Finite Group Databasebeta

← #12271860

Subgroups — #12271860

Order 1280.

3038 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#534C211yesmaximal, characteristic
2C22×D4×Dic5C211yesmaximal, characteristic, complemented
3#10615774C211yesmaximal, characteristic, complemented
4#10615774C211yesmaximal, characteristic, complemented
5C2×#65509C211yesmaximal, characteristic, complemented
6#10614621C212yesmaximal, complemented
7#10614597C212yesmaximal, complemented
8#10614575C214yesmaximal, complemented
9#10614387C214yesmaximal, complemented
10#10614386C214yesmaximal, complemented
11#10614333C212yesmaximal, complemented
12#10614324C212yesmaximal, complemented
13#10614316C214yesmaximal, complemented
14#10613826C211yesmaximal, characteristic, complemented
15C2×#65235C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic, complemented
20C5×#534—28no—
21C2×C5×#123C2212yes—
22C2×C5×#123C2212yes—
23C2×C5×#121C2212yes—
24C2×C5×#121C2212yes—
25C2×C5×#120C2212yes—
26C2×C5×#120C2212yes—
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic, complemented
32C22×C22⋊Dic5C2212yescomplemented
33C2×#4081C2214yescomplemented
34C2×D4×Dic5—28no—
35C2×D4×Dic5C2214yes—
36C2×D4×Dic5C2214yescomplemented
37C22×C4⋊Dic5C2211yescharacteristic, complemented
38C22×#683C2212yescomplemented
39C22×C4×Dic5C2211yescharacteristic, complemented
40#65536C2212yescomplemented
41#65536C2212yescomplemented
42#65511C2214yescomplemented
43#65511C2214yescomplemented
44#65509C2214yes—
45#65509C2212yes—
46#65509C2212yes—
47#65509C2212yes—
48#65509C2212yes—
49#65509C2214yescomplemented
50#65509C2214yescomplemented
51#65509C2214yescomplemented
52#65509C2214yescomplemented
53#65500C2212yescomplemented
54#65500C2212yescomplemented
55#65499C2212yescomplemented
56#65499C2212yescomplemented
57C2×#3963C2212yescomplemented
58C2×#3963C2212yescomplemented
59#65275C2214yescomplemented
60#65272C2214yescomplemented
61#65267C2214yescomplemented
62#65267C2214yescomplemented
63#65242C2214yescomplemented
64#65241C2214yescomplemented
65#65241C2214yescomplemented
66#65238C2214yescomplemented
67#65235C2214yescomplemented
68#65235C2214yescomplemented
69#65235C2212yescomplemented
70#65235C2212yescomplemented
71#65235C2212yescomplemented
72#65235C2212yescomplemented
73#65233C2214yescomplemented
74#65233C2214yescomplemented
75#65232C2214yescomplemented
76#65231C2214yescomplemented
77#34983—51nomaximal, Sylow
78C25×C5C2311yescharacteristic
79C25×C5C2311yescharacteristic
80C25×C5C2311yescharacteristic
81C22×C5×D4—24no—
82C22×C5×D4—24no—
83C22×C5×D4—24no—
84C22×C5×D4—24no—
85C22×C5×D4—24no—
86C22×C5×D4D418yes—
87C22×C5×D4C2312yes—
88C22×C5×D4C2312yes—
89C22×C5×D4C2312yes—
90C22×C5×D4C2312yes—
91C22×C5×D4C2312yes—
92C22×C5×D4C2312yes—
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C23×Dic5—24no—
98C23×Dic5—24no—
99C23×Dic5—44no—
100C23×Dic5—44no—
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2312yes—
103C23×Dic5C2312yes—
104C23×Dic5C2314yes—
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2312yes—
107C23×Dic5C2311yescharacteristic
108C23×Dic5C2311yescharacteristic
109C23×Dic5C2312yes—
110C5×#123—28no—
111C5×#123—28no—
112C5×#121—28no—
113C5×#121—28no—
114C5×#120—28no—
115C5×#120—28no—
116C2×C5×C4⋊C4C2312yes—
