Finite Group Databasebeta

← D5×#3499 #13007708

Subgroups — D5×#3499 #13007708

Order 1280.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×2−1+4C212yesmaximal, complemented
2C5×#3499C211yesmaximal, characteristic, complemented
3#10619193C212yesmaximal, complemented
4D4×Q8×D5C214yesmaximal, complemented
5#10618647C214yesmaximal, complemented
6D5×#547C2112yesmaximal, complemented
7#10618580C2112yesmaximal, complemented
8D5×#536C216yesmaximal, complemented
9#10618241C216yesmaximal, complemented
10#10618144C213yesmaximal, complemented
11D5×#532C213yesmaximal, complemented
12#10618115C213yesmaximal, complemented
13C2×D5×C4⋊Q8C213yesmaximal, complemented
14C4×D5×#41C211yesmaximal, characteristic, complemented
15#10617728C211yesmaximal, characteristic, complemented
16C2×C5×2−1+4C2212yescomplemented
17D5×2−1+4—232no—
18C2×#4150C2216yescomplemented
19C2×#4150C2212yescomplemented
20C2×#4150C22112yescomplemented
21C2×D5×#41C2216yes—
22C2×D5×#41C22112yes—
23C2×D5×#41C2211yescharacteristic
24C2×#4147C2216yescomplemented
25C2×#4147C2214yescomplemented
26C22×Q8×D5C2214yes—
27C22×Q8×D5C2216yes—
28C5×D4×Q8C2214yescomplemented
29C5×#547C22112yescomplemented
30C5×#536C2216yescomplemented
31C5×#532C2213yescomplemented
32C2×C5×C4⋊Q8C2213yescomplemented
33C4×C5×#41C2211yescharacteristic, complemented
34#66166C2216yescomplemented
35#41×Dic5C2211yescharacteristic, complemented
36#66159C2216yescomplemented
37#66158C22124yescomplemented
38#66150C2216yescomplemented
39Q8×C22⋊D5C2218yescomplemented
40C2×#4090C2216yescomplemented
41#66061C22112yescomplemented
42#66060C22112yescomplemented
43#66059C2213yescomplemented
44#66058C22112yescomplemented
45D5×C4⋊Q8C2213yes—
46D5×C4⋊Q8C22112yes—
47D5×C4⋊Q8C2216yes—
48D5×C4⋊Q8C2216yescomplemented
49D5×C4⋊Q8C22112yescomplemented
50D5×C4⋊Q8C2216yescomplemented
51#66050C2213yescomplemented
52D5×#127C2211yescharacteristic
53#66009C22112yescomplemented
54D5×#124C2216yes—
55#66002C2216yescomplemented
56#65989C22148yescomplemented
57D5×#123C22124yes—
58#65982C22124yescomplemented
59#65966C22124yescomplemented
60#65965C22124yescomplemented
61#65962C22124yescomplemented
62D5×C22⋊Q8C22124yes—
63#65945C22124yescomplemented
64D5×#121C22112yes—
65#65930C22112yescomplemented
66Q8×D20C2214yescomplemented
67C4×#713C2212yescomplemented
68C4×Q8×D5C2212yes—
69#65889C22112yescomplemented
70#65885C22112yescomplemented
71#65882C22112yescomplemented
72C4×D4×D5C22112yes—
73C4×D4×D5C2216yes—
74D4×Dic10C22112yescomplemented
75C4×#711C2216yescomplemented
76#65860C2216yescomplemented
77#65856C2213yescomplemented
78D5×#117C2213yes—
79#65841C22124yescomplemented
80C2×D5×C4⋊C4C22112yes—
81C2×#4034C22112yescomplemented
82#65811C2213yescomplemented
83C4×#709C2213yescomplemented
