Finite Group Databasebeta

← C5×#24140 #11946860

Subgroups — C5×#24140 #11946860

Order 1280.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3505C211yesmaximal, characteristic, complemented
2C5×#2848C211yesmaximal, characteristic, complemented
3C5×#2847C211yesmaximal, characteristic, complemented
4C4×C5×#120C211yesmaximal, characteristic, complemented
5C5×#2044C212yesmaximal, complemented
6C5×#2021C212yesmaximal, complemented
7C5×#1996C211yesmaximal, characteristic, complemented
8C5×#1964C211yesmaximal, characteristic, complemented
9C5×#1889C212yesmaximal, complemented
10C5×#1867C212yesmaximal, complemented
11C5×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C5C2211yescharacteristic
13C5×#553—21no—
14C5×#553—22no—
15C5×#552—21no—
16C5×#551—22no—
17C5×#548—21no—
18C5×#546—21no—
19C5×#539—21no—
20C5×#538—21no—
21C5×#534C2212yes—
22C5×#529—21no—
23C5×#525—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×#121—21no—
27C2×C5×#121C2211yescharacteristic
28C2×C5×#120C2211yescharacteristic
29C2×C5×#120C2212yes—
30C5×#518C2212yes—
31C2×C4×C5×D4—21no—
32C2×C4×C5×D4C2211yescharacteristic
33C2×C5×#99C2212yes—
34C2×C5×#99C2212yes—
35C2×C5×#99C2212yes—
36C5×#386—21no—
37C5×#386—22no—
38C5×#386C2211yescharacteristic
39C5×#386C2212yes—
40C5×#385—21no—
41C5×#385—22no—
42C5×#385C2212yes—
43C5×#385C2211yescharacteristic
44C5×#380—21no—
45C5×#380—21no—
46C5×#380C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C5×#379C2212yes—
49C5×#379C2211yescharacteristic
50C4×C5×C22⋊C4—21no—
51C4×C5×C22⋊C4C2211yescharacteristic
52C5×#342C2212yes—
53C5×#342C2212yes—
54C5×#342C2212yes—
55#24140C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C2×C5×#41—21no—
58C22×C5×Q8D411yescharacteristic, complemented
59C22×C5×D4—21no—
60C22×C5×D4—22no—
61C22×C5×D4D411yescharacteristic, complemented
62C22×C5×D4C2311yescharacteristic
63C22×C5×D4C2312yes—
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5—44no—
71C23×C4×C5D411yescharacteristic, complemented
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C5×#126—22no—
75C5×#126—22no—
76C5×#126—22no—
77C5×#125—21no—
78C5×#125—22no—
79C5×#124—21no—
80C5×#124—22no—
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—22no—
84C5×#123—22no—
85C5×#123—22no—
86C5×C22⋊Q8—21no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8—21no—
92C5×C22⋊Q8—44no—
93C5×#121—21no—
94C5×#121—22no—
95C5×#121—21no—
96C5×#121—21no—
97C5×#121—21no—
98C5×#121—21no—
99C5×#121—22no—
100C5×#121—22no—
101C5×#121—44no—
102C5×#120—22no—
103C5×#120—22no—
104C5×#120—22no—
105C5×#120—22no—
106C5×#120—24no—
107C5×#120—42no—
108C4×C5×Q8—21no—
109C4×C5×D4—22no—
110C4×C5×D4—21no—
111C4×C5×D4—21no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4—22no—
116C4×C5×D4—22no—
117C4×C5×D4—22no—
118C4×C5×D4—22no—
119C4×C5×D4—44no—
120C5×#117—21no—
121C5×#117—22no—
122C5×#117—22no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—22no—
127C2×C5×C4⋊C4D411yescharacteristic, complemented
128C2×C5×C4⋊C4D411yescharacteristic, complemented
129C2×C5×C4⋊C4D411yescharacteristic, complemented
130C2×C5×C4⋊C4D412yescomplemented
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—21no—
134C2×C5×C22⋊C4—22no—
135C2×C5×C22⋊C4—21no—
136C2×C5×C22⋊C4—22no—
137C2×C5×C22⋊C4—21no—
138C2×C5×C22⋊C4—22no—
139C2×C5×C22⋊C4—22no—
