Finite Group Databasebeta

← D5×#3586 #13013143

Subgroups — D5×#3586 #13013143

Order 1280.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#585C211yesmaximal, characteristic, complemented
2C2×D5×2−1+4C211yesmaximal, characteristic, complemented
3C5×#3586C211yesmaximal, characteristic, complemented
4#10619200C211yesmaximal, characteristic, complemented
5#10619188C211yesmaximal, characteristic, complemented
6#10619112C218yesmaximal, complemented
7D5×#578C218yesmaximal, complemented
8#10619109C218yesmaximal, complemented
9D5×#577C218yesmaximal, complemented
10#10619102C216yesmaximal, complemented
11D5×#575C216yesmaximal, complemented
12#10619098C216yesmaximal, complemented
13C2×D5×#137C216yesmaximal, complemented
14#10619069C211yesmaximal, characteristic, complemented
15D5×#568C211yesmaximal, characteristic, complemented
16C5×#585C2211yescharacteristic, complemented
17C2×C5×2−1+4C2211yescharacteristic, complemented
18#66287—21no—
19#66287C2214yescomplemented
20D5×2−1+4—24no—
21D5×2−1+4—24no—
22D5×2−1+4—21no—
23D5×2−1+4C2218yescomplemented
24D5×2−1+4C2214yescomplemented
25D5×2−1+4C2218yescomplemented
26#66285—23no—
27#66285C2214yescomplemented
28D5×H(5,𝔽2)—23no—
29D5×H(5,𝔽2)C2214yescomplemented
30#66283—24no—
31#66283C2216yescomplemented
32#66283C2211yescharacteristic, complemented
33C2×#4150—23no—
34C2×#4150C2213yescomplemented
35C2×#4150C2211yescharacteristic, complemented
36C2×D5×#41—24no—
37C2×D5×#41—23no—
38C2×D5×#41C2216yes—
39C2×D5×#41C2211yescharacteristic
40C2×D5×#41C2213yescomplemented
41C2×#4147—21no—
42C2×#4147C2213yescomplemented
43C22×Q8×D5—21no—
44C22×Q8×D5C2213yescomplemented
45C5×#578C2218yescomplemented
46C5×#577C2218yescomplemented
47C5×#575C2216yescomplemented
48C2×C5×#137C2216yescomplemented
49C5×#568C2211yescharacteristic, complemented
50#66172C2218yescomplemented
51#66172C2218yescomplemented
52#66171C2218yescomplemented
53#66170C2218yescomplemented
54C2×#4097C2216yescomplemented
55#66156C2216yescomplemented
56#66156C2216yescomplemented
57#66153C2211yescharacteristic, complemented
58C2×#4088C2216yescomplemented
59#66113C22124yescomplemented
60#66113C22124yescomplemented
61#66112C22124yescomplemented
62#66111C22112yescomplemented
63#66111C22112yescomplemented
64D5×#137C22112yescomplemented
65D5×#137C22124yescomplemented
66D5×#137C22112yescomplemented
67D5×#137C22124yescomplemented
68D5×#137C22124yescomplemented
69#66109C22124yescomplemented
70#66107C22112yescomplemented
71#66107C22112yescomplemented
72D5×AGL(1,ℤ/8)C2214yescomplemented
73D5×AGL(1,ℤ/8)C22112yescomplemented
74#66105C22124yescomplemented
75#66104C22124yescomplemented
76#66102C22124yescomplemented
77D5×#135C22124yescomplemented
78#66100C22124yescomplemented
79C2×#4064C22112yescomplemented
80C2×D5×Q16C22112yescomplemented
81#66096C22124yescomplemented
82C2×#4061C22112yescomplemented
83C2×D5×SD16C22112yescomplemented
84#66087C2218yescomplemented
85#66085C2218yescomplemented
86#66084C2218yescomplemented
87D5×#131C2218yescomplemented
88#66082C2216yescomplemented
89C2×#4055C2216yescomplemented
90#66079C2216yescomplemented
91C2×D5×M16C2216yescomplemented
92C2×#3586—51nomaximal, Sylow
93C5×2−1+4—24no—
94C5×2−1+4—21no—
95C5×2−1+4C2318yescomplemented
96C5×2−1+4C2314yescomplemented
97C5×H(5,𝔽2)—23no—
98C5×H(5,𝔽2)C2314yescomplemented
99C2×C5×#41—24no—
100C2×C5×#41—23no—
101C2×C5×#41C2316yes—
102C2×C5×#41C2311yescharacteristic
103C2×C5×#41C2313yescomplemented
104C22×C5×Q8—21no—
105C22×C5×Q8C2313yescomplemented
106#4150—24no—
107#4150—24no—
108#4150—224no—
109#4150—224no—
110#4150—212no—
111#4150—212no—
112#4150—26no—
113#4150C23124yescomplemented
114#4150C23112yescomplemented
115#4150C2318yescomplemented
116#4150C2314yescomplemented
117#4149—24no—
