Finite Group Databasebeta

← #13007695

Subgroups — #13007695

Order 1280.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3503C211yesmaximal, characteristic, complemented
2#10618944C212yesmaximal, complemented
3#10618941C212yesmaximal, complemented
4#10618924C212yesmaximal, complemented
5#10618917C212yesmaximal, complemented
6#10618834C216yesmaximal, complemented
7#10618825C216yesmaximal, complemented
8#10618649C216yesmaximal, complemented
9D4×#713C216yesmaximal, complemented
10#10618498C216yesmaximal, complemented
11#10618483C216yesmaximal, complemented
12#10618162C213yesmaximal, complemented
13#10618158C213yesmaximal, complemented
14#10618106C213yesmaximal, complemented
15C2×#66059C213yesmaximal, complemented
16#10617801C212yesmaximal, complemented
17#10617787C212yesmaximal, complemented
18#10617747C211yesmaximal, characteristic, complemented
19C4×D5×#41C211yesmaximal, characteristic, complemented
20C2×#4149C2212yes—
21C2×D5×#41C2211yescharacteristic
22C22×#713C2216yescomplemented
23C5×Q82C2212yescomplemented
24C5×#557C2212yescomplemented
25C5×#554C2216yescomplemented
26C5×D4×Q8C2216yescomplemented
27C5×#544C2216yescomplemented
28C5×#533C2213yescomplemented
29C2×C5×C4⋊Q8C2213yescomplemented
30C5×#520C2212yes—
31C4×C5×#41C2211yescharacteristic
32#41×Dic5C2211yescharacteristic
33#66151C22112yescomplemented
34C2×#4093C2216yescomplemented
35#66068C22112yescomplemented
36#66068C2216yescomplemented
37#66067C22112yescomplemented
38#66067C22112yescomplemented
39#66066C2216yescomplemented
40#66064C2216yescomplemented
41#66062C2211yescharacteristic, complemented
42#66062C2213yescomplemented
43#66060C2216yescomplemented
44#66060C22112yescomplemented
45#66059C2216yescomplemented
46#66059C22112yescomplemented
47#66059C2216yescomplemented
48#66059C2213yescomplemented
49#66059C2213yescomplemented
50#66059C2216yescomplemented
51#66059C2216yescomplemented
52#66059C2216yescomplemented
53#66059C2216yescomplemented
54#66059C2216yescomplemented
55#66032C22112yescomplemented
56#66032C22112yescomplemented
57#66029C22112yescomplemented
58#66029C22112yescomplemented
59#66025C22112yescomplemented
60#66025C2216yescomplemented
61#66025C2216yescomplemented
62#65978C22124yescomplemented
63#65971C22124yescomplemented
64#65964C22112yescomplemented
65#65964C22124yescomplemented
66#65964C22112yescomplemented
67#65961C2216yescomplemented
68#65961C22124yescomplemented
69#65961C2216yescomplemented
70#65958C2216yescomplemented
71#65958C2216yescomplemented
72#65919C2216yescomplemented
73#65919C2216yescomplemented
74#65914C2216yescomplemented
75#65914C2216yescomplemented
76#65911C2216yescomplemented
77#65911C2212yescomplemented
78#65911C2214yescomplemented
79#65911C2216yescomplemented
80#65911C2212yescomplemented
81#65910C2214yescomplemented
82#65908C2214yescomplemented
83C4×#713C2216yescomplemented
84C4×#713C2214yescomplemented
85C4×#713C2211yescharacteristic, complemented
86C4×#713C2216yescomplemented
87C4×#713C2211yescharacteristic, complemented
88C4×Q8×D5C2211yescharacteristic, complemented
