Finite Group Databasebeta

← #12976511

Subgroups — #12976511

Order 1280.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617940C211yesmaximal, characteristic, complemented
2#10617619C211yesmaximal, characteristic, complemented
3C5×#3092C211yesmaximal, characteristic, complemented
4#10614653C211yesmaximal, characteristic, complemented
5C22×#3941C211yesmaximal, characteristic, complemented
6#10613217C212yesmaximal, complemented
7#10613216C212yesmaximal, complemented
8#10613177C212yesmaximal, complemented
9#10613176C212yesmaximal, complemented
10#10613074C212yesmaximal, complemented
11#10613073C212yesmaximal, complemented
12#10613034C212yesmaximal, complemented
13#10613033C212yesmaximal, complemented
14#10610973C211yesmaximal, characteristic, complemented
15#10610950C211yesmaximal, characteristic, complemented
16#10610944C211yesmaximal, characteristic, complemented
17#10610932C211yesmaximal, characteristic, complemented
18#10610642C211yesmaximal, characteristic, complemented
19#10610617C211yesmaximal, characteristic, complemented
20#10610613C211yesmaximal, characteristic, complemented
21#10610607C211yesmaximal, characteristic, complemented
22#10610368C211yesmaximal, characteristic, complemented
23#10610357C211yesmaximal, characteristic, complemented
24C2×#4149C2211yescharacteristic
25C23×D20C2211yescharacteristic
26C5×#525C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic, complemented
28#66164C2211yescharacteristic
29C2×#4096C2211yescharacteristic, complemented
30#66125—22no—
31#66125C2211yescharacteristic
32#66125C2211yescharacteristic, complemented
33C23×#168C2211yescharacteristic, complemented
34C2×#4054C2211yescharacteristic
35C2×#4054C2211yescharacteristic, complemented
36C2×#4053C2211yescharacteristic, complemented
37#65987—22no—
38#65964C2212yes—
39#65964C2212yes—
40#65943C2212yes—
41#65943C2212yes—
42D5×#120—22no—
43#65884—21no—
44#65884—21no—
45D4×D20—21no—
46D4×D20—21no—
47#65859C2211yescharacteristic
48#65855C2211yescharacteristic
49#65849—22no—
50#65848—21no—
51#65848C2212yescomplemented
52#65847—21no—
53#65847C2212yescomplemented
54#65845—21no—
55#65845C2212yescomplemented
56#65844C2211yescharacteristic, complemented
57#65841—21no—
58#65841C2212yescomplemented
59#65838C2211yescharacteristic, complemented
60#65838C2211yescharacteristic, complemented
61#65834C2211yescharacteristic, complemented
62C5×#484C2212yescomplemented
63C5×#483C2212yescomplemented
64C5×#481C2212yescomplemented
65C5×#480C2212yescomplemented
66C5×#428C2211yescharacteristic, complemented
67C5×#428C2211yescharacteristic, complemented
68C5×#417C2211yescharacteristic, complemented
69C5×#417C2211yescharacteristic, complemented
70C5×#407C2211yescharacteristic, complemented
71#65522C2211yescharacteristic, complemented
72#65420C2211yescharacteristic
73#65420C2211yescharacteristic, complemented
74#65418C2211yescharacteristic, complemented
75#65411C2211yescharacteristic, complemented
76#65408C2211yescharacteristic, complemented
77#65340C2211yescharacteristic, complemented
78#65340C2211yescharacteristic, complemented
79#65337C2211yescharacteristic, complemented
80#65337C2211yescharacteristic, complemented
81#65330C2211yescharacteristic, complemented
82#65330C2211yescharacteristic, complemented
83#65327C2211yescharacteristic, complemented
84#65327C2211yescharacteristic, complemented
85#65291C2211yescharacteristic, complemented
86#65287C2211yescharacteristic, complemented
87C2×#3941C2211yescharacteristic
88C2×#3941C2211yescharacteristic
89C2×#3941C2211yescharacteristic, complemented
90C2×#3941C2211yescharacteristic, complemented
91C2×#3941C2212yescomplemented
92C2×#3941C2212yescomplemented
93C2×#3941C2212yescomplemented
94C2×#3941C2212yescomplemented
95#65180C2212yescomplemented
96#65179C2212yescomplemented
97#65178C2212yescomplemented
98#65175C2212yescomplemented