140C2×C5×C22⋊C4D411yescharacteristic, complemented
141C2×C5×C22⋊C4D412yescomplemented
142C2×C5×C22⋊C4C2311yescharacteristic
143C2×C5×C22⋊C4C2312yes—
144C2×C5×C22⋊C4C2312yes—
145C2×C5×C22⋊C4C2311yescharacteristic
146C2×C5×C22⋊C4C2312yes—
147C2×C5×C22⋊C4C2311yescharacteristic
148C2×C42×C5—21no—
149C2×C42×C5D411yescharacteristic, complemented
150C5×#99—24no—
151C5×#99—42no—
152C5×#99—42no—
153C5×#95—21no—
154C5×#95—21no—
155C5×#95—21no—
156C5×#95—22no—
157C5×#95—22no—
158C5×#95—21no—
159C5×#95—21no—
160#3505C2×C511yescharacteristic, complemented
161#2848C2×C511yescharacteristic, complemented
162#2847C2×C511yescharacteristic, complemented
163C4×#120C2×C511yescharacteristic, complemented
164#2044C2×C512yescomplemented
165#2021C2×C512yescomplemented
166#1996C2×C511yescharacteristic, complemented
167#1964C2×C511yescharacteristic, complemented
168#1889C2×C512yescomplemented
169#1867C2×C512yescomplemented
170#1799C2×C511yescharacteristic, complemented
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—42no—
178C24×C5—42no—
179C24×C5C2×D412yes—
180C24×C5C2×D411yescharacteristic
181C24×C5#4112yescomplemented
182C24×C5C2411yescharacteristic
183C5×#41—82no—
184C2×C5×Q8—21no—
185C2×C5×Q8—21no—
186C2×C5×Q8—42no—
187C2×C5×D4—24no—
188C2×C5×D4—21no—
189C2×C5×D4—22no—
190C2×C5×D4—21no—
191C2×C5×D4—22no—
192C2×C5×D4—21no—
193C2×C5×D4—21no—
194C2×C5×D4—22no—
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4—22no—
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—42no—
205C2×C5×D4—42no—
206C2×C5×D4—42no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—44no—
210C22×C4×C5—24no—
211C22×C4×C5—24no—
212C22×C4×C5—24no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—42no—
225C22×C4×C5—42no—
226C22×C4×C5—42no—
227C22×C4×C5—42no—
228C22×C4×C5—42no—
229C22×C4×C5—42no—
230C22×C4×C5—42no—
231C22×C4×C5—42no—
232C22×C4×C5—42no—
233C22×C4×C5—42no—
234C22×C4×C5—42no—
235C22×C4×C5—42no—
236C22×C4×C5—41no—
237C22×C4×C5—41no—
238C22×C4×C5—41no—
239C22×C4×C5—41no—
240C22×C4×C5C2×D411yescharacteristic
241C22×C4×C5C2×D412yes—
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2×D412yes—
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2×D411yescharacteristic
251C22×C4×C5C2×D411yescharacteristic
252C5×C4⋊C4—22no—
253C5×C4⋊C4—22no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—22no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—22no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—22no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—42no—
265C5×C4⋊C4—42no—
266C5×C4⋊C4—42no—
267C5×C4⋊C4—44no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—22no—
270C5×C22⋊C4—24no—
271C5×C22⋊C4—22no—
272C5×C22⋊C4—22no—
273C5×C22⋊C4—22no—
274C5×C22⋊C4—22no—
275C5×C22⋊C4—21no—
276C5×C22⋊C4—22no—
277C5×C22⋊C4—21no—
278C5×C22⋊C4—22no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—22no—
281C5×C22⋊C4—21no—
282C5×C22⋊C4—21no—
283C5×C22⋊C4—22no—
284C5×C22⋊C4—22no—
285C5×C22⋊C4—22no—
286C5×C22⋊C4—22no—
287C5×C22⋊C4—21no—
288C5×C22⋊C4—22no—
289C5×C22⋊C4—21no—
290C5×C22⋊C4—44no—
291C5×C22⋊C4—42no—
292C5×C22⋊C4—44no—
293C5×C22⋊C4—44no—
294C5×C22⋊C4—42no—
295C5×C22⋊C4—42no—
296C5×C22⋊C4—44no—
297C5×C22⋊C4#4112yescomplemented
298C42×C5—22no—
299C42×C5—22no—
300C42×C5—21no—
301C42×C5—21no—
302C42×C5—42no—