117C2×C5×C4⋊C4C2312yes—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4C2312yes—
120C2×C5×C22⋊C4C2312yes—
121C2×C5×C22⋊C4C2312yes—
122C2×C5×C22⋊C4C2312yes—
123C2×C5×C22⋊C4C2312yes—
124C2×C5×C22⋊C4C2312yes—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5—44no—
130C2×C22⋊Dic5C2312yes—
131C2×C22⋊Dic5C2312yes—
132C2×C22⋊Dic5C2312yes—
133C2×C22⋊Dic5C2312yes—
134C2×C22⋊Dic5C2314yes—
135C2×C22⋊Dic5C2312yes—
136C2×C22⋊Dic5C2314yes—
137C2×C22⋊Dic5C2312yes—
138C2×C22⋊Dic5C2314yes—
139C2×C22⋊Dic5C2314yes—
140C2×C22⋊Dic5C2314yes—
141C2×C22⋊Dic5C2314yes—
142C2×C22⋊Dic5C2314yes—
143#4081—48no—
144D4×Dic5—216no—
145D4×Dic5—216no—
146C2×C4⋊Dic5—24no—
147C2×C4⋊Dic5C2314yes—
148C2×#683—44no—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165C2×#534D511yescharacteristic
166C22×C4×D4—51no—
167#2853—52no—
168#2849—52no—
169#2623—52no—
170#2622—52no—
171#2444—54no—
172#2443—54no—
173#2419—54no—
174#2418—54no—
175#2315—51no—
176#2308—51no—
177#2308—51no—
178C2×#386—51no—
179C2×#385—51no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—42no—
186C24×C5—42no—
187C24×C5—42no—
188C24×C5—42no—
189C24×C5—42no—
190C24×C5—42no—
191C24×C5C2×D414yes—
192C24×C5C2×D414yes—
193C24×C5#4114yes—
194C24×C5#4114yes—
195C24×C5C2412yes—
196C24×C5C2412yes—
197C24×C5C2411yescharacteristic
198C24×C5C2411yescharacteristic
199C24×C5C2411yescharacteristic
200C2×C5×D4—232no—
201C2×C5×D4—24no—
202C2×C5×D4—24no—
203C2×C5×D4—24no—
204C2×C5×D4—24no—
205C2×C5×D4—24no—
206C2×C5×D4—24no—
207C2×C5×D4—24no—
208C2×C5×D4—24no—
209C2×C5×D4—24no—
210C2×C5×D4—24no—
211C2×C5×D4—24no—
212C2×C5×D4—24no—
213C2×C5×D4—44no—
214C2×C5×D4—44no—
215C2×C5×D4—416no—
216C2×C5×D4C2×D418yes—
217C2×C5×D4C2×D418yes—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—42no—
226C22×C4×C5—42no—
227C22×C4×C5C2×D414yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×Dic5—22no—
233C22×Dic5—24no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—28no—
238C22×Dic5—24no—
239C22×Dic5—24no—
240C22×Dic5—24no—
241C22×Dic5—24no—
242C22×Dic5—24no—
243C22×Dic5—24no—
244C22×Dic5—28no—
245C22×Dic5—42no—
246C22×Dic5—44no—
247C22×Dic5—42no—
248C22×Dic5—42no—
249C22×Dic5—42no—
250C22×Dic5—42no—
251C22×Dic5—42no—
252C22×Dic5—42no—
253C22×Dic5—42no—
254C22×Dic5—42no—
255C22×Dic5—416no—
256C22×Dic5—416no—
257C22×Dic5C2414yes—
258C22×Dic5C2414yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C5×C4⋊C4—24no—
264C5×C4⋊C4—24no—
265C5×C22⋊C4—24no—
266C5×C22⋊C4—24no—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C5×C22⋊C4—24no—
270C5×C22⋊C4—24no—
271C22⋊Dic5—28no—
272C22⋊Dic5—24no—
273C22⋊Dic5—24no—
274C22⋊Dic5—24no—
275C22⋊Dic5—24no—
276C22⋊Dic5—24no—
277C22⋊Dic5—24no—
278C22⋊Dic5—28no—
279C22⋊Dic5—44no—
280C22⋊Dic5—44no—
281C22⋊Dic5—44no—
282C22⋊Dic5—44no—
283C22⋊Dic5—44no—
284C4⋊Dic5—28no—
285#683—28no—
286#683—44no—
287#683—44no—
288#683—44no—
289C4×Dic5—28no—
290C23×D4C2×D511yescharacteristic
291C23×D4C2×D511yescharacteristic
292C24×C4—51no—
293C24×C4—51no—
294#534—28no—
295C2×#123—54no—
296C2×#123C2×D512yes—
297C2×#123C2×D512yes—
298C2×#121C2×D512yes—
299C2×#121C2×D512yes—
300C2×#120C2×D512yes—
301C2×#120C2×D512yes—
302C2×C4×D4—54no—
303C2×C4×D4—54no—
304C2×C4×D4—108no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4—52no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—52no—