89C4×Q8×D5C2211yescharacteristic, complemented
90#65888C22112yescomplemented
91D4×D20C2216yescomplemented
92D4×D20C22112yescomplemented
93D4×D20C2216yescomplemented
94#65879C22112yescomplemented
95C4×D4×D5C2213yescomplemented
96C4×D4×D5C22112yescomplemented
97C4×D4×D5C2213yescomplemented
98C4×#711C2213yescomplemented
99C4×#711C2213yescomplemented
100#65859C2216yescomplemented
101#65859C2216yescomplemented
102#65858C2216yescomplemented
103#65856C2216yescomplemented
104#65856C2213yescomplemented
105#65855C2216yescomplemented
106D5×#117C2213yescomplemented
107#65848C22112yescomplemented
108#65844C2216yescomplemented
109C2×#4041C2216yescomplemented
110C2×#4041C2216yescomplemented
111#65838C2216yescomplemented
112C2×#4039C2216yescomplemented
113C2×#4039C2216yescomplemented
114#65811C2213yescomplemented
115C2×#4020C2213yescomplemented
116C4×#709C2213yescomplemented
117C2×C42×D5C2213yescomplemented
118#62800—51nomaximal, Sylow
119C2×C5×#41C2311yescharacteristic
120C22×C5×Q8C2316yes—
121#4149—216no—
122D5×#41—28no—
123C2×#713—424no—
124C2×#713C2316yes—
125C2×#713C2311yescharacteristic
126C2×#713C2314yes—
127C2×#713C23112yes—
128C2×#713C23112yes—
129C2×#713C23112yes—
130C2×#713C2316yes—
131C2×Q8×D5C2311yescharacteristic
132C2×#711C2313yes—
133C2×D4×D5C2313yes—
134C2×D4×D5C23112yes—
135C2×#709C2313yes—
136C2×#709C2316yes—
137C22×D20C2316yes—
138C22×D20C2316yes—
139C22×D20C2316yes—
140C22×D20C23112yes—
141C22×C4×D5C2313yes—
142C22×C4×D5C2313yes—
143C22×C4×D5C2313yes—
144C22×C4×D5C23112yes—
145C5×C4⋊Q8C2313yes—
146C5×C4⋊Q8C2311yescharacteristic
147C5×C4⋊Q8C2316yes—
148C5×C4⋊Q8C2316yes—
149C5×C4⋊Q8C2316yes—
150C5×C4⋊Q8C23112yes—
151C5×#125C2316yes—
152C5×#125C23112yes—
153C5×C22⋊Q8C2316yes—
154C5×C22⋊Q8C2316yes—
155C5×C22⋊Q8C23124yes—
156C4×C5×Q8C2311yescharacteristic
157C4×C5×Q8C2311yescharacteristic
158C4×C5×Q8C2314yes—
159C4×C5×Q8C2316yes—
160C4×C5×Q8C2316yes—
161C4×C5×D4C2313yes—
162C4×C5×D4C2313yes—
163C4×C5×D4C23112yes—
164C5×#117C2313yes—
165C5×#117C2316yes—
166C2×C5×C4⋊C4C2316yes—
167C2×C5×C4⋊C4C2316yes—
168C2×C42×C5C2313yes—
169#4093C2316yes—
170#4093C23112yes—
171#4093C23112yes—
172#4093C23112yes—
173#4093C23124yes—
174#4093C2316yes—
175#4092C2316yes—
176#4092C23124yes—
177#4092C2312yes—
178Q8×Dic5C2316yes—
179Q8×Dic5C2312yes—
180Q8×Dic5C2311yescharacteristic
181Q8×Dic5C2311yescharacteristic
182D4×Dic5C2313yes—
183D4×Dic5C2313yes—
184#4076C2316yes—
185#4076C2316yes—
186#4076C23124yes—
187C4×C22⋊D5C2316yes—
188C4×C22⋊D5C2316yes—
189C4×C22⋊D5C23124yes—
190C2×#685C23112yes—
191C2×#685C23112yes—
192#4072C2313yes—
193C2×C4×Dic5C2313yes—
194C2×C4×Dic5C2313yes—
195C2×C4×Dic5C2313yes—
196#4044C23124yes—
197#4044C23112yes—
198#4044C23112yes—
199#4043C2316yes—
200#4043C2312yes—
201#4043C23112yes—
202#4041C2316yes—
203#4041C2316yes—
204#4041C23112yes—
205#4041C23112yes—
206#4041C23112yes—
207#4041C23112yes—
208#4041C23112yes—
209#4041C23112yes—
210#4041C23112yes—
211#4041C23112yes—
212#4041C23124yes—
213#4041C2316yes—
214#4041C2316yes—
215#4041C23112yes—
216#4041C23124yes—
217#4040C23112yes—
218#4040C23124yes—
219#4040C23124yes—
