Finite Group Databasebeta

← #12994871

Subgroups — #12994871

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3475C211yesmaximal, characteristic
2#10617731C211yesmaximal, characteristic, complemented
3#10615407C212yesmaximal, complemented
4#10615377C212yesmaximal, complemented
5#10615360C212yesmaximal, complemented
6#10615321C214yesmaximal, complemented
7#10615241C212yesmaximal, complemented
8#10615225C214yesmaximal, complemented
9#10615104C211yesmaximal, characteristic, complemented
10#10615054C211yesmaximal, characteristic, complemented
11#10614886C212yesmaximal, complemented
12#10614853C212yesmaximal, complemented
13#10614265C212yesmaximal, complemented
14#10614251C211yesmaximal, characteristic, complemented
15#10614238C212yesmaximal, complemented
16#10614045C211yesmaximal, characteristic, complemented
17C2×#65296C211yesmaximal, characteristic, complemented
18C5×#556C2211yescharacteristic
19C5×#555C2211yescharacteristic
20C5×#554C2211yescharacteristic
21C5×#553—21no—
22C5×#552—21no—
23C5×#552C2212yes—
24C5×#551—22no—
25C5×#547C2211yescharacteristic
26C5×#546C2212yes—
27C5×#533C2211yescharacteristic
28C5×#529—22no—
29C5×#529C2212yes—
30C5×#525—21no—
31C4×C5×#41C2212yes—
32C4×C5×#41C2211yescharacteristic
33C2×C4×C5×D4C2211yescharacteristic
34C2×C5×#117—21no—
35#66159—21no—
36#65901—21no—
37#65901C2212yescomplemented
38#65876—21no—
39#65876C2212yescomplemented
40#65875—22no—
41#65875C2214yes—
42#65852—22no—
43#65850—21no—
44#65804C2211yescharacteristic
45#65804C2212yescomplemented
46#65804C2212yescomplemented
47C2×#4015C2211yescharacteristic
48#65528C2214yes—
49#65522C2214yes—
50#65507C2212yes—
51C2×#3964C2212yes—
52#65380C2212yescomplemented
53#65379C2212yescomplemented
54#65370C2212yescomplemented
55#65368C2212yescomplemented
56#65353C2214yescomplemented
57#65352C2214yescomplemented
58#65345C2214yes—
59#65343C2214yes—
60#65340C2214yes—
61#65340C2214yescomplemented
62#65334C2214yescomplemented
63#65332C2214yes—
64#65330C2214yes—
65#65324C2214yes—
66#65320C2212yescomplemented
67C4×#689C2214yescomplemented
68Q8×#168C2212yescomplemented
69#65311C2214yescomplemented
70#65310C2212yescomplemented
71#65309C2212yescomplemented
72#65309C2212yescomplemented
73#65308C2211yescharacteristic
74#65308C2211yescharacteristic
75C4×#687C2212yes—
76C4×#687C2212yes—
77C4×#687C2214yes—
78D4×#168C2214yes—
79D4×#168C2212yescomplemented
80#65298C2214yes—
81#65297C2211yescharacteristic
82#65297C2211yescharacteristic
83#65296C2212yes—
84#65296C2212yes—
85#65296C2212yes—
86#65296C2212yes—
87#65287C2214yescomplemented
88#65285C2214yescomplemented
89#65260C2212yes—
90C2×#3939C2212yes—
91#65214C2211yescharacteristic
92#65214C2212yescomplemented
93C2×C4⋊#168C2211yescharacteristic
94C2×C4⋊#168C2212yescomplemented
95#62097—51nomaximal, Sylow
96C2×C5×#41D411yescharacteristic
97C2×C5×#41C2312yes—
98C22×C5×D4C2311yescharacteristic
99C23×C4×C5—21no—
100C22×Dic10—21no—
101C5×C4⋊Q8C2311yescharacteristic
102C5×C4⋊Q8C2311yescharacteristic
103C5×#126—22no—
104C5×#126—22no—
105C5×#126—22no—
106C5×#125—22no—
