Finite Group Databasebeta

← #12969799

Subgroups — #12969799

Order 1280.

1902 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3510C211yesmaximal, characteristic, complemented
2#10617751C211yesmaximal, characteristic, complemented
3#10615188C214yesmaximal, complemented
4#10615187C214yesmaximal, complemented
5#10615131C212yesmaximal, complemented
6#10615110C212yesmaximal, complemented
7#10615072C211yesmaximal, characteristic, complemented
8#10615066C211yesmaximal, characteristic, complemented
9#10614869C212yesmaximal, complemented
10#10614868C212yesmaximal, complemented
11#10614867C212yesmaximal, complemented
12#10614866C212yesmaximal, complemented
13#10614674C211yesmaximal, characteristic, complemented
14C2×#65344C211yesmaximal, characteristic, complemented
15#10614278C212yesmaximal, complemented
16#10614268C212yesmaximal, complemented
17#10614242C211yesmaximal, characteristic, complemented
18C5×#559—21no—
19C5×#559—21no—
20C5×#556—21no—
21C5×#556—21no—
22C5×#551—22no—
23C5×#551—22no—
24C5×#542C2212yes—
25C5×#542C2212yes—
26C5×#536C2211yescharacteristic
27C5×#535C2211yescharacteristic
28C5×#533C2211yescharacteristic
29C5×#529C2212yes—
30C5×#529C2212yes—
31C2×C5×#124C2211yescharacteristic
32C5×#519C2211yescharacteristic
33C5×#518C2211yescharacteristic
34C4×C5×#41C2211yescharacteristic
35#66167C2212yes—
36C2×#4094C2212yes—
37C2×#4088C2212yes—
38C2×#4078C2212yes—
39#65918—21no—
40#65913—21no—
41#65899—22no—
42#65897—21no—
43#65886—22no—
44#65885—21no—
45#65868C2214yescomplemented
46#65857C2212yes—
47#65811C2211yescharacteristic
48#65811C2212yescomplemented
49#65804C2212yescomplemented
50C2×#4015C2211yescharacteristic
51C2×#3967C2212yes—
52C2×#3964C2212yes—
53#65378C2212yescomplemented
54#65378C2212yescomplemented
55#65368C2212yescomplemented
56#65367C2212yescomplemented
57#65358C2211yescharacteristic, complemented
58#65358C2211yescharacteristic, complemented
59#65356C2211yescharacteristic, complemented
60#65356C2211yescharacteristic, complemented
61#65354C2212yescomplemented
62#65354C2212yescomplemented
63#65349C2212yes—
64#65348C2214yes—
65#65347C2212yes—
66#65344C2212yes—
67#65344C2212yes—
68#65344C2214yes—
69#65341C2214yescomplemented
70#65340C2214yescomplemented
71#65338C2214yescomplemented
72#65337C2214yescomplemented
73#65331C2214yes—
74#65330C2214yes—
75#65328C2214yes—
76#65327C2214yes—
77#65319C2214yescomplemented
78C4×#689C2214yescomplemented
79#65315C2214yescomplemented
80C4×#688C2214yescomplemented
81#65307C2214yes—
82C4×#687C2214yes—
83#65303C2214yes—
84C4×#686C2214yes—
85#65291C2212yes—
86#65291C2212yes—
87#65286C2212yes—
88#65286C2214yescomplemented
89#65284C2212yes—
90#65284C2212yes—
91C4×#681C2211yescharacteristic
92C4×#681C2212yescomplemented
93C2×#3935C2211yescharacteristic
94C2×#3935C2212yescomplemented
95#60727—51nomaximal, Sylow
96C2×C5×#41C2311yescharacteristic
97C22×C5×Q8C2311yescharacteristic
98C22×C5×D4C2311yescharacteristic
99C2×#709—22no—
100C2×#709C2312yes—
101C22×Dic10—21no—
102C5×C4⋊Q8—21no—
103C5×C4⋊Q8C2311yescharacteristic
104C5×C4⋊Q8C2311yescharacteristic