99#65174C2212yescomplemented
100#65172C2212yescomplemented
101#65171C2212yescomplemented
102#65161C2212yescomplemented
103#65160C2212yescomplemented
104#65159C2212yescomplemented
105#65158C2212yescomplemented
106#65155C2212yescomplemented
107#65154C2212yescomplemented
108#65153C2212yescomplemented
109#65152C2212yescomplemented
110#65141C2212yescomplemented
111#65108C2212yescomplemented
112#65100C2212yescomplemented
113#65099C2212yescomplemented
114#65093C2212yescomplemented
115#65092C2212yescomplemented
116#65089C2212yescomplemented
117#65087C2212yescomplemented
118#65084C2212yescomplemented
119#65075C2212yescomplemented
120#65065C2212yescomplemented
121#65062C2212yescomplemented
122#65059C2212yescomplemented
123D5×#102C2212yescomplemented
124#65053C2212yescomplemented
125#65051C2212yescomplemented
126#65049C2212yescomplemented
127#65021C2212yescomplemented
128#65021C2212yescomplemented
129#65020C2212yescomplemented
130#65020C2212yescomplemented
131#65019C2212yescomplemented
132#65019C2212yescomplemented
133#65014C2212yescomplemented
134#65014C2212yescomplemented
135#61167—51nomaximal, Sylow
136C24×D5—21no—
137C2×C5×#41C2311yescharacteristic
138C23×C4×C5—21no—
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—22no—
148C2×#709—21no—
149C2×#709C2311yescharacteristic
150C2×#709C2311yescharacteristic
151C22×D20—24no—
152C22×D20—21no—
153C22×D20—21no—
154C22×D20—21no—
155C22×D20—21no—
156C22×D20—42no—
157C22×D20C2311yescharacteristic
158C22×D20C2312yes—
159C22×D20C2312yes—
160C22×D20C2311yescharacteristic
161C2×C5×M16C2311yescharacteristic
162C2×C5×M16C2311yescharacteristic
163C5×#123—21no—
164C5×C22⋊Q8C2311yescharacteristic
165C5×C22⋊Q8C2311yescharacteristic
166C5×#121C2311yescharacteristic
167C5×#121C2311yescharacteristic
168C5×#120—21no—
169C4×C5×D4—21no—
170C4×C5×D4—21no—
171C5×#117C2311yescharacteristic
172C2×C5×C4⋊C4—21no—
173C2×C5×C4⋊C4—21no—
174C2×C5×C4⋊C4—21no—
175C2×C5×C4⋊C4C2311yescharacteristic
176C2×C5×C4⋊C4C2311yescharacteristic
177C2×C5×C4⋊C4C2312yes—
178C2×C5×C4⋊C4C2312yes—
179#4099—21no—
180#4099D412yes—
181#4096—42no—
182#4093C2312yes—
183C2×#689C2311yescharacteristic, complemented
184C2×#688C2311yescharacteristic, complemented
185#4086C2312yes—
186#4083—22no—
187#4083—22no—
188#4083—22no—
189C2×#687C2311yescharacteristic, complemented
190C2×#686C2311yescharacteristic, complemented
191#4076—22no—
192#4076—22no—
193#4076—21no—
194#4076—21no—
195#4076D411yescharacteristic
196#4076D411yescharacteristic
197#4076C2311yescharacteristic
198#4076C2311yescharacteristic
199#4075—21no—
200#4075—22no—
201#4075—22no—
202#4075D412yes—
203C4×C22⋊D5—21no—
204C4×C22⋊D5—21no—
205C4×C22⋊D5—22no—
206C4×C22⋊D5—22no—
207C4×C22⋊D5—22no—
208C4×C22⋊D5—22no—
209C4×C22⋊D5C2312yes—
210C4×C22⋊D5C2312yes—
211#4072—22no—
212#4072C2311yescharacteristic
213#4072C2311yescharacteristic
214#4070—22no—
215#4070—22no—
216#4070D411yescharacteristic
217#4070D411yescharacteristic
218#4070C2311yescharacteristic
219#4070C2311yescharacteristic
220C22×#168—42no—
221C22×#168C2311yescharacteristic
222C22×#168C2311yescharacteristic
223C22×#168C2311yescharacteristic
224C22×#168C2311yescharacteristic
225C22×#168C2311yescharacteristic
226C22×#168C2311yescharacteristic
227#4054—24no—
228#4054—42no—
229#4053—42no—
230C2×D40C2312yes—
231C2×D40C2312yes—
232C2×#677C2312yes—
233C2×#677C2312yes—
234C2×#676C2312yescomplemented
235C2×C8×D5C2312yescomplemented
236#4044—22no—
237#4044—22no—
238#4043—21no—
239#4043C2312yescomplemented
240#4042—22no—
241#4042—22no—
242#4041—21no—
243#4041—22no—
244#4041—22no—
245#4041C2312yes—
246#4041C2312yes—
247#4041C2312yescomplemented
248#4040—22no—
249#4040—22no—
250#4040—22no—
251#4040—22no—
252#4039—21no—
253#4039C2312yes—
254#4039C2312yes—
255#4039C2312yescomplemented
256#4038—21no—
257#4038C2312yescomplemented
258D5×C4⋊C4—21no—
259D5×C4⋊C4C2312yescomplemented
260#4036—21no—