303C24×C4C22×C511yescharacteristic
304#553—21no—
305#553—22no—
306#552—21no—
307#551—22no—
308#548—21no—
309#546—21no—
310#539—21no—
311#538—21no—
312#534C22×C512yes—
313#529—21no—
314#525—21no—
315C2×C22⋊Q8—21no—
316C2×C22⋊Q8C22×C511yescharacteristic
317C2×#121—21no—
318C2×#121C22×C511yescharacteristic
319C2×#120C22×C511yescharacteristic
320C2×#120C22×C512yes—
321#518C22×C512yes—
322C2×C4×D4—21no—
323C2×C4×D4C22×C511yescharacteristic
324C2×#99C22×C512yes—
325C2×#99C22×C512yes—
326C2×#99C22×C512yes—
327#386—22no—
328#386—21no—
329#386C22×C512yes—
330#386C22×C511yescharacteristic
331#385—22no—
332#385—21no—
333#385C22×C512yes—
334#385C22×C511yescharacteristic
335#380—21no—
336#380—21no—
337#380C22×C511yescharacteristic
338#380C22×C511yescharacteristic
339#379C22×C512yes—
340#379C22×C511yescharacteristic
341C4×C22⋊C4—21no—
342C4×C22⋊C4C22×C511yescharacteristic
343#342C22×C512yes—
344#342C22×C512yes—
345#342C22×C512yes—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—21no—
356C23×C5—22no—
357C23×C5—21no—
358C23×C5—21no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—41no—
362C23×C5—44no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—44no—
371C23×C5—44no—
372C23×C5—44no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5—42no—
376C23×C5—42no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5—41no—
380C23×C5—41no—
381C23×C5C22×D411yescharacteristic
382C23×C5C22×D411yescharacteristic
383C23×C5C22×D411yescharacteristic
384C23×C5C2×#4111yescharacteristic
385C23×C5C2×#4111yescharacteristic
386C23×C5H(5,𝔽2)11yescharacteristic
387C23×C52−1+411yescharacteristic
388C5×Q8—42no—
389C5×Q8—81no—
390C5×D4—48no—
391C5×D4—42no—
392C5×D4—42no—
393C5×D4—41no—
394C5×D4—41no—
395C5×D4—41no—
396C5×D4—42no—
397C5×D4—41no—
398C5×D4—42no—
399C5×D4—42no—
400C5×D4—81no—
401C5×D4—82no—
402C5×D4—82no—
403C5×D4—88no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—21no—
411C2×C4×C5—22no—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—21no—
417C2×C4×C5—22no—
418C2×C4×C5—21no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—44no—
434C2×C4×C5—42no—
435C2×C4×C5—41no—
436C2×C4×C5—42no—
437C2×C4×C5—41no—
438C2×C4×C5—42no—
439C2×C4×C5—41no—
440C2×C4×C5—42no—
441C2×C4×C5—42no—
442C2×C4×C5—42no—
443C2×C4×C5—41no—
444C2×C4×C5—42no—
445C2×C4×C5—41no—
446C2×C4×C5—42no—
447C2×C4×C5—42no—
448C2×C4×C5—81no—
449C2×C4×C5—82no—
450C2×C4×C5—82no—
451C2×C4×C5#12011yescharacteristic
452C2×C4×C5#12011yescharacteristic
453C2×C4×C5#12011yescharacteristic
454C2×C4×C5#12011yescharacteristic
455C25C23×C511yescharacteristic
456C2×#41—21no—
457C22×Q8C5×D411yescharacteristic, complemented
458C22×D4—21no—
459C22×D4—22no—
460C22×D4C5×D411yescharacteristic, complemented
461C22×D4C23×C511yescharacteristic
462C22×D4C23×C512yes—
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—44no—
470C23×C4C5×D411yescharacteristic, complemented
471C23×C4C23×C511yescharacteristic
472C23×C4C23×C511yescharacteristic
473#126—22no—
474#126—22no—
475#126—22no—
476#125—21no—
477#125—22no—
478#124—21no—
479#124—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—44no—
492#121—21no—
493#121—22no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—22no—
499#121—22no—
500#121—44no—
501#120—22no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—24no—