118#4149—212no—
119#4149—26no—
120#4149C23112yescomplemented
121#4149C2314yescomplemented
122D5×#41—24no—
123D5×#41—24no—
124D5×#41—24no—
125D5×#41—212no—
126D5×#41—212no—
127D5×#41—224no—
128D5×#41—224no—
129D5×#41—212no—
130D5×#41—26no—
131D5×#41—26no—
132D5×#41—26no—
133D5×#41—26no—
134D5×#41—26no—
135D5×#41—26no—
136D5×#41D414yes—
137D5×#41D414yes—
138D5×#41C23112yes—
139D5×#41C23112yes—
140D5×#41C23112yes—
141D5×#41C2314yes—
142D5×#41C23112yes—
143D5×#41C2314yes—
144D5×#41C2314yes—
145D5×#41C23112yescomplemented
146#4147—21no—
147#4147—28no—
148#4147—28no—
149#4147—24no—
150#4147—24no—
151#4147—212no—
152#4147C23124yescomplemented
153#4147C23112yescomplemented
154C2×#713—24no—
155C2×#713—23no—
156C2×#713D411yescharacteristic
157C2×#713C2316yes—
158C2×#713C2313yescomplemented
159C2×Q8×D5—21no—
160C2×Q8×D5—28no—
161C2×Q8×D5—28no—
162C2×Q8×D5—24no—
163C2×Q8×D5—23no—
164C2×Q8×D5—23no—
165C2×Q8×D5—26no—
166C2×Q8×D5—26no—
167C2×Q8×D5—23no—
168C2×Q8×D5D411yescharacteristic
169C2×Q8×D5C23112yes—
170C2×Q8×D5C2316yes—
171C2×Q8×D5C2313yes—
172C2×Q8×D5C23112yescomplemented
173C2×Q8×D5C2316yescomplemented
174#4144—23no—
175#4144—212no—
176#4144—212no—
177#4144—212no—
178#4144C23112yescomplemented
179C2×#711—23no—
180C2×#711—26no—
181C2×#711—26no—
182C2×#711—23no—
183C2×#711—212no—
184C2×#711D413yes—
185C2×#711C2316yes—
186C2×#711C2313yescomplemented
187C2×D4×D5—23no—
188C2×D4×D5—26no—
189C2×D4×D5—212no—
190C2×D4×D5D413yes—
191C2×D4×D5C2316yes—
192C2×D4×D5C2311yescharacteristic
193C2×#709—26no—
194C2×#709—212no—
195C2×#709—23no—
196C2×#709—23no—
197C2×#709—26no—
198C2×#709C2313yes—
199C2×#709C2316yes—
200C2×#709C2313yescomplemented
201C22×C4×D5—23no—
202C22×C4×D5—23no—
203C22×C4×D5—26no—
204C22×C4×D5C2313yes—
205C22×Dic10—23no—
206C22×Dic10—23no—
207C22×Dic10C2313yescomplemented
208C5×#137C23112yescomplemented
209C5×#137C23124yescomplemented
210C5×#137C23112yescomplemented
211C5×AGL(1,ℤ/8)C2314yescomplemented
212C5×AGL(1,ℤ/8)C23112yescomplemented
213C5×#135C23124yescomplemented
214C2×C5×Q16C23112yescomplemented
215C2×C5×SD16C23112yescomplemented
216C5×#131C2318yescomplemented
217C2×C5×M16C2316yescomplemented
218#4097C23124yescomplemented
219#4097C23112yescomplemented
220#4097C23112yescomplemented
221#4096C23124yescomplemented
222#4096C23124yescomplemented
223#4095C23112yescomplemented
224#4095C2314yescomplemented
225#4094C2318yescomplemented
226C2×#689C23112yescomplemented
227C2×#689C23112yescomplemented
228#4088C23124yescomplemented
229#4088C23112yescomplemented
230#4088C23112yescomplemented
231C2×#688C23112yescomplemented
232C2×#687C23112yescomplemented
233#4078C23112yescomplemented
234#4078C2314yescomplemented
235C2×#681C2316yescomplemented
236#4065C23124yescomplemented
237#4064C23124yescomplemented
238#4064C23148yescomplemented
239#4064C23124yescomplemented
240D5×Q16C23124yes—
241D5×Q16C23148yescomplemented
242#4062C23124yescomplemented
243#4062C23124yescomplemented
244#4061C23124yescomplemented
245#4061C23148yescomplemented
246#4061C23124yescomplemented
247#4060C23124yescomplemented
248#4060C2318yescomplemented
249D5×SD16C23124yes—
250D5×SD16C2318yes—
251D5×SD16C23148yescomplemented
252#4058C23124yescomplemented
253#4057C2318yescomplemented
254#4057C23124yescomplemented
255D5×D8C2318yes—
256#4055C23112yescomplemented
257#4055C23124yescomplemented
258#4055C23112yescomplemented
259#4054C2314yescomplemented
260#4054C23112yescomplemented
261#4053C23124yescomplemented
262D5×M16C2314yes—
263D5×M16C23112yes—
264D5×M16C23112yescomplemented
265D5×M16C23112yescomplemented
266C2×Dic20C23112yescomplemented
267#4050C23124yescomplemented
268C2×#677C23112yescomplemented
269#4047C23124yescomplemented
270C2×#676C23112yescomplemented
