Finite Group Databasebeta

← #12970415

Subgroups — #12970415

Order 1280.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3489C211yesmaximal, characteristic, complemented
2#10619176C211yesmaximal, characteristic, complemented
3#10615845C211yesmaximal, characteristic, complemented
4#10615844C211yesmaximal, characteristic, complemented
5#10615805C211yesmaximal, characteristic, complemented
6#10615157C212yesmaximal, complemented
7#10615156C212yesmaximal, complemented
8#10615155C211yesmaximal, characteristic, complemented
9#10615149C211yesmaximal, characteristic, complemented
10#10615139C212yesmaximal, complemented
11#10615138C212yesmaximal, complemented
12#10615135C211yesmaximal, characteristic, complemented
13#10615128C211yesmaximal, characteristic, complemented
14#10614663C212yesmaximal, complemented
15#10614662C212yesmaximal, complemented
16#10614655C211yesmaximal, characteristic, complemented
17#10614654C211yesmaximal, characteristic, complemented
18#10614470C212yesmaximal, complemented
19#10614469C212yesmaximal, complemented
20#10614463C211yesmaximal, characteristic, complemented
21C2×#65338C211yesmaximal, characteristic, complemented
22#10614298C211yesmaximal, characteristic, complemented
23#10614297C211yesmaximal, characteristic, complemented
24C2×C5×2−1+4C2211yescharacteristic, complemented
25C22×C5×#41C2211yescharacteristic
26C2×#4149C2211yescharacteristic
27C5×D4×Q8—21no—
28C5×#548—21no—
29C5×#547—22no—
30C5×#547—21no—
31C5×#546—22no—
32C5×#546—21no—
33C5×#537C2211yescharacteristic
34C5×#537C2212yescomplemented
35C5×#536C2211yescharacteristic
36C5×#536C2212yescomplemented
37C5×#525C2211yescharacteristic, complemented
38C5×#525C2212yescomplemented
39C2×C5×C22⋊Q8C2211yescharacteristic, complemented
40C2×C5×C22⋊Q8C2212yescomplemented
41C5×#520C2211yescharacteristic, complemented
42#66168—21no—
43#66167C2211yescharacteristic
44#66167C2212yes—
45#66164C2211yescharacteristic
46#66164C2212yes—
47#66163—22no—
48#66163—21no—
49#66161C2211yescharacteristic
50C2×#4096C2211yescharacteristic, complemented
51C2×#4095C2211yescharacteristic, complemented
52#66151—21no—
53C2×#4088C2211yescharacteristic, complemented
54C22×#688C2211yescharacteristic, complemented
55D4×C22⋊D5—22no—
56D4×C22⋊D5—21no—
57#66125C2211yescharacteristic
58#66125C2212yes—
59C2×#4076C2211yescharacteristic
60C2×#4076C2212yes—
61C22×#681C2211yescharacteristic, complemented
62C22×#681C2211yescharacteristic, complemented
63#65528C2212yescomplemented
64#65527C2212yescomplemented
65#65527C2212yescomplemented
66#65527C2212yescomplemented
67#65523C2211yescharacteristic
68#65523C2211yescharacteristic
69#65523C2211yescharacteristic, complemented
70#65523C2211yescharacteristic, complemented
71#65523C2212yescomplemented
72#65523C2212yescomplemented
73#65522C2211yescharacteristic, complemented
74#65521C2211yescharacteristic, complemented
75#65517C2212yescomplemented
76#65516C2212yescomplemented
77#65516C2212yescomplemented
78#65516C2212yescomplemented
79#65514C2211yescharacteristic, complemented
80C2×#3967C2211yescharacteristic, complemented
81#65496C2212yescomplemented
82#65496C2212yescomplemented
83#65341C2211yescharacteristic, complemented
84#65341C2211yescharacteristic, complemented
85#65341C2212yescomplemented
86#65340C2212yescomplemented
87#65338C2211yescharacteristic, complemented
88#65338C2212yescomplemented
89#65338C2212yescomplemented
90#65338C2211yescharacteristic, complemented
91#65338C2212yescomplemented
92#65338C2212yescomplemented
93#65338C2212yescomplemented
94#65338C2212yescomplemented
95#65337C2212yescomplemented
96#65337C2212yescomplemented
97#65336C2212yescomplemented
98#65336C2212yescomplemented
99#65336C2212yescomplemented
100#65335C2212yescomplemented
101#65335C2212yescomplemented