84C2×C42×D5C2213yes—
85C2×#4015C2213yescomplemented
86C2×#3499—51nomaximal, Sylow
87C5×2−1+4—216no—
88C2×C5×#41C23112yes—
89C2×C5×#41C2316yes—
90C2×C5×#41C2311yescharacteristic
91C22×C5×Q8C2316yes—
92C22×C5×Q8C2314yes—
93#4150—216no—
94#4150—296no—
95#4150—248no—
96D5×#41—296no—
97D5×#41—248no—
98D5×#41D4116yescomplemented
99#4147—232no—
100#4147—248no—
101C2×#713C2316yes—
102C2×#713C23112yes—
103C2×#713C2311yescharacteristic
104C2×Q8×D5—232no—
105C2×Q8×D5—248no—
106C2×Q8×D5C2316yes—
107C2×Q8×D5C23112yes—
108C2×Q8×D5C23112yes—
109C2×Q8×D5C23112yes—
110C2×Q8×D5C23112yes—
111C2×Q8×D5C2314yes—
112C2×Q8×D5C2311yescharacteristic
113C2×#711C2316yes—
114C2×#711C23112yes—
115C2×#711C23112yes—
116C2×#711C23124yes—
117C2×#711C2313yes—
118C2×D4×D5C2314yes—
119C2×D4×D5C2312yes—
120C2×D4×D5C23112yes—
121C2×D4×D5C2313yes—
122C2×#709C2316yes—
123C2×#709C23124yes—
124C2×#709C23112yes—
125C2×#709C23112yes—
126C2×#709C2313yes—
127C22×C4×D5C2316yes—
128C22×C4×D5C23112yes—
129C22×C4×D5C23112yes—
130C22×C4×D5C2313yes—
131C22×Dic10C2316yes—
132C22×Dic10C23112yes—
133C22×Dic10C23112yes—
134C5×C4⋊Q8C2313yes—
135C5×C4⋊Q8C2316yes—
136C5×C4⋊Q8C23112yes—
137C5×#127C2311yescharacteristic
138C5×#124C2316yes—
139C5×#123C23124yes—
140C5×C22⋊Q8C23124yes—
141C5×#121C23112yes—
142C4×C5×Q8C2312yes—
143C4×C5×D4C2316yes—
144C4×C5×D4C23112yes—
145C5×#117C2313yes—
146C2×C5×C4⋊C4C23112yes—
147C2×C42×C5C2313yes—
148#4093C2316yes—
149#4092C23124yes—
150Q8×Dic5C2312yes—
151#4090C2316yes—
152#4090C23112yes—
153#4090C23124yes—
154#4086C2314yes—
155#4086C2312yes—
156#4085C23124yes—
157#4084C23112yes—
158#4082C2316yes—
159#4081C23124yes—
160D4×Dic5C23112yes—
161D4×Dic5C2316yes—
162#4076C23112yes—
163#4075C23124yes—
164C4×C22⋊D5C23112yes—
165C4×C22⋊D5C23124yes—
166#4072C2313yes—
167C2×C4⋊Dic5C23112yes—
168#4070C23124yes—
169C2×#683C23124yes—
170C2×C4×Dic5C2316yes—
171C2×C4×Dic5C2313yes—
172#4043C23124yes—
173#4042C23148yes—
174#4041C23112yes—
175#4040C23148yes—
176#4039C23112yes—
177#4039C2316yes—
178#4038C2316yes—
179D5×C4⋊C4C23112yes—
180D5×C4⋊C4C23124yes—
181D5×C4⋊C4C23124yes—
182D5×C4⋊C4C23124yes—
183D5×C4⋊C4C2316yes—
184#4034C23112yes—
185#4034C23124yes—
186#4034C23124yes—
187#4034C23124yes—
188#4033C2316yes—
189#4032C23124yes—
190#4031C23124yes—
191#4030C23124yes—
192#4029C23148yes—
193#4027C23112yes—
194#4027C23124yes—
195D5×C22⋊C4C2316yes—
196D5×C22⋊C4C23124yes—
197#4024C23148yes—
198#4023C2316yes—
199#4021C2316yes—
200#4020C2311yescharacteristic
201C4×D20C2316yes—
202C4×D20C23112yes—
203#4018C2316yes—
204C42×D5C2311yescharacteristic
205C42×D5C2313yes—
206C42×D5C2313yes—
207C42×D5C2316yes—
208C42×D5C2313yes—
209C42×D5C2316yes—
210#4015C2313yes—
211#4015C2316yes—
212#4015C23112yes—