271C2×C8×D5C23112yes—
272C2×#585—51no—
273C22×2−1+4—51no—
274#3586—51no—
275#3586—51no—
276#3586—58no—
277#3586—58no—
278#3586—56no—
279#3586—56no—
280#3586—51no—
281#3586D511yescharacteristic, direct product factor
282C2×#578—58no—
283C2×#577—58no—
284C2×#575—56no—
285C22×#137—56no—
286C2×#568—51no—
287C23×D5—21no—
288C23×D5—26no—
289C23×D5C2×D413yes—
290C5×#41—24no—
291C5×#41—212no—
292C5×#41—224no—
293C5×#41—26no—
294C5×#41—26no—
295C5×#41—26no—
296C5×#41C2×D414yes—
297C5×#41C24112yes—
298C5×#41C24112yes—
299C5×#41C2414yes—
300C5×#41C2414yes—
301C2×C5×Q8—28no—
302C2×C5×Q8—24no—
303C2×C5×Q8—23no—
304C2×C5×Q8—26no—
305C2×C5×Q8C2×D411yescharacteristic
306C2×C5×Q8C24112yes—
307C2×C5×Q8C2416yes—
308C2×C5×Q8C2413yes—
309C2×C5×D4—23no—
310C2×C5×D4—26no—
311C2×C5×D4—212no—
312C2×C5×D4C2×D413yes—
313C2×C5×D4C2416yes—
314C2×C5×D4C2411yescharacteristic
315C22×C4×C5—23no—
316C22×C4×C5—23no—
317C22×C4×C5—26no—
318C22×C4×C5C2413yes—
319C2×C22⋊D5—23no—
320C2×C22⋊D5—26no—
321C2×C22⋊D5—23no—
322C2×C22⋊D5—26no—
323C2×C22⋊D5—224no—
324C2×C22⋊D5—21no—
325C2×C22⋊D5—26no—
326C2×C22⋊D5C2×D416yes—
327C22×Dic5—23no—
328C22×Dic5—23no—
329C22×Dic5—26no—
330C22×Dic5C2×D413yes—
331#713—24no—
332#713—224no—
333#713—212no—
334#713—26no—
335#713—26no—
336#713—26no—
337#713C2×D414yes—
338#713C2×D414yes—
339#713C2414yes—
340#713C24112yes—
341#713C24112yes—
342Q8×D5—28no—
343Q8×D5—24no—
344Q8×D5—23no—
345Q8×D5—212no—
346Q8×D5—23no—
347Q8×D5—212no—
348Q8×D5—212no—
349Q8×D5—26no—
350Q8×D5—212no—
351Q8×D5—212no—
352Q8×D5—26no—
353Q8×D5—224no—
354Q8×D5—212no—
355Q8×D5C2×D414yes—
356Q8×D5C2×D414yes—
357Q8×D5C2416yes—
358Q8×D5C2414yes—
359Q8×D5C2416yes—
360Q8×D5C24124yes—
361Q8×D5C24112yes—
362#711—212no—
363#711—224no—
364#711—224no—
365#711—248no—
366#711—24no—
367#711—212no—
368#711—212no—
369#711—212no—
370#711—212no—
371#711—212no—
372#711—26no—
373#711—26no—
374#711—26no—
375#711—212no—
376#711C2×D4112yes—
377#711C2×D4112yes—
378#711C2414yes—
379#711C24112yes—
380#711C24112yes—
381D4×D5—24no—
382D4×D5—212no—
383D4×D5—212no—
384D4×D5—212no—
385D4×D5—212no—
386D4×D5—212no—
387D4×D5—212no—
388D4×D5—224no—
389D4×D5—212no—
390D4×D5—26no—
391D4×D5—26no—
392D4×D5—21no—
393D4×D5—21no—
394D4×D5C2×D4112yes—
395D4×D5C2×D4112yes—
396D4×D5C2414yes—
397D4×D5C24112yes—
398D4×D5C2412yes—
399D4×D5C2412yes—
400#709—26no—
401#709—26no—
402#709—26no—
403#709—224no—
404#709—248no—
405#709—212no—
406#709—224no—
407#709—212no—
408#709—24no—
409#709—212no—
410#709—212no—
411#709—212no—
412#709—212no—
413#709—212no—
414#709C2×D4112yes—
415#709C24112yes—
416#709C24112yes—
417#709C24112yes—
418#709C2414yes—
419C2×D20—23no—
420C2×D20—26no—
421C2×D20—212no—
422C2×D20C2×D413yes—
423C2×D20C2416yes—
424C2×D20C2411yescharacteristic
425C2×C4×D5—23no—
426C2×C4×D5—26no—
427C2×C4×D5—26no—
428C2×C4×D5—212no—
429C2×C4×D5—212no—
430C2×C4×D5—26no—
431C2×C4×D5—23no—
432C2×C4×D5—23no—
433C2×C4×D5—26no—
434C2×C4×D5—24no—
435C2×C4×D5—212no—
436C2×C4×D5—212no—
437C2×C4×D5—212no—
438C2×C4×D5—212no—
439C2×C4×D5—212no—
440C2×C4×D5C2×D413yes—
441C2×C4×D5C2×D416yes—
442C2×C4×D5C2×D413yes—
443C2×C4×D5C2×D416yes—
444C2×C4×D5C2411yescharacteristic
445C2×C4×D5C2413yes—
446C2×C4×D5C2416yes—
447C2×C4×D5C2416yes—
448C2×Dic10—23no—
449C2×Dic10—26no—
450C2×Dic10—23no—
451C2×Dic10—26no—
452C2×Dic10—212no—
453C2×Dic10—212no—
454C2×Dic10—26no—
455C2×Dic10—224no—
456C2×Dic10—212no—
457C2×Dic10C2×D413yes—
458C2×Dic10C2413yes—
459C2×Dic10C24112yes—
460C2×Dic10C2416yes—
461C5×Q16C24124yes—
462C5×SD16C24124yes—
463C5×SD16C2418yes—
464C5×D8C2418yes—
465C5×M16C2414yes—
466C5×M16C24112yes—
467C2×C5×C8C24112yes—
468#689C24124yes—
469#689C24124yes—
470#688C2418yes—
471#688C24124yes—
472#687C2418yes—
473#687C24124yes—
474#686C2418yes—
