Finite Group Databasebeta

← #12977378

Subgroups — #12977378

Order 1280.

2150 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3498C211yesmaximal, characteristic
2#10618125C211yesmaximal, characteristic, complemented
3#10615836C212yesmaximal, complemented
4#10615830C212yesmaximal, complemented
5#10615306C212yesmaximal, complemented
6#10615304C214yesmaximal, complemented
7#10615301C212yesmaximal, complemented
8#10615217C212yesmaximal, complemented
9#10615215C214yesmaximal, complemented
10#10615214C212yesmaximal, complemented
11#10615108C212yesmaximal, complemented
12#10615107C212yesmaximal, complemented
13#10615008C211yesmaximal, characteristic, complemented
14C2×#65364C211yesmaximal, characteristic, complemented
15#10614890C211yesmaximal, characteristic, complemented
16C4×#4097C211yesmaximal, characteristic, complemented
17#10614238C211yesmaximal, characteristic, complemented
18C2×C5×H(5,𝔽2)C2212yes—
19C5×#550C2212yes—
20C5×#550C2212yes—
21C5×D42—22no—
22C5×D42—22no—
23C5×D42C2212yes—
24C5×D42C2212yes—
25C5×#535—22no—
26C5×#535C2212yes—
27C5×#532—21no—
28C5×#532C2211yescharacteristic
29C2×C5×#127—21no—
30C2×C5×#127C2211yescharacteristic
31C4×C5×#41C2211yescharacteristic
32#66161C2212yescomplemented
33#66159C2212yescomplemented
34C2×#4097C2211yescharacteristic
35C2×#4094C2212yescomplemented
36C22×#687C2212yescomplemented
37#66055—21no—
38#66047—21no—
39#66005—22no—
40#65936—22no—
41#65934—22no—
42#65877C2212yescomplemented
43#65876C2212yescomplemented
44#65875C2214yescomplemented
45#65804C2211yescharacteristic, complemented
46C2×C4×Dic10C2211yescharacteristic, complemented
47#65528C2214yescomplemented
48#65528C2214yescomplemented
49#65523C2212yescomplemented
50#65522C2212yes—
51#65522C2214yescomplemented
52#65521C2211yescharacteristic
53#65521C2214yescomplemented
54#65507C2214yescomplemented
55#65507C2214yescomplemented
56#65504C2212yescomplemented
57#65504C2214yescomplemented
58#65504C2212yescomplemented
59C2×#3964C2212yescomplemented
60C2×#3964C2214yescomplemented
61#65364C2212yescomplemented
62#65364C2214yescomplemented
63#65364C2212yescomplemented
64#65360C2214yescomplemented
65#65359C2212yescomplemented
66#65359C2212yescomplemented
67#65331C2214yescomplemented
68#65331C2214yescomplemented
69#65330C2214yescomplemented
70#65330C2214yescomplemented
71#65324C2214yescomplemented
72#65324C2214yescomplemented
73#65323C2214yescomplemented
74#65322C2214yescomplemented
75#65319C2212yescomplemented
76C4×#689C2212yescomplemented
77#65311C2212yescomplemented
78#65310C2211yescharacteristic, complemented
79#65309C2211yescharacteristic, complemented
80#65307C2212yescomplemented
81C4×#687C2212yescomplemented
82#65301C2212yescomplemented
83#65300C2214yescomplemented