220#4040C23112yes—
221#4040C23124yes—
222#4039C2313yes—
223#4039C2316yes—
224#4039C2316yes—
225#4039C23112yes—
226#4039C23112yes—
227#4039C23112yes—
228#4039C23112yes—
229#4039C23112yes—
230#4039C23112yes—
231#4039C23112yes—
232#4039C2316yes—
233#4039C2316yes—
234#4039C2313yes—
235#4039C23112yes—
236#4038C2316yes—
237#4038C2312yes—
238#4038C23112yes—
239#4038C2313yes—
240#4038C23112yes—
241#4038C2313yes—
242#4038C23112yes—
243D5×C4⋊C4C2313yes—
244D5×C4⋊C4C23112yes—
245D5×C4⋊C4C2313yes—
246#4036C2316yes—
247#4036C2312yes—
248#4033C2316yes—
249#4033C2312yes—
250#4033C2313yes—
251#4033C2313yes—
252#4032C23112yes—
253#4028C23112yes—
254#4028C23124yes—
255#4028C23124yes—
256#4027C2316yes—
257#4027C2316yes—
258#4027C23112yes—
259#4027C23112yes—
260D5×C22⋊C4C2316yes—
261D5×C22⋊C4C23124yes—
262#4023C2316yes—
263#4021C2316yes—
264#4021C23112yes—
265#4020C2313yes—
266#4020C2316yes—
267#4020C2316yes—
268#4020C2316yes—
269#4020C23112yes—
270C4×D20C2313yes—
271C4×D20C2316yes—
272C4×D20C23112yes—
273C4×D20C23112yes—
274C4×D20C2313yes—
275C4×D20C2316yes—
276C4×D20C23112yes—
277C4×D20C23112yes—
278#4018C2316yes—
279#4018C23112yes—
280C42×D5C2311yescharacteristic
281C42×D5C2313yes—
282C42×D5C2313yes—
283C42×D5C2313yes—
284C42×D5C2313yes—
285C42×D5C2313yes—
286C42×D5C2313yes—
287C42×D5C2313yes—
288C42×D5C23112yes—
289#4015C2311yescharacteristic
290C4×Dic10C2313yes—
291C4×Dic10C2313yes—
292#3522—52no—
293#3519—56no—
294#3517—52no—
295#3514—56no—
296#3511—53no—
297#3508—53no—
298#3503D511yescharacteristic, complemented
299#3498—51no—
300#3494—56no—
301#3488—52no—
302#3483—52no—
303#3481—56no—
304#3480—52no—
305D4×#41—56no—
306#3460—56no—
307#3444—53no—
308C2×#532—53no—
309C4×H(5,𝔽2)—52no—
310C2×C4×#41—51no—
311C23×D5C2413yes—
312C23×D5C24112yes—
313C5×#41#4118yescomplemented
314C2×C5×Q8—412no—
315C2×C5×Q8C2412yes—
316C2×C5×Q8C2416yes—
317C2×C5×Q8C24112yes—
318C2×C5×Q8C2411yescharacteristic
319C2×C5×D4C2413yes—
320C22×C4×C5C2413yes—
321C22×C4×C5C2413yes—
322C22×C4×C5C24112yes—
323C22×C4×C5C2413yes—
324C2×C22⋊D5C24112yes—
325C2×C22⋊D5C2416yes—
326C22×Dic5C2413yes—
327C22×Dic5C2413yes—
328C22×Dic5C2413yes—
329#713—24no—
330#713—216no—
331#713—224no—
332#713—424no—
333#713—424no—
334#713—424no—
335#713—412no—
336Q8×D5—24no—
337#711—212no—
338D4×D5—212no—
339D4×D5—248no—
340#709—212no—
341#709—224no—
342C2×D20—224no—
343C2×D20—412no—
344C2×D20—412no—
345C2×D20—424no—
346C2×D20C2416yes—
347C2×D20C2416yes—
348C2×D20C24112yes—
349C2×D20C2416yes—
350C2×D20C24112yes—
351C2×D20C2413yes—
352C2×D20C24112yes—
353C2×D20C24124yes—
354C2×D20C24112yes—
355C2×D20C24112yes—
356C2×C4×D5—212no—
357C2×C4×D5—212no—
358C2×C4×D5—424no—
359C2×C4×D5—46no—
360C2×C4×D5C2411yescharacteristic
361C2×C4×D5C2411yescharacteristic
362C2×C4×D5C24112yes—
363C2×C4×D5C2413yes—
364C2×C4×D5C2413yes—
365C2×C4×D5C2413yes—
366C2×C4×D5C2413yes—
367C2×C4×D5C2413yes—
368C2×C4×D5C2413yes—
369C2×C4×D5C2413yes—
370C2×C4×D5C24112yes—
371C2×C4×D5C24124yes—
372C2×C4×D5C2413yes—
373C2×C4×D5C2413yes—
374C2×C4×D5C24112yes—
375C2×C4×D5C2411yescharacteristic