102#65335C2212yescomplemented
103#65334C2212yescomplemented
104#65334C2212yescomplemented
105#65334C2212yescomplemented
106#65333C2212yescomplemented
107#65333C2212yescomplemented
108#65332C2212yescomplemented
109#65331C2211yescharacteristic, complemented
110#65331C2211yescharacteristic, complemented
111#65328C2211yescharacteristic, complemented
112#65328C2211yescharacteristic, complemented
113#65328C2212yescomplemented
114#65327C2212yescomplemented
115#65326C2212yescomplemented
116#65325C2212yescomplemented
117#65324C2212yescomplemented
118#65322C2212yescomplemented
119#65292C2212yescomplemented
120#65292C2212yescomplemented
121#65292C2212yescomplemented
122#65291C2211yescharacteristic, complemented
123#65290C2211yescharacteristic, complemented
124#65287C2211yescharacteristic, complemented
125#65285C2212yescomplemented
126#65284C2211yescharacteristic, complemented
127#65259C2212yescomplemented
128#65257C2212yescomplemented
129#65256C2212yescomplemented
130#65256C2212yescomplemented
131#65255C2211yescharacteristic, complemented
132C2×#3941C2211yescharacteristic, complemented
133#65253C2211yescharacteristic, complemented
134C2×#3939C2211yescharacteristic, complemented
135#60772—51nomaximal, Sylow
136C5×2−1+4—42no—
137C5×2−1+4—42no—
138C2×C5×#41—22no—
139C2×C5×#41—21no—
140C2×C5×#41—42no—
141C2×C5×#41—42no—
142C2×C5×#41D412yes—
143C2×C5×#41D411yescharacteristic
144C2×C5×#41D411yescharacteristic
145C2×C5×#41C2311yescharacteristic
146C2×C5×#41C2312yes—
147C2×C5×#41C2311yescharacteristic
148C2×C5×#41C2311yescharacteristic
149C2×C5×#41C2312yes—
150C22×C5×Q8—21no—
151C22×C5×Q8D411yescharacteristic
152C22×C5×Q8C2311yescharacteristic
153C22×C5×Q8C2312yes—
154C22×C5×D4D411yescharacteristic
155C22×C5×D4D412yes—
156C23×C4×C5C2311yescharacteristic
157C23×C4×C5C2312yes—
158C22×C22⋊D5—21no—
159C22×C22⋊D5—22no—
160#4149—42no—
161#4149—42no—
162C2×#713—21no—
163C2×D4×D5—22no—
164C2×D4×D5—21no—
165C2×#709C2311yescharacteristic
166C2×#709C2312yes—
167C22×D20C2311yescharacteristic
168C22×D20C2312yes—
169C5×C4⋊Q8—21no—
170C5×C4⋊Q8—22no—
171C5×#124—21no—
172C5×#124—22no—
173C5×#123—22no—
174C5×#123—22no—
175C5×#123—22no—
176C5×#123—21no—
177C5×#123—22no—
178C5×C22⋊Q8—21no—
179C5×C22⋊Q8—22no—
180C5×C22⋊Q8—21no—
181C5×C22⋊Q8—22no—
182C5×C22⋊Q8—21no—
183C5×C22⋊Q8—22no—
184C5×C22⋊Q8C2312yes—
185C5×C22⋊Q8C2312yes—
186C5×C22⋊Q8C2312yes—
187C5×C22⋊Q8C2311yescharacteristic
188C5×C22⋊Q8C2312yes—
189C5×C22⋊Q8C2311yescharacteristic
190C5×C22⋊Q8C2312yes—
191C5×#121—22no—
192C5×#121—21no—
193C5×#121—22no—
194C5×#121—22no—
195C5×#121—22no—
196C5×#121C2312yes—
197C5×#121C2311yescharacteristic
198C5×#121C2311yescharacteristic
199C5×#120—21no—
200C5×#120—22no—
201C4×C5×Q8—21no—
202C4×C5×D4—22no—
203C4×C5×D4—21no—
204C4×C5×D4—21no—
205C4×C5×D4—22no—
206C4×C5×D4—21no—
207C4×C5×D4—22no—
208C5×#117C2311yescharacteristic
209C5×#117C2312yes—
210C2×C5×C4⋊C4—21no—
211C2×C5×C4⋊C4—22no—
212C2×C5×C4⋊C4C2311yescharacteristic
213C2×C5×C4⋊C4C2312yes—
214C2×C5×C22⋊C4—21no—
215C2×C5×C22⋊C4—22no—
216#4099—21no—
217#4099—22no—
218#4096—42no—
219#4095—42no—
220#4093—21no—
221#4093—22no—
222#4092—21no—
223#4092—22no—
224Q8×Dic5—21no—
225C2×#689C2312yes—
226C2×#689C2311yescharacteristic
227#4088—42no—
228C2×#688—42no—
229C2×#688C2312yes—
230C2×#688C2311yescharacteristic
231C2×#688C2312yes—
232C2×#688C2312yes—
233C2×#688C2312yes—
234#4086—21no—
235#4086—22no—
236#4085—22no—
237#4085—22no—
238#4085—22no—
239#4084—21no—
240#4084—22no—
241#4083—22no—
242#4083—22no—
243#4083—22no—
244D4×Dic5—22no—
245D4×Dic5—21no—
246C2×#687C2311yescharacteristic
247C2×#686C2311yescharacteristic
248C2×#686C2312yes—
249#4076—21no—
250#4076—22no—
251#4076—21no—
252#4076—22no—
253#4076C2312yes—
254#4076C2312yes—
255#4076C2312yes—
256#4076C2312yes—