475#686C2418yes—
476#681C24112yes—
477#681C2414yes—
478C2×#168C24112yes—
479Dic20C24124yes—
480D40C2418yes—
481#677C24124yes—
482#677C2418yes—
483#676C2418yes—
484#676C24124yes—
485C8×D5C2418yes—
486C8×D5C24124yes—
487#585—54no—
488#585—54no—
489#585—56no—
490#585—51no—
491#585—104no—
492#585—103no—
493#585—101no—
494#585C2×D511yescharacteristic, complemented
495C2×2−1+4—58no—
496C2×2−1+4—58no—
497C2×2−1+4—54no—
498C2×2−1+4—51no—
499C2×2−1+4—53no—
500C2×2−1+4—53no—
501C2×2−1+4—101no—
502C2×2−1+4—101no—
503C2×2−1+4—103no—
504C2×2−1+4—104no—
505C2×2−1+4—104no—
506C2×2−1+4C2×D511yescharacteristic, complemented
507C2×H(5,𝔽2)—54no—
508C2×H(5,𝔽2)—103no—
509C22×#41—51no—
510C22×#41—56no—
511C22×#41—53no—
512C22×#41—103no—
513C22×#41—104no—
514C23×Q8—53no—
515C23×Q8—101no—
516#578—58no—
517#578—58no—
518#578—524no—
519#578—524no—
520#578—524no—
521#578—524no—
522#578—58no—
523#578C2×D518yescomplemented
524#577—58no—
525#577—58no—
526#577—524no—
527#577—524no—
528#577—524no—
529#577—524no—
530#577—58no—
531#577C2×D518yescomplemented
532#575—56no—
533#575—56no—
534#575—512no—
535#575—512no—
536#575—512no—
537#575—512no—
538#575—524no—
539#575—56no—
540#575C2×D516yescomplemented
541C2×#137—56no—
542C2×#137—56no—
543C2×#137—524no—
544C2×#137—524no—
545C2×#137—512no—
546C2×#137—524no—
547C2×#137—512no—
548C2×#137—512no—
549C2×#137—512no—
550C2×#137—56no—
551C2×#137C2×D516yescomplemented
552C2×AGL(1,ℤ/8)—54no—
553C2×AGL(1,ℤ/8)—512no—
554C2×#135—524no—
555C22×Q16—512no—
556C22×SD16—512no—
557#568—51no—
558#568—58no—
559#568—56no—
560#568C2×D511yescharacteristic, complemented
561C2×#131—58no—
562C22×M16—56no—
563C23×C5—21no—
564C23×C5—26no—
565C23×C5C22×D413yes—
566C22×D5—21no—
567C22×D5—26no—
568C22×D5—22no—
569C22×D5—22no—
570C22×D5—24no—
571C22×D5—212no—
572C22×D5—46no—
573C22×D5—44no—
574C22×D5—812no—
575C22×D5C22×D411yescharacteristic
576C22×D5C22×D416yes—
577C22×D5C22×D413yes—
578C22×D5C22×D416yes—
579C5×Q8—212no—
580C5×Q8—23no—
581C5×Q8—26no—
582C5×Q8C22×D414yes—
583C5×Q8C2516yes—
584C5×Q8C2514yes—
585C5×D4—24no—
586C5×D4—212no—
587C5×D4—212no—
588C5×D4—26no—
589C5×D4—21no—
590C5×D4C22×D4112yes—
591C5×D4C2512yes—
592C5×D4C2514yes—
593C2×C4×C5—23no—
594C2×C4×C5—212no—
595C2×C4×C5—26no—
596C2×C4×C5—212no—
597C2×C4×C5—212no—
598C2×C4×C5—24no—
599C2×C4×C5C22×D413yes—
600C2×C4×C5C22×D416yes—
601C2×C4×C5C2516yes—
602C2×C4×C5C2511yescharacteristic
603C22⋊D5—212no—
604C22⋊D5—24no—
605C22⋊D5—212no—
606C22⋊D5—212no—
607C22⋊D5—24no—
608C22⋊D5—212no—
609C22⋊D5—22no—
610C22⋊D5—22no—
611C22⋊D5—24no—
612C22⋊D5—212no—
613C22⋊D5C22×D4124yes—
614C2×Dic5—23no—
615C2×Dic5—212no—
616C2×Dic5—26no—
617C2×Dic5—212no—
618C2×Dic5—212no—
619C2×Dic5—24no—
620C2×Dic5C22×D411yescharacteristic
621C2×Dic5C22×D416yes—
622C2×Dic5C22×D413yes—
623C2×Dic5C22×D416yes—
624D20—24no—
625D20—212no—
626D20—212no—
627D20—26no—
628D20—21no—
629D20C22×D4112yes—
630D20C2514yes—
631D20C2512yes—
632C4×D5—24no—
633C4×D5—26no—
634C4×D5—26no—
635C4×D5—212no—
636C4×D5—224no—
637C4×D5—24no—
638C4×D5—212no—
639C4×D5—212no—
640C4×D5—24no—
641C4×D5—212no—
642C4×D5—212no—
643C4×D5C22×D411yescharacteristic
644C4×D5C22×D416yes—
645C4×D5C22×D416yes—
646C4×D5C22×D416yes—
647C4×D5C22×D416yes—
648C4×D5C22×D411yescharacteristic
649C4×D5C22×D416yes—
650C4×D5C2511yescharacteristic
651C4×D5C2516yes—
652C4×D5C2511yescharacteristic
653Dic10—212no—
654Dic10—23no—
655Dic10—26no—
656Dic10—26no—
657Dic10—224no—
658Dic10—26no—
659Dic10—24no—
660Dic10—212no—
661Dic10C22×D4112yes—
662Dic10C2516yes—
663Dic10C2514yes—
664C5×C8C2518yes—
665#168C2518yes—
6662−1+4—24no—
6672−1+4—21no—
6682−1+4—524no—
6692−1+4—58no—
6702−1+4—512no—
6712−1+4—54no—
6722−1+4—524no—
6732−1+4—512no—
6742−1+4—104no—
6752−1+4—108no—