107C5×#125—21no—
108C5×#125C2312yes—
109C5×#124—22no—
110C5×#124C2312yes—
111C5×#123—22no—
112C5×#123—22no—
113C5×#123—22no—
114C5×#123—22no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8—21no—
117C5×C22⋊Q8—21no—
118C5×C22⋊Q8—22no—
119C5×C22⋊Q8C2312yes—
120C5×C22⋊Q8C2312yes—
121C5×#121—21no—
122C5×#121—21no—
123C5×#121—22no—
124C5×#121C2312yes—
125C5×#120—22no—
126C4×C5×Q8—21no—
127C4×C5×Q8D411yescharacteristic
128C4×C5×Q8C2312yes—
129C4×C5×Q8C2312yes—
130C4×C5×Q8C2311yescharacteristic
131C4×C5×D4—22no—
132C4×C5×D4—22no—
133C4×C5×D4—22no—
134C4×C5×D4—21no—
135C4×C5×D4—21no—
136C4×C5×D4D412yes—
137C4×C5×D4D411yescharacteristic
138C4×C5×D4C2311yescharacteristic
139C4×C5×D4C2311yescharacteristic
140C4×C5×D4C2311yescharacteristic
141C4×C5×D4C2311yescharacteristic
142C4×C5×D4C2312yes—
143C4×C5×D4C2312yes—
144C4×C5×D4C2311yescharacteristic
145C5×#117—21no—
146C5×#117—21no—
147C5×#117—21no—
148C5×#117—22no—
149C5×#117—22no—
150C5×#117—22no—
151C5×#117D411yescharacteristic
152C5×#117D412yes—
153C5×#117C2312yes—
154C2×C5×C4⋊C4—21no—
155C2×C5×C4⋊C4—21no—
156C2×C5×C4⋊C4C2311yescharacteristic
157C2×C5×C22⋊C4—21no—
158C2×C5×C22⋊C4—22no—
159C2×C42×C5—22no—
160C2×C42×C5C2311yescharacteristic
161C2×C42×C5C2312yes—
162#4090—22no—
163C2×#689C2314yes—
164#4082—22no—
165#4081—24no—
166C2×#687C2312yes—
167C2×#687C2312yes—
168#4072—21no—
169#4072—22no—
170#4072C2314yes—
171C2×C4⋊Dic5—21no—
172C2×C4⋊Dic5C2312yes—
173#4070—21no—
174#4070—22no—
175#4070—22no—
176#4070—22no—
177#4070C2314yes—
178#4070C2312yes—
179C22×#168C2314yes—
180C22×#168C2312yes—
181#4035—24no—
182#4035—24no—
183#4033—22no—
184#4033—22no—
185#4025—24no—
186#4025—24no—
187#4023—24no—
188#4016—21no—
189#4016—22no—
190#4016C2314yes—
191#4015—21no—
192#4015—21no—
193#4015C2311yescharacteristic
194#4015C2312yes—
195#4015C2312yes—
196#4015C2311yescharacteristic
197C4×Dic10—21no—
198C4×Dic10—22no—
199C4×Dic10—22no—
200C4×Dic10—22no—
201C4×Dic10C2312yes—
202C4×Dic10C2314yes—
203#3967C2314yes—
204#3967C2314yes—
205#3967C2314yes—
206#3964C2314yes—
207#3964C2314yes—
208#3964C2312yes—
209#3964C2312yes—
210C22⋊#168C2314yes—
211C22⋊#168C2312yes—
212#3942C2312yes—
213#3942C2314yes—
214#3942C2312yes—
215#3940C2314yes—
216#3940C2312yes—
217#3940C2314yes—
218#3940C2312yes—
219#3939C2314yes—
220#3939C2314yes—
221#3939C2314yes—
222C4⋊#168C2312yes—
223C4⋊#168C2312yes—
224C4⋊#168C2311yescharacteristic
225C4⋊#168C2311yescharacteristic
226C4⋊#168C2314yes—
227C4×#168C2314yes—
228C4×#168C2312yes—
229#3509—51no—
230#3475D511yescharacteristic
231#3381—52no—
232#3364—52no—
233#3340—52no—
234#3336—54no—
235#3302—52no—
236#3296—54no—
237#3249—51no—
238#3248—52no—
239#3233—52no—
240#3229—51no—
241#3107—52no—
242#3101—51no—
243#3076—52no—
244C2×#474—51no—
245#2988—51no—
246C24×C5—21no—
247C5×#41—24no—
248C5×#41—24no—
249C5×#41—42no—
250C2×C5×Q8—21no—
251C2×C5×Q8C2×D411yescharacteristic
252C2×C5×Q8C2412yes—
253C2×C5×D4—22no—
254C2×C5×D4—22no—
255C2×C5×D4—22no—
256C2×C5×D4—21no—
257C2×C5×D4—41no—
258C2×C5×D4C2×D412yes—
259C2×C5×D4C2×D411yescharacteristic