257#4076C2311yescharacteristic
258#4076C2311yescharacteristic
259#4076C2312yes—
260#4075—21no—
261#4075—22no—
262C4×C22⋊D5—21no—
263C4×C22⋊D5—22no—
264C4×C22⋊D5—21no—
265C4×C22⋊D5—22no—
266C2×#685—21no—
267C2×#685—22no—
268#4072C2311yescharacteristic
269#4072C2312yes—
270C2×C4⋊Dic5C2311yescharacteristic
271C2×C4⋊Dic5C2312yes—
272#4070C2312yes—
273#4070C2311yescharacteristic
274#4070C2311yescharacteristic
275C2×#681—42no—
276C2×#681—42no—
277C2×#681C2311yescharacteristic
278C2×#681C2311yescharacteristic
279C2×#681C2311yescharacteristic
280C2×#681C2312yes—
281C2×#681C2311yescharacteristic
282C2×#681C2311yescharacteristic
283C2×#681C2311yescharacteristic
284C22×#168C2311yescharacteristic
285C22×#168C2311yescharacteristic
286C22×#168C2312yes—
287#3967C2312yes—
288#3967C2312yes—
289#3967C2311yescharacteristic
290#3967C2312yes—
291#3967C2312yes—
292#3967C2312yes—
293#3967C2311yescharacteristic
294#3964C2311yescharacteristic
295#3964C2312yes—
296#3964C2311yescharacteristic
297C22⋊#168C2312yes—
298C22⋊#168C2312yes—
299C22⋊#168C2312yes—
300C22⋊#168C2312yes—
301C22⋊#168C2312yes—
302C22⋊#168C2312yes—
303C22⋊#168C2312yes—
304C22⋊#168C2312yes—
305#3942C2311yescharacteristic
306#3942C2312yes—
307#3942C2311yescharacteristic
308#3941C2312yes—
309#3941C2312yes—
310#3941C2311yescharacteristic
311#3941C2311yescharacteristic
312#3941C2312yes—
313#3941C2312yes—
314#3941C2312yes—
315#3940C2312yes—
316#3940C2311yescharacteristic
317#3940C2311yescharacteristic
318#3940C2312yes—
319#3939C2312yes—
320#3939C2312yes—
321#3939C2311yescharacteristic
322#3939C2311yescharacteristic
323#3939C2312yes—
324#3939C2312yes—
325#3489D511yescharacteristic, complemented
326#3488—51no—
327#3203—52no—
328#3201—52no—
329#3200—52no—
330#3198—52no—
331#3197—52no—
332#3196—52no—
333#3194—52no—
334#3193—52no—
335#3098—51no—
336#3098—51no—
337#3097—51no—
338#3096—51no—
339#3056—51no—
340#3055—51no—
341#3054—51no—
342C2×#468—51no—
343#3013—51no—
344#3012—51no—
345#3010—51no—
346#3009—51no—
347#2879—51no—
348C24×C5C2×D411yescharacteristic
349C24×C5C2×D412yes—
350C23×D5—22no—
351C23×D5—21no—
352C5×#41—22no—
353C5×#41—22no—
354C5×#41—22no—
355C5×#41—22no—
356C5×#41—22no—
357C5×#41—22no—
358C5×#41—42no—
359C5×#41—42no—
360C5×#41—44no—
361C5×#41—42no—
362C5×#41—42no—
363C5×#41—42no—
364C5×#41—42no—
365C5×#41—48no—
366C5×#41—44no—
367C2×C5×Q8—22no—
368C2×C5×Q8—21no—
369C2×C5×Q8—22no—
370C2×C5×Q8—22no—
371C2×C5×Q8—42no—
372C2×C5×Q8—42no—
373C2×C5×Q8—42no—
374C2×C5×Q8—44no—
375C2×C5×Q8C2×D411yescharacteristic
376C2×C5×Q8C2×D411yescharacteristic
377C2×C5×Q8C2×D412yes—
378C2×C5×Q8C2412yes—
379C2×C5×Q8C2411yescharacteristic
380C2×C5×D4—21no—
381C2×C5×D4—22no—
382C2×C5×D4—21no—
383C2×C5×D4—22no—
384C2×C5×D4—21no—
385C2×C5×D4—42no—
386C2×C5×D4—44no—
387C2×C5×D4C2×D412yes—
388C2×C5×D4C2×D411yescharacteristic
389C2×C5×D4C2×D412yes—
390C2×C5×D4C2×D411yescharacteristic
391C2×C5×D4C2×D412yes—
392C2×C5×D4C2×D412yes—
393C2×C5×D4C2×D412yes—
394C2×C5×D4C2411yescharacteristic
395C22×C4×C5—22no—
396C22×C4×C5—22no—
397C22×C4×C5—22no—
398C22×C4×C5—21no—
399C22×C4×C5—22no—
400C22×C4×C5—21no—
401C22×C4×C5—22no—
402C22×C4×C5—21no—
403C22×C4×C5—42no—
404C22×C4×C5—42no—
405C22×C4×C5C2×D411yescharacteristic
406C22×C4×C5C2×D411yescharacteristic
407C22×C4×C5C2×D411yescharacteristic
408C22×C4×C5C2×D412yes—
409C22×C4×C5C2×D412yes—
410C22×C4×C5C2×D412yes—
411C22×C4×C5C2412yes—
412C22×C4×C5C2412yes—
413C22×C4×C5C2411yescharacteristic
414C22×C4×C5C2411yescharacteristic
415C22×C4×C5C2411yescharacteristic
416C2×C22⋊D5—22no—
417C2×C22⋊D5—21no—
418C2×C22⋊D5—21no—
419C2×C22⋊D5—22no—
420C2×C22⋊D5—21no—
421C2×C22⋊D5—22no—
422C2×C22⋊D5—22no—
423C2×C22⋊D5—22no—
424C2×C22⋊D5—22no—
425C2×C22⋊D5—82no—
426C2×C22⋊D5—84no—
427C22×Dic5—22no—
428C22×Dic5—21no—
429#713—44no—
430D4×D5—48no—