213C4×Dic10C2316yes—
214C22×2−1+4—52no—
215#3499—52no—
216#3499—54no—
217#3499—512no—
218#3499—56no—
219#3499—53no—
220#3499—53no—
221#3499—51no—
222#3499D511yescharacteristic, direct product factor
223C2×D4×Q8—54no—
224C2×#547—512no—
225C2×#536—56no—
226C2×#532—53no—
227C22×C4⋊Q8—53no—
228C2×C4×#41—51no—
229C23×D5C2414yes—
230C23×D5C2413yes—
231C5×#41—248no—
232C5×#41—224no—
233C5×#41C2×D418yescomplemented
234C2×C5×Q8—216no—
235C2×C5×Q8—224no—
236C2×C5×Q8C24112yes—
237C2×C5×Q8C2416yes—
238C2×C5×Q8C2411yescharacteristic
239C2×C5×D4C2414yes—
240C2×C5×D4C24112yes—
241C2×C5×D4C2412yes—
242C2×C5×D4C2413yes—
243C22×C4×C5C2416yes—
244C22×C4×C5C24112yes—
245C22×C4×C5C24112yes—
246C22×C4×C5C2413yes—
247C2×C22⋊D5C24112yes—
248C2×C22⋊D5C2414yes—
249C2×C22⋊D5C24112yes—
250C2×C22⋊D5C2418yes—
251C2×C22⋊D5C2416yes—
252C22×Dic5C24112yes—
253C22×Dic5C24112yes—
254C22×Dic5C2416yes—
255C22×Dic5C2413yes—
256#713—248no—
257#713—224no—
258#713C2×D418yescomplemented
259Q8×D5—216no—
260Q8×D5—248no—
261Q8×D5—224no—
262Q8×D5—248no—
263Q8×D5—248no—
264Q8×D5—248no—
265Q8×D5C2×D418yes—
266#711—248no—
267#711—296no—
268#711—248no—
269#711—224no—
270#711C2×D4124yescomplemented
271D4×D5—248no—
272D4×D5—28no—
273D4×D5—216no—
274D4×D5C2×D4124yes—
275#709—224no—
276#709—296no—
277#709—248no—
278#709—248no—
279#709C2×D4124yescomplemented
280C2×D20C2412yes—
281C2×D20C24112yes—
282C2×D20C2414yes—
283C2×D20C2413yes—
284C2×C4×D5—248no—
285C2×C4×D5—248no—
286C2×C4×D5—224no—
287C2×C4×D5C2×D4124yes—
288C2×C4×D5C24112yes—
289C2×C4×D5C24112yes—
290C2×C4×D5C24112yes—
291C2×C4×D5C24124yes—
292C2×C4×D5C2416yes—
293C2×C4×D5C2416yes—
294C2×C4×D5C2416yes—
295C2×C4×D5C2413yes—
296C2×C4×D5C2411yescharacteristic
297C2×C4×D5C2413yes—
298C2×C4×D5C2413yes—
299C2×C4×D5C2412yes—
300C2×Dic10—224no—
301C2×Dic10—248no—
302C2×Dic10—248no—
303C2×Dic10C2416yes—
304C2×Dic10C24112yes—
305C2×Dic10C24124yes—
306C2×Dic10C24112yes—
307C2×Dic10C2413yes—
308C5×C4⋊C4C24112yes—
309C5×C4⋊C4C24124yes—
310C5×C4⋊C4C2416yes—
311C5×C22⋊C4C2416yes—
312C5×C22⋊C4C24124yes—
313C42×C5C2411yescharacteristic
314C42×C5C2413yes—
315C42×C5C2416yes—
316C22⋊Dic5C2416yes—
317C22⋊Dic5C24124yes—
318#685C24112yes—
319#685C24124yes—
320#685C24124yes—
321C4⋊Dic5C2416yes—
322C4⋊Dic5C24112yes—
323C4⋊Dic5C24124yes—
324#683C24112yes—
325#683C24148yes—
326#683C24124yes—
327C4×Dic5C2416yes—
328C4×Dic5C2412yes—
329C4×Dic5C2411yescharacteristic
330C4×Dic5C2413yes—
331C4×Dic5C2416yes—
332C4×Dic5C2416yes—
333C4×Dic5C2416yes—
334C2×2−1+4—56no—
335C2×2−1+4—512no—
336C2×2−1+4—52no—
337C2×2−1+4—54no—
338C2×2−1+4—56no—
339C2×2−1+4—1032no—
340C2×2−1+4C2×D512yescomplemented
341C22×#41—51no—
342C22×#41—56no—
343C22×#41—512no—
344C23×Q8—56no—
345C23×Q8—54no—