105C5×#127—21no—
106C5×#126—22no—
107C5×#126—22no—
108C5×#126—22no—
109C5×#126—22no—
110C5×#125C2311yescharacteristic
111C5×#125C2311yescharacteristic
112C5×#124—21no—
113C5×#124—21no—
114C5×#124—22no—
115C5×#124—22no—
116C5×#124—21no—
117C5×#124—21no—
118C5×#124C2312yes—
119C5×#124C2312yes—
120C5×#123—22no—
121C5×#123—22no—
122C5×#123—22no—
123C5×#123—22no—
124C5×#123—22no—
125C5×C22⋊Q8—21no—
126C5×C22⋊Q8—21no—
127C5×C22⋊Q8—22no—
128C5×C22⋊Q8—22no—
129C5×C22⋊Q8C2312yes—
130C5×C22⋊Q8C2312yes—
131C5×#121C2312yes—
132C5×#121C2312yes—
133C5×#120—22no—
134C4×C5×Q8—21no—
135C4×C5×Q8—21no—
136C4×C5×Q8—21no—
137C4×C5×Q8—21no—
138C4×C5×Q8D411yescharacteristic
139C4×C5×Q8D411yescharacteristic
140C4×C5×Q8C2312yes—
141C4×C5×Q8C2312yes—
142C4×C5×D4—22no—
143C4×C5×D4—22no—
144C4×C5×D4—21no—
145C4×C5×D4—21no—
146C4×C5×D4D411yescharacteristic
147C4×C5×D4D412yes—
148C4×C5×D4D411yescharacteristic
149C4×C5×D4D412yes—
150C4×C5×D4C2312yes—
151C4×C5×D4C2312yes—
152C5×#117—22no—
153C5×#117—22no—
154C5×#117—22no—
155C5×#117C2311yescharacteristic
156C5×#117C2311yescharacteristic
157C5×#117C2311yescharacteristic
158C5×#117C2312yes—
159C2×C5×C22⋊C4—21no—
160C2×C5×C22⋊C4—21no—
161C2×C5×C22⋊C4—22no—
162C2×C42×C5C2311yescharacteristic
163C2×C42×C5C2312yes—
164#4094—28no—
165#4092—22no—
166C2×#689C2314yes—
167#4088—28no—
168C2×#688C2314yes—
169#4085—24no—
170#4084—22no—
171C2×#687C2314yes—
172#4078—28no—
173C2×#686C2314yes—
174#4076—21no—
175#4076—21no—
176#4076—22no—
177#4076C2314yes—
178#4072—22no—
179C2×C4⋊Dic5—21no—
180C2×C4⋊Dic5C2312yes—
181#4070—22no—
182#4070C2314yes—
183C2×#681C2314yes—
184C2×#681C2312yes—
185C22×#168C2312yes—
186C22×#168C2314yes—
187#4044—24no—
188#4042—24no—
189#4038—22no—
190D5×C4⋊C4—22no—
191#4031—24no—
192#4029—24no—
193#4027—24no—
194#4021—22no—
195#4021C2312yes—
196#4020C2311yescharacteristic
197C4×D20—21no—
198C4×D20—21no—
199C4×D20—22no—
200C4×D20C2314yes—
201#4016—22no—
202#4015—21no—
203#4015—21no—
204#4015C2311yescharacteristic
205#4015C2312yes—
206#4015C2312yes—
207C4×Dic10—22no—
208C4×Dic10C2314yes—
209#3967C2314yes—
210#3967C2314yes—
211#3964C2314yes—
212#3964C2314yes—
213#3942C2312yes—
214#3942C2312yes—
215#3942C2312yes—
216#3942C2312yes—
217#3941C2312yes—
218#3941C2312yes—
219#3941C2312yes—
220#3941C2312yes—
221#3940C2314yes—
222#3940C2314yes—
223#3939C2314yes—
224#3939C2314yes—
225#3935C2314yes—
226#3935C2312yes—
227#3935C2311yescharacteristic
228#3935C2311yescharacteristic
229#3935C2312yes—
230C4×#168C2314yes—
231C4×#168C2312yes—
232#3511—51no—
233#3510D511yescharacteristic, complemented
234#3181—52no—
235#3180—52no—
236#3175—54no—
237#3173—54no—
238#3172—52no—
239#3171—52no—
240#3165—51no—
241#3153—51no—
242#3135—51no—
243C2×#489—51no—
244#3063—52no—
245#3062—52no—
246#2947—52no—
247#2946—52no—
248#2875—51no—
249C24×C5—21no—
250C5×#41—24no—
251C2×C5×Q8—21no—
252C2×C5×Q8—21no—
253C2×C5×Q8—21no—
254C2×C5×Q8—24no—
255C2×C5×Q8C2×D411yescharacteristic
256C2×C5×Q8C2412yes—
257C2×C5×D4—22no—
258C2×C5×D4—22no—
259C2×C5×D4—21no—
260C2×C5×D4—24no—
261C2×C5×D4C2×D412yes—
262C2×C5×D4C2×D411yescharacteristic