431D4×D5—44no—
432#709—22no—
433#709—22no—
434#709—42no—
435#709—42no—
436C2×D20—22no—
437C2×D20—22no—
438C2×D20—22no—
439C2×D20—21no—
440C2×D20—42no—
441C2×D20—42no—
442C2×D20C2412yes—
443C2×D20C2411yescharacteristic
444C2×C4×D5—22no—
445C2×C4×D5—21no—
446C2×Dic10C2411yescharacteristic
447C5×C4⋊C4—22no—
448C5×C4⋊C4—21no—
449C5×C4⋊C4—22no—
450C5×C4⋊C4—22no—
451C5×C4⋊C4—22no—
452C5×C4⋊C4—22no—
453C5×C4⋊C4—21no—
454C5×C4⋊C4—22no—
455C5×C4⋊C4—21no—
456C5×C4⋊C4C2412yes—
457C5×C4⋊C4C2411yescharacteristic
458C5×C4⋊C4C2411yescharacteristic
459C5×C22⋊C4—22no—
460C5×C22⋊C4—21no—
461C5×C22⋊C4—22no—
462C5×C22⋊C4—22no—
463C5×C22⋊C4—22no—
464C5×C22⋊C4—22no—
465C5×C22⋊C4—21no—
466C5×C22⋊C4—22no—
467C5×C22⋊C4—21no—
468C5×C22⋊C4—21no—
469C5×C22⋊C4—22no—
470C5×C22⋊C4—21no—
471C42×C5—22no—
472C42×C5—21no—
473C22⋊Dic5—21no—
474C22⋊Dic5—21no—
475C22⋊Dic5—22no—
476C22⋊Dic5—22no—
477C22⋊Dic5—21no—
478#689—41no—
479#689—42no—
480#688—41no—
481#688—42no—
482#688—42no—
483#688—42no—
484#688—42no—
485#687—41no—
486#686—41no—
487#686—42no—
488#685—22no—
489#685—21no—
490#685—22no—
491#685—22no—
492#685—22no—
493#685—22no—
494#685—21no—
495C4⋊Dic5—22no—
496C4⋊Dic5—21no—
497C4⋊Dic5C2412yes—
498C4⋊Dic5C2411yescharacteristic
499C4⋊Dic5C2411yescharacteristic
500#683—21no—
501#683—22no—
502#683—21no—
503C4×Dic5—22no—
504C4×Dic5—21no—
505#681—22no—
506#681—22no—
507#681—41no—
508#681—41no—
509#681—41no—
510#681—41no—
511#681—42no—
512C2×#168—22no—
513C2×#168—22no—
514C2×#168—42no—
515C2×#168C2411yescharacteristic
516C2×#168C2411yescharacteristic
517C2×#168C2411yescharacteristic
518C2×#168C2412yes—
519C2×#168C2412yes—
520C2×#168C2411yescharacteristic
521C2×2−1+4C2×D511yescharacteristic, complemented
522C2×H(5,𝔽2)—51no—
523C22×#41C2×D511yescharacteristic
524C2×#137—51no—
525C2×AGL(1,ℤ/8)—51no—
526C2×#135—51no—
527C22×SD16—51no—
528C22×M16—51no—
529C22×M16—51no—
530#550—101no—
531D4×Q8—21no—
532#548—21no—
533#548—101no—
534#547—22no—
535#547—21no—
536#546—22no—
537#546—21no—
538#546—102no—
539#546—101no—
540D42—102no—
541D42—101no—
542#537—51no—
543#537—52no—
544#537C2×D511yescharacteristic
545#537C2×D512yescomplemented
546#536C2×D511yescharacteristic
547#536C2×D512yescomplemented
548#535—51no—
549#535—52no—
550#525—52no—
551#525—51no—
552#525C2×D512yescomplemented
553#525C2×D511yescharacteristic, complemented
554C2×C22⋊Q8C2×D512yescomplemented
555C2×C22⋊Q8C2×D511yescharacteristic, complemented
556C2×#121—52no—
557C2×#121—51no—
558#520—51no—
559#520C2×D511yescharacteristic, complemented
560#485—52no—
561#485—52no—
562#485—52no—
563#485—52no—
564#484—52no—
565#484—52no—
566#484—52no—
567#483—52no—
568#482—52no—
569#482—52no—
570#482—52no—
571#482—52no—
572#481—52no—
573#480—52no—
574#480—52no—
575#480—52no—
576#470—51no—
577#470—52no—
578#470—51no—
579#469—51no—
580#469—52no—
581#469—51no—
582#468—51no—
583#468—52no—
584#468—52no—
585#468—52no—
586#468—52no—
587#468—52no—
588#468—51no—
589#468—52no—
590#468—51no—
591#468—51no—
592#467—52no—
593#466—52no—
594#465—52no—
595#465—52no—
596#452—52no—
597#452—52no—
598#452—52no—
599#452—52no—
600#451—52no—
601#450—52no—
602#450—52no—
603#450—52no—
604#449—52no—
605#449—52no—
606#449—52no—
607#449—52no—
608#448—52no—
609#448—52no—
610#448—52no—
611#447—52no—
612#428—51no—
613#428—51no—
614#427—51no—
615C2×#107—51no—
616#419—51no—
617#418—51no—
618#417—51no—
619#417—51no—
620#416—51no—
621#416—51no—
622C2×#103—51no—
623C2×#102—51no—
624#408—51no—
625#408—51no—
626#408—51no—
627#408—51no—
628#408—52no—
629#408—52no—
630#407—52no—
631#407—52no—
632C23×C5—22no—
633C23×C5—21no—
634C23×C5—41no—
635C23×C5—42no—
636C23×C5—42no—
637C23×C5—41no—
638C23×C5—42no—
639C23×C5C22×D412yes—
640C23×C5C22×D411yescharacteristic
641C23×C5C22×D411yescharacteristic
642C23×C5C22×D412yes—