260C2×C5×D4C2411yescharacteristic
261C2×C5×D4C2411yescharacteristic
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—22no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—22no—
269C22×C4×C5—44no—
270C22×C4×C5C2×D412yes—
271C22×C4×C5C2×D411yescharacteristic
272C22×C4×C5C2×D412yes—
273C22×C4×C5C2×D411yescharacteristic
274C22×C4×C5C2411yescharacteristic
275C22×C4×C5C2412yes—
276C22×Dic5—22no—
277C2×Dic10—22no—
278C2×Dic10—22no—
279C2×Dic10—21no—
280C2×Dic10—44no—
281C2×Dic10C2412yes—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—22no—
285C5×C4⋊C4—22no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—22no—
288C5×C4⋊C4—22no—
289C5×C4⋊C4—22no—
290C5×C4⋊C4—22no—
291C5×C4⋊C4—21no—
292C5×C4⋊C4C2×D411yescharacteristic
293C5×C4⋊C4C2×D411yescharacteristic
294C5×C4⋊C4C2×D412yes—
295C5×C4⋊C4C2×D412yes—
296C5×C4⋊C4C2411yescharacteristic
297C5×C4⋊C4C2411yescharacteristic
298C5×C4⋊C4C2412yes—
299C5×C22⋊C4—22no—
300C5×C22⋊C4—22no—
301C5×C22⋊C4—22no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4—22no—
304C5×C22⋊C4—22no—
305C5×C22⋊C4—21no—
306C5×C22⋊C4—21no—
307C5×C22⋊C4—21no—
308C5×C22⋊C4—22no—
309C5×C22⋊C4—22no—
310C5×C22⋊C4C2×D412yes—
311C5×C22⋊C4C2×D412yes—
312C5×C22⋊C4C2×D412yes—
313C42×C5—22no—
314C42×C5—22no—
315C42×C5—22no—
316C42×C5C2×D412yes—
317C42×C5C2×D412yes—
318C42×C5C2×D411yescharacteristic
319C42×C5C2×D411yescharacteristic
320C42×C5C2411yescharacteristic
321C42×C5C2411yescharacteristic
322C42×C5C2412yes—
323C22⋊Dic5—22no—
324C22⋊Dic5—24no—
325C22⋊Dic5—24no—
326#689—44no—
327#687—24no—
328#687—42no—
329C4⋊Dic5—21no—
330C4⋊Dic5—21no—
331C4⋊Dic5—22no—
332C4⋊Dic5—21no—
333C4⋊Dic5—22no—
334C4⋊Dic5—22no—
335C4⋊Dic5C2414yes—
336C4⋊Dic5C2412yes—
337#683—24no—
338#683—22no—
339#683—24no—
340#683—24no—
341#683—22no—
342#683—24no—
343C4×Dic5—24no—
344C4×Dic5—24no—
345C4×Dic5—22no—
346C2×#168—44no—
347C2×#168—42no—
348C2×#168C2412yes—
349C2×#168C2414yes—
350C2×#168C2412yes—
351#557—52no—
352#557—101no—
353#556—52no—
354#556—101no—
355#556C2×D511yescharacteristic
356#555C2×D511yescharacteristic
357#554C2×D511yescharacteristic
358#553—21no—
359#552—21no—
360#552—54no—
361#552—102no—
362#552C2×D512yes—
363#551—22no—
364#547C2×D511yescharacteristic
365#546C2×D512yes—
366#541—102no—
367#536—101no—
368#533—52no—
369#533—51no—
370#533—52no—
371#533C2×D511yescharacteristic
372C2×C4⋊Q8—51no—
373#529—22no—
374#529C2×D512yes—
375#525—21no—
376#519—101no—
377C4×#41C2×D512yes—
378C4×#41C2×D511yescharacteristic
379C2×C4×D4C2×D511yescharacteristic
380C2×#117—21no—
381#499—54no—
382#498—52no—
383#488—54no—
384#487—52no—
385#485—54no—
386#485—54no—
387#483—54no—
388#483—52no—
389#482—54no—
390#479—54no—
391#479—54no—
392#478—54no—
393#477—52no—
394#477—52no—
395#476—51no—
396#476—51no—
397#475—52no—
398#475—52no—
399#474—52no—
400#474—52no—
401#474—52no—
402#474—52no—
403#467—54no—
404#467—54no—
405#465—54no—
406#464—54no—
407#462—52no—
408#462—52no—
409#461—51no—
410#461—51no—
411#452—54no—
412#450—52no—
413C8×Q8—52no—
414C4×Q16—54no—
415C4×SD16—52no—