263C2×C5×D4C2412yes—
264C22×C4×C5—21no—
265C22×C4×C5—22no—
266C22×C4×C5—22no—
267C22×C4×C5C2×D411yescharacteristic
268C22×C4×C5C2×D411yescharacteristic
269C22×C4×C5C2×D412yes—
270C22×C4×C5C2×D412yes—
271C22×C4×C5C2412yes—
272C22×C4×C5C2411yescharacteristic
273C2×C22⋊D5—22no—
274C2×C22⋊D5—24no—
275C22×Dic5—22no—
276#709—24no—
277#709—24no—
278#709—84no—
279C2×D20—21no—
280C2×D20—21no—
281C2×D20C2412yes—
282C2×C4×D5—22no—
283C2×C4×D5—24no—
284C2×Dic10—22no—
285C2×Dic10—22no—
286C2×Dic10—82no—
287C2×Dic10C2412yes—
288C5×C4⋊C4—21no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—22no—
291C5×C4⋊C4—22no—
292C5×C4⋊C4—22no—
293C5×C4⋊C4—22no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—21no—
297C5×C4⋊C4—21no—
298C5×C4⋊C4C2×D411yescharacteristic
299C5×C4⋊C4C2×D411yescharacteristic
300C5×C4⋊C4C2×D412yes—
301C5×C4⋊C4C2×D412yes—
302C5×C4⋊C4C2411yescharacteristic
303C5×C4⋊C4C2411yescharacteristic
304C5×C4⋊C4C2411yescharacteristic
305C5×C4⋊C4C2411yescharacteristic
306C5×C22⋊C4—21no—
307C5×C22⋊C4—21no—
308C5×C22⋊C4—22no—
309C5×C22⋊C4—22no—
310C5×C22⋊C4—22no—
311C5×C22⋊C4—22no—
312C5×C22⋊C4—22no—
313C5×C22⋊C4—22no—
314C5×C22⋊C4—22no—
315C5×C22⋊C4—22no—
316C5×C22⋊C4—22no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4C2×D412yes—
319C5×C22⋊C4C2×D412yes—
320C5×C22⋊C4C2×D412yes—
321C42×C5—22no—
322C42×C5—22no—
323C42×C5—21no—
324C42×C5—21no—
325C42×C5C2×D412yes—
326C42×C5C2×D412yes—
327C42×C5C2×D411yescharacteristic
328C42×C5C2×D411yescharacteristic
329C42×C5C2411yescharacteristic
330C42×C5C2412yes—
331C42×C5C2411yescharacteristic
332C22⋊Dic5—24no—
333#689—28no—
334#688—28no—
335#687—28no—
336#686—28no—
337#685—24no—
338#685—22no—
339#685—22no—
340#685—24no—
341C4⋊Dic5—21no—
342C4⋊Dic5—22no—
343C4⋊Dic5—22no—
344C4⋊Dic5—22no—
345C4⋊Dic5—21no—
346C4⋊Dic5C2414yes—
347#683—24no—
348#683—24no—
349C4×Dic5—24no—
350#681—28no—
351#681#4118yescomplemented
352C2×#168—24no—
353C2×#168—28no—
354C2×#168C2412yes—
355C2×#168C2412yes—
356C2×#168C2414yes—
357C2×#137—52no—
358C2×AGL(1,ℤ/8)—52no—
359C2×#131—52no—
360#559—21no—
361#559—21no—
362#556—21no—
363#556—21no—
364#556—101no—
365#555—101no—
366#554—101no—
367#553—102no—
368#551—22no—
369#551—22no—
370#548—102no—
371#547—101no—
372#542—54no—
373#542C2×D512yes—
374#542C2×D512yes—
375#537—52no—
376#536C2×D511yescharacteristic
377#535C2×D511yescharacteristic
378#533—52no—
379#533C2×D511yescharacteristic
380#532—52no—
381#532—51no—
382C2×C4⋊Q8—51no—
383#529C2×D512yes—
384#529C2×D512yes—
385C2×#124C2×D511yescharacteristic
386#520—52no—
387#519C2×D511yescharacteristic
388#518C2×D511yescharacteristic
389C4×#41C2×D511yescharacteristic
390#501—52no—
391#501—52no—
392#500—52no—
393#498—52no—
394#497—52no—
395#496—52no—
396#495—54no—
397#491—51no—
398#491—51no—
399#490—51no—
400#490—51no—
401#489—52no—
402#489—52no—
403#489—52no—
404#489—54no—
405#489—52no—
406#470—54no—
407#469—54no—
408#468—54no—
409#468—54no—
410#467—54no—
411#466—54no—
412#465—54no—
413#465—54no—
414#442—54no—
415#441—54no—
416#440—54no—
417#440—54no—
418C4×Q16—54no—
419C4×SD16—54no—
420C4×SD16—54no—