643C23×C5C22×D411yescharacteristic
644C22×D5—22no—
645C22×D5—21no—
646C22×D5—44no—
647C22×D5—42no—
648C22×D5—81no—
649C22×D5—82no—
650C22×D5—81no—
651C22×D5—82no—
652C5×Q8—22no—
653C5×Q8—22no—
654C5×Q8—22no—
655C5×Q8—21no—
656C5×Q8—22no—
657C5×Q8—21no—
658C5×Q8—42no—
659C5×Q8—44no—
660C5×Q8—42no—
661C5×D4—24no—
662C5×D4—24no—
663C5×D4—22no—
664C5×D4—22no—
665C5×D4—21no—
666C5×D4—21no—
667C5×D4—42no—
668C5×D4—42no—
669C5×D4—42no—
670C5×D4—42no—
671C5×D4—44no—
672C5×D4—42no—
673C5×D4—82no—
674C5×D4—81no—
675C2×C4×C5—22no—
676C2×C4×C5—22no—
677C2×C4×C5—22no—
678C2×C4×C5—21no—
679C2×C4×C5—21no—
680C2×C4×C5—21no—
681C2×C4×C5—21no—
682C2×C4×C5—22no—
683C2×C4×C5—22no—
684C2×C4×C5—22no—
685C2×C4×C5—22no—
686C2×C4×C5—21no—
687C2×C4×C5—22no—
688C2×C4×C5—21no—
689C2×C4×C5—22no—
690C2×C4×C5—21no—
691C2×C4×C5—42no—
692C2×C4×C5—42no—
693C2×C4×C5—42no—
694C2×C4×C5—44no—
695C2×C4×C5—44no—
696C2×C4×C5—42no—
697C2×C4×C5—42no—
698C2×C4×C5—81no—
699C2×C4×C5—82no—
700C2×C4×C5C22×D412yes—
701C2×C4×C5C22×D412yes—
702C2×C4×C5C22×D411yescharacteristic
703C2×C4×C5C22×D411yescharacteristic
704C2×C4×C5C22×D411yescharacteristic
705C2×C4×C5H(5,𝔽2)12yes—
706C2×C4×C5H(5,𝔽2)12yes—
707C2×C4×C5C2511yescharacteristic
708C22⋊D5—44no—
709C22⋊D5—44no—
710C22⋊D5—42no—
711C22⋊D5—42no—
712C22⋊D5—81no—
713C22⋊D5—82no—
714C22⋊D5—82no—
715C22⋊D5—82no—
716C22⋊D5—82no—
717C2×Dic5—21no—
718C2×Dic5—22no—
719C2×Dic5—21no—
720C2×Dic5—21no—
721C2×Dic5—81no—
722C2×Dic5—82no—
723D20—22no—
724D20—21no—
725D20—22no—
726D20—21no—
727D20—44no—
728D20—42no—
729C4×D5—44no—
730C4×D5—42no—
731Dic10—21no—
732Dic10—21no—
733#168—21no—
734#168—21no—
735#168—21no—
736#168—21no—
737#168—22no—
738#168—22no—
7392−1+4—42no—
7402−1+4—42no—
741H(5,𝔽2)—202no—
742H(5,𝔽2)—202no—
743C2×#41—22no—
744C2×#41—21no—
745C2×#41—42no—
746C2×#41—42no—
747C2×#41—51no—
748C2×#41—52no—
749C2×#41—101no—
750C2×#41C22⋊D512yes—
751C2×#41C22⋊D511yescharacteristic
752C2×#41C22⋊D511yescharacteristic
753C2×#41C22×D511yescharacteristic
754C2×#41C22×D512yes—
755C2×#41C22×D511yescharacteristic
756C2×#41C22×D511yescharacteristic
757C2×#41C22×D512yes—
758C22×Q8—21no—
759C22×Q8C22⋊D511yescharacteristic
760C22×Q8C22×D511yescharacteristic
761C22×Q8C22×D512yes—
762C22×D4—51no—
763C22×D4—52no—
764C22×D4—101no—
765C22×D4—102no—
766C22×D4—102no—
767C22×D4—101no—
768C22×D4C22⋊D511yescharacteristic
769C22×D4C22⋊D512yes—
770C23×C4C22×D511yescharacteristic
771C23×C4C22×D512yes—
772#137—202no—
773AGL(1,ℤ/8)—202no—
774#135—202no—
775C2×Q16—51no—
776C2×Q16—52no—
777C2×SD16—52no—
778C2×SD16—52no—
779C2×SD16—51no—
780C2×SD16—52no—
781C2×SD16—52no—
782C2×SD16—51no—
783C2×SD16—202no—
784C2×D8—51no—
785C2×D8—52no—
786C2×M16—51no—
787C2×M16—51no—
788C2×M16—51no—
789C2×M16—52no—
790C2×M16—51no—
791C2×M16—51no—
792C2×M16—51no—
793C2×M16—202no—
794C2×M16—202no—
795C22×C8—51no—
796C22×C8—51no—
797C22×C8—52no—
798C4⋊Q8—21no—
799C4⋊Q8—22no—
800#127—101no—
801#127—102no—
802#124—21no—
803#124—22no—
804#124—101no—
805#124—102no—
806#123—22no—
807#123—22no—
808#123—22no—
809#123—21no—
810#123—22no—
811#123—101no—
812#123—102no—
813C22⋊Q8—21no—
814C22⋊Q8—22no—
815C22⋊Q8—21no—
816C22⋊Q8—22no—
817C22⋊Q8—21no—
818C22⋊Q8—22no—
819C22⋊Q8—51no—
820C22⋊Q8—52no—
821C22⋊Q8—51no—
822C22⋊Q8—101no—
823C22⋊Q8—102no—
824C22⋊Q8C22×D511yescharacteristic
825C22⋊Q8C22×D512yes—
826C22⋊Q8C22×D512yes—
827C22⋊Q8C22×D512yes—
828C22⋊Q8C22×D512yes—
829C22⋊Q8C22×D512yes—
830C22⋊Q8C22×D511yescharacteristic
831#121—22no—
832#121—21no—
833#121—22no—
834#121—22no—
835#121—22no—
836#121—51no—
837#121—52no—
838#121—52no—
839#121—52no—
840#121—52no—
841#121—52no—
842#121—51no—
843#121—102no—
844#121—102no—
845#121—102no—
846#121—101no—
847#121—102no—
848#121—101no—
849#121—102no—
850#121—101no—
851#121—102no—