84D4×#168C2212yescomplemented
85#65298C2212yescomplemented
86#65297C2211yescharacteristic, complemented
87#65296C2211yescharacteristic, complemented
88#65293C2211yescharacteristic, complemented
89#65287C2212yescomplemented
90#65284C2211yescharacteristic, complemented
91C2×C4⋊#168C2211yescharacteristic, complemented
92C4×#681C2211yescharacteristic, complemented
93#61206—51nomaximal, Sylow
94C5×H(5,𝔽2)—28no—
95C5×H(5,𝔽2)—44no—
96C2×C5×#41—22no—
97C2×C5×#41C2314yes—
98C2×C5×#41C2311yescharacteristic
99C2×C5×#41C2312yes—
100C22×C5×D4—22no—
101C22×C5×D4—24no—
102C22×C5×D4—22no—
103C22×C5×D4—22no—
104C22×C5×D4—21no—
105C22×C5×D4—21no—
106C22×C5×D4C2312yes—
107C22×C5×D4C2314yes—
108C22×Dic10C2311yescharacteristic
109C5×C4⋊Q8D411yescharacteristic
110C5×#127—22no—
111C5×#127—22no—
112C5×#127—22no—
113C5×#127—21no—
114C5×#127—21no—
115C5×#127D411yescharacteristic
116C5×#127C2312yes—
117C5×#127C2312yes—
118C5×#124—22no—
119C5×#124D412yes—
120C5×#121—22no—
121C5×#121—22no—
122C5×#121—24no—
123C5×#121—24no—
124C5×#121D412yes—
125C5×#121D412yes—
126C5×#121C2314yes—
127C5×#121C2314yes—
128C5×#120—24no—
129C5×#120—24no—
130C5×#120—24no—
131C4×C5×Q8C2311yescharacteristic
132C4×C5×Q8C2311yescharacteristic
133C4×C5×D4—21no—
134C4×C5×D4—21no—
135C4×C5×D4—22no—
136C4×C5×D4—22no—
137C4×C5×D4C2311yescharacteristic
138C4×C5×D4C2311yescharacteristic
139C4×C5×D4C2312yes—
140C4×C5×D4C2312yes—
141C5×#117—21no—
142C5×#117C2311yescharacteristic
143C2×C42×C5—21no—
144C2×C42×C5C2311yescharacteristic
145#4097—24no—
146#4094—44no—
147Q8×Dic5—22no—
148#4090—22no—
149C2×#689C2312yes—
150#4082—22no—
151#4082—22no—
152#4081—24no—
153#4081—24no—
154D4×Dic5—22no—
155D4×Dic5—24no—
156D4×Dic5—22no—
157C2×#687—44no—
158C2×#687C2312yes—
159C2×#687C2314yes—
160C2×#687C2314yes—
161#4072C2312yes—
162#4072C2314yes—
163C2×C4⋊Dic5C2311yescharacteristic
164C2×C4⋊Dic5C2314yes—
165#4070—21no—
166#4070—21no—
167#4070C2314yes—
168#4070C2314yes—
169C2×#683—21no—
170C2×C4×Dic5—21no—
171C2×#681C2311yescharacteristic
172C2×#681C2311yescharacteristic
173C2×#681C2314yes—
174C22×#168C2312yes—
175C22×#168C2314yes—
176#4036—22no—
177#4035—24no—
178#4033—22no—
179#4025—24no—
180#4025—24no—
181#4024—24no—
182#4023—24no—
183#4016C2312yes—
184#4015C2311yescharacteristic
185#4015C2311yescharacteristic
186C4×Dic10—21no—
187C4×Dic10—21no—
188C4×Dic10—21no—
189C4×Dic10—21no—
190C4×Dic10C2312yes—
191C4×Dic10C2312yes—
192#3967C2312yes—
193#3967C2312yes—
194#3967C2312yes—
195#3964C2312yes—
196#3964C2312yes—
197#3964C2312yes—
198#3964C2314yes—
199#3964C2314yes—
200#3964C2314yes—
201#3964C2314yes—
202#3964C2314yes—
203#3964C2314yes—
204C22⋊#168C2314yes—
205C22⋊#168C2314yes—
206#3942C2312yes—
207#3942C2312yes—
208#3940C2312yes—