416C4×SD16—52no—
417C4×SD16—54no—
418C8×D4—54no—
419C8×D4—52no—
420#431—51no—
421#431—52no—
422#427—54no—
423C2×#107—52no—
424C2×C4⋊C8—52no—
425C2×C4⋊C8—51no—
426#416—54no—
427C2×#102—52no—
428C23×C5—21no—
429C23×C5—21no—
430C23×C5—42no—
431C23×C5—42no—
432C23×C5—81no—
433C23×C5C22×D412yes—
434C23×C5C22×D411yescharacteristic
435C5×Q8—22no—
436C5×Q8—22no—
437C5×Q8—22no—
438C5×Q8—81no—
439C5×D4—24no—
440C5×D4—22no—
441C5×D4—21no—
442C5×D4—21no—
443C5×D4—21no—
444C5×D4—42no—
445C5×D4—44no—
446C5×D4—82no—
447C5×D42−1+412yes—
448C2×C4×C5—24no—
449C2×C4×C5—21no—
450C2×C4×C5—22no—
451C2×C4×C5—21no—
452C2×C4×C5—22no—
453C2×C4×C5—21no—
454C2×C4×C5—22no—
455C2×C4×C5—22no—
456C2×C4×C5—21no—
457C2×C4×C5—42no—
458C2×C4×C5—41no—
459C2×C4×C5—44no—
460C2×C4×C5—42no—
461C2×C4×C5—42no—
462C2×C4×C5—42no—
463C2×C4×C5—42no—
464C2×C4×C5—42no—
465C2×C4×C5—82no—
466C2×C4×C5#13514yes—
467C2×C4×C5C22×D412yes—
468C2×C4×C5C22×D412yes—
469C2×C4×C5C22×D412yes—
470C2×C4×C5C22×D411yescharacteristic
471C2×C4×C5C22×D411yescharacteristic
472C2×C4×C5C22×D411yescharacteristic
473C2×C4×C5C22×D411yescharacteristic
474C2×C4×C5C22×D411yescharacteristic
475C2×C4×C5C2511yescharacteristic
476C2×Dic5—22no—
477C2×Dic5—22no—
478C2×Dic5—24no—
479C2×Dic5—44no—
480Dic10—22no—
481Dic10—22no—
482Dic10—42no—
483Dic10—44no—
484Dic10—44no—
485#168—22no—
486#168—22no—
487#168—24no—
488C2×#41C22⋊D511yescharacteristic
489C2×#41C22×D512yes—
490C22×Q8—101no—
491C22×D4C22×D511yescharacteristic
492C23×C4—21no—
493C2×Q16—54no—
494C2×SD16—52no—
495C2×SD16—52no—
496C22×C8—52no—
497C22×C8—54no—
498C4⋊Q8—52no—
499C4⋊Q8—52no—
500C4⋊Q8—51no—
501C4⋊Q8—51no—
502C4⋊Q8—102no—
503C4⋊Q8—101no—
504C4⋊Q8—101no—
505C4⋊Q8C22×D511yescharacteristic
506C4⋊Q8C22×D511yescharacteristic
507#126—22no—
508#126—22no—
509#126—22no—
510#126—104no—
511#126—104no—
512#125—22no—
513#125—21no—
514#125—54no—
515#125—104no—
516#125—104no—
517#125—101no—
518#125—102no—
519#125C22×D512yes—
520#124—22no—
521#124—102no—
522#124C22×D512yes—
523#123—22no—
524#123—22no—
525#123—22no—
526#123—22no—
527#123—104no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—22no—
532C22⋊Q8—52no—
533C22⋊Q8—54no—
534C22⋊Q8—102no—
535C22⋊Q8—102no—
536C22⋊Q8—101no—
537C22⋊Q8—102no—
538C22⋊Q8C22×D512yes—
539C22⋊Q8C22×D512yes—
540#121—21no—
541#121—21no—
542#121—22no—
543#121C22×D512yes—
544#120—22no—
545C4×Q8—21no—
546C4×Q8—54no—
547C4×Q8—52no—
548C4×Q8—102no—
549C4×Q8—102no—
550C4×Q8—102no—
551C4×Q8—102no—
552C4×Q8—102no—
553C4×Q8—101no—
554C4×Q8C22⋊D511yescharacteristic
555C4×Q8C22×D512yes—
556C4×Q8C22×D512yes—
557C4×Q8C22×D511yescharacteristic
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4C22⋊D512yes—
564C4×D4C22⋊D511yescharacteristic
565C4×D4C22×D511yescharacteristic
566C4×D4C22×D511yescharacteristic
567C4×D4C22×D511yescharacteristic
568C4×D4C22×D511yescharacteristic
569C4×D4C22×D512yes—
570C4×D4C22×D512yes—
571C4×D4C22×D511yescharacteristic
572#117—21no—
573#117—21no—
574#117—21no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—54no—
579#117—101no—
580#117—102no—