376C2×Dic10C2412yes—
377C2×Dic10C2413yes—
378C5×C4⋊C4C2416yes—
379C5×C4⋊C4C2416yes—
380C5×C4⋊C4C24112yes—
381C5×C4⋊C4C24112yes—
382C5×C4⋊C4C2412yes—
383C5×C4⋊C4C2413yes—
384C5×C4⋊C4C2413yes—
385C5×C4⋊C4C2412yes—
386C5×C4⋊C4C24112yes—
387C5×C4⋊C4C24112yes—
388C5×C22⋊C4C2416yes—
389C5×C22⋊C4C24112yes—
390C42×C5C2411yescharacteristic
391C42×C5C2413yes—
392C42×C5C2413yes—
393C42×C5C2413yes—
394C42×C5C24112yes—
395C22⋊Dic5C2416yes—
396#685C24112yes—
397#685C2416yes—
398#685C2416yes—
399#685C24112yes—
400#685C2414yes—
401#685C24112yes—
402#685C24112yes—
403#685C24112yes—
404#685C24124yes—
405#685C24112yes—
406#685C24112yes—
407#685C24124yes—
408C4⋊Dic5C2413yes—
409C4⋊Dic5C2413yes—
410C4⋊Dic5C2412yes—
411C4⋊Dic5C2412yes—
412C4⋊Dic5C2414yes—
413C4⋊Dic5C24112yes—
414#683C2416yes—
415#683C2416yes—
416#683C2414yes—
417#683C24112yes—
418C4×Dic5C2413yes—
419C4×Dic5C2413yes—
420C4×Dic5C2413yes—
421C4×Dic5C2411yescharacteristic
422C4×Dic5C2411yescharacteristic
423C4×Dic5C2411yescharacteristic
424C4×Dic5C2414yes—
425C4×Dic5C2413yes—
426C4×Dic5C2413yes—
427C4×Dic5C2413yes—
428C4×Dic5C2413yes—
429C4×Dic5C2413yes—
430C4×Dic5C2413yes—
431C4×Dic5C24112yes—
432C2×H(5,𝔽2)—52no—
433C22×#41—51no—
434C22×#41—56no—
435#559—56no—
436#559—56no—
437Q82C2×D512yescomplemented
438#557C2×D512yescomplemented
439#556—56no—
440#555—512no—
441#555—56no—
442#554—56no—
443#554C2×D516yescomplemented
444#553—512no—
445#553—512no—
446#553—512no—
447#551—524no—
448#550—56no—
449#550—52no—
450#550—54no—
451#550—52no—
452#550—56no—
453D4×Q8C2×D516yescomplemented
454#548—512no—
455#548—54no—
456#547—512no—
457#547—56no—
458#546—524no—
459#546—512no—
460#546—512no—
461#546—512no—
462D42—512no—
463D42—56no—
464D42—56no—
465#544C2×D516yescomplemented
466#542—512no—
467#542—512no—
468#540—512no—
469#540—512no—
470#538—524no—
471#537—56no—
472#535—56no—
473#535—56no—
474#533—51no—
475#533—53no—
476#533C2×D513yescomplemented
477#532—53no—
478#532—56no—
479#532—56no—
480#532—56no—
481#532—56no—
482#532—56no—
483#532—56no—
484#532—56no—
485#532—53no—
486#532—512no—
487#532—53no—
488C2×C4⋊Q8C2×D513yescomplemented
489C2×#127—53no—
490#529—56no—
491#529—56no—
492#529—512no—
493#529—56no—
494#529—56no—
495#529—56no—
496#529—56no—
497C2×#124—56no—
498#525—56no—
499#525—56no—
500#525—524no—
501#525—56no—
502C2×#121—56no—
503C2×#121—56no—
504#520—54no—
505#520—56no—
506#520C2×D512yes—
507#518—512no—
508#518—56no—
509C4×#41—51no—
510C4×#41—51no—
511C4×#41—51no—
512C4×#41—54no—
513C4×#41—56no—
514C4×#41—56no—
515C4×#41—53no—
516C4×#41—53no—
517C4×#41—53no—
518C4×#41—56no—
519C4×#41—53no—
520C4×#41C2×D511yescharacteristic
521C2×C4×Q8—51no—
522C2×C4×Q8—51no—
523C2×C4×D4—53no—
524C2×C4×D4—53no—
525C2×C4×D4—512no—
526C2×C4×D4—56no—
527C2×C4×D4—56no—
528C2×#117—53no—
529C22×C42—53no—
530C23×C5C2513yes—
531C22×D5—26no—
532C22×D5—224no—
533C22×D5—26no—
534C22×D5—43no—
535C22×D5—412no—
536C22×D5—412no—
537C22×D5C25112yes—
538C22×D5C2513yes—
539C22×D5C2511yescharacteristic
540C5×Q8—212no—
541C5×Q8—24no—
542C5×Q8—412no—
543C5×Q8C2×#4114yescomplemented