209#3940C2312yes—
210#3940C2312yes—
211#3939C2312yes—
212#3939C2312yes—
213#3939C2312yes—
214C4⋊#168C2311yescharacteristic
215C4⋊#168C2311yescharacteristic
216C4⋊#168C2312yes—
217#3935C2312yes—
218C4×#168C2312yes—
219#3507—51no—
220#3498D511yescharacteristic
221#3333—52no—
222#3324—52no—
223#3317—54no—
224#3310—54no—
225#3304—52no—
226#3295—52no—
227#3138—51no—
228#3096—52no—
229#3076—51no—
230#3057—52no—
231C2×#460—51no—
232#3009—52no—
233C4×#137—51no—
234#2935—51no—
235#2897—52no—
236C24×C5—24no—
237C24×C5—22no—
238C5×#41—24no—
239C5×#41—22no—
240C5×#41—24no—
241C5×#41—28no—
242C5×#41—44no—
243C5×#41—48no—
244C5×#41#4114yes—
245C2×C5×Q8C2×D412yes—
246C2×C5×Q8C2411yescharacteristic
247C2×C5×D4—21no—
248C2×C5×D4—28no—
249C2×C5×D4—24no—
250C2×C5×D4—24no—
251C2×C5×D4—24no—
252C2×C5×D4—22no—
253C2×C5×D4—22no—
254C2×C5×D4—24no—
255C2×C5×D4—22no—
256C2×C5×D4—22no—
257C2×C5×D4—22no—
258C2×C5×D4—24no—
259C2×C5×D4—24no—
260C2×C5×D4—44no—
261C2×C5×D4—48no—
262C2×C5×D4—416no—
263C2×C5×D4—82no—
264C2×C5×D4—84no—
265C2×C5×D4—82no—
266C2×C5×D4—84no—
267C2×C5×D4C2×D412yes—
268C2×C5×D4C2×D414yes—
269C2×C5×D4C2×D412yes—
270C2×C5×D4C2×D412yes—
271C2×C5×D4C2414yes—
272C2×C5×D4C2411yescharacteristic
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—24no—
277C22×C4×C5C2×D411yescharacteristic
278C22×C4×C5C2×D411yescharacteristic
279C22×C4×C5C2414yes—
280C22×C4×C5C2411yescharacteristic
281C22×Dic5—21no—
282C22×Dic5—24no—
283C22×Dic5—21no—
284C2×Dic10—22no—
285C2×Dic10—22no—
286C2×Dic10—21no—
287C2×Dic10—21no—
288C2×Dic10—21no—
289C2×Dic10C2412yes—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—21no—
292C5×C4⋊C4C2×D412yes—
293C5×C4⋊C4C2×D412yes—
294C5×C4⋊C4C2411yescharacteristic
295C5×C4⋊C4C2411yescharacteristic
296C5×C22⋊C4—21no—
297C5×C22⋊C4—21no—
298C5×C22⋊C4—21no—
299C5×C22⋊C4—24no—
300C5×C22⋊C4—24no—
301C5×C22⋊C4C2×D414yes—
302C5×C22⋊C4C2×D414yes—
303C42×C5—21no—
304C42×C5—21no—
305C42×C5—21no—
306C42×C5C2×D411yescharacteristic
307C42×C5C2×D411yescharacteristic
308C42×C5C2411yescharacteristic
309C42×C5C2411yescharacteristic
310C22⋊Dic5—24no—
311C22⋊Dic5—24no—
312C22⋊Dic5—24no—
313C22⋊Dic5—22no—
314#689—24no—
315#687—24no—
316#687—44no—
317#687—44no—
318C4⋊Dic5—21no—
319C4⋊Dic5—21no—
320C4⋊Dic5—21no—
321C4⋊Dic5—24no—
322C4⋊Dic5C2412yes—
323C4⋊Dic5C2412yes—
324C4⋊Dic5C2412yes—
325#683—22no—
326#683—22no—
327#683—22no—
328#683—22no—
329#683—24no—
330#683—24no—
331C4×Dic5—22no—
332C4×Dic5—22no—
333C4×Dic5—22no—
334C4×Dic5—24no—
335#681—22no—
336#681—22no—
337#681—44no—
338C2×#168—24no—
339C2×#168—44no—
340C2×#168C2412yes—
341C2×#168C2412yes—
342C2×#168C2412yes—
343C2×#168C2412yes—
344C2×H(5,𝔽2)C2×D512yes—
345C2×#137—51no—
346C22×SD16—52no—
347C2×#131—52no—
348#559—101no—
349#557—101no—
