Finite Group Databasebeta

← #12976705

Subgroups — #12976705

Order 1280.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617940C211yesmaximal, characteristic, complemented
2#10617927C211yesmaximal, characteristic, complemented
3C5×#3054C211yesmaximal, characteristic, complemented
4#10615643C211yesmaximal, characteristic, complemented
5#10615632C211yesmaximal, characteristic, complemented
6C2×#65420C211yesmaximal, characteristic, complemented
7#10615487C211yesmaximal, characteristic, complemented
8#10614658C211yesmaximal, characteristic, complemented
9#10614646C211yesmaximal, characteristic, complemented
10#10612655C212yesmaximal, complemented
11#10612645C212yesmaximal, complemented
12#10612615C212yesmaximal, complemented
13#10612607C212yesmaximal, complemented
14#10612572C212yesmaximal, complemented
15#10612571C212yesmaximal, complemented
16#10612556C212yesmaximal, complemented
17#10612552C212yesmaximal, complemented
18#10610928C211yesmaximal, characteristic, complemented
19#10610905C211yesmaximal, characteristic, complemented
20#10610571C211yesmaximal, characteristic, complemented
21#10610562C211yesmaximal, characteristic, complemented
22#10610558C211yesmaximal, characteristic, complemented
23#10610551C211yesmaximal, characteristic, complemented
24C2×#4149C2211yescharacteristic
25C23×D20C2211yescharacteristic
26C2×C5×#135C2211yescharacteristic, complemented
27C22×C5×M16C2211yescharacteristic, complemented
28C5×#525C2211yescharacteristic
29C5×#525C2211yescharacteristic, complemented
30#66167C2211yescharacteristic, complemented
31#66164C2211yescharacteristic
32#66161C2211yescharacteristic, complemented
33C2×#4095C2211yescharacteristic
34C2×#4095C2211yescharacteristic, complemented
35#66125C2211yescharacteristic
36C2×#4072C2211yescharacteristic, complemented
37C2×#4047C2211yescharacteristic, complemented
38#65987—22no—
39#65983—22no—
40#65975C2212yescomplemented
41#65973C2212yescomplemented
42#65964C2212yes—
43#65964C2212yes—
44#65950C2212yescomplemented
45#65948C2212yescomplemented
46#65943C2212yes—
47#65943C2212yes—
48#65927—22no—
49D5×#120—22no—
50#65899—21no—
51#65897—21no—
52#65884—21no—
53#65884—21no—
54D4×D20—21no—
55D4×D20—21no—
56#65876—21no—
57#65875—21no—
58#65859C2211yescharacteristic
59#65857C2211yescharacteristic, complemented
60#65855C2211yescharacteristic
61#65853C2211yescharacteristic, complemented
62C5×#470C2211yescharacteristic, complemented
63C5×#470C2211yescharacteristic, complemented
64C5×#469C2211yescharacteristic, complemented
65C5×#469C2211yescharacteristic, complemented
66C5×#468C2211yescharacteristic, complemented
67C5×#468C2211yescharacteristic, complemented
68C5×#468C2211yescharacteristic, complemented
69C5×#468C2211yescharacteristic, complemented
70C5×#427C2211yescharacteristic, complemented
71C5×#416C2211yescharacteristic, complemented
72C5×#416C2211yescharacteristic, complemented
73#65521C2211yescharacteristic, complemented
74#65521C2211yescharacteristic, complemented
75#65496C2211yescharacteristic, complemented
76#65476C2212yescomplemented
77#65474C2212yescomplemented
78#65461C2212yescomplemented
79#65458C2212yescomplemented
80#65454C2212yescomplemented
81#65452C2212yescomplemented
82#65445C2212yescomplemented
83#65439C2212yescomplemented
84#65420C2212yescomplemented
85#65420C2212yescomplemented
86#65420C2212yescomplemented
87#65420C2212yescomplemented
88#65417C2212yescomplemented
89#65417C2212yescomplemented
90#65416C2212yescomplemented
91#65416C2212yescomplemented
92C2×#3953C2211yescharacteristic
93C2×#3953C2211yescharacteristic
94C2×#3953C2211yescharacteristic, complemented
95C2×#3953C2211yescharacteristic, complemented
96#65399C2211yescharacteristic, complemented
97#65391C2211yescharacteristic, complemented
98#65390C2211yescharacteristic, complemented
99#65335C2212yescomplemented
100#65335C2212yescomplemented
101#65334C2212yescomplemented
102#65334C2212yescomplemented
103#65325C2212yescomplemented
104#65325C2212yescomplemented
105#65324C2212yescomplemented
106#65324C2212yescomplemented