544C5×D4C2×#41112yescomplemented
545C2×C4×C5—26no—
546C2×C4×C5—26no—
547C2×C4×C5—412no—
548C2×C4×C5C2×#41112yescomplemented
549C2×C4×C5C2513yes—
550C2×C4×C5C2513yes—
551C2×C4×C5C2514yes—
552C2×C4×C5C25112yes—
553C2×C4×C5C2511yescharacteristic
554C2×C4×C5C2513yes—
555C2×C4×C5C2511yescharacteristic
556C2×C4×C5C2511yescharacteristic
557C22⋊D5—224no—
558C22⋊D5—212no—
559C2×Dic5—26no—
560C2×Dic5—26no—
561C2×Dic5—43no—
562C2×Dic5C2511yescharacteristic
563C2×Dic5C2513yes—
564C2×Dic5C2511yescharacteristic
565C2×Dic5C2513yes—
566C2×Dic5C2514yes—
567C2×Dic5C2513yes—
568C2×Dic5C2511yescharacteristic
569D20—224no—
570D20—212no—
571D20—224no—
572D20—26no—
573D20—212no—
574D20—212no—
575D20—412no—
576D20—412no—
577D20—424no—
578D20—412no—
579C4×D5—26no—
580C4×D5—22no—
581C4×D5—26no—
582C4×D5—26no—
583C4×D5—26no—
584C4×D5—224no—
585C4×D5—26no—
586C4×D5—22no—
587C4×D5—26no—
588C4×D5—26no—
589C4×D5—224no—
590C4×D5—43no—
591C4×D5—43no—
592C4×D5—424no—
593C4×D5—412no—
594C4×D5H(5,𝔽2)14yescomplemented
595Dic10—24no—
596Dic10—26no—
597H(5,𝔽2)—1016no—
598C2×#41—51no—
599C2×#41—54no—
600C2×#41—56no—
601C2×#41—56no—
602C2×#41—512no—
603C2×#41—512no—
604C2×#41—512no—
605C2×#41—53no—
606C2×#41—53no—
607C2×#41—56no—
608C2×#41—108no—
609C2×#41—2024no—
610C2×#41C22×D511yescharacteristic
611C22×Q8—51no—
612C22×Q8C22×D516yes—
613C22×D4—53no—
614C22×D4—512no—
615C22×D4—56no—
616C22×D4—56no—
617C22×D4—512no—
618C22×D4—56no—
619C23×C4—53no—
620C23×C4—53no—
621C23×C4—512no—
622C23×C4—53no—
623C4⋊Q8—51no—
624C4⋊Q8C22×D513yes—
625C4⋊Q8C22×D516yes—
626C4⋊Q8C22×D516yes—
627C4⋊Q8C22×D516yes—
628C4⋊Q8C22×D511yescharacteristic
629C4⋊Q8C22×D5112yes—
630#127—53no—
631#127—56no—
632#127—56no—
633#127—56no—
634#127—512no—
635#126—512no—
636#126—512no—
637#126—524no—
638#125—52no—
639#125—56no—
640#125C22×D516yes—
641#125C22×D5112yes—
642#124—56no—
643#124—512no—
644#124—512no—
645#124—512no—
646#124—56no—
647#124—524no—
648#124—56no—
649#124—512no—
650#123—512no—
651#123—512no—
652#123—524no—
653#123—524no—
654#123—524no—
655#123—512no—
656C22⋊Q8—52no—
657C22⋊Q8—56no—
658C22⋊Q8—524no—
659C22⋊Q8—52no—
660C22⋊Q8—56no—
661C22⋊Q8—512no—
662C22⋊Q8C22×D516yes—
663C22⋊Q8C22×D516yes—
664C22⋊Q8C22×D5124yes—
665#121—56no—
666#121—56no—
667#121—524no—
668#121—56no—
669#121—56no—
670#121—512no—
671#121—512no—
672#121—512no—
673#121—512no—
674#121—512no—
675#121—512no—
676#121—56no—
677#121—56no—
678#121—524no—
679#121—512no—
680#121—512no—
681#121—512no—
682#121—524no—
683#120—512no—
684#120—524no—
685#120—524no—
686C4×Q8—51no—
687C4×Q8—51no—
688C4×Q8—52no—
689C4×Q8—56no—
690C4×Q8—53no—
691C4×Q8—53no—
692C4×Q8—52no—
693C4×Q8—56no—
694C4×Q8—53no—
695C4×Q8—53no—
696C4×Q8C22×D511yescharacteristic
697C4×Q8C22×D511yescharacteristic
698C4×Q8C22×D514yes—
699C4×Q8C22×D516yes—
700C4×Q8C22×D516yes—
701C4×D4—53no—
702C4×D4—53no—
703C4×D4—56no—
704C4×D4—56no—
705C4×D4—524no—
706C4×D4—512no—
707C4×D4—56no—
708C4×D4—56no—
709C4×D4—53no—
710C4×D4—53no—
711C4×D4—512no—
712C4×D4—512no—
713C4×D4—512no—
714C4×D4—512no—
715C4×D4—512no—
716C4×D4—56no—
717C4×D4—512no—