261#4036C2312yescomplemented
262#4035—22no—
263#4035—22no—
264#4034—21no—
265#4034C2312yescomplemented
266#4033—21no—
267#4033C2312yescomplemented
268#4030—22no—
269#4030—22no—
270#4028—22no—
271#4028—22no—
272#4028—22no—
273#4028—22no—
274#4028—22no—
275D5×C22⋊C4—22no—
276D5×C22⋊C4—22no—
277D5×C22⋊C4—22no—
278#4021—21no—
279#4020—21no—
280C4×D20—21no—
281C4×D20—21no—
282C5×#107C2312yescomplemented
283C5×#107C2312yescomplemented
284C5×#106C2312yescomplemented
285C5×#106C2312yescomplemented
286C5×#103C2312yescomplemented
287C5×#103C2312yescomplemented
288C5×#102C2312yescomplemented
289C5×#102C2312yescomplemented
290C5×C22⋊C8C2312yes—
291C5×C22⋊C8C2312yes—
292#3967C2311yescharacteristic, complemented
293#3967C2311yescharacteristic, complemented
294#3964C2311yescharacteristic, complemented
295#3964C2311yescharacteristic, complemented
296#3953C2312yes—
297#3953C2312yes—
298#3953C2312yes—
299#3953C2312yes—
300#3952C2312yescomplemented
301#3952C2312yescomplemented
302#3947C2312yescomplemented
303#3946C2312yescomplemented
304#3946C2312yescomplemented
305C8×Dic5C2312yescomplemented
306#3942C2311yescharacteristic, complemented
307#3942C2311yescharacteristic, complemented
308#3941C2312yes—
309#3941C2312yes—
310#3941C2312yes—
311#3941C2312yes—
312#3941C2312yes—
313#3941C2312yes—
314#3941C2312yes—
315#3941C2312yes—
316#3941C2311yescharacteristic, complemented
317#3941C2311yescharacteristic, complemented
318#3940C2311yescharacteristic, complemented
319#3940C2311yescharacteristic, complemented
320#3939C2311yescharacteristic, complemented
321#3939C2311yescharacteristic, complemented
322#3492—51no—
323#3484—51no—
324#3318—52no—
325#3314—52no—
326#3310—52no—
327#3306—52no—
328#3297—52no—
329#3296—52no—
330#3295—52no—
331#3294—52no—
332#3136—51no—
333#3096—51no—
334#3092D511yescharacteristic, complemented
335#3081—51no—
336#3062—51no—
337#3050—51no—
338#3045—51no—
339#3012—51no—
340#3003—51no—
341#2946—51no—
342#2929—51no—
343#2897—51no—
344C22×#102—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—
356C2×C5×Q8C2411yescharacteristic
357C2×C5×D4—21no—
358C2×C5×D4—21no—
359C2×C5×D4—21no—
360C2×C5×D4C2411yescharacteristic
361C22×C4×C5—22no—
362C22×C4×C5—22no—
363C22×C4×C5—22no—
364C22×C4×C5—21no—
365C22×C4×C5—22no—
366C22×C4×C5—21no—
367C22×C4×C5—21no—
368C22×C4×C5—82no—
369C22×C4×C5C2×D411yescharacteristic
370C22×C4×C5C2×D411yescharacteristic
371C22×C4×C5C2×D411yescharacteristic
372C22×C4×C5C2411yescharacteristic
373C22×C4×C5C2411yescharacteristic
374C22×C4×C5C2411yescharacteristic
375C2×C22⋊D5—21no—
376C2×C22⋊D5—21no—
377C2×C22⋊D5—21no—
378C2×C22⋊D5—22no—
379C2×C22⋊D5—22no—
380C2×C22⋊D5—22no—
381C2×C22⋊D5C2×D412yes—
382C2×C22⋊D5C2×D412yes—
383C2×C22⋊D5C2×D412yes—
384#713—24no—
385#713—42no—
386D4×D5—24no—
387D4×D5—42no—
388D4×D5—48no—
389D4×D5—84no—
390D4×D5—84no—
391#709—22no—
392#709—22no—
393#709—22no—
394#709—22no—
395#709—44no—
396#709—84no—
397C2×D20—21no—
398C2×D20—22no—
399C2×D20—22no—
400C2×D20—22no—
401C2×D20—24no—
402C2×D20—24no—
403C2×D20—22no—
404C2×D20—21no—
405C2×D20—22no—
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#4114yescomplemented
418C2×D20C2412yes—
419C2×D20C2411yescharacteristic
420C2×D20C2412yes—
421C2×C4×D5—21no—
422C2×C4×D5—22no—
423C2×C4×D5—22no—
424C2×C4×D5—22no—
425C2×C4×D5—22no—
426C2×C4×D5—22no—
427C2×C4×D5C2412yes—
428C2×Dic10—22no—
429C2×Dic10C2×D411yescharacteristic
430C2×Dic10C2411yescharacteristic
431C5×M16—22no—
432C5×M16—22no—
433C2×C5×C8C2412yes—
434C2×C5×C8C2412yes—
435C5×C4⋊C4—21no—
436C5×C4⋊C4—21no—
437C5×C4⋊C4—22no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—21no—
440C5×C4⋊C4—21no—
441C5×C4⋊C4C2412yes—
442C5×C4⋊C4C2412yes—
443C5×C4⋊C4C2411yescharacteristic
444C5×C4⋊C4C2411yescharacteristic
445C5×C22⋊C4—21no—
446C5×C22⋊C4—21no—
447C5×C22⋊C4—21no—
448C5×C22⋊C4—21no—
449C5×C22⋊C4—21no—
450C42×C5—21no—
451C22⋊Dic5—21no—