107#65290C2211yescharacteristic
108#65290C2211yescharacteristic, complemented
109#65284C2211yescharacteristic, complemented
110#65284C2211yescharacteristic, complemented
111#65180C2212yescomplemented
112#65179C2212yescomplemented
113#65174C2212yescomplemented
114#65171C2212yescomplemented
115#65160C2212yescomplemented
116#65159C2212yescomplemented
117#65155C2212yescomplemented
118#65152C2212yescomplemented
119#65106C2212yescomplemented
120#65101C2212yescomplemented
121#65096C2212yescomplemented
122#65093C2212yescomplemented
123#65092C2212yescomplemented
124#65089C2212yescomplemented
125#65084C2212yescomplemented
126#65077C2212yescomplemented
127#65074C2212yescomplemented
128#65071C2212yescomplemented
129#65064C2212yescomplemented
130#65059C2212yescomplemented
131D5×#102C2212yescomplemented
132#65053C2212yescomplemented
133#65049C2212yescomplemented
134#65045C2212yescomplemented
135#61175—51nomaximal, Sylow
136C24×D5—21no—
137C2×C5×#41C2311yescharacteristic
138C2×C5×#41C2311yescharacteristic
139C23×C4×C5C2311yescharacteristic
140#4149—24no—
141#4149—42no—
142C2×#713C2312yes—
143C2×D4×D5—22no—
144C2×D4×D5—22no—
145C2×D4×D5—22no—
146C2×D4×D5C2312yes—
147C2×#709—21no—
148C2×#709C2311yescharacteristic
149C22×D20—24no—
150C22×D20—21no—
151C22×D20—21no—
152C22×D20—21no—
153C22×D20—21no—
154C22×D20—42no—
155C22×D20C2311yescharacteristic
156C22×D20C2312yes—
157C22×D20C2312yes—
158C22×D20C2311yescharacteristic
159C5×#135—42no—
160C2×C5×Q16C2311yescharacteristic, complemented
161C2×C5×SD16C2311yescharacteristic, complemented
162C2×C5×SD16C2311yescharacteristic, complemented
163C2×C5×D8C2311yescharacteristic, complemented
164C2×C5×M16—42no—
165C2×C5×M16C2311yescharacteristic
166C2×C5×M16C2311yescharacteristic
167C2×C5×M16C2311yescharacteristic
168C2×C5×M16C2311yescharacteristic
169C22×C5×C8C2311yescharacteristic
170C22×C5×C8C2311yescharacteristic
171C5×#123—21no—
172C5×#123—21no—
173C5×C22⋊Q8C2311yescharacteristic
174C5×C22⋊Q8C2311yescharacteristic
175C5×C22⋊Q8C2311yescharacteristic
176C5×C22⋊Q8C2311yescharacteristic
177C5×#121C2311yescharacteristic
178C5×#121C2311yescharacteristic
179C5×#121C2311yescharacteristic
180C5×#121C2311yescharacteristic
181C5×#120—21no—
182C5×#120—21no—
183C4×C5×D4—21no—
184C4×C5×D4—21no—
185C4×C5×D4—21no—
186C4×C5×D4—21no—
187C5×#117C2311yescharacteristic
188C5×#117C2311yescharacteristic
189#4099D412yes—
190C2×C22⋊Dic5—21no—
191#4095—24no—
192#4095—42no—
193#4093C2312yes—
194#4092C2312yescomplemented
195Q8×Dic5C2312yescomplemented
196C2×#688C2312yes—
197C2×#688C2312yes—
198#4086C2312yes—
199#4085—22no—
200#4085—22no—
201#4084—22no—
202#4084C2312yescomplemented
203#4083—22no—
204#4083—22no—
205#4083—22no—
206#4082—22no—
207#4081—22no—
208D4×Dic5—22no—
209D4×Dic5C2312yescomplemented
210C2×#686C2312yes—
211C2×#686C2312yes—
212#4076—21no—
213#4076—21no—
214#4076—21no—
215#4076D411yescharacteristic
216#4076D411yescharacteristic
217#4075D412yes—
218C4×C22⋊D5C2312yes—
219C4×C22⋊D5C2312yes—
220#4072—21no—
221#4072—21no—
222#4072—21no—
223#4072C2312yes—
224#4072C2312yes—
225#4072C2311yescharacteristic
226C2×C4⋊Dic5—21no—
227C2×C4⋊Dic5C2311yescharacteristic
228C2×C4⋊Dic5C2311yescharacteristic
229#4070—21no—
230#4070D411yescharacteristic
231#4070D411yescharacteristic
232C2×C4×Dic5—21no—
233C2×#681C2311yescharacteristic
234C2×#681C2311yescharacteristic
235#4047—42no—
236C2×#676C2312yescomplemented
237C2×C8×D5C2312yescomplemented
238#4044—22no—
239#4041—22no—
240#4041—22no—
241#4041C2312yes—
242#4041C2312yes—
243#4040—22no—
244#4040—22no—
245#4039C2312yes—
246#4039C2312yes—
247#4038—22no—
248#4038C2312yescomplemented
249D5×C4⋊C4C2312yescomplemented
250#4036C2312yescomplemented
251#4035—22no—
252#4034C2312yescomplemented
253#4033—22no—
254#4031—22no—
255#4031—22no—
256#4030—22no—
257#4030—22no—
258#4029—22no—
259#4028—22no—
260#4028—22no—
261#4028—22no—
262#4028—22no—
263#4028—22no—
264#4027—22no—
265#4027—22no—
266D5×C22⋊C4—22no—
267D5×C22⋊C4—22no—
268D5×C22⋊C4—22no—
269#4025—22no—
270#4025—22no—
271#4025—22no—