852#121C22×D511yescharacteristic
853#121C22×D512yes—
854#121C22×D511yescharacteristic
855#120—21no—
856#120—22no—
857#120—101no—
858#120—102no—
859#120—102no—
860#120—102no—
861#120—102no—
862C4×Q8—21no—
863C4×Q8—101no—
864C4×D4—22no—
865C4×D4—21no—
866C4×D4—21no—
867C4×D4—22no—
868C4×D4—21no—
869C4×D4—22no—
870C4×D4—102no—
871C4×D4—101no—
872C4×D4—101no—
873C4×D4—102no—
874C4×D4—101no—
875C4×D4—102no—
876#117—51no—
877#117—52no—
878#117C22×D511yescharacteristic
879#117C22×D512yes—
880C2×C4⋊C4—21no—
881C2×C4⋊C4—22no—
882C2×C4⋊C4—51no—
883C2×C4⋊C4—52no—
884C2×C4⋊C4C22×D511yescharacteristic
885C2×C4⋊C4C22×D512yes—
886C2×C22⋊C4—21no—
887C2×C22⋊C4—22no—
888C2×C22⋊C4—101no—
889C2×C22⋊C4—102no—
890#107—52no—
891#107—52no—
892#107—51no—
893#107—51no—
894#107—52no—
895#107—52no—
896#106—51no—
897#106—51no—
898#106—52no—
899#106—52no—
900#103—52no—
901#103—52no—
902#103—51no—
903#103—51no—
904#103—52no—
905#103—52no—
906#103—52no—
907#103—51no—
908#103—51no—
909#103—52no—
910#102—51no—
911#102—51no—
912#102—52no—
913#102—52no—
914#102—52no—
915#102—51no—
916#102—51no—
917#102—52no—
918#102—52no—
919#102—52no—
920C22⋊C8—52no—
921C22⋊C8—52no—
922C22⋊C8—52no—
923C22⋊C8—52no—
924C22⋊C8—52no—
925C22⋊C8—52no—
926C22⋊C8—52no—
927C22⋊C8—52no—
928C22×C5—21no—
929C22×C5—21no—
930C22×C5—22no—
931C22×C5—21no—
932C22×C5—22no—
933C22×C5—21no—
934C22×C5—21no—
935C22×C5—22no—
936C22×C5—21no—
937C22×C5—22no—
938C22×C5—22no—
939C22×C5—21no—
940C22×C5—21no—
941C22×C5—22no—
942C22×C5—41no—
943C22×C5—41no—
944C22×C5—41no—
945C22×C5—82no—
946C22×C5—84no—
947C22×C5#53412yes—
948C22×C5C23×D411yescharacteristic
949C2×D5—42no—
950C2×D5—41no—
951C2×D5—42no—
952C2×D5—41no—
953C2×D5—42no—
954C2×D5—41no—
955C2×D5—162no—
956C2×D5—164no—
957C4×C5—22no—
958C4×C5—21no—
959C4×C5—21no—
960C4×C5—22no—
961C4×C5—42no—
962C4×C5—41no—
963C4×C5—41no—
964C4×C5—42no—
965C4×C5—41no—
966C4×C5#53412yes—
967C4×C5C2×H(5,𝔽2)11yescharacteristic
968C4×C5C2×H(5,𝔽2)11yescharacteristic
969Dic5—42no—
970Dic5—41no—
971Dic5—41no—
972Dic5—41no—
973C24—102no—
974C24—101no—
975C24C2×C22⋊D511yescharacteristic
976C24C2×C22⋊D512yes—
977#41—22no—
978#41—22no—
979#41—22no—
980#41—22no—
981#41—22no—
982#41—22no—
983#41—42no—
984#41—42no—
985#41—44no—
986#41—42no—
987#41—42no—
988#41—42no—
989#41—42no—
990#41—48no—
991#41—44no—
992#41—102no—
993#41—102no—
994#41—202no—
995#41—202no—
996#41—204no—
997C2×Q8—22no—
998C2×Q8—21no—
999C2×Q8—22no—
1000C2×Q8—22no—
1001C2×Q8—42no—
1002C2×Q8—42no—
1003C2×Q8—42no—
1004C2×Q8—44no—
1005C2×Q8—51no—
1006C2×Q8C2×C22⋊D511yescharacteristic
1007C2×Q8C2×C22⋊D511yescharacteristic
1008C2×Q8C2×C22⋊D512yes—
1009C2×Q8C23×D512yes—
1010C2×Q8C23×D511yescharacteristic
1011C2×D4—21no—
1012C2×D4—22no—
1013C2×D4—21no—
1014C2×D4—22no—
1015C2×D4—21no—
1016C2×D4—42no—
1017C2×D4—44no—
1018C2×D4—52no—
1019C2×D4—51no—
1020C2×D4—101no—
1021C2×D4—102no—
1022C2×D4—102no—
1023C2×D4—101no—
1024C2×D4—101no—
1025C2×D4—102no—
1026C2×D4—102no—
1027C2×D4—102no—
1028C2×D4—102no—
1029C2×D4—102no—
1030C2×D4—102no—
1031C2×D4—102no—
1032C2×D4—101no—
1033C2×D4—202no—
1034C2×D4—202no—
1035C2×D4—208no—
1036C2×D4—204no—
1037C2×D4—402no—
1038C2×D4—404no—
1039C2×D4C2×C22⋊D512yes—
1040C2×D4C2×C22⋊D511yescharacteristic
1041C2×D4C2×C22⋊D512yes—
1042C2×D4C2×C22⋊D511yescharacteristic
1043C2×D4C2×C22⋊D512yes—
1044C2×D4C2×C22⋊D512yes—
1045C2×D4C2×C22⋊D512yes—
1046C2×D4C23×D511yescharacteristic
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—21no—
1051C22×C4—22no—
1052C22×C4—21no—
1053C22×C4—22no—
1054C22×C4—21no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—102no—
1058C22×C4—101no—
1059C22×C4—102no—
1060C22×C4—101no—
1061C22×C4C2×C22⋊D511yescharacteristic
1062C22×C4C2×C22⋊D511yescharacteristic
1063C22×C4C2×C22⋊D511yescharacteristic
1064C22×C4C2×C22⋊D512yes—