506#120—42no—
507C4×Q8—21no—
508C4×D4—22no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—44no—
519#117—21no—
520#117—22no—
521#117—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4C5×D411yescharacteristic, complemented
527C2×C4⋊C4C5×D411yescharacteristic, complemented
528C2×C4⋊C4C5×D411yescharacteristic, complemented
529C2×C4⋊C4C5×D412yescomplemented
530C2×C22⋊C4—22no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4C5×D411yescharacteristic, complemented
540C2×C22⋊C4C5×D412yescomplemented
541C2×C22⋊C4C23×C512yes—
542C2×C22⋊C4C23×C511yescharacteristic
543C2×C22⋊C4C23×C512yes—
544C2×C22⋊C4C23×C511yescharacteristic
545C2×C22⋊C4C23×C512yes—
546C2×C22⋊C4C23×C511yescharacteristic
547C2×C42—21no—
548C2×C42C5×D411yescharacteristic, complemented
549#99—24no—
550#99—42no—
551#99—42no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—22no—
556#95—22no—
557#95—21no—
558#95—21no—
559C22×C5—21no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—24no—
566C22×C5—24no—
567C22×C5—24no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—41no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5—42no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—42no—
582C22×C5—42no—
583C22×C5—42no—
584C22×C5—42no—
585C22×C5—41no—
586C22×C5—42no—
587C22×C5—41no—
588C22×C5—42no—
589C22×C5—42no—
590C22×C5—41no—
591C22×C5—82no—
592C22×C5—81no—
593C22×C5—82no—
594C22×C5C2×#12011yescharacteristic
595C22×C5#52511yescharacteristic
596C22×C5#53711yescharacteristic
597C22×C5#54611yescharacteristic
598C22×C5#54711yescharacteristic
599C22×C5#54811yescharacteristic
600C22×C5#55011yescharacteristic
601C4×C5—21no—
602C4×C5—21no—
603C4×C5—21no—
604C4×C5—42no—
605C4×C5—41no—
606C4×C5—42no—
607C4×C5—42no—
608C4×C5—41no—
609C4×C5—42no—
610C4×C5—41no—
611C4×C5—42no—
612C4×C5—82no—
613C4×C5—81no—
614C4×C5—82no—
615C4×C5B(4,𝔽2)12yes—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—42no—
623C24—42no—
624C24C2×C5×D412yes—
625C24C2×C5×D411yescharacteristic
626C24C5×#4112yescomplemented
627C24C24×C511yescharacteristic
628#41—82no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—42no—
632C2×D4—24no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—44no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4C2×C5×D411yescharacteristic
686C22×C4C2×C5×D412yes—
687C22×C4C2×C5×D411yescharacteristic
688C22×C4C2×C5×D411yescharacteristic
689C22×C4C2×C5×D411yescharacteristic
690C22×C4C2×C5×D411yescharacteristic
691C22×C4C2×C5×D412yes—
692C22×C4C2×C5×D411yescharacteristic
693C22×C4C2×C5×D412yes—
694C22×C4C2×C5×D411yescharacteristic
695C22×C4C2×C5×D411yescharacteristic
696C22×C4C2×C5×D411yescharacteristic
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—21no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—22no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—44no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—24no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—21no—
721C22⋊C4—22no—
722C22⋊C4—21no—
723C22⋊C4—22no—
724C22⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—21no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—21no—
735C22⋊C4—44no—
736C22⋊C4—42no—
737C22⋊C4—44no—
738C22⋊C4—42no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—42no—
742C22⋊C4C5×#4112yescomplemented
743C42—22no—