272#4024—22no—
273#4023—22no—
274#4021—21no—
275#4020—21no—
276C4×D20—21no—
277C4×D20—21no—
278C4×D20—21no—
279#4016—21no—
280#4015—21no—
281C4×Dic10—21no—
282C5×#107C2311yescharacteristic, complemented
283C5×#107C2311yescharacteristic, complemented
284C5×#106C2311yescharacteristic, complemented
285C5×#106C2311yescharacteristic, complemented
286C5×#103C2311yescharacteristic, complemented
287C5×#103C2311yescharacteristic, complemented
288C5×#103C2311yescharacteristic, complemented
289C5×#103C2311yescharacteristic, complemented
290C5×#102C2311yescharacteristic, complemented
291C5×#102C2311yescharacteristic, complemented
292C5×#102C2311yescharacteristic, complemented
293C5×#102C2311yescharacteristic, complemented
294#3967C2312yescomplemented
295#3967C2312yescomplemented
296#3964C2312yescomplemented
297#3964C2312yescomplemented
298C22⋊#168C2312yes—
299C22⋊#168C2312yes—
300#3953C2312yes—
301#3953C2312yes—
302#3953C2312yes—
303#3953C2312yes—
304#3953C2312yes—
305#3953C2312yes—
306#3953C2312yes—
307#3953C2312yes—
308#3952C2312yescomplemented
309#3952C2312yescomplemented
310#3947C2312yescomplemented
311#3946C2312yescomplemented
312#3946C2312yescomplemented
313C8×Dic5C2312yescomplemented
314#3941C2312yes—
315#3941C2312yes—
316#3941C2312yes—
317#3941C2312yes—
318#3940C2312yescomplemented
319#3940C2312yescomplemented
320#3939C2312yescomplemented
321#3939C2312yescomplemented
322#3493—51no—
323#3484—51no—
324#3325—52no—
325#3324—52no—
326#3323—52no—
327#3322—52no—
328#3319—52no—
329#3318—52no—
330#3311—52no—
331#3310—52no—
332#3136—51no—
333#3096—51no—
334#3093—51no—
335#3081—51no—
336#3062—51no—
337#3054D511yescharacteristic, complemented
338#3045—51no—
339#3012—51no—
340#3003—51no—
341#2946—51no—
342#2930—51no—
343#2897—51no—
344C2×#418—51no—
345C24×C5C2×D411yescharacteristic
346C23×D5—21no—
347C23×D5—22no—
348C23×D5—22no—
349C23×D5—21no—
350C23×D5—22no—
351C23×D5—44no—
352C23×D5—82no—
353C23×D5—82no—
354C5×#41—22no—
355C5×#41—22no—
356C5×#41—22no—
357C5×#41—22no—
358C2×C5×Q8C2411yescharacteristic
359C2×C5×Q8C2411yescharacteristic
360C2×C5×D4—21no—
361C2×C5×D4—21no—
362C2×C5×D4—21no—
363C2×C5×D4—21no—
364C2×C5×D4—21no—
365C2×C5×D4—21no—
366C2×C5×D4C2411yescharacteristic
367C2×C5×D4C2411yescharacteristic
368C22×C4×C5—22no—
369C22×C4×C5—22no—
370C22×C4×C5—21no—
371C22×C4×C5—21no—
372C22×C4×C5C2×D411yescharacteristic
373C22×C4×C5C2×D411yescharacteristic
374C22×C4×C5C2×D411yescharacteristic
375C22×C4×C5C2411yescharacteristic
376C22×C4×C5C2411yescharacteristic
377C22×C4×C5C2411yescharacteristic
378C2×C22⋊D5—22no—
379C2×C22⋊D5—22no—
380C2×C22⋊D5—22no—
381C2×C22⋊D5—22no—
382C2×C22⋊D5C2×D412yes—
383C2×C22⋊D5C2×D412yes—
384C2×C22⋊D5C2×D412yes—
385C22×Dic5—21no—
386C22×Dic5—21no—
387C22×Dic5—22no—
388#713—24no—
389#713—42no—
390D4×D5—24no—
391D4×D5—42no—
392D4×D5—48no—
393D4×D5—84no—
394D4×D5—84no—
395#709—22no—
396#709—22no—
397#709—44no—
398C2×D20—21no—
399C2×D20—22no—
400C2×D20—22no—
401C2×D20—22no—
402C2×D20—24no—
403C2×D20—24no—
404C2×D20—22no—
405C2×D20—21no—
406C2×D20—22no—
407C2×D20—22no—
408C2×D20—22no—
409C2×D20—22no—
410C2×D20—42no—
411C2×D20—42no—
412C2×D20—44no—
413C2×D20—44no—
414C2×D20—44no—
415C2×D20—44no—
416C2×D20C2×D411yescharacteristic
417C2×D20#4114yes—
418C2×D20C2412yes—
419C2×D20C2412yes—
420C2×C4×D5—22no—
421C2×C4×D5—22no—
422C2×C4×D5—22no—
423C2×C4×D5—22no—
424C2×C4×D5C2412yes—
425C2×Dic10—22no—
426C2×Dic10C2×D411yescharacteristic
427C5×Q16—41no—
428C5×SD16—41no—
429C5×SD16—41no—
430C5×D8—41no—
431C5×M16—41no—
432C5×M16—41no—
433C5×M16—41no—
434C5×M16—41no—
435C2×C5×C8—22no—
436C2×C5×C8—22no—
437C2×C5×C8C2411yescharacteristic
438C2×C5×C8C2411yescharacteristic
439C2×C5×C8C2411yescharacteristic
440C2×C5×C8C2411yescharacteristic
441C5×C4⋊C4—21no—
442C5×C4⋊C4—21no—
443C5×C4⋊C4—21no—
444C5×C4⋊C4—21no—
445C5×C4⋊C4C2411yescharacteristic
446C5×C4⋊C4C2411yescharacteristic
447C5×C4⋊C4C2411yescharacteristic
448C5×C4⋊C4C2411yescharacteristic
449C5×C22⋊C4—21no—
450C5×C22⋊C4—21no—
451C5×C22⋊C4—21no—
452C5×C22⋊C4—21no—