1065C22×C4C2×C22⋊D512yes—
1066C22×C4C2×C22⋊D512yes—
1067C22×C4C23×D512yes—
1068C22×C4C23×D512yes—
1069C22×C4C23×D511yescharacteristic
1070C22×C4C23×D511yescharacteristic
1071C22×C4C23×D511yescharacteristic
1072Q16—201no—
1073Q16—202no—
1074SD16—201no—
1075SD16—202no—
1076SD16—202no—
1077SD16—201no—
1078SD16—202no—
1079SD16—202no—
1080D8—201no—
1081D8—202no—
1082M16—102no—
1083M16—102no—
1084M16—201no—
1085M16—201no—
1086M16—201no—
1087M16—201no—
1088M16—202no—
1089C2×C8—52no—
1090C2×C8—51no—
1091C2×C8—51no—
1092C2×C8—51no—
1093C2×C8—51no—
1094C2×C8—52no—
1095C2×C8—102no—
1096C2×C8—102no—
1097C2×C8—202no—
1098C4⋊C4—22no—
1099C4⋊C4—21no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—21no—
1105C4⋊C4—22no—
1106C4⋊C4—21no—
1107C4⋊C4—51no—
1108C4⋊C4—51no—
1109C4⋊C4—52no—
1110C4⋊C4—102no—
1111C4⋊C4—101no—
1112C4⋊C4—101no—
1113C4⋊C4—102no—
1114C4⋊C4—101no—
1115C4⋊C4C23×D511yescharacteristic
1116C4⋊C4C23×D512yes—
1117C4⋊C4C23×D511yescharacteristic
1118C22⋊C4—22no—
1119C22⋊C4—21no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—21no—
1125C22⋊C4—22no—
1126C22⋊C4—21no—
1127C22⋊C4—21no—
1128C22⋊C4—22no—
1129C22⋊C4—21no—
1130C22⋊C4—102no—
1131C22⋊C4—101no—
1132C22⋊C4—101no—
1133C22⋊C4—101no—
1134C22⋊C4—102no—
1135C22⋊C4—102no—
1136C22⋊C4—101no—
1137C22⋊C4—102no—
1138C22⋊C4—102no—
1139C22⋊C4—102no—
1140C22⋊C4—102no—
1141C22⋊C4—101no—
1142C42—22no—
1143C42—21no—
1144C42—102no—
1145C42—101no—
1146C2×C5—22no—
1147C2×C5—42no—
1148C2×C5—42no—
1149C2×C5—41no—
1150C2×C5—41no—
1151C2×C5—81no—
1152C2×C5C2×#53411yescharacteristic
1153C2×C5#358511yescharacteristic
1154C2×C5#358611yescharacteristic
1155D5—82no—
1156D5—81no—
1157C23—22no—
1158C23—21no—
1159C23—42no—
1160C23—41no—
1161C23—42no—
1162C23—41no—
1163C23—42no—
1164C23—102no—
1165C23—101no—
1166C23—204no—
1167C23—202no—
1168C23—401no—
1169C23—402no—
1170C23—401no—
1171C23—402no—
1172C23C22×C22⋊D512yes—
1173C23C22×C22⋊D511yescharacteristic
1174C23C22×C22⋊D511yescharacteristic
1175C23C22×C22⋊D512yes—
1176C23C22×C22⋊D511yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—21no—
1181Q8—22no—
1182Q8—21no—
1183Q8—42no—
1184Q8—44no—
1185Q8—42no—
1186Q8—101no—
1187Q8—101no—
1188D4—24no—
1189D4—24no—
1190D4—22no—
1191D4—22no—
1192D4—21no—
1193D4—21no—
1194D4—42no—
1195D4—42no—
1196D4—42no—
1197D4—44no—
1198D4—42no—
1199D4—42no—
1200D4—82no—
1201D4—81no—
1202D4—102no—
1203D4—101no—
1204D4—102no—
1205D4—101no—
1206D4—204no—
1207D4—204no—
1208D4—204no—
1209D4—202no—
1210D4—202no—
1211D4—202no—
1212D4—402no—
1213D4—402no—
1214D4—402no—
1215D4—401no—
1216D4—402no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—81no—
1241C2×C4—82no—
1242C2×C4—101no—
1243C2×C4—102no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—204no—
1247C2×C4—202no—
1248C2×C4—401no—
1249C2×C4—402no—
1250C2×C4#414412yes—
1251C2×C4#414412yes—
1252C2×C4C22×C22⋊D512yes—
1253C2×C4C22×C22⋊D512yes—
1254C2×C4C22×C22⋊D511yescharacteristic
1255C2×C4C22×C22⋊D511yescharacteristic
1256C2×C4C22×C22⋊D511yescharacteristic
1257C2×C4C24×D511yescharacteristic
1258C8—101no—
1259C8—101no—
1260C8—101no—
1261C8—101no—
1262C8—102no—
1263C8—102no—
1264C5#6077211yescharacteristic, complemented, Sylow
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—22no—
1270C22—22no—
1271C22—21no—
1272C22—21no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—21no—
1278C22—21no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—82no—
1283C22—84no—
1284C22—202no—
1285C22—201no—
1286C22—202no—
1287C22—201no—
1288C22—202no—
1289C22—201no—
1290C22—802no—
1291C22—804no—
1292C22#6613812yes—
1293C22C23×C22⋊D511yescharacteristic
1294C4—21no—
1295C4—21no—
1296C4—22no—
1297C4—22no—
1298C4—42no—
1299C4—41no—
1300C4—41no—
1301C4—42no—
1302C4—41no—
1303C4—201no—
1304C4—201no—
1305C4—202no—
1306C4—201no—