350#556—52no—
351#556—102no—
352#554—52no—
353#552—54no—
354#550C2×D512yes—
355#550C2×D512yes—
356D42—22no—
357D42—22no—
358D42C2×D512yes—
359D42C2×D512yes—
360#539—102no—
361#536—52no—
362#535—22no—
363#535C2×D512yes—
364#533—51no—
365#532—21no—
366#532C2×D511yescharacteristic
367C2×#127—21no—
368C2×#127C2×D511yescharacteristic
369#529—102no—
370#520—52no—
371C4×#41C2×D511yescharacteristic
372C2×C4×Q8—51no—
373#490—54no—
374#486—52no—
375#486—52no—
376#482—54no—
377#482—54no—
378#481—54no—
379#480—54no—
380#479—52no—
381#478—52no—
382#477—51no—
383#476—51no—
384#475—51no—
385#474—51no—
386#468—54no—
387#468—54no—
388#465—54no—
389#465—54no—
390#460—52no—
391#460—52no—
392#460—54no—
393#452—54no—
394#452—54no—
395#450—54no—
396#450—54no—
397#441—52no—
398#440—52no—
399C4×Q16—52no—
400C4×SD16—52no—
401#436—52no—
402#435—54no—
403C8×D4—52no—
404#428—51no—
405#427—52no—
406C2×C4⋊C8—51no—
407#419—51no—
408#418—52no—
409#418—52no—
410#418—54no—
411#417—54no—
412#417—51no—
413#416—52no—
414#416—54no—
415C2×#102—52no—
416C2×#102—54no—
417#408—52no—
418C4×M16—51no—
419C23×C5—21no—
420C23×C5—24no—
421C23×C5—48no—
422C23×C5—44no—
423C23×C5—82no—
424C23×C5—82no—
425C23×C5—84no—
426C23×C5—84no—
427C23×C5C22×D414yes—
428C23×C5C22×D411yescharacteristic
429C5×Q8—24no—
430C5×Q8—21no—
431C5×Q8C2×#4112yes—
432C5×D4—24no—
433C5×D4—28no—
434C5×D4—24no—
435C5×D4—24no—
436C5×D4—24no—
437C5×D4—21no—
438C5×D4—24no—
439C5×D4—42no—
440C5×D4—48no—
441C5×D4—48no—
442C5×D4—44no—
443C5×D4—44no—
444C5×D4—44no—
445C5×D4—82no—
446C5×D4—82no—
447C5×D4—84no—
448C5×D4—84no—
449C5×D4C2×#4112yes—
450C2×C4×C5—21no—
451C2×C4×C5—24no—
452C2×C4×C5—22no—
453C2×C4×C5—24no—
454C2×C4×C5—24no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—41no—
458C2×C4×C5—48no—
459C2×C4×C5—42no—
460C2×C4×C5—42no—
461C2×C4×C5C22×D411yescharacteristic
462C2×C4×C5C22×D414yes—
463C2×C4×C5C22×D411yescharacteristic
464C2×C4×C5C22×D411yescharacteristic
465C2×C4×C5C22×D411yescharacteristic
466C2×C4×C5C22×D411yescharacteristic
467C2×C4×C5C2×#4112yes—
468C2×C4×C5H(5,𝔽2)12yes—
469C2×C4×C5C2511yescharacteristic
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—22no—
473C2×Dic5—22no—
474C2×Dic5—42no—
475C2×Dic5—84no—
476C2×Dic5—81no—
477Dic10—22no—
478Dic10—22no—
479Dic10—42no—
480Dic10—42no—
481Dic10—81no—
482#168—22no—
483#168—22no—
484#168—22no—
485#168—22no—
486H(5,𝔽2)—28no—
487H(5,𝔽2)—44no—
488C2×#41—22no—
489C2×#41C22×D514yes—
490C2×#41C22×D511yescharacteristic
491C2×#41C22×D512yes—
492C22×Q8—51no—
493C22×D4—22no—
494C22×D4—24no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C22×D512yes—
500C22×D4C22×D514yes—
501#137—104no—
502C2×Q16—52no—
503C2×SD16—52no—
504C2×SD16—54no—
505C2×SD16—54no—
506C2×SD16—204no—