744C42—22no—
745C42—21no—
746C42—21no—
747C42—42no—
748C2×C5—21no—
749C2×C5—21no—
750C2×C5—21no—
751C2×C5—21no—
752C2×C5—21no—
753C2×C5—21no—
754C2×C5—44no—
755C2×C5—81no—
756C2×C5—82no—
757C2×C5#240711yescharacteristic
758C2×C5C2×B(4,𝔽2)11yescharacteristic
759C2×C5#302511yescharacteristic
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—21no—
770C23—22no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—22no—
775C23—41no—
776C23—44no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—42no—
790C23—42no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23C22×C5×D411yescharacteristic
796C23C22×C5×D411yescharacteristic
797C23C22×C5×D411yescharacteristic
798C23C2×C5×#4111yescharacteristic
799C23C2×C5×#4111yescharacteristic
800C23C5×H(5,𝔽2)11yescharacteristic
801C23C5×2−1+411yescharacteristic
802Q8—42no—
803Q8—81no—
804D4—48no—
805D4—42no—
806D4—42no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—42no—
811D4—42no—
812D4—41no—
813D4—42no—
814D4—81no—
815D4—82no—
816D4—82no—
817D4—88no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—81no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4C5×#12011yescharacteristic
866C2×C4C5×#12011yescharacteristic
867C2×C4C5×#12011yescharacteristic
868C2×C4C5×#12011yescharacteristic
869C5#2414011yescharacteristic, direct product factor, Sylow
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×C5×#12011yescharacteristic
906C22C5×#52511yescharacteristic
907C22C5×#53711yescharacteristic
908C22C5×#54611yescharacteristic
909C22C5×#54711yescharacteristic
910C22C5×#54811yescharacteristic
911C22C5×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C5×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C5×#240711yescharacteristic
937C2C2×C5×B(4,𝔽2)11yescharacteristic
938C2C5×#302511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3505C2semidirect
2. C5×#2848C2semidirect
3. C5×#2847C2semidirect
4. C4×C5×#120C2semidirect
5. C5×#2044C2semidirect
6. C5×#2021C2semidirect
7. C5×#1996C2semidirect
8. C5×#1964C2semidirect
9. C5×#1889C2semidirect
10. C5×#1867C2semidirect
11. C5×#1799C2semidirect
55. #24140C5direct (N × H)
58. C22×C5×Q8D4semidirect
61. C22×C5×D4D4semidirect
71. C23×C4×C5D4semidirect
127. C2×C5×C4⋊C4D4semidirect
128. C2×C5×C4⋊C4D4semidirect
129. C2×C5×C4⋊C4D4semidirect
130. C2×C5×C4⋊C4D4semidirect
140. C2×C5×C22⋊C4D4semidirect
141. C2×C5×C22⋊C4D4semidirect
149. C2×C42×C5D4semidirect
160. #3505C2×C5semidirect
161. #2848C2×C5semidirect
162. #2847C2×C5semidirect
163. C4×#120C2×C5semidirect
164. #2044C2×C5semidirect
165. #2021C2×C5semidirect
166. #1996C2×C5semidirect
167. #1964C2×C5semidirect
168. #1889C2×C5semidirect
169. #1867C2×C5semidirect
170. #1799C2×C5semidirect
181. C24×C5#41semidirect
297. C5×C22⋊C4#41semidirect
457. C22×Q8C5×D4semidirect
460. C22×D4C5×D4semidirect
470. C23×C4C5×D4semidirect
526. C2×C4⋊C4C5×D4semidirect
527. C2×C4⋊C4C5×D4semidirect
528. C2×C4⋊C4C5×D4semidirect
529. C2×C4⋊C4C5×D4semidirect
539. C2×C22⋊C4C5×D4semidirect
540. C2×C22⋊C4C5×D4semidirect
548. C2×C42C5×D4semidirect
626. C24C5×#41semidirect
742. C22⋊C4C5×#41semidirect
869. C5#24140direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35052
C5×#28482
C5×#28472
C4×C5×#1202
C5×#20442
C5×#20212
C5×#19962
C5×#19642
C5×#18892
C5×#18672
C5×#17992
#241405