453C5×C22⋊C4—21no—
454C5×C22⋊C4—21no—
455C5×C22⋊C4—21no—
456C5×C22⋊C4—21no—
457C5×C22⋊C4—21no—
458C5×C22⋊C4—21no—
459C42×C5—21no—
460C42×C5—21no—
461C22⋊Dic5—22no—
462C22⋊Dic5—22no—
463C22⋊Dic5—22no—
464C22⋊Dic5—22no—
465C22⋊Dic5C2×D412yes—
466C22⋊Dic5C2×D412yes—
467C22⋊Dic5C2×D412yes—
468#688—24no—
469#688—42no—
470#686—24no—
471#686—42no—
472#685—22no—
473#685—22no—
474#685—22no—
475#685—22no—
476#685—22no—
477#685—22no—
478#685—22no—
479#685—22no—
480#685C2×D412yes—
481#685C2×D412yes—
482C4⋊Dic5—21no—
483C4⋊Dic5—21no—
484C4⋊Dic5—22no—
485C4⋊Dic5—22no—
486C4⋊Dic5C2×D411yescharacteristic
487C4⋊Dic5C2×D411yescharacteristic
488C4⋊Dic5C2412yes—
489C4⋊Dic5C2412yes—
490#683—22no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683C2×D412yes—
495#683C2×D412yes—
496C4×Dic5—22no—
497C4×Dic5—22no—
498C4×Dic5—22no—
499C4×Dic5—22no—
500C4×Dic5C2412yes—
501#681—22no—
502#681—22no—
503C2×#168C2412yes—
504C2×#168C2412yes—
505#676—42no—
506C8×D5—42no—
507C2×H(5,𝔽2)—51no—
508C23×D4—51no—
509C2×AGL(1,ℤ/8)—51no—
510C2×AGL(1,ℤ/8)—51no—
511C2×#135C2×D511yescharacteristic, complemented
512C2×#131—51no—
513C22×M16C2×D511yescharacteristic, complemented
514#556—52no—
515#556—101no—
516#555—52no—
517#555—101no—
518#553—52no—
519#553—101no—
520#552—52no—
521#552—101no—
522#546—52no—
523#546—52no—
524#546—101no—
525#546—101no—
526D42—52no—
527D42—52no—
528D42—101no—
529D42—101no—
530#544—51no—
531#538—102no—
532#537—51no—
533#535—51no—
534#535—51no—
535#534—102no—
536#529—102no—
537#525—51no—
538#525C2×D511yescharacteristic
539#525C2×D511yescharacteristic, complemented
540C2×#120—102no—
541#520—51no—
542#520—51no—
543#518—51no—
544C2×#117—51no—
545#490—52no—
546#489—52no—
547#488—52no—
548#486—52no—
549#485—52no—
550#485—52no—
551#482—52no—
552#482—52no—
553#482—52no—
554#482—52no—
555#481—52no—
556#480—52no—
557#478—52no—
558#478—52no—
559#476—52no—
560#474—52no—
561#470C2×D511yescharacteristic, complemented
562#470C2×D511yescharacteristic, complemented
563#469—52no—
564#469C2×D511yescharacteristic, complemented
565#469C2×D511yescharacteristic, complemented
566#468—52no—
567#468C2×D511yescharacteristic, complemented
568#468C2×D511yescharacteristic, complemented
569#468C2×D511yescharacteristic, complemented
570#468C2×D511yescharacteristic, complemented
571#466—52no—
572#465—52no—
573#464—52no—
574#463—52no—
575#460—52no—
576#459—52no—
577#452—52no—
578#450—52no—
579#450—52no—
580#450—52no—
581#449—52no—
582#447—52no—
583#447—52no—
584#447—52no—
585#442—52no—
586#440—52no—
587C4×SD16—52no—
588C4×D8—52no—
589#436—52no—
590#436—52no—
591#435—52no—
592#435—52no—
593#428—51no—
594#428—51no—
595#427C2×D511yescharacteristic, complemented
596#424—51no—
597#418—52no—
598#418—52no—
599#418—52no—
600#418—52no—
601#418—51no—
602#418—51no—
603#418—52no—
604#417—51no—
605#417—51no—
606#417—52no—
607#416—52no—
608#416C2×D511yescharacteristic, complemented
609#416C2×D511yescharacteristic, complemented
610C2×#102—51no—
611C2×#102—51no—
612C2×#102—51no—
613C2×#102—51no—
614C2×#102—52no—
615#408—51no—
616#407—51no—
617#405—51no—
618C23×C5—22no—
619C23×C5—21no—
620C23×C5—21no—
621C23×C5—41no—
622C23×C5—41no—
623C23×C5C22×D411yescharacteristic
624C23×C5C22×D411yescharacteristic
625C23×C5C22×D411yescharacteristic
626C22×D5—22no—
627C22×D5—24no—
628C22×D5—22no—
629C22×D5—44no—
630C22×D5—44no—
631C22×D5—44no—
632C22×D5—44no—
633C22×D5—44no—
634C22×D5—42no—
635C22×D5—82no—
636C22×D5—82no—
637C22×D5—81no—
638C22×D5—81no—
639C22×D5—82no—
640C22×D5—82no—
641C22×D5—81no—
642C22×D5—81no—
643C22×D5—816no—
644C22×D5C22×D412yes—
645C5×Q8—21no—
646C5×Q8—21no—
647C5×Q8—21no—
648C5×Q8—21no—
649C5×D4—21no—
650C5×D4—21no—
651C5×D4—21no—
652C5×D4—21no—
653C5×D4—42no—
654C5×D4—42no—
655C5×D4—42no—
656C5×D4—42no—
657C5×D4—81no—
658C5×D4—81no—
659C2×C4×C5—22no—
660C2×C4×C5—22no—
661C2×C4×C5—22no—
662C2×C4×C5—21no—
663C2×C4×C5—21no—
664C2×C4×C5—21no—
665C2×C4×C5—21no—
666C2×C4×C5—21no—
667C2×C4×C5—21no—
668C2×C4×C5—21no—
669C2×C4×C5—21no—
670C2×C4×C5—21no—
671C2×C4×C5—21no—
672C2×C4×C5—42no—