581#117—104no—
582#117C22⋊D511yescharacteristic
583#117C22⋊D512yes—
584#117C22×D512yes—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—52no—
588C2×C4⋊C4—101no—
589C2×C4⋊C4C22×D511yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—22no—
592C2×C42—22no—
593C2×C42C22×D511yescharacteristic
594C2×C42C22×D512yes—
595#107—54no—
596#107—54no—
597#107—54no—
598#106—52no—
599#106—54no—
600#106—54no—
601#106—52no—
602C4⋊C8—51no—
603C4⋊C8—52no—
604C4⋊C8—52no—
605C4⋊C8—54no—
606C4⋊C8—51no—
607#103—54no—
608#103—54no—
609#103—54no—
610#103—52no—
611#103—52no—
612#103—54no—
613#102—54no—
614#102—54no—
615#102—52no—
616#102—52no—
617C22⋊C8—52no—
618C22⋊C8—54no—
619C4×C8—52no—
620C4×C8—54no—
621C22×C5—21no—
622C22×C5—21no—
623C22×C5—22no—
624C22×C5—22no—
625C22×C5—22no—
626C22×C5—22no—
627C22×C5—41no—
628C22×C5—41no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—84no—
633C22×C5C2×#13512yes—
634C22×C5C23×D411yescharacteristic
635C4×C5—21no—
636C4×C5—22no—
637C4×C5—21no—
638C4×C5—22no—
639C4×C5—21no—
640C4×C5—22no—
641C4×C5—42no—
642C4×C5—42no—
643C4×C5—41no—
644C4×C5—41no—
645C4×C5C2×#13512yes—
646C4×C5C2×#13512yes—
647C4×C5C2×2−1+411yescharacteristic
648C4×C5#58511yescharacteristic
649Dic5—42no—
650Dic5—42no—
651Dic5—44no—
652C24—21no—
653#41—24no—
654#41—24no—
655#41—42no—
656C2×Q8—21no—
657C2×Q8—52no—
658C2×Q8—101no—
659C2×Q8—102no—
660C2×Q8—102no—
661C2×Q8—204no—
662C2×Q8C2×C22⋊D511yescharacteristic
663C2×Q8C23×D512yes—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4C2×C22⋊D512yes—
670C2×D4C2×C22⋊D511yescharacteristic
671C2×D4C23×D511yescharacteristic
672C2×D4C23×D511yescharacteristic
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—44no—
681C22×C4—102no—
682C22×C4C2×C22⋊D512yes—
683C22×C4C2×C22⋊D511yescharacteristic
684C22×C4C2×C22⋊D512yes—
685C22×C4C2×C22⋊D511yescharacteristic
686C22×C4C23×D511yescharacteristic
687C22×C4C23×D512yes—
688Q16—204no—
689SD16—104no—
690SD16—202no—
691C2×C8—52no—
692C2×C8—54no—
693C2×C8—52no—
694C2×C8—204no—
695C2×C8—202no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—21no—
706C4⋊C4—54no—
707C4⋊C4—52no—
708C4⋊C4—102no—
709C4⋊C4—102no—
710C4⋊C4—102no—
711C4⋊C4—101no—
712C4⋊C4—104no—
713C4⋊C4—101no—
714C4⋊C4—101no—
715C4⋊C4—104no—
716C4⋊C4—104no—
717C4⋊C4—102no—
718C4⋊C4—102no—
719C4⋊C4—104no—
720C4⋊C4C2×C22⋊D511yescharacteristic
721C4⋊C4C2×C22⋊D511yescharacteristic
722C4⋊C4C2×C22⋊D512yes—
723C4⋊C4C2×C22⋊D512yes—
724C4⋊C4C23×D512yes—
725C4⋊C4C23×D511yescharacteristic
726C4⋊C4C23×D511yescharacteristic
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—21no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—104no—
739C22⋊C4—102no—
740C22⋊C4—104no—
741C22⋊C4C2×C22⋊D512yes—
742C22⋊C4C2×C22⋊D512yes—
743C22⋊C4C2×C22⋊D512yes—
744C42—22no—
745C42—22no—
746C42—22no—
747C42—104no—
748C42—104no—
749C42—102no—
750C42C2×C22⋊D512yes—
751C42C2×C22⋊D512yes—
752C42C2×C22⋊D511yescharacteristic
753C42C2×C22⋊D511yescharacteristic
754C42C23×D511yescharacteristic
755C42C23×D512yes—
756C42C23×D511yescharacteristic
757C2×C5—22no—
758C2×C5—42no—