718C4×D4—512no—
719C4×D4—56no—
720C4×D4—512no—
721C4×D4—56no—
722C4×D4—56no—
723C4×D4—512no—
724C4×D4—53no—
725C4×D4—53no—
726C4×D4—512no—
727C4×D4—512no—
728C4×D4—512no—
729C4×D4—512no—
730C4×D4—56no—
731C4×D4—56no—
732C4×D4C22×D513yes—
733C4×D4C22×D513yes—
734C4×D4C22×D5112yes—
735#117—53no—
736#117—53no—
737#117—53no—
738#117—52no—
739#117—512no—
740#117—512no—
741#117—56no—
742#117—512no—
743#117—56no—
744#117—56no—
745#117—512no—
746#117C22×D513yes—
747#117C22×D516yes—
748C2×C4⋊C4—53no—
749C2×C4⋊C4—53no—
750C2×C4⋊C4—512no—
751C2×C4⋊C4C22×D516yes—
752C2×C4⋊C4C22×D516yes—
753C2×C22⋊C4—512no—
754C2×C22⋊C4—512no—
755C2×C22⋊C4—56no—
756C2×C22⋊C4—524no—
757C2×C42—53no—
758C2×C42—53no—
759C2×C42—53no—
760C2×C42—53no—
761C2×C42—53no—
762C2×C42—53no—
763C2×C42—512no—
764C2×C42—53no—
765C2×C42—53no—
766C2×C42—53no—
767C2×C42—53no—
768C2×C42—51no—
769C2×C42C22×D513yes—
770C22×C5—23no—
771C22×C5—23no—
772C22×C5C22×#4116yes—
773C22×C5C2611yescharacteristic
774C2×D5—21no—
775C2×D5—21no—
776C2×D5—23no—
777C2×D5—212no—
778C2×D5—23no—
779C2×D5—212no—
780C2×D5—23no—
781C2×D5—212no—
782C2×D5—412no—
783C2×D5—824no—
784C2×D5C2×H(5,𝔽2)12yes—
785C4×C5—23no—
786C4×C5—212no—
787C4×C5—24no—
788C4×C5—23no—
789C4×C5C22×#4112yes—
790C4×C5C22×#4116yes—
791C4×C5C2×H(5,𝔽2)12yes—
792C4×C5#58512yes—
793Dic5—23no—
794Dic5—24no—
795Dic5—21no—
796Dic5—23no—
797Dic5—23no—
798Dic5—21no—
799Dic5C2×H(5,𝔽2)12yes—
800C24—53no—
801C24—512no—
802#41—1024no—
803#41—104no—
804#41—1016no—
805#41—1012no—
806#41—1012no—
807#41—1024no—
808#41—2024no—
809#41—2024no—
810#41—2024no—
811#41—2012no—
812#41#71318yescomplemented
813C2×Q8—412no—
814C2×Q8—53no—
815C2×Q8—52no—
816C2×Q8—104no—
817C2×Q8C23×D512yes—
818C2×Q8C23×D516yes—
819C2×Q8C23×D5112yes—
820C2×Q8C23×D511yescharacteristic
821C2×D4—56no—
822C2×D4—512no—
823C2×D4—56no—
824C2×D4—512no—
825C2×D4—56no—
826C2×D4—53no—
827C2×D4—512no—
828C2×D4—56no—
829C2×D4—512no—
830C2×D4—512no—
831C2×D4—512no—
832C2×D4—524no—
833C2×D4—1012no—
834C2×D4—1048no—
835C2×D4—1024no—
836C2×D4—2012no—
837C2×D4—2012no—
838C2×D4—2024no—
839C2×D4C23×D513yes—
840C22×C4—51no—
841C22×C4—53no—
842C22×C4—53no—
843C22×C4—53no—
844C22×C4—51no—
845C22×C4—51no—
846C22×C4—53no—
847C22×C4—53no—
848C22×C4—53no—
849C22×C4—53no—
850C22×C4—53no—
851C22×C4—53no—
852C22×C4—53no—
853C22×C4—512no—
854C22×C4—512no—
855C22×C4—53no—
856C22×C4—53no—
857C22×C4—512no—
858C22×C4—524no—
859C22×C4—1012no—
860C22×C4—1012no—
861C22×C4—206no—
862C22×C4—2024no—
863C22×C4C23×D513yes—
864C22×C4C23×D513yes—
865C22×C4C23×D5112yes—
866C22×C4C23×D513yes—
867C4⋊C4—53no—
868C4⋊C4—512no—
869C4⋊C4—53no—
870C4⋊C4—56no—
871C4⋊C4—56no—
872C4⋊C4—52no—
873C4⋊C4—54no—
874C4⋊C4—54no—
875C4⋊C4—52no—
876C4⋊C4—512no—
877C4⋊C4C23×D5112yes—
878C4⋊C4C23×D513yes—
879C4⋊C4C23×D513yes—
880C4⋊C4C23×D516yes—
881C4⋊C4C23×D516yes—
882C4⋊C4C23×D5112yes—
883C4⋊C4C23×D512yes—
884C4⋊C4C23×D5112yes—
885C4⋊C4C23×D5112yes—
886C4⋊C4C23×D512yes—
887C22⋊C4—56no—
888C22⋊C4—512no—
889C22⋊C4—512no—
890C22⋊C4—524no—
891C22⋊C4—512no—
892C22⋊C4—56no—
893C22⋊C4—56no—
894C22⋊C4—524no—