1307C4#6613812yes—
1308C4C2×#414411yescharacteristic
1309C4C2×#414411yescharacteristic
1310C2—22no—
1311C2—41no—
1312C2—42no—
1313C2—41no—
1314C2—42no—
1315C2—81no—
1316C2—402no—
1317C2—401no—
1318C2C2×#6613811yescharacteristic
1319C2#1061918811yescharacteristic
1320C2#1061919911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3489C2
socleC22×C5C23×D4
hypercenter#3489D5
hypocenterC5#60772
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C5×#3489C2semidirect
2. #10619176C2semidirect
3. #10615845C2semidirect
4. #10615844C2semidirect
5. #10615805C2semidirect
6. #10615157C2semidirect
7. #10615156C2semidirect
8. #10615155C2semidirect
9. #10615149C2semidirect
10. #10615139C2semidirect
11. #10615138C2semidirect
12. #10615135C2semidirect
13. #10615128C2semidirect
14. #10614663C2semidirect
15. #10614662C2semidirect
16. #10614655C2semidirect
17. #10614654C2semidirect
18. #10614470C2semidirect
19. #10614469C2semidirect
20. #10614463C2semidirect
21. C2×#65338C2semidirect
22. #10614298C2semidirect
23. #10614297C2semidirect
24. C2×C5×2−1+4C22semidirect
34. C5×#537C22semidirect
36. C5×#536C22semidirect
37. C5×#525C22semidirect
38. C5×#525C22semidirect
39. C2×C5×C22⋊Q8C22semidirect
40. C2×C5×C22⋊Q8C22semidirect
41. C5×#520C22semidirect
50. C2×#4096C22semidirect
51. C2×#4095C22semidirect
53. C2×#4088C22semidirect
54. C22×#688C22semidirect
61. C22×#681C22semidirect
62. C22×#681C22semidirect
63. #65528C22semidirect
64. #65527C22semidirect
65. #65527C22semidirect
66. #65527C22semidirect
69. #65523C22semidirect
70. #65523C22semidirect
71. #65523C22semidirect
72. #65523C22semidirect
73. #65522C22semidirect
74. #65521C22semidirect
75. #65517C22semidirect
76. #65516C22semidirect
77. #65516C22semidirect
78. #65516C22semidirect
79. #65514C22semidirect
80. C2×#3967C22semidirect
81. #65496C22semidirect
82. #65496C22semidirect
83. #65341C22semidirect
84. #65341C22semidirect
85. #65341C22semidirect
86. #65340C22semidirect
87. #65338C22semidirect
88. #65338C22semidirect
89. #65338C22semidirect
90. #65338C22semidirect
91. #65338C22semidirect
92. #65338C22semidirect
93. #65338C22semidirect
94. #65338C22semidirect
95. #65337C22semidirect
96. #65337C22semidirect
97. #65336C22semidirect
98. #65336C22semidirect
99. #65336C22semidirect
100. #65335C22semidirect
101. #65335C22semidirect
102. #65335C22semidirect
103. #65334C22semidirect
104. #65334C22semidirect
105. #65334C22semidirect
106. #65333C22semidirect
107. #65333C22semidirect
108. #65332C22semidirect
109. #65331C22semidirect
110. #65331C22semidirect
111. #65328C22semidirect
112. #65328C22semidirect
113. #65328C22semidirect
114. #65327C22semidirect
115. #65326C22semidirect
116. #65325C22semidirect
117. #65324C22semidirect
118. #65322C22semidirect
119. #65292C22semidirect
120. #65292C22semidirect
121. #65292C22semidirect
122. #65291C22semidirect
123. #65290C22semidirect
124. #65287C22semidirect
125. #65285C22semidirect
126. #65284C22semidirect
127. #65259C22semidirect
128. #65257C22semidirect
129. #65256C22semidirect
130. #65256C22semidirect
131. #65255C22semidirect
132. C2×#3941C22semidirect
133. #65253C22semidirect
134. C2×#3939C22semidirect
325. #3489D5semidirect
521. C2×2−1+4C2×D5semidirect
545. #537C2×D5semidirect
547. #536C2×D5semidirect
552. #525C2×D5semidirect
553. #525C2×D5semidirect
554. C2×C22⋊Q8C2×D5semidirect
555. C2×C22⋊Q8C2×D5semidirect
559. #520C2×D5semidirect
1264. C5#60772semidirect

Maximal subgroups

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

subgroupindex
C5×#34892
#106191762
#106158452
#106158442
#106158052
#106151572
#106151562
#106151552
#106151492
#106151392
#106151382
#106151352
#106151282
#106146632
#106146622
#106146552
#106146542
#106144702
#106144692
#106144632
C2×#653382
#106142982
#106142972
#607725