673C2×C4×C5—42no—
674C2×C4×C5C22×D411yescharacteristic
675C2×C4×C5C22×D411yescharacteristic
676C2×C4×C5C22×D411yescharacteristic
677C2×C4×C5C2×#4112yes—
678C2×C4×C5H(5,𝔽2)12yes—
679C2×C4×C5C2511yescharacteristic
680C22⋊D5—24no—
681C22⋊D5—42no—
682C22⋊D5—42no—
683C22⋊D5—44no—
684C22⋊D5—82no—
685C22⋊D5—82no—
686C22⋊D5—82no—
687C2×Dic5—22no—
688C2×Dic5—22no—
689C2×Dic5—82no—
690C2×Dic5—81no—
691C2×Dic5—81no—
692C2×Dic5C22×D412yes—
693C2×Dic5C22×D412yes—
694C2×Dic5C22×D412yes—
695D20—24no—
696D20—22no—
697D20—22no—
698D20—22no—
699D20—22no—
700D20—44no—
701D20—44no—
702D20—44no—
703D20—42no—
704D20—82no—
705D20—82no—
706D20C2×#4114yes—
707C4×D5—22no—
708C4×D5—22no—
709C4×D5—44no—
710C4×D5—82no—
711C4×D5—82no—
712C4×D5—82no—
713Dic10—22no—
714Dic10—82no—
715C5×C8—21no—
716C5×C8—21no—
717C5×C8—21no—
718C5×C8—21no—
719#168—22no—
720#168—22no—
721C25—101no—
722H(5,𝔽2)—104no—
723H(5,𝔽2)—202no—
724C2×#41—51no—
725C2×#41—52no—
726C2×#41—101no—
727C2×#41C22×D511yescharacteristic
728C2×#41C22×D511yescharacteristic
729C22×D4—52no—
730C22×D4—51no—
731C22×D4—51no—
732C22×D4—52no—
733C22×D4—52no—
734C22×D4—104no—
735C22×D4—101no—
736C22×D4—102no—
737C22×D4—102no—
738C22×D4—102no—
739C22×D4—101no—
740C22×D4—101no—
741C22×D4—101no—
742C22×D4—202no—
743C23×C4C22×D511yescharacteristic
744AGL(1,ℤ/8)—104no—
745AGL(1,ℤ/8)—202no—
746#135—42no—
747C2×Q16C22×D511yescharacteristic, complemented
748C2×SD16—52no—
749C2×SD16—52no—
750C2×SD16C22×D511yescharacteristic, complemented
751C2×SD16C22×D511yescharacteristic, complemented
752C2×D8—52no—
753C2×D8—52no—
754C2×D8C22×D511yescharacteristic, complemented
755#131—202no—
756C2×M16—42no—
757C2×M16—51no—
758C2×M16—51no—
759C2×M16—52no—
760C2×M16C22×D511yescharacteristic
761C2×M16C22×D511yescharacteristic
762C2×M16C22×D511yescharacteristic
763C2×M16C22×D511yescharacteristic
764C22×C8—52no—
765C22×C8C22×D511yescharacteristic
766C22×C8C22×D511yescharacteristic
767C4⋊Q8—52no—
768C4⋊Q8—101no—
769#127—52no—
770#127—101no—
771#126—102no—
772#126—102no—
773#126—102no—
774#126—102no—
775#125—52no—
776#125—101no—
777#125—102no—
778#124—52no—
779#124—101no—
780#124—102no—
781#124—102no—
782#124—102no—
783#123—21no—
784#123—21no—
785#123—52no—
786#123—102no—
787#123—102no—
788#123—102no—
789#123—102no—
790C22⋊Q8—51no—
791C22⋊Q8—51no—
792C22⋊Q8—52no—
793C22⋊Q8—102no—
794C22⋊Q8—101no—
795C22⋊Q8C22×D511yescharacteristic
796C22⋊Q8C22×D511yescharacteristic
797C22⋊Q8C22×D511yescharacteristic
798C22⋊Q8C22×D511yescharacteristic
799#121—51no—
800#121—51no—
801#121—52no—
802#121—52no—
803#121—52no—
804#121—102no—
805#121—102no—
806#121—102no—
807#121—102no—
808#121—101no—
809#121—101no—
810#121—101no—
811#121—102no—
812#121—102no—
813#121—102no—
814#121C22×D511yescharacteristic
815#121C22×D511yescharacteristic
816#121C22×D511yescharacteristic
817#121C22×D511yescharacteristic
818#120—21no—
819#120—21no—
820#120—52no—
821#120—102no—
822#120—102no—
823#120—102no—
824#120—102no—
825#120—102no—
826#120—102no—
827#120—102no—
828#120—102no—
829C4×Q8—52no—
830C4×Q8—101no—
831C4×Q8—102no—
832C4×D4—21no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—52no—
837C4×D4—52no—
838C4×D4—52no—
839C4×D4—52no—
840C4×D4—52no—
841C4×D4—101no—
842C4×D4—101no—
843C4×D4—101no—
844C4×D4—102no—
845C4×D4—102no—
846C4×D4—102no—
847#117—51no—
848#117—52no—
849#117—52no—
850#117—52no—
851#117—102no—
852#117—102no—
853#117—101no—
854#117—101no—
855#117—101no—
856#117C22×D511yescharacteristic
857#117C22×D511yescharacteristic
858C2×C4⋊C4—51no—
859C2×C4⋊C4—51no—
860C2×C4⋊C4—52no—
861C2×C4⋊C4—101no—
862C2×C22⋊C4—102no—
863C2×C22⋊C4—102no—
864C2×C22⋊C4—102no—
865C2×C22⋊C4—101no—
866C2×C42—101no—
867#107—52no—
868#107—52no—
869#107C22×D511yescharacteristic, complemented
870#107C22×D511yescharacteristic, complemented
871#106—52no—
872#106—52no—
873#106C22×D511yescharacteristic, complemented
874#106C22×D511yescharacteristic, complemented
875C4⋊C8—52no—
876C4⋊C8—52no—
877#103—52no—
878#103—52no—
879#103C22×D511yescharacteristic, complemented