346D4×Q8—58no—
347D4×Q8—512no—
348D4×Q8—524no—
349D4×Q8—54no—
350D4×Q8—512no—
351D4×Q8C2×D514yescomplemented
352#547—524no—
353#547—512no—
354#547—548no—
355#547—524no—
356#547—524no—
357#547—512no—
358#547—512no—
359#547—524no—
360#547C2×D5112yescomplemented
361#536—56no—
362#536—56no—
363#536—512no—
364#536—512no—
365#536—524no—
366#536—524no—
367#536—56no—
368#536C2×D516yescomplemented
369#532—56no—
370#532—53no—
371#532—53no—
372#532—56no—
373#532—512no—
374#532—512no—
375#532—53no—
376#532C2×D513yescomplemented
377C2×C4⋊Q8—56no—
378C2×C4⋊Q8—53no—
379C2×C4⋊Q8—56no—
380C2×C4⋊Q8—512no—
381C2×C4⋊Q8—56no—
382C2×C4⋊Q8—56no—
383C2×C4⋊Q8—512no—
384C2×C4⋊Q8—512no—
385C2×C4⋊Q8—53no—
386C2×C4⋊Q8C2×D513yescomplemented
387C2×#127—51no—
388C2×#124—56no—
389C2×#123—524no—
390C2×C22⋊Q8—524no—
391C2×#121—512no—
392C4×#41—51no—
393C4×#41—52no—
394C4×#41—56no—
395C4×#41—53no—
396C4×#41—53no—
397C4×#41C2×D511yescharacteristic, complemented
398C2×C4×Q8—52no—
399C2×C4×D4—56no—
400C2×C4×D4—512no—
401C2×#117—53no—
402C22×C4⋊C4—512no—
403C22×C42—53no—
404C23×C5C2514yes—
405C23×C5C2513yes—
406C22×D5—212no—
407C22×D5—28no—
408C22×D5—216no—
409C22×D5C22×D4112yes—
410C22×D5C2514yes—
411C22×D5C2513yes—
412C22×D5C2511yescharacteristic
413C5×Q8—212no—
414C5×Q8—224no—
415C5×Q8C22×D414yes—
416C5×D4—224no—
417C5×D4—24no—
418C5×D4—28no—
419C5×D4C22×D4112yes—
420C2×C4×C5—224no—
421C2×C4×C5—224no—
422C2×C4×C5—212no—
423C2×C4×C5C22×D4112yes—
424C2×C4×C5C2516yes—
425C2×C4×C5C25112yes—
426C2×C4×C5C2511yescharacteristic
427C2×C4×C5C2513yes—
428C2×C4×C5C2512yes—
429C22⋊D5—224no—
430C22⋊D5—224no—
431C22⋊D5—28no—
432C22⋊D5—216no—
433C22⋊D5C22×D4124yes—
434C2×Dic5—224no—
435C2×Dic5—224no—
436C2×Dic5—212no—
437C2×Dic5C22×D4112yes—
438C2×Dic5C2516yes—
439C2×Dic5C25112yes—
440C2×Dic5C2511yescharacteristic
441C2×Dic5C2513yes—
442C2×Dic5C2512yes—
443D20—224no—
444D20—24no—
445D20—28no—
446D20C22×D4112yes—
447C4×D5—224no—
448C4×D5—248no—
449C4×D5—212no—
450C4×D5—224no—
451C4×D5—212no—
452C4×D5—224no—
453C4×D5—212no—
454C4×D5C22×D4112yes—
455C4×D5C22×D414yes—
456C4×D5C22×D4112yes—
457C4×D5C22×D4112yes—
458C4×D52−1+418yescomplemented
459Dic10—212no—
460Dic10—224no—
461Dic10—224no—
462Dic10—248no—
463Dic10C22×D4112yes—
4642−1+4—216no—
4652−1+4—1032no—
4662−1+4—1048no—
4672−1+4—1096no—
4682−1+4—1048no—
4692−1+4—1016no—
470C2×#41—516no—
471C2×#41—51no—
472C2×#41—56no—
473C2×#41—512no—
474C2×#41—53no—
475C2×#41—512no—
476C2×#41—56no—
477C2×#41—512no—
478C2×#41—524no—
479C2×#41—53no—
480C2×#41—512no—
481C2×#41—56no—
482C2×#41—512no—
483C2×#41—524no—
484C2×#41—1048no—
485C2×#41—1096no—
486C2×#41C22×D516yes—
487C2×#41C22×D5112yes—
488C2×#41C22×D511yescharacteristic
489C22×Q8—51no—
490C22×Q8—512no—
491C22×Q8—56no—