452C22⋊Dic5—21no—
453C22⋊Dic5—21no—
454C22⋊Dic5C2×D412yes—
455C22⋊Dic5C2×D412yes—
456C22⋊Dic5C2×D412yes—
457#689—41no—
458#688—41no—
459#687—41no—
460#686—41no—
461#685—22no—
462#685—22no—
463#685—21no—
464#685—21no—
465#685—22no—
466#685—22no—
467#685—22no—
468#685—22no—
469#685—22no—
470#685—22no—
471#685—22no—
472#685—22no—
473#685C2×D412yes—
474#685C2×D412yes—
475C4⋊Dic5—22no—
476C4⋊Dic5—22no—
477C4⋊Dic5C2×D411yescharacteristic
478C4⋊Dic5C2×D411yescharacteristic
479C4⋊Dic5C2411yescharacteristic
480C4⋊Dic5C2411yescharacteristic
481#683—21no—
482#683—21no—
483#683—22no—
484#683—22no—
485#683—22no—
486#683—22no—
487#683C2×D412yes—
488#683C2×D412yes—
489C4×Dic5—21no—
490C4×Dic5—22no—
491C4×Dic5—22no—
492C4×Dic5C2412yes—
493C2×#168—22no—
494C2×#168—22no—
495C2×#168—41no—
496C2×#168—41no—
497C2×#168—41no—
498C2×#168—41no—
499C2×#168C2411yescharacteristic
500C2×#168C2411yescharacteristic
501C2×#168C2411yescharacteristic
502C2×#168C2411yescharacteristic
503D40—24no—
504D40—42no—
505#677—24no—
506#677—42no—
507#676—42no—
508C8×D5—42no—
509C2×H(5,𝔽2)—51no—
510C23×D4—51no—
511C2×AGL(1,ℤ/8)—51no—
512C2×AGL(1,ℤ/8)—51no—
513C2×#135—51no—
514C2×#131—51no—
515C23×C8—51no—
516#554—52no—
517#554—101no—
518#553—52no—
519#553—101no—
520#552—52no—
521#552—101no—
522#547—52no—
523#547—101no—
524#546—52no—
525#546—52no—
526#546—101no—
527#546—101no—
528D42—52no—
529D42—52no—
530D42—101no—
531D42—101no—
532#544—51no—
533#539—102no—
534#537—51no—
535#535—51no—
536#535—51no—
537#534—102no—
538#525—51no—
539#525—51no—
540#525—102no—
541#525C2×D511yescharacteristic
542C2×#120—102no—
543#520—51no—
544#520—51no—
545#518—51no—
546C22×C4⋊C4C2×D511yescharacteristic, complemented
547#490—52no—
548#489—52no—
549#488—52no—
550#486—52no—
551#484C2×D512yescomplemented
552#483C2×D512yescomplemented
553#482—52no—
554#482—52no—
555#481—52no—
556#481C2×D512yescomplemented
557#480—52no—
558#480C2×D512yescomplemented
559#478—52no—
560#478—52no—
561#476—52no—
562#474—52no—
563#469—52no—
564#468—52no—
565#467—51no—
566#467—51no—
567#466—51no—
568#466—51no—
569#466—52no—
570#465—51no—
571#465—51no—
572#465—51no—
573#465—51no—
574#465—52no—
575#464—52no—
576#463—52no—
577#460—52no—
578#459—52no—
579#452—52no—
580#450—52no—
581#450—52no—
582#450—52no—
583#449—52no—
584#447—52no—
585#447—52no—
586#447—52no—
587#442—52no—
588#440—52no—
589C4×SD16—52no—
590C4×D8—52no—
591#435—52no—
592#435—52no—
593C8×D4—52no—
594C8×D4—52no—
595#428C2×D511yescharacteristic, complemented
596#428C2×D511yescharacteristic, complemented
597#427—51no—
598#424—51no—
599#418—51no—
600#418—51no—
601#418—52no—
602#417—52no—
603#417C2×D511yescharacteristic, complemented
604#417C2×D511yescharacteristic, complemented
605#416—51no—
606#416—51no—
607#416—52no—
608C2×#102—51no—
609C2×#102—51no—
610C2×#102—51no—
611C2×#102—51no—
612C2×#102—52no—
613C2×#102—52no—
614C2×#102—52no—
615C2×#102—52no—
616C2×#102—52no—
617#408—51no—
618#407C2×D511yescharacteristic, complemented
619#405—51no—
620C23×C5—22no—
621C23×C5—22no—
622C23×C5—22no—
623C23×C5—21no—
624C23×C5C22×D411yescharacteristic
625C23×C5C22×D411yescharacteristic
626C23×C5C22×D411yescharacteristic
627C22×D5—22no—
628C22×D5—24no—
629C22×D5—21no—
630C22×D5—22no—
631C22×D5—44no—
632C22×D5—44no—
633C22×D5—44no—
634C22×D5—42no—
635C22×D5—44no—
636C22×D5—44no—
637C22×D5—82no—
638C22×D5—82no—
639C22×D5—81no—
640C22×D5—82no—
641C22×D5—81no—
642C22×D5—82no—
643C22×D5—81no—
644C22×D5—81no—
645C22×D5—816no—
646C22×D5C22×D412yes—
647C5×Q8—21no—
648C5×Q8—21no—
649C5×D4—21no—
650C5×D4—21no—
651C5×D4—42no—
652C5×D4—42no—
653C5×D4—42no—
654C2×C4×C5—22no—
655C2×C4×C5—22no—
656C2×C4×C5—22no—
657C2×C4×C5—21no—
658C2×C4×C5—21no—
659C2×C4×C5—21no—
660C2×C4×C5—21no—
661C2×C4×C5—22no—
662C2×C4×C5—22no—
663C2×C4×C5—21no—
664C2×C4×C5—21no—
665C2×C4×C5—21no—
666C2×C4×C5—44no—
667C2×C4×C5—42no—
668C2×C4×C5—81no—