880#103C22×D511yescharacteristic, complemented
881#103C22×D511yescharacteristic, complemented
882#103C22×D511yescharacteristic, complemented
883#102—52no—
884#102—52no—
885#102—52no—
886#102—52no—
887#102—52no—
888#102—52no—
889#102—52no—
890#102—52no—
891#102—52no—
892#102—52no—
893#102—52no—
894#102—52no—
895#102—52no—
896#102—52no—
897#102C22×D511yescharacteristic, complemented
898#102C22×D511yescharacteristic, complemented
899#102C22×D511yescharacteristic, complemented
900#102C22×D511yescharacteristic, complemented
901C22⋊C8—52no—
902C22⋊C8—52no—
903C22⋊C8—52no—
904C22⋊C8—52no—
905#97—52no—
906C4×C8—52no—
907C22×C5—21no—
908C22×C5—21no—
909C22×C5—21no—
910C22×C5—21no—
911C22×C5—21no—
912C22×C5—21no—
913C22×C5—21no—
914C22×C5—21no—
915C22×C5—44no—
916C22×C5—41no—
917C22×C5—41no—
918C22×C5—41no—
919C22×C5—41no—
920C22×C5—41no—
921C22×C5—41no—
922C22×C5#54612yes—
923C22×C5C23×D411yescharacteristic
924C2×D5—22no—
925C2×D5—22no—
926C2×D5—22no—
927C2×D5—24no—
928C2×D5—42no—
929C2×D5—42no—
930C2×D5—42no—
931C2×D5—42no—
932C2×D5—42no—
933C2×D5—84no—
934C2×D5—88no—
935C2×D5—88no—
936C2×D5—84no—
937C2×D5—164no—
938C4×C5—21no—
939C4×C5—21no—
940C4×C5—41no—
941C4×C5—41no—
942C4×C5—41no—
943C4×C5—41no—
944C4×C5—41no—
945C4×C5—41no—
946C4×C5#54612yes—
947C4×C5C22×#4111yescharacteristic
948C4×C5C2×H(5,𝔽2)11yescharacteristic
949Dic5—22no—
950Dic5—22no—
951Dic5—22no—
952Dic5—42no—
953Dic5—42no—
954C24—102no—
955C24—101no—
956C24—102no—
957C24—102no—
958C24—101no—
959C24—204no—
960C24—402no—
961C24—402no—
962C24D4×D511yescharacteristic
963#41—22no—
964#41—22no—
965#41—22no—
966#41—22no—
967#41—102no—
968#41—102no—
969#41—104no—
970#41—204no—
971#41—202no—
972C2×Q8—51no—
973C2×Q8—102no—
974C2×Q8C23×D511yescharacteristic
975C2×Q8C23×D511yescharacteristic
976C2×D4—21no—
977C2×D4—21no—
978C2×D4—21no—
979C2×D4—21no—
980C2×D4—21no—
981C2×D4—21no—
982C2×D4—52no—
983C2×D4—52no—
984C2×D4—52no—
985C2×D4—51no—
986C2×D4—54no—
987C2×D4—52no—
988C2×D4—52no—
989C2×D4—104no—
990C2×D4—104no—
991C2×D4—102no—
992C2×D4—102no—
993C2×D4—102no—
994C2×D4—102no—
995C2×D4—102no—
996C2×D4—102no—
997C2×D4—104no—
998C2×D4—102no—
999C2×D4—101no—
1000C2×D4—102no—
1001C2×D4—102no—
1002C2×D4—101no—
1003C2×D4—102no—
1004C2×D4—102no—
1005C2×D4—102no—
1006C2×D4—202no—
1007C2×D4—202no—
1008C2×D4—204no—
1009C2×D4—204no—
1010C2×D4—204no—
1011C2×D4—204no—
1012C2×D4—202no—
1013C2×D4—208no—
1014C2×D4—404no—
1015C2×D4—404no—
1016C2×D4C23×D511yescharacteristic
1017C2×D4C23×D511yescharacteristic
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—52no—
1023C22×C4—102no—
1024C22×C4—102no—
1025C22×C4—102no—
1026C22×C4—102no—
1027C22×C4—102no—
1028C22×C4—101no—
1029C22×C4—101no—
1030C22×C4D4×D511yescharacteristic
1031C22×C4D4×D511yescharacteristic
1032C22×C4D4×D511yescharacteristic
1033C22×C4C23×D511yescharacteristic
1034C22×C4C23×D511yescharacteristic
1035C22×C4C23×D511yescharacteristic
1036Q16—41no—
1037SD16—41no—
1038SD16—41no—
1039SD16—104no—
1040SD16—202no—
1041D8—41no—
1042D8—104no—
1043D8—202no—
1044M16—41no—
1045M16—41no—
1046M16—41no—
1047M16—41no—
1048M16—102no—
1049M16—102no—
1050M16—202no—
1051C2×C8—22no—
1052C2×C8—22no—
1053C2×C8—52no—
1054C2×C8—52no—
1055C2×C8—202no—
1056C2×C8C23×D511yescharacteristic
1057C2×C8C23×D511yescharacteristic
1058C2×C8C23×D511yescharacteristic
1059C2×C8C23×D511yescharacteristic
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—51no—
1065C4⋊C4—51no—
1066C4⋊C4—52no—
1067C4⋊C4—52no—
1068C4⋊C4—52no—
1069C4⋊C4—52no—
1070C4⋊C4—102no—
1071C4⋊C4—102no—
1072C4⋊C4—102no—
1073C4⋊C4—102no—
1074C4⋊C4—102no—
1075C4⋊C4—102no—
1076C4⋊C4—101no—
1077C4⋊C4—101no—
1078C4⋊C4C23×D511yescharacteristic
1079C4⋊C4C23×D511yescharacteristic
1080C4⋊C4C23×D511yescharacteristic
1081C4⋊C4C23×D511yescharacteristic
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—21no—
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—21no—
1088C22⋊C4—21no—
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—52no—
1093C22⋊C4—52no—
1094C22⋊C4—52no—
1095C22⋊C4—52no—
1096C22⋊C4—52no—