312C22×C22⋊C4C2×D511yescharacteristic
313C22×C42—51no—
314#400—54no—
315#399—54no—
316#398—54no—
317#397—54no—
318#397—54no—
319#397—54no—
320#394—54no—
321#394—54no—
322#388—54no—
323#388—54no—
324#387—54no—
325#387—54no—
326#386—52no—
327#386—52no—
328#386—54no—
329#386—54no—
330#386—54no—
331#386—52no—
332#386—54no—
333#386—52no—
334#386—54no—
335#385—52no—
336#385—52no—
337#385—52no—
338#385—52no—
339#385—52no—
340#385—54no—
341#385—52no—
342#385—54no—
343#381—52no—
344#381—52no—
345#381—54no—
346#380—54no—
347#379—52no—
348#379—52no—
349C2×#95—52no—
350C2×#95—52no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—28no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—24no—
361C23×C5—24no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—24no—
366C23×C5—24no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5—48no—
372C23×C5—48no—
373C23×C5—48no—
374C23×C5—48no—
375C23×C5—48no—
376C23×C5—44no—
377C23×C5—82no—
378C23×C5—82no—
379C23×C5—84no—
380C23×C5#123116yescomplemented
381C23×C5C22×D414yes—
382C23×C5C22×D412yes—
383C23×C5C22×D412yes—
384C23×C5C22×D412yes—
385C23×C5C2×#4112yes—
386C23×C5C2×#4112yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5C2511yescharacteristic
392C5×D4—216no—
393C5×D4—216no—
394C5×D4—48no—
395C5×D4—48no—
396C5×D4—84no—
397C5×D4—84no—
398C2×C4×C5—28no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—24no—
407C2×C4×C5—24no—
408C2×C4×C5—44no—
409C2×C4×C5—82no—
410C2×C4×C5—82no—
411C2×C4×C5C22×D414yes—
412C2×Dic5—28no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—24no—
419C2×Dic5—24no—
420C2×Dic5—24no—
421C2×Dic5—22no—
422C2×Dic5—24no—
423C2×Dic5—24no—
424C2×Dic5—22no—
425C2×Dic5—24no—
426C2×Dic5—24no—
427C2×Dic5—24no—
428C2×Dic5—48no—
429C2×Dic5—48no—
430C2×Dic5—416no—
431C2×Dic5—48no—
432C2×Dic5—44no—
433C2×Dic5—44no—
434C2×Dic5—44no—
435C2×Dic5—84no—
436C2×Dic5H(5,𝔽2)14yes—
437C25C22×D511yescharacteristic
438C25C22×D511yescharacteristic
439C25C22×D511yescharacteristic
440C22×D4—24no—
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—24no—
445C22×D4C22⋊D518yes—
446C22×D4C22×D512yes—
447C22×D4C22×D512yes—
448C22×D4C22×D512yes—
449C22×D4C22×D512yes—
450C22×D4C22×D512yes—
451C22×D4C22×D512yes—
452C23×C4—51no—
453C23×C4—52no—
454C23×C4—52no—
455C23×C4—54no—
456C23×C4—52no—
457C23×C4—51no—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—52no—
461C23×C4—104no—
462C23×C4—104no—
463C23×C4—204no—
464C23×C4—204no—
465C23×C4C22×D511yescharacteristic
466C23×C4C22×D511yescharacteristic
467C23×C4C22×D511yescharacteristic
468C23×C4C22×D511yescharacteristic
469#123—28no—
470#123—28no—
471#123—208no—
472#121—28no—
473#121—28no—
474#120—28no—
475#120—28no—
476C4×D4—1016no—
477C4×D4—1016no—
478C2×C4⋊C4—54no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—204no—
485C2×C4⋊C4C22×D512yes—
486C2×C4⋊C4C22×D512yes—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—52no—
489C2×C22⋊C4—52no—
490C2×C22⋊C4—54no—
491C2×C22⋊C4—54no—
492C2×C22⋊C4—52no—
493C2×C22⋊C4—52no—
494C2×C22⋊C4—52no—
495C2×C22⋊C4—52no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—104no—
502C2×C22⋊C4—104no—
503C2×C22⋊C4—104no—
504C2×C22⋊C4—104no—
505C2×C22⋊C4—204no—
506C2×C22⋊C4C22×D512yes—
507C2×C22⋊C4C22×D512yes—