669C2×C4×C5—82no—
670C2×C4×C5—81no—
671C2×C4×C5C22×D411yescharacteristic
672C2×C4×C5C22×D411yescharacteristic
673C2×C4×C5C22×D411yescharacteristic
674C2×C4×C5C2×#4112yes—
675C2×C4×C5H(5,𝔽2)12yes—
676C2×C4×C5C2511yescharacteristic
677C22⋊D5—24no—
678C22⋊D5—24no—
679C22⋊D5—24no—
680C22⋊D5—44no—
681C22⋊D5—42no—
682C22⋊D5—42no—
683C22⋊D5—42no—
684C22⋊D5—82no—
685C22⋊D5—82no—
686C2×Dic5—21no—
687C2×Dic5—21no—
688C2×Dic5—21no—
689C2×Dic5C22×D412yes—
690C2×Dic5C22×D412yes—
691C2×Dic5C22×D412yes—
692D20—24no—
693D20—22no—
694D20—21no—
695D20—22no—
696D20—22no—
697D20—22no—
698D20—21no—
699D20—44no—
700D20—44no—
701D20—44no—
702D20—42no—
703D20—82no—
704D20—82no—
705D20—82no—
706D20C2×#4114yes—
707C4×D5—22no—
708C4×D5—22no—
709C4×D5—44no—
710C4×D5—42no—
711C4×D5—82no—
712C4×D5—82no—
713C4×D5—82no—
714C4×D5—82no—
715Dic10—22no—
716Dic10—21no—
717Dic10—21no—
718Dic10—82no—
719C5×C8—22no—
720C5×C8—22no—
721#168—21no—
722#168—21no—
723#168—21no—
724#168—21no—
725C25—101no—
726H(5,𝔽2)—104no—
727H(5,𝔽2)—202no—
728C2×#41—51no—
729C2×#41—52no—
730C2×#41—51no—
731C2×#41—102no—
732C2×#41—101no—
733C2×#41C22×D511yescharacteristic
734C22×D4—52no—
735C22×D4—51no—
736C22×D4—51no—
737C22×D4—52no—
738C22×D4—52no—
739C22×D4—104no—
740C22×D4—101no—
741C22×D4—102no—
742C22×D4—102no—
743C22×D4—102no—
744C22×D4—101no—
745C22×D4—101no—
746C22×D4—101no—
747C22×D4—202no—
748C23×C4—21no—
749C23×C4C22×D511yescharacteristic
750AGL(1,ℤ/8)—104no—
751AGL(1,ℤ/8)—202no—
752#135—202no—
753C2×Q16—51no—
754C2×SD16—51no—
755C2×SD16—51no—
756C2×SD16—52no—
757C2×SD16—52no—
758C2×D8—51no—
759C2×D8—52no—
760C2×D8—52no—
761#131—202no—
762C2×M16—52no—
763C2×M16C22×D511yescharacteristic
764C2×M16C22×D511yescharacteristic
765C22×C8—51no—
766C22×C8—51no—
767C22×C8—51no—
768C22×C8—51no—
769C22×C8—51no—
770C22×C8—51no—
771C22×C8—52no—
772C22×C8—202no—
773C4⋊Q8—52no—
774C4⋊Q8—101no—
775#127—52no—
776#127—101no—
777#126—102no—
778#126—102no—
779#125—52no—
780#125—102no—
781#125—102no—
782#125—101no—
783#124—52no—
784#124—101no—
785#123—21no—
786#123—52no—
787#123—102no—
788#123—102no—
789#123—102no—
790#123—102no—
791#123—102no—
792#123—102no—
793#123—101no—
794C22⋊Q8—51no—
795C22⋊Q8—51no—
796C22⋊Q8—51no—
797C22⋊Q8—51no—
798C22⋊Q8—52no—
799C22⋊Q8—102no—
800C22⋊Q8—102no—
801C22⋊Q8—102no—
802C22⋊Q8—102no—
803C22⋊Q8—101no—
804C22⋊Q8C22×D511yescharacteristic
805C22⋊Q8C22×D511yescharacteristic
806#121—51no—
807#121—51no—
808#121—51no—
809#121—51no—
810#121—52no—
811#121—52no—
812#121—52no—
813#121—102no—
814#121—102no—
815#121—102no—
816#121—102no—
817#121—101no—
818#121—101no—
819#121—101no—
820#121—102no—
821#121—102no—
822#121C22×D511yescharacteristic
823#121C22×D511yescharacteristic
824#120—21no—
825#120—52no—
826#120—102no—
827#120—102no—
828#120—102no—
829#120—102no—
830#120—102no—
831#120—102no—
832#120—102no—
833#120—102no—
834#120—101no—
835C4×Q8—52no—
836C4×Q8—101no—
837C4×D4—21no—
838C4×D4—21no—
839C4×D4—52no—
840C4×D4—52no—
841C4×D4—52no—
842C4×D4—52no—
843C4×D4—52no—
844C4×D4—101no—
845C4×D4—101no—
846C4×D4—102no—
847C4×D4—102no—
848C4×D4—101no—
849C4×D4—102no—
850C4×D4—102no—
851C4×D4—101no—
852C4×D4—101no—
853#117—51no—
854#117—51no—
855#117—52no—
856#117—102no—
857#117—101no—
858#117C22×D511yescharacteristic
859C2×C4⋊C4—21no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—21no—
862C2×C4⋊C4—52no—
863C2×C4⋊C4—101no—
864C2×C4⋊C4C22×D511yescharacteristic
865C2×C4⋊C4C22×D511yescharacteristic
866C2×C4⋊C4C22×D512yes—
867C2×C4⋊C4C22×D512yes—
868C2×C22⋊C4—102no—
869C2×C22⋊C4—102no—
870C2×C22⋊C4—102no—
871#107—51no—
872#107—51no—
873#107C22×D512yescomplemented
874#107C22×D512yescomplemented
875#106—51no—
876#106—51no—
877#106C22×D512yescomplemented
878#106C22×D512yescomplemented
879C4⋊C8—52no—
880C4⋊C8—52no—
881#103—51no—
882#103—51no—
883#103—51no—
884#103—51no—
885#103C22×D512yescomplemented