1097C22⋊C4—102no—
1098C22⋊C4—102no—
1099C22⋊C4—102no—
1100C22⋊C4—102no—
1101C22⋊C4—102no—
1102C22⋊C4—102no—
1103C22⋊C4—102no—
1104C22⋊C4—102no—
1105C22⋊C4—102no—
1106C22⋊C4—102no—
1107C22⋊C4—102no—
1108C22⋊C4—102no—
1109C42—21no—
1110C42—21no—
1111C42—52no—
1112C42—102no—
1113C42—102no—
1114C42—102no—
1115C42—102no—
1116C2×C5—22no—
1117C2×C5—41no—
1118C2×C5—41no—
1119C2×C5—81no—
1120C2×C5—81no—
1121C2×C5C2×#54611yescharacteristic
1122C2×C5#358511yescharacteristic
1123C2×C5#358511yescharacteristic
1124D5—42no—
1125D5—44no—
1126D5—82no—
1127C23—22no—
1128C23—21no—
1129C23—21no—
1130C23—41no—
1131C23—41no—
1132C23—52no—
1133C23—102no—
1134C23—104no—
1135C23—102no—
1136C23—204no—
1137C23—204no—
1138C23—204no—
1139C23—204no—
1140C23—204no—
1141C23—202no—
1142C23—401no—
1143C23—401no—
1144C23—401no—
1145C23—401no—
1146C23—402no—
1147C23—402no—
1148C23—402no—
1149C23—402no—
1150C23—4016no—
1151C23C2×D4×D511yescharacteristic
1152C23C2×D4×D511yescharacteristic
1153C23C2×D4×D511yescharacteristic
1154Q8—21no—
1155Q8—21no—
1156Q8—21no—
1157Q8—21no—
1158Q8—102no—
1159Q8—402no—
1160D4—21no—
1161D4—21no—
1162D4—21no—
1163D4—21no—
1164D4—42no—
1165D4—42no—
1166D4—42no—
1167D4—42no—
1168D4—54no—
1169D4—81no—
1170D4—81no—
1171D4—104no—
1172D4—104no—
1173D4—102no—
1174D4—102no—
1175D4—102no—
1176D4—102no—
1177D4—204no—
1178D4—204no—
1179D4—204no—
1180D4—202no—
1181D4—202no—
1182D4—204no—
1183D4—202no—
1184D4—402no—
1185D4—402no—
1186D4—402no—
1187D4—402no—
1188D4—402no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—52no—
1205C2×C4—52no—
1206C2×C4—52no—
1207C2×C4—102no—
1208C2×C4—102no—
1209C2×C4—102no—
1210C2×C4—102no—
1211C2×C4—204no—
1212C2×C4—402no—
1213C2×C4—402no—
1214C2×C4—402no—
1215C2×C4—402no—
1216C2×C4—401no—
1217C2×C4—401no—
1218C2×C4C2×D4×D511yescharacteristic
1219C2×C4C2×D4×D511yescharacteristic
1220C2×C4C2×D4×D511yescharacteristic
1221C2×C4#414412yes—
1222C2×C4D5×#4112yes—
1223C2×C4C24×D511yescharacteristic
1224C8—21no—
1225C8—21no—
1226C8—21no—
1227C8—21no—
1228C8—102no—
1229C8—102no—
1230C5#6117511yescharacteristic, complemented, Sylow
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—21no—
1238C22—21no—
1239C22—44no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—102no—
1247C22—102no—
1248C22—102no—
1249C22—104no—
1250C22—202no—
1251C22—202no—
1252C22—202no—
1253C22—202no—
1254C22—202no—
1255C22—404no—
1256C22—404no—
1257C22—408no—
1258C22—408no—
1259C22—804no—
1260C22#6594412yes—
1261C22C22×D4×D511yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—102no—
1271C4—102no—
1272C4—102no—
1273C4—202no—
1274C4—202no—
1275C4#6594412yes—
1276C4C2×#414411yescharacteristic
1277C4C2×D5×#4111yescharacteristic
1278C2—22no—
1279C2—41no—
1280C2—41no—
1281C2—81no—
1282C2—81no—
1283C2—202no—
1284C2—204no—
1285C2—402no—
1286C2C2×#6594411yescharacteristic
1287C2#1061910111yescharacteristic
1288C2#1061910111yescharacteristic
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3054C2
socleC22×C5C23×D4
hypercenter#3054D5
hypocenterC5#61175
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3054

Complements

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

NH ≅ G/Ntype
1. #10617940C2semidirect
2. #10617927C2semidirect
3. C5×#3054C2semidirect
4. #10615643C2semidirect
5. #10615632C2semidirect
6. C2×#65420C2semidirect
7. #10615487C2semidirect
8. #10614658C2semidirect
9. #10614646C2semidirect
10. #10612655C2semidirect
11. #10612645C2semidirect
12. #10612615C2semidirect
13. #10612607C2semidirect
14. #10612572C2semidirect
15. #10612571C2semidirect
16. #10612556C2semidirect
17. #10612552C2semidirect
18. #10610928C2semidirect
19. #10610905C2semidirect
20. #10610571C2semidirect
21. #10610562C2semidirect
22. #10610558C2semidirect
23. #10610551C2semidirect
26. C2×C5×#135C22semidirect
27. C22×C5×M16C22semidirect
29. C5×#525C22semidirect
30. #66167C22semidirect
32. #66161C22semidirect
34. C2×#4095C22semidirect
36. C2×#4072C22semidirect
37. C2×#4047C22semidirect
40. #65975C22semidirect
41. #65973C22semidirect
44. #65950C22semidirect