759C2×C5—42no—
760C2×C5—81no—
761C2×C5#348911yescharacteristic
762C2×C5C22×#13511yescharacteristic
763C2×C5#358611yescharacteristic
764C23—21no—
765C23—21no—
766C23—42no—
767C23—42no—
768C23—81no—
769C23C22×C22⋊D512yes—
770C23C22×C22⋊D511yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—81no—
775Q8—102no—
776Q8—102no—
777Q8—202no—
778Q8—204no—
779Q8—204no—
780D4—24no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—21no—
785D4—42no—
786D4—44no—
787D4—82no—
788D4#415012yes—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—82no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—104no—
810C2×C4—204no—
811C2×C4#409614yes—
812C2×C4C22×C22⋊D512yes—
813C2×C4C22×C22⋊D512yes—
814C2×C4C22×C22⋊D511yescharacteristic
815C2×C4C22×C22⋊D511yescharacteristic
816C2×C4C22×C22⋊D511yescharacteristic
817C2×C4C22×C22⋊D512yes—
818C2×C4C22×C22⋊D511yescharacteristic
819C2×C4C22×C22⋊D511yescharacteristic
820C2×C4C24×D511yescharacteristic
821C8—102no—
822C8—102no—
823C8—104no—
824C5#6209711yescharacteristic, complemented, Sylow
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22C2×#409612yes—
838C22C23×C22⋊D511yescharacteristic
839C4—22no—
840C4—22no—
841C4—21no—
842C4—21no—
843C4—22no—
844C4—21no—
845C4—41no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—204no—
850C4—202no—
851C4—202no—
852C4C2×#409612yes—
853C4C2×#409612yes—
854C4C2×#415011yescharacteristic
855C4#6628311yescharacteristic
856C2—22no—
857C2—42no—
858C2—42no—
859C2—81no—
860C2C22×#409611yescharacteristic
861C2#1061916511yescharacteristic
862C2#1061920011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC5×#3475C2
socleC22×C5C23×D4
hypercenter#3475D5
hypocenterC5#62097
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
2. #10617731C2semidirect
3. #10615407C2semidirect
4. #10615377C2semidirect
5. #10615360C2semidirect
6. #10615321C2semidirect
7. #10615241C2semidirect
8. #10615225C2semidirect
9. #10615104C2semidirect
10. #10615054C2semidirect
11. #10614886C2semidirect
12. #10614853C2semidirect
13. #10614265C2semidirect
14. #10614251C2semidirect
15. #10614238C2semidirect
16. #10614045C2semidirect
17. C2×#65296C2semidirect
37. #65901C22semidirect
39. #65876C22semidirect
45. #65804C22semidirect
46. #65804C22semidirect
52. #65380C22semidirect
53. #65379C22semidirect
54. #65370C22semidirect
55. #65368C22semidirect
56. #65353C22semidirect
57. #65352C22semidirect
61. #65340C22semidirect
62. #65334C22semidirect
66. #65320C22semidirect
67. C4×#689C22semidirect
68. Q8×#168C22semidirect
69. #65311C22semidirect
70. #65310C22semidirect
71. #65309C22semidirect
72. #65309C22semidirect
79. D4×#168C22semidirect
87. #65287C22semidirect
88. #65285C22semidirect
92. #65214C22semidirect
94. C2×C4⋊#168C22semidirect
824. C5#62097semidirect

Maximal subgroups

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

subgroupindex
C5×#34752
#106177312
#106154072
#106153772
#106153602
#106153212
#106152412
#106152252
#106151042
#106150542
#106148862
#106148532
#106142652
#106142512
#106142382
#106140452
C2×#652962
#620975