886#103C22×D512yescomplemented
887#102—51no—
888#102—51no—
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#102—52no—
898#102—52no—
899#102—52no—
900#102—52no—
901#102—51no—
902#102—51no—
903#102C22×D512yescomplemented
904#102C22×D512yescomplemented
905C22⋊C8—52no—
906C22⋊C8—52no—
907C22⋊C8C22×D512yes—
908C22⋊C8C22×D512yes—
909#97—52no—
910C4×C8—52no—
911C22×C5—28no—
912C22×C5—21no—
913C22×C5—21no—
914C22×C5—21no—
915C22×C5—21no—
916C22×C5—21no—
917C22×C5—21no—
918C22×C5—41no—
919C22×C5—41no—
920C22×C5—41no—
921C22×C5#54612yes—
922C22×C5#57612yes—
923C22×C5#57712yes—
924C22×C5C23×D411yescharacteristic
925C2×D5—22no—
926C2×D5—24no—
927C2×D5—22no—
928C2×D5—22no—
929C2×D5—42no—
930C2×D5—42no—
931C2×D5—41no—
932C2×D5—42no—
933C2×D5—41no—
934C2×D5—42no—
935C2×D5—42no—
936C2×D5—41no—
937C2×D5—84no—
938C2×D5—88no—
939C2×D5—88no—
940C2×D5—84no—
941C2×D5—164no—
942C4×C5—21no—
943C4×C5—21no—
944C4×C5—41no—
945C4×C5—42no—
946C4×C5—41no—
947C4×C5—42no—
948C4×C5—41no—
949C4×C5#54612yes—
950C4×C5C22×#4111yescharacteristic
951C4×C5C2×H(5,𝔽2)11yescharacteristic
952Dic5—22no—
953Dic5—22no—
954Dic5—22no—
955Dic5—41no—
956Dic5—41no—
957Dic5—41no—
958C24—102no—
959C24—101no—
960C24—102no—
961C24—102no—
962C24—101no—
963C24—204no—
964C24—402no—
965C24—402no—
966C24D4×D511yescharacteristic
967#41—22no—
968#41—22no—
969#41—102no—
970#41—102no—
971#41—104no—
972#41—102no—
973#41—102no—
974#41—204no—
975#41—202no—
976#41—404no—
977C2×Q8—51no—
978C2×Q8—51no—
979C2×Q8—102no—
980C2×Q8C23×D511yescharacteristic
981C2×D4—21no—
982C2×D4—21no—
983C2×D4—21no—
984C2×D4—52no—
985C2×D4—52no—
986C2×D4—52no—
987C2×D4—51no—
988C2×D4—54no—
989C2×D4—52no—
990C2×D4—52no—
991C2×D4—51no—
992C2×D4—104no—
993C2×D4—104no—
994C2×D4—102no—
995C2×D4—102no—
996C2×D4—102no—
997C2×D4—102no—
998C2×D4—102no—
999C2×D4—102no—
1000C2×D4—102no—
1001C2×D4—104no—
1002C2×D4—101no—
1003C2×D4—101no—
1004C2×D4—101no—
1005C2×D4—101no—
1006C2×D4—102no—
1007C2×D4—102no—
1008C2×D4—101no—
1009C2×D4—102no—
1010C2×D4—102no—
1011C2×D4—102no—
1012C2×D4—202no—
1013C2×D4—202no—
1014C2×D4—204no—
1015C2×D4—204no—
1016C2×D4—204no—
1017C2×D4—204no—
1018C2×D4—202no—
1019C2×D4—208no—
1020C2×D4—404no—
1021C2×D4—404no—
1022C2×D4C23×D511yescharacteristic
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—21no—
1027C22×C4—22no—
1028C22×C4—21no—
1029C22×C4—21no—
1030C22×C4—52no—
1031C22×C4—82no—
1032C22×C4—102no—
1033C22×C4—102no—
1034C22×C4—102no—
1035C22×C4—102no—
1036C22×C4—102no—
1037C22×C4—101no—
1038C22×C4D4×D511yescharacteristic
1039C22×C4D4×D511yescharacteristic
1040C22×C4D4×D511yescharacteristic
1041C22×C4C23×D511yescharacteristic
1042C22×C4C23×D511yescharacteristic
1043C22×C4C23×D511yescharacteristic
1044Q16—201no—
1045SD16—104no—
1046SD16—202no—
1047SD16—201no—
1048SD16—201no—
1049D8—104no—
1050D8—202no—
1051D8—201no—
1052M16—22no—
1053M16—22no—
1054M16—202no—
1055C2×C8—51no—
1056C2×C8—51no—
1057C2×C8—51no—
1058C2×C8—51no—
1059C2×C8—102no—
1060C2×C8—102no—
1061C2×C8—202no—
1062C2×C8—201no—
1063C2×C8—201no—
1064C2×C8—201no—
1065C2×C8—201no—
1066C2×C8C23×D512yes—
1067C2×C8C23×D512yes—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—51no—
1075C4⋊C4—51no—
1076C4⋊C4—52no—
1077C4⋊C4—52no—
1078C4⋊C4—51no—
1079C4⋊C4—51no—
1080C4⋊C4—102no—
1081C4⋊C4—102no—
1082C4⋊C4—102no—
1083C4⋊C4—102no—
1084C4⋊C4—102no—
1085C4⋊C4—102no—
1086C4⋊C4—101no—
1087C4⋊C4—101no—
1088C4⋊C4C23×D512yes—
1089C4⋊C4C23×D512yes—
1090C4⋊C4C23×D511yescharacteristic
1091C4⋊C4C23×D511yescharacteristic
1092C22⋊C4—21no—
1093C22⋊C4—21no—
1094C22⋊C4—21no—
1095C22⋊C4—21no—
1096C22⋊C4—21no—
1097C22⋊C4—52no—
1098C22⋊C4—52no—
1099C22⋊C4—52no—
1100C22⋊C4—52no—
1101C22⋊C4—52no—
1102C22⋊C4—102no—
1103C22⋊C4—102no—
1104C22⋊C4—102no—
1105C22⋊C4—102no—
1106C22⋊C4—102no—
1107C22⋊C4—102no—
1108C22⋊C4—102no—
1109C22⋊C4—102no—
1110C22⋊C4—102no—
1111C22⋊C4—102no—
1112C22⋊C4—101no—