421C4×D8—54no—
422#428—52no—
423#428—52no—
424#416—52no—
425#416—52no—
426C2×#103—52no—
427C2×#102—52no—
428#405—52no—
429#405—54no—
430C4×M16—51no—
431C4×M16—52no—
432C2×#97—51no—
433C2×#97—52no—
434C23×C5—22no—
435C23×C5—42no—
436C23×C5—81no—
437C23×C5—81no—
438C23×C5C22×D412yes—
439C23×C5C22×D411yescharacteristic
440C22×D5—22no—
441C5×Q8—22no—
442C5×Q8—24no—
443C5×Q8—42no—
444C5×Q8—81no—
445C5×Q8—81no—
446C5×D4—24no—
447C5×D4—22no—
448C5×D4—24no—
449C5×D4—42no—
450C5×D4—82no—
451C5×D4—82no—
452C2×C4×C5—24no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—22no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—41no—
459C2×C4×C5—42no—
460C2×C4×C5—42no—
461C2×C4×C5—41no—
462C2×C4×C5—42no—
463C2×C4×C5—82no—
464C2×C4×C5—82no—
465C2×C4×C5C22×D412yes—
466C2×C4×C5C22×D412yes—
467C2×C4×C5C22×D412yes—
468C2×C4×C5C22×D411yescharacteristic
469C2×C4×C5C22×D411yescharacteristic
470C2×C4×C5C22×D411yescharacteristic
471C2×C4×C5C22×D411yescharacteristic
472C2×C4×C5C22×D411yescharacteristic
473C2×C4×C5C2×#4114yes—
474C2×C4×C5C2511yescharacteristic
475C22⋊D5—44no—
476C22⋊D5—84no—
477C2×Dic5—22no—
478C2×Dic5—24no—
479C2×Dic5—82no—
480D20—22no—
481D20—22no—
482D20—42no—
483D20—42no—
484C4×D5—44no—
485C4×D5—84no—
486Dic10—22no—
487Dic10—22no—
488Dic10—44no—
489Dic10—82no—
490#168—22no—
491#168—22no—
492#168C2×#4118yes—
493C2×#41—52no—
494C2×#41—102no—
495C2×#41C22×D511yescharacteristic
496C22×Q8—101no—
497C22×Q8C22×D511yescharacteristic
498C22×D4C22×D511yescharacteristic
499#137—108no—
500AGL(1,ℤ/8)—108no—
501C2×Q16—54no—
502C2×SD16—54no—
503C2×SD16—54no—
504C2×D8—54no—
505#131—108no—
506C2×M16—52no—
507C2×M16—54no—
508C22×C8—52no—
509C22×C8—54no—
510C4⋊Q8—21no—
511C4⋊Q8—52no—
512C4⋊Q8—52no—
513C4⋊Q8—51no—
514C4⋊Q8—101no—
515C4⋊Q8—101no—
516C4⋊Q8C22×D511yescharacteristic
517C4⋊Q8C22×D511yescharacteristic
518#127—21no—
519#127—51no—
520#126—22no—
521#126—22no—
522#126—22no—
523#126—22no—
524#126—104no—
525#125—102no—
526#125C22×D511yescharacteristic
527#125C22×D511yescharacteristic
528#124—21no—
529#124—21no—
530#124—22no—
531#124—22no—
532#124—21no—
533#124—21no—
534#124—52no—
535#124—104no—
536#124—102no—
537#124C22×D512yes—
538#124C22×D512yes—
539#123—22no—
540#123—22no—
541#123—22no—
542#123—22no—
543#123—22no—
544#123—104no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—54no—
550C22⋊Q8—102no—
551C22⋊Q8—102no—
552C22⋊Q8—104no—
553C22⋊Q8C22×D512yes—
554C22⋊Q8C22×D512yes—
555#121—54no—
556#121—102no—
557#121—104no—
558#121—101no—
559#121—101no—
560#121—102no—
561#121C22×D512yes—
562#121C22×D512yes—
563#120—22no—
564C4×Q8—21no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—54no—
569C4×Q8—102no—
570C4×Q8C22⋊D511yescharacteristic
571C4×Q8C22⋊D511yescharacteristic
572C4×Q8C22×D512yes—
573C4×Q8C22×D512yes—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—54no—
579C4×D4—104no—
580C4×D4—101no—
581C4×D4—102no—
582C4×D4—101no—
583C4×D4C22⋊D511yescharacteristic
584C4×D4C22⋊D512yes—
585C4×D4C22⋊D512yes—
586C4×D4C22⋊D511yescharacteristic
587C4×D4C22×D512yes—
588C4×D4C22×D512yes—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—102no—