508C2×C22⋊C4C22×D512yes—
509C2×C22⋊C4C22×D512yes—
510C2×C22⋊C4C22×D512yes—
511C2×C22⋊C4C22×D512yes—
512C2×C42—54no—
513C2×C42—104no—
514#95—54no—
515#95—54no—
516#95—54no—
517#95—54no—
518#95—54no—
519#95—54no—
520#95—54no—
521#95—54no—
522#95—54no—
523#95—54no—
524C22×C5—24no—
525C22×C5—24no—
526C22×C5—24no—
527C22×C5—22no—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—22no—
531C22×C5—22no—
532C22×C5—22no—
533C22×C5—24no—
534C22×C5—24no—
535C22×C5—24no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—416no—
540C22×C5—416no—
541C22×C5—44no—
542C22×C5—44no—
543C22×C5—42no—
544C22×C5—44no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—44no—
548C22×C5—88no—
549C22×C5C2×#12314yes—
550C22×C5C2×#12314yes—
551C22×C5C2×#12314yes—
552C22×C5C23×D411yescharacteristic
553C22×C5C22×#4111yescharacteristic
554C22×C5C22×#4111yescharacteristic
555C22×C5C2×H(5,𝔽2)12yes—
556C22×C5#58512yes—
557C4×C5—24no—
558C4×C5—42no—
559C4×C5—42no—
560C4×C5—42no—
561Dic5—24no—
562Dic5—44no—
563Dic5—42no—
564Dic5—42no—
565Dic5—42no—
566Dic5—44no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24—42no—
576C24—42no—
577C24—42no—
578C24#71114yes—
579C24#71114yes—
580C24C2×C22⋊D514yes—
581C24C2×C22⋊D514yes—
582C24C23×D512yes—
583C24C23×D512yes—
584C24C23×D511yescharacteristic
585C24C23×D511yescharacteristic
586C24C23×D511yescharacteristic
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—232no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—416no—
603C2×D4C2×C22⋊D518yes—
604C2×D4C2×C22⋊D518yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—52no—
615C22×C4—54no—
616C22×C4—54no—
617C22×C4—52no—
618C22×C4—52no—
619C22×C4—52no—
620C22×C4—104no—
621C22×C4—104no—
622C22×C4—104no—
623C22×C4—108no—
624C22×C4—102no—
625C22×C4—104no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—108no—
630C22×C4—104no—
631C22×C4—104no—
632C22×C4—104no—
633C22×C4—202no—
634C22×C4—202no—
635C22×C4—204no—
636C22×C4—202no—
637C22×C4—202no—
638C22×C4—202no—
639C22×C4—202no—
640C22×C4—202no—
641C22×C4—202no—
642C22×C4—202no—
643C22×C4—2016no—
644C22×C4—2016no—
645C22×C4C2×C22⋊D514yes—
646C22×C4C23×D512yes—
647C22×C4C23×D512yes—
648C22×C4C23×D512yes—
649C22×C4C23×D512yes—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—108no—
653C4⋊C4—108no—
654C4⋊C4—204no—
655C4⋊C4—204no—
656C4⋊C4—204no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—108no—
664C22⋊C4—104no—
665C22⋊C4—104no—
666C22⋊C4—104no—
667C22⋊C4—104no—
668C22⋊C4—108no—
669C22⋊C4—104no—
670C22⋊C4—104no—
671C22⋊C4—204no—
672C22⋊C4—204no—
673C22⋊C4—204no—
674C22⋊C4—204no—
675C22⋊C4—204no—
676C42—108no—
677C2×C5—24no—
678C2×C5—24no—
679C2×C5—24no—
680C2×C5—44no—
681C2×C5—82no—
682C2×C5C22×#12311yescharacteristic
683C2×C5#345912yes—
684C2×C5#348411yescharacteristic
685C2×C5#348511yescharacteristic
686C2×C5#350512yes—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—24no—
702C23—22no—
703C23—44no—
704C23—44no—
705C23—48no—
706C23—48no—
707C23—44no—
708C23—44no—
709C23—48no—
710C23—48no—
711C23—48no—
712C23—44no—
713C23—82no—
714C23—82no—
715C23—84no—
716C23#4081116yescomplemented
717C23C2×#71112yes—
718C23C2×#71112yes—
719C23C2×#71112yes—
720C23C2×#71112yes—
721C23C2×#71112yes—
722C23C2×#71112yes—
723C23C22×C22⋊D514yes—