1113C22⋊C4—101no—
1114C22⋊C4—101no—
1115C22⋊C4—101no—
1116C22⋊C4—101no—
1117C42—21no—
1118C42—52no—
1119C42—102no—
1120C42—102no—
1121C42—101no—
1122C2×C5—22no—
1123C2×C5—22no—
1124C2×C5—22no—
1125C2×C5—81no—
1126C2×C5C2×#54611yescharacteristic
1127C2×C5C2×#57611yescharacteristic
1128C2×C5C2×#57711yescharacteristic
1129D5—42no—
1130D5—44no—
1131D5—81no—
1132D5—82no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—21no—
1137C23—52no—
1138C23—102no—
1139C23—104no—
1140C23—101no—
1141C23—102no—
1142C23—204no—
1143C23—204no—
1144C23—204no—
1145C23—204no—
1146C23—204no—
1147C23—202no—
1148C23—401no—
1149C23—402no—
1150C23—401no—
1151C23—401no—
1152C23—402no—
1153C23—401no—
1154C23—4016no—
1155C23—402no—
1156C23—402no—
1157C23C2×D4×D511yescharacteristic
1158C23C2×D4×D511yescharacteristic
1159C23C2×D4×D511yescharacteristic
1160Q8—21no—
1161Q8—21no—
1162Q8—102no—
1163Q8—101no—
1164Q8—101no—
1165Q8—402no—
1166D4—21no—
1167D4—21no—
1168D4—42no—
1169D4—42no—
1170D4—42no—
1171D4—54no—
1172D4—104no—
1173D4—104no—
1174D4—104no—
1175D4—104no—
1176D4—102no—
1177D4—101no—
1178D4—102no—
1179D4—102no—
1180D4—101no—
1181D4—102no—
1182D4—204no—
1183D4—204no—
1184D4—204no—
1185D4—204no—
1186D4—202no—
1187D4—202no—
1188D4—202no—
1189D4—202no—
1190D4—402no—
1191D4—402no—
1192D4—402no—
1193D4—402no—
1194D4—402no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—44no—
1208C2×C4—42no—
1209C2×C4—52no—
1210C2×C4—52no—
1211C2×C4—52no—
1212C2×C4—81no—
1213C2×C4—82no—
1214C2×C4—81no—
1215C2×C4—102no—
1216C2×C4—102no—
1217C2×C4—101no—
1218C2×C4—101no—
1219C2×C4—101no—
1220C2×C4—204no—
1221C2×C4—202no—
1222C2×C4—402no—
1223C2×C4—402no—
1224C2×C4—402no—
1225C2×C4—402no—
1226C2×C4C2×D4×D511yescharacteristic
1227C2×C4C2×D4×D511yescharacteristic
1228C2×C4C2×D4×D511yescharacteristic
1229C2×C4D5×#4112yes—
1230C2×C4#414912yes—
1231C2×C4C24×D511yescharacteristic
1232C8—22no—
1233C8—22no—
1234C8—101no—
1235C8—101no—
1236C8—101no—
1237C8—101no—
1238C5#6116711yescharacteristic, complemented, Sylow
1239C22—28no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—21no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—102no—
1250C22—104no—
1251C22—102no—
1252C22—102no—
1253C22—202no—
1254C22—202no—
1255C22—201no—
1256C22—202no—
1257C22—201no—
1258C22—202no—
1259C22—201no—
1260C22—202no—
1261C22—404no—
1262C22—408no—
1263C22—408no—
1264C22—404no—
1265C22—804no—
1266C22#6598812yes—
1267C22#6610812yes—
1268C22#6611212yes—
1269C22C22×D4×D511yescharacteristic
1270C4—21no—
1271C4—21no—
1272C4—41no—
1273C4—42no—
1274C4—42no—
1275C4—41no—
1276C4—41no—
1277C4—102no—
1278C4—102no—
1279C4—102no—
1280C4—201no—
1281C4—201no—
1282C4—201no—
1283C4#6598812yes—
1284C4C2×D5×#4111yescharacteristic
1285C4C2×#414911yescharacteristic
1286C2—22no—
1287C2—22no—
1288C2—22no—
1289C2—81no—
1290C2—202no—
1291C2—204no—
1292C2—402no—
1293C2—401no—
1294C2C2×#6598811yescharacteristic
1295C2C2×#6610811yescharacteristic
1296C2C2×#6611211yescharacteristic
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3092C2
socleC22×C5C23×D4
hypercenter#3092D5
hypocenterC5#61167
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
1. #10617940C2semidirect
2. #10617619C2semidirect
3. C5×#3092C2semidirect
4. #10614653C2semidirect
5. C22×#3941C2semidirect
6. #10613217C2semidirect
7. #10613216C2semidirect
8. #10613177C2semidirect
9. #10613176C2semidirect
10. #10613074C2semidirect
11. #10613073C2semidirect
12. #10613034C2semidirect
13. #10613033C2semidirect
14. #10610973C2semidirect
15. #10610950C2semidirect
16. #10610944C2semidirect
17. #10610932C2semidirect
18. #10610642C2semidirect
19. #10610617C2semidirect
20. #10610613C2semidirect
21. #10610607C2semidirect
22. #10610368C2semidirect
23. #10610357C2semidirect
27. C22×C5×C4⋊C4C22semidirect
29. C2×#4096C22semidirect
32. #66125C22semidirect
33. C23×#168C22semidirect
35. C2×#4054C22semidirect