507#131—204no—
508C2×M16—51no—
509C2×M16—51no—
510C2×M16—54no—
511C22×C8—52no—
512C22×C8—54no—
513C4⋊Q8—51no—
514C4⋊Q8—51no—
515C4⋊Q8—102no—
516C4⋊Q8C22⋊D511yescharacteristic
517#127—22no—
518#127—22no—
519#127—22no—
520#127—21no—
521#127—21no—
522#127C22⋊D511yescharacteristic
523#127C22×D512yes—
524#127C22×D512yes—
525#126—104no—
526#126—104no—
527#125—52no—
528#125—102no—
529#125—104no—
530#124—22no—
531#124—102no—
532#124—102no—
533#124C22⋊D512yes—
534#123—104no—
535#123—104no—
536C22⋊Q8—54no—
537C22⋊Q8—54no—
538C22⋊Q8—101no—
539C22⋊Q8—101no—
540C22⋊Q8—104no—
541#121—22no—
542#121—22no—
543#121—24no—
544#121—24no—
545#121C22⋊D512yes—
546#121C22⋊D512yes—
547#121C22×D514yes—
548#121C22×D514yes—
549#120—24no—
550#120—24no—
551#120—24no—
552C4×Q8—52no—
553C4×Q8—52no—
554C4×Q8—102no—
555C4×Q8—102no—
556C4×Q8—101no—
557C4×Q8—101no—
558C4×Q8—101no—
559C4×Q8—101no—
560C4×Q8C22×D511yescharacteristic
561C4×Q8C22×D511yescharacteristic
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—104no—
567C4×D4—102no—
568C4×D4—102no—
569C4×D4C22×D511yescharacteristic
570C4×D4C22×D511yescharacteristic
571C4×D4C22×D512yes—
572C4×D4C22×D512yes—
573#117—21no—
574#117—52no—
575#117—54no—
576#117—104no—
577#117C22×D511yescharacteristic
578C2×C4⋊C4—51no—
579C2×C4⋊C4—54no—
580C2×C4⋊C4—101no—
581C2×C42—21no—
582C2×C42—101no—
583C2×C42C22×D511yescharacteristic
584#107—52no—
585#107—52no—
586#107—52no—
587#106—52no—
588#106—52no—
589#106—52no—
590C4⋊C8—51no—
591C4⋊C8—52no—
592C4⋊C8—51no—
593#103—52no—
594#103—52no—
595#103—52no—
596#103—52no—
597#103—52no—
598#102—52no—
599#102—54no—
600#102—52no—
601#102—54no—
602#102—54no—
603#102—52no—
604#102—54no—
605#102—54no—
606#102—54no—
607C22⋊C8—54no—
608C22⋊C8—54no—
609#97—52no—
610C4×C8—52no—
611C22×C5—21no—
612C22×C5—21no—
613C22×C5—24no—
614C22×C5—24no—
615C22×C5—22no—
616C22×C5—24no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—44no—
620C22×C5—44no—
621C22×C5—44no—
622C22×C5—164no—
623C22×C5—168no—
624C22×C5#54612yes—
625C22×C5C23×D411yescharacteristic
626C4×C5—21no—
627C4×C5—21no—
628C4×C5—22no—
629C4×C5—24no—
630C4×C5—21no—
631C4×C5—41no—
632C4×C5—41no—
633C4×C5#54612yes—
634C4×C5#57712yes—
635C4×C5C22×#4111yescharacteristic
636C4×C5C2×H(5,𝔽2)11yescharacteristic
637Dic5—42no—
638Dic5—42no—
639Dic5—42no—
640Dic5—42no—
641C24—24no—
642C24—22no—
643#41—24no—
644#41—24no—
645#41—22no—
646#41—28no—
647#41—44no—
648#41—48no—
649#41#71114yes—
650C2×Q8—52no—
651C2×Q8—101no—
652C2×Q8—101no—
653C2×Q8—101no—
654C2×Q8—102no—
655C2×Q8—102no—
656C2×Q8C2×C22⋊D512yes—
657C2×Q8C23×D511yescharacteristic
658C2×D4—21no—
659C2×D4—28no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—24no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—44no—