492C22×Q8—512no—
493C22×Q8—512no—
494C22×Q8—512no—
495C22×Q8—54no—
496C22×Q8—512no—
497C22×Q8—56no—
498C22×Q8—512no—
499C22×Q8—1048no—
500C22×Q8—1032no—
501C22×Q8C22×D516yes—
502C22×Q8C22×D514yes—
503C22×D4—53no—
504C22×D4—54no—
505C22×D4—512no—
506C22×D4—52no—
507C23×C4—53no—
508C23×C4—56no—
509C23×C4—512no—
510C23×C4—512no—
511C4⋊Q8—56no—
512C4⋊Q8—512no—
513C4⋊Q8—524no—
514C4⋊Q8—512no—
515C4⋊Q8—524no—
516C4⋊Q8—524no—
517C4⋊Q8—524no—
518C4⋊Q8—53no—
519C4⋊Q8—56no—
520C4⋊Q8—512no—
521C4⋊Q8C22×D513yes—
522C4⋊Q8C22×D516yes—
523C4⋊Q8C22×D5112yes—
524#127—52no—
525#127—54no—
526#127—51no—
527#127C22×D511yescharacteristic
528#124—56no—
529#124—56no—
530#124—524no—
531#124—56no—
532#124C22×D516yes—
533#123—524no—
534#123—524no—
535#123—548no—
536#123—548no—
537#123—524no—
538#123C22×D5124yes—
539C22⋊Q8—524no—
540C22⋊Q8—524no—
541C22⋊Q8—548no—
542C22⋊Q8—524no—
543C22⋊Q8—548no—
544C22⋊Q8C22×D5124yes—
545#121—512no—
546#121—524no—
547#121—512no—
548#121—512no—
549#121—524no—
550#121C22×D5112yes—
551C4×Q8—52no—
552C4×Q8—56no—
553C4×Q8—56no—
554C4×Q8C22×D512yes—
555C4×D4—56no—
556C4×D4—512no—
557C4×D4—512no—
558C4×D4—524no—
559C4×D4—56no—
560C4×D4—512no—
561C4×D4—512no—
562C4×D4—524no—
563C4×D4—56no—
564C4×D4—512no—
565C4×D4C22×D516yes—
566C4×D4C22×D5112yes—
567#117—53no—
568#117—56no—
569#117—56no—
570#117—56no—
571#117C22×D513yes—
572C2×C4⋊C4—524no—
573C2×C4⋊C4—512no—
574C2×C4⋊C4—512no—
575C2×C4⋊C4—524no—
576C2×C4⋊C4—524no—
577C2×C4⋊C4—524no—
578C2×C4⋊C4—56no—
579C2×C4⋊C4C22×D5112yes—
580C2×C22⋊C4—56no—
581C2×C22⋊C4—524no—
582C2×C42—56no—
583C2×C42—53no—
584C2×C42—53no—
585C2×C42—56no—
586C2×C42—56no—
587C2×C42—53no—
588C2×C42—53no—
589C2×C42—51no—
590C2×C42C22×D513yes—
591C22×C5—26no—
592C22×C5—24no—
593C22×C5—28no—
594C22×C5C23×D416yes—
595C22×C5C2611yescharacteristic
596C2×D5—26no—
597C2×D5—224no—
598C2×D5—24no—
599C2×D5—28no—
600C2×D5—416no—
601C2×D5C23×D416yes—
602C2×D5C23×D412yes—
603C2×D5C2×2−1+414yes—
604C4×C5—212no—
605C4×C5—26no—
606C4×C5C23×D412yes—
607C4×C5C23×D416yes—
608C4×C5C2×2−1+414yescomplemented
609Dic5—212no—
610Dic5—26no—
611Dic5C23×D412yes—
612Dic5C23×D416yes—
613Dic5C2×2−1+414yescomplemented
614C24—53no—
615C24—54no—
616#41—248no—
617#41—224no—
618#41—58no—
619#41—524no—
620#41—524no—
621#41—1048no—
622#41—1096no—
623#41—1048no—
624#41—1048no—
625#41—1024no—
626#41—1024no—
627#41—1096no—
628#41—1048no—
629#41—1048no—
630#41—1024no—
631#41D4×D518yescomplemented
632C2×Q8—216no—
633C2×Q8—224no—
634C2×Q8—58no—
635C2×Q8—53no—
636C2×Q8—524no—
637C2×Q8—512no—
638C2×Q8—512no—
639C2×Q8—56no—
640C2×Q8—1048no—
641C2×Q8—1048no—
642C2×Q8—1024no—
643C2×Q8—1048no—
644C2×Q8—1048no—
645C2×Q8—1048no—
646C2×Q8—1048no—
647C2×Q8—1016no—
648C2×Q8—1024no—