593#117—102no—
594#117C22×D511yescharacteristic
595#117C22×D511yescharacteristic
596#117C22×D511yescharacteristic
597#117C22×D512yes—
598C2×C4⋊C4—52no—
599C2×C4⋊C4—101no—
600C2×C4⋊C4—102no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C42C22×D511yescharacteristic
605C2×C42C22×D512yes—
606#107—54no—
607#107—54no—
608#106—54no—
609#106—54no—
610#103—54no—
611#103—54no—
612#103—52no—
613#103—52no—
614#103—52no—
615#103—52no—
616#102—54no—
617#102—54no—
618#102—52no—
619#102—52no—
620#102—52no—
621#102—52no—
622#97—51no—
623#97—51no—
624#97—52no—
625#97—54no—
626#97—52no—
627C4×C8—54no—
628C4×C8—52no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5—22no—
632C22×C5—22no—
633C22×C5—22no—
634C22×C5—42no—
635C22×C5—42no—
636C22×C5—42no—
637C22×C5—162no—
638C22×C5#53212yes—
639C22×C5C23×D411yescharacteristic
640C2×D5—42no—
641C2×D5—42no—
642C2×D5—42no—
643C4×C5—21no—
644C4×C5—21no—
645C4×C5—22no—
646C4×C5—21no—
647C4×C5—22no—
648C4×C5—21no—
649C4×C5—22no—
650C4×C5—41no—
651C4×C5—41no—
652C4×C5—41no—
653C4×C5—41no—
654C4×C5—42no—
655C4×C5#53212yes—
656C4×C5C22×#4112yes—
657Dic5—44no—
658Dic5—42no—
659C24—21no—
660#41—24no—
661#41—104no—
662#41—104no—
663#41—404no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—24no—
668C2×Q8—52no—
669C2×Q8—102no—
670C2×Q8—102no—
671C2×Q8—402no—
672C2×Q8C2×C22⋊D511yescharacteristic
673C2×Q8C23×D512yes—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—24no—
677C2×D4—21no—
678C2×D4—52no—
679C2×D4—102no—
680C2×D4—104no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4C2×C22⋊D512yes—
684C2×D4C2×C22⋊D511yescharacteristic
685C2×D4C23×D512yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—104no—
692C22×C4C2×C22⋊D511yescharacteristic
693C22×C4C2×C22⋊D511yescharacteristic
694C22×C4C2×C22⋊D512yes—
695C22×C4C2×C22⋊D512yes—
696C22×C4C23×D512yes—
697C22×C4C23×D511yescharacteristic
698Q16—108no—
699SD16—108no—
700SD16—108no—
701D8—108no—
702M16—58no—
703M16—108no—
704C2×C8—54no—
705C2×C8—52no—
706C2×C8—52no—
707C2×C8—108no—
708C2×C8—104no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—54no—
720C4⋊C4—102no—
721C4⋊C4—102no—
722C4⋊C4—104no—
723C4⋊C4—102no—
724C4⋊C4—101no—
725C4⋊C4—101no—
726C4⋊C4—104no—
727C4⋊C4C2×C22⋊D511yescharacteristic
728C4⋊C4C2×C22⋊D511yescharacteristic
729C4⋊C4C2×C22⋊D512yes—
730C4⋊C4C2×C22⋊D512yes—
731C4⋊C4C23×D511yescharacteristic
732C4⋊C4C23×D511yescharacteristic
733C4⋊C4C23×D511yescharacteristic
734C4⋊C4C23×D511yescharacteristic
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—104no—
748C22⋊C4—104no—
749C22⋊C4—104no—
750C22⋊C4—102no—
751C22⋊C4—102no—
752C22⋊C4C2×C22⋊D512yes—
753C22⋊C4C2×C22⋊D512yes—
754C22⋊C4C2×C22⋊D512yes—
755C42—22no—
756C42—22no—
757C42—21no—
758C42—21no—
759C42—104no—
760C42C2×C22⋊D512yes—
761C42C2×C22⋊D512yes—
762C42C2×C22⋊D511yescharacteristic
763C42C2×C22⋊D511yescharacteristic
764C42C23×D512yes—
765C42C23×D511yescharacteristic
766C42C23×D511yescharacteristic
767C2×C5—22no—
768C2×C5—42no—
769C2×C5—82no—
770C2×C5C2×#53211yescharacteristic
771C2×C5#358511yescharacteristic
