—
1082C24—53no—
1083C24—56no—
1084#41—24no—
1085#41—28no—
1086#41—412no—
1087#41—1012no—
1088#41—1024no—
1089#41—1012no—
1090#41—1024no—
1091#41—104no—
1092#41—108no—
1093#41—2012no—
1094#41—2024no—
1095#41—2012no—
1096#41—2024no—
1097#41—2012no—
1098C2×Q8—58no—
1099C2×Q8—53no—
1100C2×Q8—56no—
1101C2×Q8—53no—
1102C2×Q8—1012no—
1103C2×Q8C23×D513yes—
1104C2×Q8C23×D511yescharacteristic
1105C2×D4—56no—
1106C2×D4—512no—
1107C2×D4—56no—
1108C2×D4—512no—
1109C2×D4—56no—
1110C2×D4—56no—
1111C2×D4—512no—
1112C2×D4—512no—
1113C2×D4—53no—
1114C2×D4—56no—
1115C2×D4—53no—
1116C2×D4—56no—
1117C2×D4—56no—
1118C2×D4—512no—
1119C2×D4—1012no—
1120C2×D4—1024no—
1121C2×D4—1012no—
1122C2×D4—2024no—
1123C2×D4—2012no—
1124C2×D4—2012no—
1125C2×D4C23×D513yes—
1126C2×D4C23×D516yes—
1127C2×D4C23×D513yes—
1128C2×D4C23×D516yes—
1129C2×D4C23×D516yes—
1130C2×D4C23×D5112yes—
1131C22×C4—53no—
1132C22×C4—51no—
1133C22×C4—53no—
1134C22×C4—53no—
1135C22×C4—56no—
1136C22×C4—53no—
1137C22×C4—512no—
1138C22×C4—51no—
1139C22×C4—51no—
1140C22×C4—52no—
1141C22×C4—53no—
1142C22×C4—53no—
1143C22×C4—53no—
1144C22×C4—53no—
1145C22×C4—53no—
1146C22×C4—53no—
1147C22×C4—56no—
1148C22×C4—52no—
1149C22×C4—56no—
1150C22×C4—56no—
1151C22×C4—53no—
1152C22×C4—53no—
1153C22×C4—512no—
1154C22×C4—512no—
1155C22×C4—1024no—
1156C22×C4—1012no—
1157C22×C4—1012no—
1158C22×C4—2024no—
1159C22×C4—206no—
1160C22×C4C23×D513yes—
1161C22×C4C23×D513yes—
1162C22×C4C23×D516yes—
1163C22×C4C23×D513yes—
1164C22×C4C23×D5112yes—
1165C4⋊C4—56no—
1166C4⋊C4—53no—
1167C4⋊C4—56no—
1168C4⋊C4—56no—
1169C4⋊C4—56no—
1170C4⋊C4—512no—
1171C4⋊C4—56no—
1172C4⋊C4—52no—
1173C4⋊C4—52no—
1174C4⋊C4—52no—
1175C4⋊C4—56no—
1176C4⋊C4—53no—
1177C4⋊C4—52no—
1178C4⋊C4—51no—
1179C4⋊C4—52no—
1180C4⋊C4—52no—
1181C4⋊C4—52no—
1182C4⋊C4—512no—
1183C4⋊C4—56no—
1184C4⋊C4—52no—
1185C4⋊C4—51no—
1186C4⋊C4—56no—
1187C4⋊C4—56no—
1188C4⋊C4—56no—
1189C4⋊C4C23×D513yes—
1190C4⋊C4C23×D516yes—
1191C4⋊C4C23×D516yes—
1192C4⋊C4C23×D512yes—
1193C4⋊C4C23×D513yes—
1194C4⋊C4C23×D511yescharacteristic
1195C4⋊C4C23×D512yes—
1196C4⋊C4C23×D516yes—
1197C4⋊C4C23×D511yescharacteristic
1198C4⋊C4C23×D516yes—
1199C22⋊C4—56no—
1200C22⋊C4—56no—
1201C22⋊C4—56no—
1202C22⋊C4—56no—
1203C22⋊C4—56no—
1204C22⋊C4—56no—
1205C22⋊C4—56no—
1206C22⋊C4—56no—
1207C22⋊C4—56no—
1208C22⋊C4—56no—
1209C22⋊C4—56no—
1210C22⋊C4—56no—
1211C22⋊C4—56no—
1212C22⋊C4—56no—
1213C22⋊C4—56no—
1214C22⋊C4—56no—
1215C22⋊C4—56no—
1216C22⋊C4—56no—
1217C22⋊C4C23×D516yes—
1218C22⋊C4C23×D516yes—
1219C22⋊C4C23×D516yes—
1220C22⋊C4C23×D516yes—
1221C22⋊C4C23×D516yes—
1222C22⋊C4C23×D516yes—
1223C42—51no—
1224C42—51no—
1225C42—51no—
1226C42—53no—
1227C42—53no—
1228C42—53no—
1229C42—53no—
1230C42—53no—
1231C42—53no—
1232C42—53no—
1233C42—53no—
1234C42—53no—
1235C42—56no—
1236C42—56no—
1237C42—56no—
1238C42C23×D511yescharacteristic
1239C42C23×D513yes—
1240C42C23×D513yes—
1241C42C23×D513yes—
1242C42C23×D516yes—
1243C2×C5—43no—
1244C2×C5—46no—
1245C2×C5C23×#4111yescharacteristic
1246C2×C5C22×H(5,𝔽2)11yescharacteristic
1247C2×C5C2×#58511yescharacteristic
1248D5—43no—
1249D5—46no—
1250D5#351714yesdirect product factor