895C22⋊C4—54no—
896C22⋊C4—512no—
897C22⋊C4—512no—
898C22⋊C4—512no—
899C22⋊C4—512no—
900C22⋊C4C23×D5112yes—
901C22⋊C4C23×D516yes—
902C42—51no—
903C42—53no—
904C42—51no—
905C42—51no—
906C42—53no—
907C42—53no—
908C42—54no—
909C42—53no—
910C42—53no—
911C42—53no—
912C42—53no—
913C42—53no—
914C42—53no—
915C42—512no—
916C42C23×D511yescharacteristic
917C42C23×D513yes—
918C42C23×D513yes—
919C42C23×D513yes—
920C42C23×D5112yes—
921C2×C5—26no—
922C2×C5C23×#4111yescharacteristic
923C2×C5C22×H(5,𝔽2)11yescharacteristic
924C2×C5C2×#58511yescharacteristic
925D5—22no—
926D5—43no—
927D5—412no—
928C23—51no—
929C23—512no—
930C23—53no—
931C23—106no—
932C23—106no—
933C23—1024no—
934C23—203no—
935C23—2012no—
936C23—2012no—
937C23C24×D513yes—
938Q8—212no—
939Q8—24no—
940Q8—412no—
941Q8—106no—
942Q8—104no—
943Q8C2×#71314yescomplemented
944D4—1024no—
945D4—1024no—
946D4—1012no—
947D4—1024no—
948D4—1012no—
949D4—106no—
950D4—1012no—
951D4—1012no—
952D4—2012no—
953D4—2024no—
954D4—2012no—
955D4—2012no—
956D4C2×#713112yescomplemented
957C2×C4—26no—
958C2×C4—26no—
959C2×C4—412no—
960C2×C4—51no—
961C2×C4—54no—
962C2×C4—51no—
963C2×C4—51no—
964C2×C4—53no—
965C2×C4—53no—
966C2×C4—54no—
967C2×C4—53no—
968C2×C4—106no—
969C2×C4—1024no—
970C2×C4—106no—
971C2×C4—106no—
972C2×C4—106no—
973C2×C4—102no—
974C2×C4—106no—
975C2×C4—106no—
976C2×C4—106no—
977C2×C4—1024no—
978C2×C4—106no—
979C2×C4—102no—
980C2×C4—106no—
981C2×C4—2024no—
982C2×C4—203no—
983C2×C4—203no—
984C2×C4—2012no—
985C2×C4—203no—
986C2×C4C2×#713112yescomplemented
987C2×C4C24×D513yes—
988C2×C4C24×D513yes—
989C2×C4C24×D514yes—
990C2×C4C24×D5112yes—
991C2×C4C24×D511yescharacteristic
992C2×C4C24×D513yes—
993C2×C4C24×D511yescharacteristic
994C2×C4C24×D511yescharacteristic
995C5#6280011yescharacteristic, complemented, Sylow
996C22—23no—
997C22—23no—
998C22—52no—
999C22—101no—
1000C22—101no—
1001C22—103no—
1002C22—1012no—
1003C22—103no—
1004C22—1012no—
1005C22—103no—
1006C22—1012no—
1007C22—2012no—
1008C22—4024no—
1009C22C22×#71316yes—
1010C22C25×D511yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—52no—
1016C4—101no—
1017C4—104no—
1018C4—103no—
1019C4—103no—
1020C4—101no—
1021C4—103no—
1022C4C22×#71316yes—
1023C4C22×#71312yes—
1024C4D5×H(5,𝔽2)12yes—
1025C4#6628712yes—
1026C2—26no—
1027C2—102no—
1028C2—203no—
1029C2—2012no—
1030C2C23×#71311yescharacteristic
1031C2C2×D5×H(5,𝔽2)11yescharacteristic
1032C2C2×#6628711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3503C2
hypercenter#3503D5
hypocenterC5#62800
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. C5×#3503C2semidirect
2. #10618944C2semidirect
3. #10618941C2semidirect
4. #10618924C2semidirect
5. #10618917C2semidirect
6. #10618834C2semidirect
7. #10618825C2semidirect
8. #10618649C2semidirect
9. D4×#713C2semidirect
10. #10618498C2semidirect
11. #10618483C2semidirect
12. #10618162C2semidirect
13. #10618158C2semidirect
14. #10618106C2semidirect
15. C2×#66059C2semidirect
16. #10617801C2semidirect
17. #10617787C2semidirect
18. #10617747C2semidirect
19. C4×D5×#41C2semidirect
22. C22×#713C22semidirect