6762−1+4—108no—
6772−1+4—1012no—
6782−1+4—104no—
6792−1+4—104no—
6802−1+4—106no—
6812−1+4—1024no—
6822−1+4—1024no—
6832−1+4—1012no—
6842−1+4—1012no—
6852−1+4—104no—
6862−1+4—101no—
6872−1+4C22×D518yescomplemented
6882−1+4C22×D514yescomplemented
689H(5,𝔽2)—23no—
690H(5,𝔽2)—512no—
691H(5,𝔽2)—54no—
692H(5,𝔽2)—512no—
693H(5,𝔽2)—1012no—
694H(5,𝔽2)—1012no—
695H(5,𝔽2)—1012no—
696H(5,𝔽2)—1012no—
697H(5,𝔽2)—106no—
698H(5,𝔽2)—104no—
699H(5,𝔽2)—103no—
700H(5,𝔽2)C22×D514yescomplemented
701C2×#41—24no—
702C2×#41—23no—
703C2×#41—54no—
704C2×#41—54no—
705C2×#41—54no—
706C2×#41—54no—
707C2×#41—51no—
708C2×#41—53no—
709C2×#41—53no—
710C2×#41—512no—
711C2×#41—512no—
712C2×#41—54no—
713C2×#41—512no—
714C2×#41—512no—
715C2×#41—512no—
716C2×#41—56no—
717C2×#41—53no—
718C2×#41—56no—
719C2×#41—53no—
720C2×#41—56no—
721C2×#41—53no—
722C2×#41—103no—
723C2×#41—106no—
724C2×#41—106no—
725C2×#41—103no—
726C2×#41—1012no—
727C2×#41—103no—
728C2×#41—106no—
729C2×#41—106no—
730C2×#41—106no—
731C2×#41—106no—
732C2×#41—106no—
733C2×#41—106no—
734C2×#41—106no—
735C2×#41—106no—
736C2×#41—1012no—
737C2×#41—103no—
738C2×#41—1012no—
739C2×#41—1024no—
740C2×#41—1024no—
741C2×#41—104no—
742C2×#41—104no—
743C2×#41—104no—
744C2×#41—1012no—
745C2×#41—1012no—
746C2×#41—104no—
747C2×#41—103no—
748C2×#41C22×D516yes—
749C2×#41C22×D511yescharacteristic
750C2×#41C22×D513yescomplemented
751C22×Q8—21no—
752C22×Q8—51no—
753C22×Q8—512no—
754C22×Q8—56no—
755C22×Q8—53no—
756C22×Q8—56no—
757C22×Q8—512no—
758C22×Q8—53no—
759C22×Q8—103no—
760C22×Q8—103no—
761C22×Q8—103no—
762C22×Q8—106no—
763C22×Q8—103no—
764C22×Q8—106no—
765C22×Q8—108no—
766C22×Q8—108no—
767C22×Q8—103no—
768C22×Q8—104no—
769C22×Q8—101no—
770C22×Q8C22×D513yescomplemented
771C22×D4—53no—
772C22×D4—56no—
773C22×D4—51no—
774C22×D4—1012no—
775C22×D4—103no—
776C22×D4—106no—
777C23×C4—53no—
778C23×C4—103no—
779C23×C4—106no—
780C23×C4—103no—
781#137—512no—
782#137—524no—
783#137—512no—
784#137—512no—
785#137—524no—
786#137—512no—
787#137—524no—
788#137—548no—
789#137—524no—
790#137—524no—
791#137—548no—
792#137—524no—
793#137—512no—
794#137—524no—
795#137—512no—
796#137C22×D5112yescomplemented
797#137C22×D5124yescomplemented
798#137C22×D5112yescomplemented
799AGL(1,ℤ/8)—54no—
800AGL(1,ℤ/8)—512no—
801AGL(1,ℤ/8)—54no—
802AGL(1,ℤ/8)—512no—
803AGL(1,ℤ/8)—58no—
804AGL(1,ℤ/8)—524no—
805AGL(1,ℤ/8)—58no—
806AGL(1,ℤ/8)—524no—
807AGL(1,ℤ/8)—54no—
808AGL(1,ℤ/8)—512no—
809AGL(1,ℤ/8)C22×D514yescomplemented
810AGL(1,ℤ/8)C22×D5112yescomplemented
811#135—524no—
812#135—524no—
813#135—524no—
814#135—524no—
815#135—524no—
816#135—524no—
817#135—524no—
818#135C22×D5124yescomplemented
819C2×Q16—512no—
820C2×Q16—512no—
821C2×Q16—524no—
822C2×Q16—548no—
823C2×Q16—512no—
824C2×Q16C22×D5112yescomplemented
825C2×SD16—512no—
826C2×SD16—512no—
827C2×SD16—524no—
828C2×SD16—548no—
829C2×SD16—58no—
830C2×SD16—512no—
831C2×SD16C22×D5112yescomplemented
832C2×D8—58no—
833#131—58no—
834#131—524no—
835#131—524no—
836#131C22×D518yescomplemented
837C2×M16—56no—
838C2×M16—54no—
839C2×M16—512no—
840C2×M16—512no—
841C2×M16—512no—
842C2×M16—512no—
843C2×M16C22×D516yescomplemented
844C22×C8—512no—
845C22×C5—22no—
846C22×C5—24no—
847C22×C5—43no—
848C22×C5—42no—
849C22×C5—86no—
850C22×C5C23×D411yescharacteristic
851C22×C5C23×D416yes—
852C2×D5—22no—
853C2×D5—212no—
854C2×D5—22no—
855C2×D5—24no—
856C2×D5—46no—
857C2×D5—43no—
858C2×D5—44no—
859C2×D5—42no—
860C2×D5—44no—
861C2×D5—48no—
862C2×D5—812no—
863C2×D5—86no—
864C2×D5C23×D411yescharacteristic
865C2×D5C23×D416yes—
866C2×D5C23×D411yescharacteristic
867C4×C5—26no—
868C4×C5—24no—
869C4×C5C23×D416yes—
870C4×C5C23×D411yescharacteristic
871C4×C5C2611yescharacteristic
872Dic5—26no—
873Dic5—24no—
874Dic5C23×D411yescharacteristic