1251C23—51no—
1252C23—53no—
1253C23—56no—
1254C23—106no—
1255C23—1012no—
1256C23—106no—
1257C23—1012no—
1258C23—106no—
1259C23—1012no—
1260C23C24×D513yes—
1261C23C24×D516yes—
1262Q8—26no—
1263Q8—512no—
1264Q8—1012no—
1265Q8—106no—
1266Q8D5×#4114yescomplemented
1267D4—26no—
1268D4—212no—
1269D4—26no—
1270D4—412no—
1271D4—46no—
1272D4—46no—
1273D4—1012no—
1274D4—1024no—
1275D4—1012no—
1276D4—106no—
1277D4—1012no—
1278D4—106no—
1279D4—2012no—
1280D4—206no—
1281D4—206no—
1282D4—2012no—
1283D4—2012no—
1284D4—2012no—
1285D4—206no—
1286D4—206no—
1287C2×C4—26no—
1288C2×C4—212no—
1289C2×C4—26no—
1290C2×C4—412no—
1291C2×C4—43no—
1292C2×C4—53no—
1293C2×C4—51no—
1294C2×C4—512no—
1295C2×C4—54no—
1296C2×C4—51no—
1297C2×C4—51no—
1298C2×C4—52no—
1299C2×C4—53no—
1300C2×C4—53no—
1301C2×C4—56no—
1302C2×C4—52no—
1303C2×C4—106no—
1304C2×C4—1012no—
1305C2×C4—106no—
1306C2×C4—102no—
1307C2×C4—104no—
1308C2×C4—106no—
1309C2×C4—102no—
1310C2×C4—1012no—
1311C2×C4—106no—
1312C2×C4—104no—
1313C2×C4—106no—
1314C2×C4—1012no—
1315C2×C4—106no—
1316C2×C4—106no—
1317C2×C4—1012no—
1318C2×C4—106no—
1319C2×C4—2012no—
1320C2×C4—2012no—
1321C2×C4—203no—
1322C2×C4—203no—
1323C2×C4—2012no—
1324C2×C4—203no—
1325C2×C4C24×D511yescharacteristic
1326C2×C4C24×D511yescharacteristic
1327C2×C4C24×D512yes—
1328C2×C4C24×D513yes—
1329C2×C4C24×D513yes—
1330C2×C4C24×D516yes—
1331C2×C4C24×D512yes—
1332C2×C4C24×D513yes—
1333C2×C4C24×D511yescharacteristic
1334C5C2×#351711yescharacteristic, complemented, Sylow
1335C22—23no—
1336C22—26no—
1337C22—23no—
1338C22—26no—
1339C22—23no—
1340C22—26no—
1341C22—52no—
1342C22—52no—
1343C22—52no—
1344C22—103no—
1345C22—106no—
1346C22—103no—
1347C22—106no—
1348C22—103no—
1349C22—106no—
1350C22—2012no—
1351C22—2024no—
1352C22C25×D511yescharacteristic
1353C4—21no—
1354C4—22no—
1355C4—23no—
1356C4—26no—
1357C4—21no—
1358C4—23no—
1359C4—22no—
1360C4—56no—
1361C4—52no—
1362C4—101no—
1363C4—102no—
1364C4—103no—
1365C4—106no—
1366C4—101no—
1367C4—103no—
1368C4—102no—
1369C4C2×D5×#4116yes—
1370C4D5×H(5,𝔽2)12yes—
1371C2—43no—
1372C2—46no—
1373C2—54no—
1374C2—203no—
1375C2—206no—
1376C2C22×D5×#4111yescharacteristic
1377C2C2×D5×H(5,𝔽2)11yescharacteristic
1378C2D5×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3517C2
hypercenter#3517D5
hypocenterC5C2×#3517
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. C5×#3517C2semidirect
2. D5×#557C2semidirect
3. #10618924C2semidirect
4. D5×#553C2semidirect
5. #10618787C2semidirect
6. D5×#550C2semidirect
7. D5×#550C2semidirect
8. D5×#550C2semidirect
9. #10618675C2semidirect
10. #10618674C2semidirect
11. #10618673C2semidirect
12. D5×#547C2semidirect
13. #10618585C2semidirect
14. D5×#540C2semidirect
15. #10618371C2semidirect
16. D5×#532C2semidirect
17. #10618129C2semidirect
18. D5×#529C2semidirect
19. #10618027C2semidirect
20. D5×#520C2semidirect
21. #10617797C2semidirect
22. #10617754C2semidirect
23. C4×D5×#41C2semidirect
27. C5×#557C22semidirect
28. C5×#553C22semidirect
29. C5×#550C22semidirect
30. C5×#550C22semidirect
31. C5×#550C22semidirect
32. C5×#547C22semidirect
33. C5×#540C22semidirect