36. C2×#4053C22semidirect
51. #65848C22semidirect
53. #65847C22semidirect
55. #65845C22semidirect
56. #65844C22semidirect
58. #65841C22semidirect
59. #65838C22semidirect
60. #65838C22semidirect
61. #65834C22semidirect
62. C5×#484C22semidirect
63. C5×#483C22semidirect
64. C5×#481C22semidirect
65. C5×#480C22semidirect
66. C5×#428C22semidirect
67. C5×#428C22semidirect
68. C5×#417C22semidirect
69. C5×#417C22semidirect
70. C5×#407C22semidirect
71. #65522C22semidirect
73. #65420C22semidirect
74. #65418C22semidirect
75. #65411C22semidirect
76. #65408C22semidirect
77. #65340C22semidirect
78. #65340C22semidirect
79. #65337C22semidirect
80. #65337C22semidirect
81. #65330C22semidirect
82. #65330C22semidirect
83. #65327C22semidirect
84. #65327C22semidirect
85. #65291C22semidirect
86. #65287C22semidirect
89. C2×#3941C22semidirect
90. C2×#3941C22semidirect
91. C2×#3941C22semidirect
92. C2×#3941C22semidirect
93. C2×#3941C22semidirect
94. C2×#3941C22semidirect
95. #65180C22semidirect
96. #65179C22semidirect
97. #65178C22semidirect
98. #65175C22semidirect
99. #65174C22semidirect
100. #65172C22semidirect
101. #65171C22semidirect
102. #65161C22semidirect
103. #65160C22semidirect
104. #65159C22semidirect
105. #65158C22semidirect
106. #65155C22semidirect
107. #65154C22semidirect
108. #65153C22semidirect
109. #65152C22semidirect
110. #65141C22semidirect
111. #65108C22semidirect
112. #65100C22semidirect
113. #65099C22semidirect
114. #65093C22semidirect
115. #65092C22semidirect
116. #65089C22semidirect
117. #65087C22semidirect
118. #65084C22semidirect
119. #65075C22semidirect
120. #65065C22semidirect
121. #65062C22semidirect
122. #65059C22semidirect
123. D5×#102C22semidirect
124. #65053C22semidirect
125. #65051C22semidirect
126. #65049C22semidirect
127. #65021C22semidirect
128. #65021C22semidirect
129. #65020C22semidirect
130. #65020C22semidirect
131. #65019C22semidirect
132. #65019C22semidirect
133. #65014C22semidirect
134. #65014C22semidirect
183. C2×#689C23semidirect
184. C2×#688C23semidirect
189. C2×#687C23semidirect
190. C2×#686C23semidirect
234. C2×#676C23semidirect
235. C2×C8×D5C23semidirect
239. #4043C23semidirect
247. #4041C23semidirect
255. #4039C23semidirect
257. #4038C23semidirect
259. D5×C4⋊C4C23semidirect
261. #4036C23semidirect
265. #4034C23semidirect
267. #4033C23semidirect
282. C5×#107C23semidirect
283. C5×#107C23semidirect
284. C5×#106C23semidirect
285. C5×#106C23semidirect
286. C5×#103C23semidirect
287. C5×#103C23semidirect
288. C5×#102C23semidirect
289. C5×#102C23semidirect
292. #3967C23semidirect
293. #3967C23semidirect
294. #3964C23semidirect
295. #3964C23semidirect
300. #3952C23semidirect
301. #3952C23semidirect
302. #3947C23semidirect
303. #3946C23semidirect
304. #3946C23semidirect
305. C8×Dic5C23semidirect
306. #3942C23semidirect
307. #3942C23semidirect
316. #3941C23semidirect
317. #3941C23semidirect
318. #3940C23semidirect
319. #3940C23semidirect
320. #3939C23semidirect
321. #3939C23semidirect
334. #3092D5semidirect
417. C2×D20#41semidirect
546. C22×C4⋊C4C2×D5semidirect
551. #484C2×D5semidirect
552. #483C2×D5semidirect
556. #481C2×D5semidirect
558. #480C2×D5semidirect
595. #428C2×D5semidirect
596. #428C2×D5semidirect
603. #417C2×D5semidirect
604. #417C2×D5semidirect
618. #407C2×D5semidirect
873. #107C22×D5semidirect
874. #107C22×D5semidirect
877. #106C22×D5semidirect
878. #106C22×D5semidirect
885. #103C22×D5semidirect
886. #103C22×D5semidirect
903. #102C22×D5semidirect
904. #102C22×D5semidirect
1238. C5#61167semidirect

Maximal subgroups

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

subgroupindex
#106179402
#106176192
C5×#30922
#106146532
C22×#39412
#106132172
#106132162
#106131772
#106131762
#106130742
#106130732
#106130342
#106130332
#106109732
#106109502
#106109442
#106109322
#106106422
#106106172
#106106132
#106106072
#106103682
#106103572
#611675