672C2×D4—48no—
673C2×D4—416no—
674C2×D4—82no—
675C2×D4—84no—
676C2×D4—82no—
677C2×D4—84no—
678C2×D4C2×C22⋊D512yes—
679C2×D4C2×C22⋊D514yes—
680C2×D4C2×C22⋊D512yes—
681C2×D4C2×C22⋊D512yes—
682C2×D4C23×D514yes—
683C2×D4C23×D511yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—101no—
689C22×C4—101no—
690C22×C4—104no—
691C22×C4C2×C22⋊D511yescharacteristic
692C22×C4C2×C22⋊D511yescharacteristic
693C22×C4C23×D514yes—
694C22×C4C23×D511yescharacteristic
695Q16—104no—
696SD16—104no—
697SD16—204no—
698SD16—204no—
699M16—102no—
700M16—102no—
701M16—204no—
702C2×C8—52no—
703C2×C8—52no—
704C2×C8—52no—
705C2×C8—52no—
706C2×C8—104no—
707C2×C8—204no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—52no—
711C4⋊C4—52no—
712C4⋊C4—52no—
713C4⋊C4—101no—
714C4⋊C4—104no—
715C4⋊C4—102no—
716C4⋊C4—102no—
717C4⋊C4—102no—
718C4⋊C4—104no—
719C4⋊C4—101no—
720C4⋊C4—104no—
721C4⋊C4—102no—
722C4⋊C4—101no—
723C4⋊C4C2×C22⋊D512yes—
724C4⋊C4C2×C22⋊D512yes—
725C4⋊C4C23×D511yescharacteristic
726C4⋊C4C23×D511yescharacteristic
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—102no—
733C22⋊C4—104no—
734C22⋊C4—104no—
735C22⋊C4—104no—
736C22⋊C4C2×C22⋊D514yes—
737C22⋊C4C2×C22⋊D514yes—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—102no—
742C42—102no—
743C42—104no—
744C42—102no—
745C42C2×C22⋊D511yescharacteristic
746C42C2×C22⋊D511yescharacteristic
747C42C23×D511yescharacteristic
748C42C23×D511yescharacteristic
749C2×C5—22no—
750C2×C5—44no—
751C2×C5—42no—
752C2×C5—84no—
753C2×C5C2×#54611yescharacteristic
754C2×C5C2×#57711yescharacteristic
755C2×C5#358511yescharacteristic
756C23—21no—
757C23—24no—
758C23—48no—
759C23—44no—
760C23—82no—
761C23—82no—
762C23—84no—
763C23—84no—
764C23C22×C22⋊D514yes—
765C23C22×C22⋊D511yescharacteristic
766Q8—24no—
767Q8—21no—
768Q8—102no—
769Q8—102no—
770Q8—202no—
771Q8—202no—
772Q8—401no—
773Q8C2×#71112yes—
774D4—24no—
775D4—28no—
776D4—24no—
777D4—24no—
778D4—24no—
779D4—21no—
780D4—24no—
781D4—42no—
782D4—48no—
783D4—48no—
784D4—44no—
785D4—44no—
786D4—44no—
787D4—82no—
788D4—82no—
789D4—84no—
790D4—84no—
791D4C2×#71112yes—
792C2×C4—21no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—41no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—202no—
808C2×C4—401no—
809C2×C4—404no—
810C2×C4C2×#71112yes—
811C2×C4#414412yes—
812C2×C4C22×C22⋊D511yescharacteristic
813C2×C4C22×C22⋊D511yescharacteristic
814C2×C4C22×C22⋊D514yes—
815C2×C4C22×C22⋊D511yescharacteristic
816C2×C4C22×C22⋊D511yescharacteristic
817C2×C4C22×C22⋊D511yescharacteristic
818C2×C4C24×D511yescharacteristic
819C8—102no—
820C8—102no—
821C8—102no—
822C8—102no—
823C5#6120611yescharacteristic, complemented, Sylow
824C22—21no—
825C22—21no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—164no—