34. C5×#532C22semidirect
35. C5×#529C22semidirect
36. C5×#520C22semidirect
37. C4×C5×#41C22semidirect
38. #66168C22semidirect
39. #66168C22semidirect
40. #66168C22semidirect
41. #66168C22semidirect
42. #66166C22semidirect
43. #66161C22semidirect
44. #41×Dic5C22semidirect
45. #66158C22semidirect
46. #66060C22semidirect
47. #66059C22semidirect
49. #66055C22semidirect
50. #66053C22semidirect
51. #66052C22semidirect
52. #66052C22semidirect
53. #66052C22semidirect
54. #66052C22semidirect
55. #66050C22semidirect
58. #66043C22semidirect
59. #66040C22semidirect
61. #66032C22semidirect
62. #66029C22semidirect
63. #66025C22semidirect
66. #66019C22semidirect
67. #66014C22semidirect
69. #66002C22semidirect
70. #65997C22semidirect
71. #65997C22semidirect
72. #65995C22semidirect
73. #65989C22semidirect
76. #65983C22semidirect
77. #65965C22semidirect
79. #65958C22semidirect
80. #65953C22semidirect
81. #65953C22semidirect
82. #65952C22semidirect
83. #65949C22semidirect
84. #65949C22semidirect
85. #65948C22semidirect
86. #65945C22semidirect
93. #65935C22semidirect
94. #65934C22semidirect
95. #65933C22semidirect
96. #65933C22semidirect
97. #65933C22semidirect
98. #65933C22semidirect
99. #65933C22semidirect
100. #65930C22semidirect
101. #65930C22semidirect
102. #65914C22semidirect
103. #65911C22semidirect
104. #65911C22semidirect
105. #65911C22semidirect
106. #65908C22semidirect
107. #65908C22semidirect
108. C4×#713C22semidirect
109. C4×#713C22semidirect
114. #65904C22semidirect
115. #65903C22semidirect
116. #65901C22semidirect
117. #65899C22semidirect
118. #65896C22semidirect
119. #65896C22semidirect
120. #65892C22semidirect
121. #65891C22semidirect
122. #65889C22semidirect
123. #65887C22semidirect
124. #65887C22semidirect
125. #65887C22semidirect
126. #65887C22semidirect
127. #65885C22semidirect
128. #65882C22semidirect
129. #65882C22semidirect
130. #65880C22semidirect
131. #65880C22semidirect
139. #65874C22semidirect
140. #65872C22semidirect
141. C4×#711C22semidirect
142. C4×#711C22semidirect
143. #65869C22semidirect
144. #65864C22semidirect
145. #65862C22semidirect
146. #65857C22semidirect
147. #65856C22semidirect
150. #65848C22semidirect
151. #65841C22semidirect
152. #65838C22semidirect
154. #65813C22semidirect
155. #65811C22semidirect
156. C4×#709C22semidirect
413. #3517D5direct (N × H)
460. Q8×D5#41semidirect
594. #557C2×D5semidirect
606. #553C2×D5semidirect
627. #550C2×D5semidirect
628. #550C2×D5semidirect
629. #550C2×D5semidirect
638. #547C2×D5semidirect
650. #540C2×D5semidirect
660. #532C2×D5semidirect
675. #529C2×D5semidirect
696. #520C2×D5semidirect
704. C4×#41C2×D5semidirect
732. C5×Q8C2×#41semidirect
802. Dic10C2×#41semidirect
1250. D5#3517direct (N × H)
1266. Q8D5×#41semidirect
1334. C5C2×#3517semidirect

Maximal subgroups

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

subgroupindex
C5×#35172
D5×#5572
#106189242
D5×#5532
#106187872
D5×#5502
#106186752
#106186742
#106186732
D5×#5472
#106185852
D5×#5402
#106183712
D5×#5322
#106181292
D5×#5292
#106180272
D5×#5202
#106177972
#106177542
C4×D5×#412
C2×#35175