45. #65948C22semidirect
59. #65857C22semidirect
61. #65853C22semidirect
62. C5×#470C22semidirect
63. C5×#470C22semidirect
64. C5×#469C22semidirect
65. C5×#469C22semidirect
66. C5×#468C22semidirect
67. C5×#468C22semidirect
68. C5×#468C22semidirect
69. C5×#468C22semidirect
70. C5×#427C22semidirect
71. C5×#416C22semidirect
72. C5×#416C22semidirect
73. #65521C22semidirect
74. #65521C22semidirect
75. #65496C22semidirect
76. #65476C22semidirect
77. #65474C22semidirect
78. #65461C22semidirect
79. #65458C22semidirect
80. #65454C22semidirect
81. #65452C22semidirect
82. #65445C22semidirect
83. #65439C22semidirect
84. #65420C22semidirect
85. #65420C22semidirect
86. #65420C22semidirect
87. #65420C22semidirect
88. #65417C22semidirect
89. #65417C22semidirect
90. #65416C22semidirect
91. #65416C22semidirect
94. C2×#3953C22semidirect
95. C2×#3953C22semidirect
96. #65399C22semidirect
97. #65391C22semidirect
98. #65390C22semidirect
99. #65335C22semidirect
100. #65335C22semidirect
101. #65334C22semidirect
102. #65334C22semidirect
103. #65325C22semidirect
104. #65325C22semidirect
105. #65324C22semidirect
106. #65324C22semidirect
108. #65290C22semidirect
109. #65284C22semidirect
110. #65284C22semidirect
111. #65180C22semidirect
112. #65179C22semidirect
113. #65174C22semidirect
114. #65171C22semidirect
115. #65160C22semidirect
116. #65159C22semidirect
117. #65155C22semidirect
118. #65152C22semidirect
119. #65106C22semidirect
120. #65101C22semidirect
121. #65096C22semidirect
122. #65093C22semidirect
123. #65092C22semidirect
124. #65089C22semidirect
125. #65084C22semidirect
126. #65077C22semidirect
127. #65074C22semidirect
128. #65071C22semidirect
129. #65064C22semidirect
130. #65059C22semidirect
131. D5×#102C22semidirect
132. #65053C22semidirect
133. #65049C22semidirect
134. #65045C22semidirect
160. C2×C5×Q16C23semidirect
161. C2×C5×SD16C23semidirect
162. C2×C5×SD16C23semidirect
163. C2×C5×D8C23semidirect
194. #4092C23semidirect
195. Q8×Dic5C23semidirect
202. #4084C23semidirect
209. D4×Dic5C23semidirect
236. C2×#676C23semidirect
237. C2×C8×D5C23semidirect
248. #4038C23semidirect
249. D5×C4⋊C4C23semidirect
250. #4036C23semidirect
252. #4034C23semidirect
282. C5×#107C23semidirect
283. C5×#107C23semidirect
284. C5×#106C23semidirect
285. C5×#106C23semidirect
286. C5×#103C23semidirect
287. C5×#103C23semidirect
288. C5×#103C23semidirect
289. C5×#103C23semidirect
290. C5×#102C23semidirect
291. C5×#102C23semidirect
292. C5×#102C23semidirect
293. C5×#102C23semidirect
294. #3967C23semidirect
295. #3967C23semidirect
296. #3964C23semidirect
297. #3964C23semidirect
308. #3952C23semidirect
309. #3952C23semidirect
310. #3947C23semidirect
311. #3946C23semidirect
312. #3946C23semidirect
313. C8×Dic5C23semidirect
318. #3940C23semidirect
319. #3940C23semidirect
320. #3939C23semidirect
321. #3939C23semidirect
337. #3054D5semidirect
511. C2×#135C2×D5semidirect
513. C22×M16C2×D5semidirect
539. #525C2×D5semidirect
561. #470C2×D5semidirect
562. #470C2×D5semidirect
564. #469C2×D5semidirect
565. #469C2×D5semidirect
567. #468C2×D5semidirect
568. #468C2×D5semidirect
569. #468C2×D5semidirect
570. #468C2×D5semidirect
595. #427C2×D5semidirect
608. #416C2×D5semidirect
609. #416C2×D5semidirect
747. C2×Q16C22×D5semidirect
750. C2×SD16C22×D5semidirect
751. C2×SD16C22×D5semidirect
754. C2×D8C22×D5semidirect
869. #107C22×D5semidirect
870. #107C22×D5semidirect
873. #106C22×D5semidirect
874. #106C22×D5semidirect
879. #103C22×D5semidirect
880. #103C22×D5semidirect
881. #103C22×D5semidirect
882. #103C22×D5semidirect
897. #102C22×D5semidirect
898. #102C22×D5semidirect
899. #102C22×D5semidirect
900. #102C22×D5semidirect
1230. C5#61175semidirect

Maximal subgroups

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

subgroupindex
#106179402
#106179272
C5×#30542
#106156432
#106156322
C2×#654202
#106154872
#106146582
#106146462
#106126552
#106126452
#106126152
#106126072
#106125722
#106125712
#106125562
#106125522
#106109282
#106109052
#106105712
#106105622
#106105582
#106105512
#611755