724C23C22×C22⋊D512yes—
725C23C22×C22⋊D512yes—
726C23C22×C22⋊D512yes—
727C23C24×D511yescharacteristic
728D4—216no—
729D4—216no—
730D4—48no—
731D4—48no—
732D4—84no—
733D4—84no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—44no—
745C2×C4—54no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—108no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—104no—
752C2×C4—104no—
753C2×C4—104no—
754C2×C4—104no—
755C2×C4—102no—
756C2×C4—104no—
757C2×C4—102no—
758C2×C4—104no—
759C2×C4—104no—
760C2×C4—104no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—208no—
765C2×C4—208no—
766C2×C4—2016no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4—204no—
770C2×C4—208no—
771C2×C4—404no—
772C2×C4C22×C22⋊D514yes—
773C5#3498311yescharacteristic, complemented, Sylow
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—416no—
790C22—416no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—88no—
799C22C2×#408114yes—
800C22C2×#408114yes—
801C22C2×#408114yes—
802C22C22×#71111yescharacteristic
803C22C22×#71111yescharacteristic
804C22D5×H(5,𝔽2)12yes—
805C22#6628512yes—
806C22C23×C22⋊D511yescharacteristic
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—104no—
812C4—202no—
813C4—202no—
814C4—202no—
815C4—204no—
816C4—204no—
817C2—24no—
818C2—24no—
819C2—24no—
820C2—44no—
821C2—82no—
822C2#1061819612yes—
823C2#1061820012yes—
824C2C22×#408111yescharacteristic
825C2#1061918111yescharacteristic
826C2#1061918511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
Fitting, prime radicalC2×C5×#534C2
hypercenterC2×#534D5
hypocenterC5#34983
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic5C2semidirect
3. #10615774C2semidirect
4. #10615774C2semidirect
5. C2×#65509C2semidirect
6. #10614621C2semidirect
7. #10614597C2semidirect
8. #10614575C2semidirect
9. #10614387C2semidirect
10. #10614386C2semidirect
11. #10614333C2semidirect
12. #10614324C2semidirect
13. #10614316C2semidirect
14. #10613826C2semidirect
15. C2×#65235C2semidirect
19. C24×Dic5C22semidirect
31. C22×C22⋊Dic5C22semidirect
32. C22×C22⋊Dic5C22semidirect
33. C2×#4081C22semidirect
36. C2×D4×Dic5C22semidirect
37. C22×C4⋊Dic5C22semidirect
38. C22×#683C22semidirect
39. C22×C4×Dic5C22semidirect
40. #65536C22semidirect
41. #65536C22semidirect
42. #65511C22semidirect
43. #65511C22semidirect
49. #65509C22semidirect
50. #65509C22semidirect
51. #65509C22semidirect
52. #65509C22semidirect
53. #65500C22semidirect
54. #65500C22semidirect
55. #65499C22semidirect
56. #65499C22semidirect
57. C2×#3963C22semidirect
58. C2×#3963C22semidirect
59. #65275C22semidirect
60. #65272C22semidirect
61. #65267C22semidirect
62. #65267C22semidirect
63. #65242C22semidirect
64. #65241C22semidirect
65. #65241C22semidirect
66. #65238C22semidirect
67. #65235C22semidirect
68. #65235C22semidirect
69. #65235C22semidirect
70. #65235C22semidirect
71. #65235C22semidirect
72. #65235C22semidirect
73. #65233C22semidirect
74. #65233C22semidirect
75. #65232C22semidirect
76. #65231C22semidirect
380. C23×C5#123semidirect
716. C23#4081semidirect
773. C5#34983semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5342
C22×D4×Dic52
#106157742
C2×#655092
#106146212
#106145972
#106145752
#106143872
#106143862
#106143332
#106143242
#106143162
#106138262
C2×#652352
#349835