875Dic5C23×D416yes—
876Dic5C23×D411yescharacteristic
877C24—53no—
878C24—101no—
879C24—106no—
880#41—24no—
881#41—212no—
882#41—224no—
883#41—26no—
884#41—26no—
885#41—26no—
886#41—54no—
887#41—54no—
888#41—512no—
889#41—512no—
890#41—512no—
891#41—512no—
892#41—512no—
893#41—512no—
894#41—54no—
895#41—512no—
896#41—512no—
897#41—54no—
898#41—512no—
899#41—512no—
900#41—54no—
901#41—104no—
902#41—1012no—
903#41—1012no—
904#41—1012no—
905#41—1012no—
906#41—1012no—
907#41—1024no—
908#41—1012no—
909#41—1048no—
910#41—1024no—
911#41—1012no—
912#41—104no—
913#41—1012no—
914#41—106no—
915#41—1012no—
916#41—1012no—
917#41—106no—
918#41—1012no—
919#41—1012no—
920#41—106no—
921#41—106no—
922#41—106no—
923#41—106no—
924#41—1024no—
925#41—1048no—
926#41—1012no—
927#41—1012no—
928#41—1024no—
929#41—104no—
930#41—1012no—
931#41—1024no—
932#41—106no—
933#41—106no—
934#41—106no—
935#41D4×D514yes—
936#41C23×D5112yes—
937#41C23×D5112yes—
938#41C23×D514yes—
939#41C23×D514yes—
940C2×Q8—28no—
941C2×Q8—24no—
942C2×Q8—23no—
943C2×Q8—26no—
944C2×Q8—54no—
945C2×Q8—54no—
946C2×Q8—53no—
947C2×Q8—56no—
948C2×Q8—54no—
949C2×Q8—524no—
950C2×Q8—512no—
951C2×Q8—56no—
952C2×Q8—512no—
953C2×Q8—56no—
954C2×Q8—53no—
955C2×Q8—103no—
956C2×Q8—106no—
957C2×Q8—1012no—
958C2×Q8—1012no—
959C2×Q8—106no—
960C2×Q8—1024no—
961C2×Q8—1012no—
962C2×Q8—103no—
963C2×Q8—103no—
964C2×Q8—1012no—
965C2×Q8—1012no—
966C2×Q8—106no—
967C2×Q8—1012no—
968C2×Q8—1012no—
969C2×Q8—1012no—
970C2×Q8—106no—
971C2×Q8—1024no—
972C2×Q8—1012no—
973C2×Q8—108no—
974C2×Q8—104no—
975C2×Q8—103no—
976C2×Q8—106no—
977C2×Q8D4×D511yescharacteristic
978C2×Q8C23×D5112yes—
979C2×Q8C23×D516yes—
980C2×Q8C23×D513yes—
981C2×D4—23no—
982C2×D4—26no—
983C2×D4—212no—
984C2×D4—56no—
985C2×D4—512no—
986C2×D4—512no—
987C2×D4—52no—
988C2×D4—54no—
989C2×D4—512no—
990C2×D4—52no—
991C2×D4—53no—
992C2×D4—56no—
993C2×D4—51no—
994C2×D4—1012no—
995C2×D4—103no—
996C2×D4—106no—
997C2×D4—106no—
998C2×D4—101no—
999C2×D4—101no—
1000C2×D4—106no—
1001C2×D4—101no—
1002C2×D4—106no—
1003C2×D4—1024no—
1004C2×D4—1012no—
1005C2×D4—104no—
1006C2×D4—1012no—
1007C2×D4—1012no—
1008C2×D4—1012no—
1009C2×D4—1012no—
1010C2×D4—1012no—
1011C2×D4—1024no—
1012C2×D4—103no—
1013C2×D4—106no—
1014C2×D4—103no—
1015C2×D4—106no—
1016C2×D4—1012no—
1017C2×D4D4×D513yes—
1018C2×D4C23×D516yes—
1019C2×D4C23×D511yescharacteristic
1020C22×C4—23no—
1021C22×C4—23no—
1022C22×C4—26no—
1023C22×C4—53no—
1024C22×C4—53no—
1025C22×C4—56no—
1026C22×C4—53no—
1027C22×C4—56no—
1028C22×C4—56no—
1029C22×C4—51no—
1030C22×C4—53no—
1031C22×C4—56no—
1032C22×C4—104no—
1033C22×C4—1012no—
1034C22×C4—103no—
1035C22×C4—1012no—
1036C22×C4—1012no—
1037C22×C4—106no—
1038C22×C4—1012no—
1039C22×C4—1012no—
1040C22×C4—103no—
1041C22×C4—106no—
1042C22×C4—106no—
1043C22×C4—1012no—
1044C22×C4—1012no—
1045C22×C4—103no—
1046C22×C4—106no—
1047C22×C4—103no—
1048C22×C4—103no—
1049C22×C4—106no—
1050C22×C4C23×D513yes—
1051Q16—524no—
1052Q16—524no—
1053Q16—524no—
1054Q16C23×D5124yes—
1055SD16—524no—
1056SD16—58no—
1057SD16—524no—
1058SD16—58no—
1059SD16—524no—
1060SD16—58no—
1061SD16C23×D5124yes—
1062SD16C23×D518yes—
1063D8—58no—
1064D8—58no—
1065D8—58no—
1066D8C23×D518yes—
1067M16—54no—
1068M16—512no—
1069M16—58no—
1070M16—524no—
1071M16C23×D514yes—
1072M16C23×D5112yes—
1073C2×C8—512no—
1074C2×C8—58no—
1075C2×C8—524no—
1076C2×C8C23×D5112yes—
1077C2×C5—21no—
1078C2×C5—26no—
1079C2×C5—42no—
1080C2×C5—44no—
1081C2×C5C24×D411yescharacteristic
1082D5—21no—
1083D5—26no—
1084D5—42no—
1085D5—44no—
1086D5#358612yesdirect product factor
1087C23—21no—
1088C23—26no—
1089C23—51no—
1090C23—56no—
1091C23—56no—
1092C23—53no—
1093C23—102no—
1094C23—102no—
1095C23—104no—
1096C23—1012no—
1097C23—101no—