649C2×Q8C23×D5112yes—
650C2×Q8C23×D516yes—
651C2×Q8C23×D511yescharacteristic
652C2×D4—56no—
653C2×D4—524no—
654C2×D4—58no—
655C2×D4—512no—
656C2×D4—512no—
657C2×D4—54no—
658C2×D4—53no—
659C2×D4—54no—
660C2×D4—512no—
661C2×D4—52no—
662C2×D4—108no—
663C2×D4—1016no—
664C2×D4—1048no—
665C2×D4C23×D514yes—
666C2×D4C23×D5112yes—
667C2×D4C23×D512yes—
668C2×D4C23×D513yes—
669C22×C4—53no—
670C22×C4—524no—
671C22×C4—52no—
672C22×C4—51no—
673C22×C4—53no—
674C22×C4—53no—
675C22×C4—53no—
676C22×C4—56no—
677C22×C4—512no—
678C22×C4—512no—
679C22×C4—56no—
680C22×C4—56no—
681C22×C4—56no—
682C22×C4—512no—
683C22×C4—524no—
684C22×C4—512no—
685C22×C4—512no—
686C22×C4—1048no—
687C22×C4—1024no—
688C22×C4—1048no—
689C22×C4C23×D516yes—
690C22×C4C23×D5112yes—
691C22×C4C23×D5112yes—
692C22×C4C23×D513yes—
693C4⋊C4—524no—
694C4⋊C4—512no—
695C4⋊C4—548no—
696C4⋊C4—524no—
697C4⋊C4—512no—
698C4⋊C4—56no—
699C4⋊C4C23×D5112yes—
700C4⋊C4C23×D5124yes—
701C4⋊C4C23×D516yes—
702C22⋊C4—56no—
703C22⋊C4—524no—
704C22⋊C4—512no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C22⋊C4C23×D516yes—
708C22⋊C4C23×D5124yes—
709C42—51no—
710C42—52no—
711C42—56no—
712C42—53no—
713C42—56no—
714C42—56no—
715C42—56no—
716C42C23×D511yescharacteristic
717C42C23×D513yes—
718C42C23×D516yes—
719C2×C5—26no—
720C2×C5—44no—
721C2×C5C24×D411yescharacteristic
722C2×C5C22×2−1+412yes—
723D5—26no—
724D5—44no—
725D5#349914yesdirect product factor
726C23—51no—
727C23—512no—
728C23—53no—
729C23—54no—
730C23—1012no—
731C23—108no—
732C23—1016no—
733C23C24×D514yes—
734C23C24×D513yes—
735Q8—224no—
736Q8—212no—
737Q8—512no—
738Q8—1024no—
739Q8—1048no—
740Q8—1024no—
741Q8—1012no—
742Q8C2×D4×D514yes—
743D4—224no—
744D4—24no—
745D4—28no—
746D4—524no—
747D4—512no—
748D4—1024no—
749D4—108no—
750D4—1016no—
751D4—1024no—
752D4—1024no—
753D4—104no—
754D4—108no—
755D4C2×D4×D5112yes—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—212no—
759C2×C4—512no—
760C2×C4—52no—
761C2×C4—51no—
762C2×C4—53no—
763C2×C4—54no—
764C2×C4—512no—
765C2×C4—512no—
766C2×C4—512no—
767C2×C4—58no—
768C2×C4—56no—
769C2×C4—512no—
770C2×C4—1024no—
771C2×C4—1012no—
772C2×C4—1024no—
773C2×C4—1048no—
774C2×C4—1012no—
775C2×C4—1024no—
776C2×C4—1012no—
777C2×C4—1024no—
778C2×C4—1024no—
779C2×C4—1012no—
780C2×C4C2×D4×D5112yes—
781C2×C4C24×D516yes—
782C2×C4C24×D5112yes—
783C2×C4C24×D511yescharacteristic
784C2×C4C24×D513yes—
785C2×C4C24×D512yes—
786C5C2×#349911yescharacteristic, complemented, Sylow
787C22—26no—
788C22—24no—
789C22—28no—
790C22—52no—
791C22—54no—
792C22—56no—
793C22—1024no—
794C22—106no—
795C22—104no—
796C22—108no—
797C22—2016no—
798C22C22×D4×D516yes—
799C22C25×D511yescharacteristic
800C4—212no—
801C4—26no—
802C4—52no—
803C4—56no—
804C4—54no—
805C4—1012no—