23. C5×Q82C22semidirect
24. C5×#557C22semidirect
25. C5×#554C22semidirect
26. C5×D4×Q8C22semidirect
27. C5×#544C22semidirect
28. C5×#533C22semidirect
29. C2×C5×C4⋊Q8C22semidirect
33. #66151C22semidirect
34. C2×#4093C22semidirect
35. #66068C22semidirect
36. #66068C22semidirect
37. #66067C22semidirect
38. #66067C22semidirect
39. #66066C22semidirect
40. #66064C22semidirect
41. #66062C22semidirect
42. #66062C22semidirect
43. #66060C22semidirect
44. #66060C22semidirect
45. #66059C22semidirect
46. #66059C22semidirect
47. #66059C22semidirect
48. #66059C22semidirect
49. #66059C22semidirect
50. #66059C22semidirect
51. #66059C22semidirect
52. #66059C22semidirect
53. #66059C22semidirect
54. #66059C22semidirect
55. #66032C22semidirect
56. #66032C22semidirect
57. #66029C22semidirect
58. #66029C22semidirect
59. #66025C22semidirect
60. #66025C22semidirect
61. #66025C22semidirect
62. #65978C22semidirect
63. #65971C22semidirect
64. #65964C22semidirect
65. #65964C22semidirect
66. #65964C22semidirect
67. #65961C22semidirect
68. #65961C22semidirect
69. #65961C22semidirect
70. #65958C22semidirect
71. #65958C22semidirect
72. #65919C22semidirect
73. #65919C22semidirect
74. #65914C22semidirect
75. #65914C22semidirect
76. #65911C22semidirect
77. #65911C22semidirect
78. #65911C22semidirect
79. #65911C22semidirect
80. #65911C22semidirect
81. #65910C22semidirect
82. #65908C22semidirect
83. C4×#713C22semidirect
84. C4×#713C22semidirect
85. C4×#713C22semidirect
86. C4×#713C22semidirect
87. C4×#713C22semidirect
88. C4×Q8×D5C22semidirect
89. C4×Q8×D5C22semidirect
90. #65888C22semidirect
91. D4×D20C22semidirect
92. D4×D20C22semidirect
93. D4×D20C22semidirect
94. #65879C22semidirect
95. C4×D4×D5C22semidirect
96. C4×D4×D5C22semidirect
97. C4×D4×D5C22semidirect
98. C4×#711C22semidirect
99. C4×#711C22semidirect
100. #65859C22semidirect
101. #65859C22semidirect
102. #65858C22semidirect
103. #65856C22semidirect
104. #65856C22semidirect
105. #65855C22semidirect
106. D5×#117C22semidirect
107. #65848C22semidirect
108. #65844C22semidirect
109. C2×#4041C22semidirect
110. C2×#4041C22semidirect
111. #65838C22semidirect
112. C2×#4039C22semidirect
113. C2×#4039C22semidirect
114. #65811C22semidirect
115. C2×#4020C22semidirect
116. C4×#709C22semidirect
117. C2×C42×D5C22semidirect
298. #3503D5semidirect
313. C5×#41#41semidirect
437. Q82C2×D5semidirect
438. #557C2×D5semidirect
443. #554C2×D5semidirect
453. D4×Q8C2×D5semidirect
465. #544C2×D5semidirect
476. #533C2×D5semidirect
488. C2×C4⋊Q8C2×D5semidirect
543. C5×Q8C2×#41semidirect
544. C5×D4C2×#41semidirect
548. C2×C4×C5C2×#41semidirect
594. C4×D5H(5,𝔽2)semidirect
812. #41#713semidirect
943. Q8C2×#713semidirect
956. D4C2×#713semidirect
986. C2×C4C2×#713semidirect
995. C5#62800semidirect

Maximal subgroups

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

subgroupindex
C5×#35032
#106189442
#106189412
#106189242
#106189172
#106188342
#106188252
#106186492
D4×#7132
#106184982
#106184832
#106181622
#106181582
#106181062
C2×#660592
#106178012
#106177872
#106177472
C4×D5×#412
#628005