1098C23—106no—
1099C23—206no—
1100C23—204no—
1101C23—4012no—
1102C23C2×D4×D513yes—
1103Q8—23no—
1104Q8—212no—
1105Q8—26no—
1106Q8—512no—
1107Q8—56no—
1108Q8—54no—
1109Q8—106no—
1110Q8—106no—
1111Q8—1024no—
1112Q8—104no—
1113Q8—1012no—
1114Q8—103no—
1115Q8—1012no—
1116Q8—106no—
1117Q8C2×D4×D514yes—
1118Q8C24×D516yes—
1119Q8C24×D514yes—
1120D4—24no—
1121D4—212no—
1122D4—212no—
1123D4—26no—
1124D4—21no—
1125D4—524no—
1126D4—512no—
1127D4—52no—
1128D4—54no—
1129D4—104no—
1130D4—1012no—
1131D4—1012no—
1132D4—104no—
1133D4—1012no—
1134D4—102no—
1135D4—102no—
1136D4—104no—
1137D4—1012no—
1138D4—1012no—
1139D4—104no—
1140D4—1012no—
1141D4—1012no—
1142D4—106no—
1143D4—101no—
1144D4C2×D4×D5112yes—
1145D4C24×D512yes—
1146D4C24×D514yes—
1147C2×C4—23no—
1148C2×C4—26no—
1149C2×C4—212no—
1150C2×C4—24no—
1151C2×C4—212no—
1152C2×C4—212no—
1153C2×C4—51no—
1154C2×C4—53no—
1155C2×C4—56no—
1156C2×C4—56no—
1157C2×C4—51no—
1158C2×C4—51no—
1159C2×C4—56no—
1160C2×C4—56no—
1161C2×C4—56no—
1162C2×C4—56no—
1163C2×C4—56no—
1164C2×C4—51no—
1165C2×C4—56no—
1166C2×C4—51no—
1167C2×C4—104no—
1168C2×C4—1012no—
1169C2×C4—1012no—
1170C2×C4—104no—
1171C2×C4—106no—
1172C2×C4—106no—
1173C2×C4—1012no—
1174C2×C4—1024no—
1175C2×C4—104no—
1176C2×C4—1012no—
1177C2×C4—1012no—
1178C2×C4—103no—
1179C2×C4—106no—
1180C2×C4—1012no—
1181C2×C4—104no—
1182C2×C4—1012no—
1183C2×C4—1012no—
1184C2×C4C2×D4×D513yes—
1185C2×C4C2×D4×D516yes—
1186C2×C4C24×D516yes—
1187C2×C4C24×D511yescharacteristic
1188C8—58no—
1189C8C24×D518yes—
1190C5C2×#358611yescharacteristic, complemented, Sylow
1191C22—22no—
1192C22—24no—
1193C22—43no—
1194C22—42no—
1195C22—51no—
1196C22—51no—
1197C22—56no—
1198C22—86no—
1199C22—102no—
1200C22—1012no—
1201C22—102no—
1202C22—104no—
1203C22—203no—
1204C22—206no—
1205C22—202no—
1206C22—204no—
1207C22—208no—
1208C22—204no—
1209C22—406no—
1210C22—4012no—
1211C22C22×D4×D511yescharacteristic
1212C22C22×D4×D516yes—
1213C4—24no—
1214C4—26no—
1215C4—51no—
1216C4—51no—
1217C4—56no—
1218C4—104no—
1219C4—106no—
1220C4C22×D4×D511yescharacteristic
1221C4C22×D4×D516yes—
1222C4C25×D511yescharacteristic
1223C2—21no—
1224C2—26no—
1225C2—42no—
1226C2—44no—
1227C2—52no—
1228C2—101no—
1229C2—106no—
1230C2—202no—
1231C2—204no—
1232C2C23×D4×D511yescharacteristic
subgroupG/H
centerC2C23×D4×D5
commutator, cosocleC4×C5C26
FrattiniC4C25×D5
FittingC5×#3586C2
socleC2×C5C24×D4
hypercenter#3586D5
hypocenterC5C2×#3586
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×#41 ◁ #3586

Complements

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

NH ≅ G/Ntype
1. D5×#585C2semidirect
2. C2×D5×2−1+4C2semidirect
3. C5×#3586C2semidirect
4. #10619200C2semidirect
5. #10619188C2semidirect
6. #10619112C2semidirect
7. D5×#578C2semidirect
8. #10619109C2semidirect
9. D5×#577C2semidirect
10. #10619102C2semidirect
11. D5×#575C2semidirect
12. #10619098C2semidirect
13. C2×D5×#137C2semidirect
14. #10619069C2semidirect
15. D5×#568C2semidirect
16. C5×#585C22semidirect
17. C2×C5×2−1+4C22semidirect
19. #66287C22semidirect
23. D5×2−1+4C22semidirect
24. D5×2−1+4C22semidirect
25. D5×2−1+4C22semidirect
27. #66285C22semidirect
29. D5×H(5,𝔽2)C22semidirect
31. #66283C22semidirect
32. #66283C22semidirect
34. C2×#4150C22semidirect
35. C2×#4150C22semidirect
40. C2×D5×#41C22semidirect
42. C2×#4147C22semidirect
44. C22×Q8×D5C22semidirect
45. C5×#578C22semidirect
46. C5×#577C22semidirect
47. C5×#575C22semidirect
48. C2×C5×#137C22semidirect
49. C5×#568C22semidirect
50. #66172C22semidirect
51. #66172C22semidirect
52. #66171C22semidirect
53. #66170C22semidirect
54. C2×#4097C22semidirect
55. #66156C22semidirect
56. #66156C22semidirect
57. #66153C22semidirect
58. C2×#4088C22semidirect
59. #66113C22semidirect
60. #66113C22semidirect