836C22—168no—
837C22#6614012yes—
838C22C23×C22⋊D511yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—22no—
843C4—24no—
844C4—41no—
845C4—41no—
846C4—202no—
847C4—202no—
848C4—202no—
849C4—202no—
850C4#6614012yes—
851C4#6617012yes—
852C4C22×#71111yescharacteristic
853C4C2×#414411yescharacteristic
854C2—22no—
855C2—44no—
856C2—42no—
857C2—84no—
858C2C2×#6614011yescharacteristic
859C2#1061917811yescharacteristic
860C2C2×#6617011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC5×#3498C2
socleC22×C5C23×D4
hypercenter#3498D5
hypocenterC5#61206
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ #532 ◁ #3498

Complements

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

NH ≅ G/Ntype
2. #10618125C2semidirect
3. #10615836C2semidirect
4. #10615830C2semidirect
5. #10615306C2semidirect
6. #10615304C2semidirect
7. #10615301C2semidirect
8. #10615217C2semidirect
9. #10615215C2semidirect
10. #10615214C2semidirect
11. #10615108C2semidirect
12. #10615107C2semidirect
13. #10615008C2semidirect
14. C2×#65364C2semidirect
15. #10614890C2semidirect
16. C4×#4097C2semidirect
17. #10614238C2semidirect
32. #66161C22semidirect
33. #66159C22semidirect
35. C2×#4094C22semidirect
36. C22×#687C22semidirect
42. #65877C22semidirect
43. #65876C22semidirect
44. #65875C22semidirect
45. #65804C22semidirect
46. C2×C4×Dic10C22semidirect
47. #65528C22semidirect
48. #65528C22semidirect
49. #65523C22semidirect
51. #65522C22semidirect
53. #65521C22semidirect
54. #65507C22semidirect
55. #65507C22semidirect
56. #65504C22semidirect
57. #65504C22semidirect
58. #65504C22semidirect
59. C2×#3964C22semidirect
60. C2×#3964C22semidirect
61. #65364C22semidirect
62. #65364C22semidirect
63. #65364C22semidirect
64. #65360C22semidirect
65. #65359C22semidirect
66. #65359C22semidirect
67. #65331C22semidirect
68. #65331C22semidirect
69. #65330C22semidirect
70. #65330C22semidirect
71. #65324C22semidirect
72. #65324C22semidirect
73. #65323C22semidirect
74. #65322C22semidirect
75. #65319C22semidirect
76. C4×#689C22semidirect
77. #65311C22semidirect
78. #65310C22semidirect
79. #65309C22semidirect
80. #65307C22semidirect
81. C4×#687C22semidirect
82. #65301C22semidirect
83. #65300C22semidirect
84. D4×#168C22semidirect
85. #65298C22semidirect
86. #65297C22semidirect
87. #65296C22semidirect
88. #65293C22semidirect
89. #65287C22semidirect
90. #65284C22semidirect
91. C2×C4⋊#168C22semidirect
92. C4×#681C22semidirect
823. C5#61206semidirect

Maximal subgroups

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

subgroupindex
C5×#34982
#106181252
#106158362
#106158302
#106153062
#106153042
#106153012
#106152172
#106152152
#106152142
#106151082
#106151072
#106150082
C2×#653642
#106148902
C4×#40972
#106142382
#612065