806C4—106no—
807C4C22×D4×D516yes—
808C4C22×D4×D512yes—
809C4D5×2−1+414yescomplemented
810C2—26no—
811C2—44no—
812C2—54no—
813C2—106no—
814C2—204no—
815C2C23×D4×D511yescharacteristic
816C2C2×D5×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3499C2
hypercenter#3499D5
hypocenterC5C2×#3499
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×D5×2−1+4C2semidirect
2. C5×#3499C2semidirect
3. #10619193C2semidirect
4. D4×Q8×D5C2semidirect
5. #10618647C2semidirect
6. D5×#547C2semidirect
7. #10618580C2semidirect
8. D5×#536C2semidirect
9. #10618241C2semidirect
10. #10618144C2semidirect
11. D5×#532C2semidirect
12. #10618115C2semidirect
13. C2×D5×C4⋊Q8C2semidirect
14. C4×D5×#41C2semidirect
15. #10617728C2semidirect
16. C2×C5×2−1+4C22semidirect
18. C2×#4150C22semidirect
19. C2×#4150C22semidirect
20. C2×#4150C22semidirect
24. C2×#4147C22semidirect
25. C2×#4147C22semidirect
28. C5×D4×Q8C22semidirect
29. C5×#547C22semidirect
30. C5×#536C22semidirect
31. C5×#532C22semidirect
32. C2×C5×C4⋊Q8C22semidirect
33. C4×C5×#41C22semidirect
34. #66166C22semidirect
35. #41×Dic5C22semidirect
36. #66159C22semidirect
37. #66158C22semidirect
38. #66150C22semidirect
39. Q8×C22⋊D5C22semidirect
40. C2×#4090C22semidirect
41. #66061C22semidirect
42. #66060C22semidirect
43. #66059C22semidirect
44. #66058C22semidirect
48. D5×C4⋊Q8C22semidirect
49. D5×C4⋊Q8C22semidirect
50. D5×C4⋊Q8C22semidirect
51. #66050C22semidirect
53. #66009C22semidirect
55. #66002C22semidirect
56. #65989C22semidirect
58. #65982C22semidirect
59. #65966C22semidirect
60. #65965C22semidirect
61. #65962C22semidirect
63. #65945C22semidirect
65. #65930C22semidirect
66. Q8×D20C22semidirect
67. C4×#713C22semidirect
69. #65889C22semidirect
70. #65885C22semidirect
71. #65882C22semidirect
74. D4×Dic10C22semidirect
75. C4×#711C22semidirect
76. #65860C22semidirect
77. #65856C22semidirect
79. #65841C22semidirect
81. C2×#4034C22semidirect
82. #65811C22semidirect
83. C4×#709C22semidirect
85. C2×#4015C22semidirect
98. D5×#41D4semidirect
222. #3499D5direct (N × H)
233. C5×#41C2×D4semidirect
258. #713C2×D4semidirect
270. #711C2×D4semidirect
279. #709C2×D4semidirect
340. C2×2−1+4C2×D5semidirect
351. D4×Q8C2×D5semidirect
360. #547C2×D5semidirect
368. #536C2×D5semidirect
376. #532C2×D5semidirect
386. C2×C4⋊Q8C2×D5semidirect
397. C4×#41C2×D5semidirect
458. C4×D52−1+4semidirect
608. C4×C5C2×2−1+4semidirect
613. Dic5C2×2−1+4semidirect
631. #41D4×D5semidirect
725. D5#3499direct (N × H)
786. C5C2×#3499semidirect
809. C4D5×2−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×D5×2−1+42
C5×#34992
#106191932
D4×Q8×D52
#106186472
D5×#5472
#106185802
D5×#5362
#106182412
#106181442
D5×#5322
#106181152
C2×D5×C4⋊Q82
C4×D5×#412
#106177282
C2×#34995