61. #66112C22semidirect
62. #66111C22semidirect
63. #66111C22semidirect
64. D5×#137C22semidirect
65. D5×#137C22semidirect
66. D5×#137C22semidirect
67. D5×#137C22semidirect
68. D5×#137C22semidirect
69. #66109C22semidirect
70. #66107C22semidirect
71. #66107C22semidirect
72. D5×AGL(1,ℤ/8)C22semidirect
73. D5×AGL(1,ℤ/8)C22semidirect
74. #66105C22semidirect
75. #66104C22semidirect
76. #66102C22semidirect
77. D5×#135C22semidirect
78. #66100C22semidirect
79. C2×#4064C22semidirect
80. C2×D5×Q16C22semidirect
81. #66096C22semidirect
82. C2×#4061C22semidirect
83. C2×D5×SD16C22semidirect
84. #66087C22semidirect
85. #66085C22semidirect
86. #66084C22semidirect
87. D5×#131C22semidirect
88. #66082C22semidirect
89. C2×#4055C22semidirect
90. #66079C22semidirect
91. C2×D5×M16C22semidirect
95. C5×2−1+4C23semidirect
96. C5×2−1+4C23semidirect
98. C5×H(5,𝔽2)C23semidirect
103. C2×C5×#41C23semidirect
105. C22×C5×Q8C23semidirect
113. #4150C23semidirect
114. #4150C23semidirect
115. #4150C23semidirect
116. #4150C23semidirect
120. #4149C23semidirect
121. #4149C23semidirect
145. D5×#41C23semidirect
152. #4147C23semidirect
153. #4147C23semidirect
158. C2×#713C23semidirect
172. C2×Q8×D5C23semidirect
173. C2×Q8×D5C23semidirect
178. #4144C23semidirect
186. C2×#711C23semidirect
200. C2×#709C23semidirect
207. C22×Dic10C23semidirect
208. C5×#137C23semidirect
209. C5×#137C23semidirect
210. C5×#137C23semidirect
211. C5×AGL(1,ℤ/8)C23semidirect
212. C5×AGL(1,ℤ/8)C23semidirect
213. C5×#135C23semidirect
214. C2×C5×Q16C23semidirect
215. C2×C5×SD16C23semidirect
216. C5×#131C23semidirect
217. C2×C5×M16C23semidirect
218. #4097C23semidirect
219. #4097C23semidirect
220. #4097C23semidirect
221. #4096C23semidirect
222. #4096C23semidirect
223. #4095C23semidirect
224. #4095C23semidirect
225. #4094C23semidirect
226. C2×#689C23semidirect
227. C2×#689C23semidirect
228. #4088C23semidirect
229. #4088C23semidirect
230. #4088C23semidirect
231. C2×#688C23semidirect
232. C2×#687C23semidirect
233. #4078C23semidirect
234. #4078C23semidirect
235. C2×#681C23semidirect
236. #4065C23semidirect
237. #4064C23semidirect
238. #4064C23semidirect
239. #4064C23semidirect
241. D5×Q16C23semidirect
242. #4062C23semidirect
243. #4062C23semidirect
244. #4061C23semidirect
245. #4061C23semidirect
246. #4061C23semidirect
247. #4060C23semidirect
248. #4060C23semidirect
251. D5×SD16C23semidirect
252. #4058C23semidirect
253. #4057C23semidirect
254. #4057C23semidirect
256. #4055C23semidirect
257. #4055C23semidirect
258. #4055C23semidirect
259. #4054C23semidirect
260. #4054C23semidirect
261. #4053C23semidirect
264. D5×M16C23semidirect
265. D5×M16C23semidirect
266. C2×Dic20C23semidirect
267. #4050C23semidirect
268. C2×#677C23semidirect
269. #4047C23semidirect
270. C2×#676C23semidirect
281. #3586D5direct (N × H)
494. #585C2×D5semidirect
506. C2×2−1+4C2×D5semidirect
523. #578C2×D5semidirect
531. #577C2×D5semidirect
540. #575C2×D5semidirect
551. C2×#137C2×D5semidirect
560. #568C2×D5semidirect
687. 2−1+4C22×D5semidirect
688. 2−1+4C22×D5semidirect
700. H(5,𝔽2)C22×D5semidirect
750. C2×#41C22×D5semidirect
770. C22×Q8C22×D5semidirect
796. #137C22×D5semidirect
797. #137C22×D5semidirect
798. #137C22×D5semidirect
809. AGL(1,ℤ/8)C22×D5semidirect
810. AGL(1,ℤ/8)C22×D5semidirect
818. #135C22×D5semidirect
824. C2×Q16C22×D5semidirect
831. C2×SD16C22×D5semidirect
836. #131C22×D5semidirect
843. C2×M16C22×D5semidirect
1086. D5#3586direct (N × H)
1190. C5C2×#3586semidirect

Maximal subgroups

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

subgroupindex
D5×#5852
C2×D5×2−1+42
C5×#35862
#106192002
#106191882
#106191122
D5×#5782
#106191092
D5×#5772
#106191022
D5×#5752
#106190982
C2×D5×#1372
#106190692
D5×#5682
C2×#35865