772C2×C5#358611yescharacteristic
773D5—82no—
774C23—22no—
775C23—42no—
776C23—81no—
777C23—81no—
778C23—102no—
779C23C22×C22⋊D512yes—
780C23C22×C22⋊D511yescharacteristic
781Q8—22no—
782Q8—24no—
783Q8—42no—
784Q8—81no—
785Q8—81no—
786Q8—102no—
787Q8—102no—
788Q8—204no—
789Q8—402no—
790D4—24no—
791D4—22no—
792D4—24no—
793D4—42no—
794D4—82no—
795D4—82no—
796D4—102no—
797D4—102no—
798D4—202no—
799D4—202no—
800D4—204no—
801D4—404no—
802C2×C4—24no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—102no—
816C2×C4—104no—
817C2×C4—204no—
818C2×C4—404no—
819C2×C4—402no—
820C2×C4D5×#4114yes—
821C2×C4C22×C22⋊D512yes—
822C2×C4C22×C22⋊D512yes—
823C2×C4C22×C22⋊D511yescharacteristic
824C2×C4C22×C22⋊D511yescharacteristic
825C2×C4C22×C22⋊D512yes—
826C2×C4C22×C22⋊D511yescharacteristic
827C2×C4C22×C22⋊D511yescharacteristic
828C2×C4C22×C22⋊D511yescharacteristic
829C2×C4C24×D511yescharacteristic
830C8—58no—
831C8—102no—
832C8—102no—
833C5#6072711yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—162no—
843C22—202no—
844C22—202no—
845C22—202no—
846C22#6616612yes—
847C22C23×C22⋊D511yescharacteristic
848C4—22no—
849C4—21no—
850C4—22no—
851C4—21no—
852C4—21no—
853C4—22no—
854C4—21no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—202no—
861C4—204no—
862C4#6616612yes—
863C4C2×D5×#4112yes—
864C2—22no—
865C2—42no—
866C2—82no—
867C2—402no—
868C2C2×#6616611yescharacteristic
869C2#1061919911yescharacteristic
870C2#1061920011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3510C2
socleC22×C5C23×D4
hypercenter#3510D5
hypocenterC5#60727
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3510

Complements

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

NH ≅ G/Ntype
1. C5×#3510C2semidirect
2. #10617751C2semidirect
3. #10615188C2semidirect
4. #10615187C2semidirect
5. #10615131C2semidirect
6. #10615110C2semidirect
7. #10615072C2semidirect
8. #10615066C2semidirect
9. #10614869C2semidirect
10. #10614868C2semidirect
11. #10614867C2semidirect
12. #10614866C2semidirect
13. #10614674C2semidirect
14. C2×#65344C2semidirect
15. #10614278C2semidirect
16. #10614268C2semidirect
17. #10614242C2semidirect
45. #65868C22semidirect
48. #65811C22semidirect
49. #65804C22semidirect
53. #65378C22semidirect
54. #65378C22semidirect
55. #65368C22semidirect
56. #65367C22semidirect
57. #65358C22semidirect
58. #65358C22semidirect
59. #65356C22semidirect
60. #65356C22semidirect
61. #65354C22semidirect
62. #65354C22semidirect
69. #65341C22semidirect
70. #65340C22semidirect
71. #65338C22semidirect
72. #65337C22semidirect
77. #65319C22semidirect
78. C4×#689C22semidirect
79. #65315C22semidirect
80. C4×#688C22semidirect
88. #65286C22semidirect
92. C4×#681C22semidirect
94. C2×#3935C22semidirect
233. #3510D5semidirect
351. #681#41semidirect
833. C5#60727semidirect

Maximal subgroups

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

subgroupindex
C5×#35102
#106177512
#106151882
#106151872
#106151312
#106151102
#106150722
#106150662
#106148692
#106148682
#106148672
#106148662
#106146742
C2×#653442
#106142782
#106142682
#106142422
#607275