Finite Group Databasebeta

← C5×#14747 #11937467

Subgroups — C5×#14747 #11937467

Order 1280.

2730 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#121C211yesmaximal, characteristic
2C2×C5×#394C211yesmaximal, characteristic, complemented
3C2×C5×#386C212yesmaximal, complemented
4C2×C5×#386C212yesmaximal, complemented
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C22×C5×#95C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1440C212yesmaximal, complemented
10C5×#1439C212yesmaximal, complemented
11C5×#1438C211yesmaximal, characteristic, complemented
12C23×C5×D4C2212yes—
13C23×C5×D4C2211yescharacteristic
14C24×C4×C5C2212yes—
15C24×C4×C5C2211yescharacteristic
16C2×C5×#121—28no—
17C2×C5×#121—24no—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2212yes—
23C22×C5×C22⋊C4C2212yes—
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2212yes—
26C22×C5×C22⋊C4C2212yes—
27C22×C5×C22⋊C4C2211yescharacteristic
28C5×#394—24no—
29C5×#386—28no—
30C5×#386—28no—
31C5×#385—24no—
32C2×C5×#95—24no—
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2212yes—
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41C2×C5×#95C2211yescharacteristic
42#14747C511yesmaximal, characteristic, direct product factor, Sylow
43C25×C5C2312yes—
44C25×C5C2311yescharacteristic
45C22×C5×D4—24no—
46C22×C5×D4—24no—
47C22×C5×D4—24no—
48C22×C5×D4—24no—
49C22×C5×D4—24no—
50C22×C5×D4—24no—
51C22×C5×D4—24no—
52C22×C5×D4—22no—
53C22×C5×D4—22no—
54C22×C5×D4—22no—
55C22×C5×D4—42no—
56C22×C5×D4D418yes—
57C23×C4×C5—24no—
58C23×C4×C5—24no—
59C23×C4×C5—24no—
60C23×C4×C5—22no—
61C23×C4×C5—24no—
62C23×C4×C5—22no—
63C23×C4×C5—24no—
64C23×C4×C5—24no—
65C23×C4×C5—42no—
66C23×C4×C5—42no—
67C23×C4×C5—42no—
68C23×C4×C5D414yes—
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2312yes—
72C23×C4×C5C2312yes—
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2312yes—
77C23×C4×C5C2311yescharacteristic
78C5×#121—232no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—42no—
86C2×C5×C22⋊C4—22no—
87C2×C5×C22⋊C4—24no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—24no—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—24no—
95C2×C5×C22⋊C4—24no—
96C2×C5×C22⋊C4—24no—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—24no—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4—24no—
101C2×C5×C22⋊C4—42no—
102C2×C5×C22⋊C4—42no—
103C2×C5×C22⋊C4—42no—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4D414yescomplemented
106C5×#95—24no—
107C5×#95—22no—
108C5×#95—22no—
109C5×#95—22no—
110C5×#95—24no—
111C5×#95—24no—
112C5×#95—24no—
113C5×#95—24no—
114C5×#95D414yescomplemented
115C22×#121C2×C511yescharacteristic
116C2×#394C2×C511yescharacteristic, complemented
117C2×#386C2×C512yescomplemented
118C2×#386C2×C512yescomplemented
119C2×#385C2×C511yescharacteristic, complemented
120C22×#95C2×C511yescharacteristic, complemented
121#1442C2×C511yescharacteristic, complemented
122#1441C2×C511yescharacteristic, complemented
123#1440C2×C512yescomplemented
124#1439C2×C512yescomplemented
125#1438C2×C511yescharacteristic, complemented
126C24×C5—21no—
127C24×C5—21no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5—21no—
131C24×C5—21no—
132C24×C5—22no—
133C24×C5—22no—
134C24×C5—22no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5—22no—
138C24×C5—22no—
139C24×C5—22no—
140C24×C5—22no—
141C24×C5—22no—
142C24×C5—22no—
143C24×C5—22no—
144C24×C5—22no—
145C24×C5—22no—
146C24×C5C2×D414yes—
147C24×C5C2×D414yes—
148C24×C5C2×D412yes—
149C24×C5C2×D412yes—
150C24×C5#4112yes—
151C24×C5#4114yes—
152C24×C5C2411yescharacteristic
153C2×C5×D4—28no—
154C2×C5×D4—216no—
155C2×C5×D4—216no—
156C2×C5×D4—216no—
157C2×C5×D4—48no—
158C2×C5×D4—48no—
159C2×C5×D4—44no—
160C2×C5×D4—48no—
161C2×C5×D4—48no—
162C2×C5×D4—48no—
163C2×C5×D4—48no—
164C2×C5×D4—44no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—216no—
168C22×C4×C5—28no—
169C22×C4×C5—21no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—21no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—22no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—21no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—21no—
201C22×C4×C5—28no—
202C22×C4×C5—21no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—22no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—22no—
211C22×C4×C5—21no—
212C22×C4×C5—44no—
213C22×C4×C5—48no—
214C22×C4×C5—48no—
215C22×C4×C5—48no—
216C22×C4×C5—48no—
217C22×C4×C5—48no—
218C22×C4×C5—48no—
219C22×C4×C5—48no—
220C22×C4×C5—48no—
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2×D412yes—
223C22×C4×C5C2×D412yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5#4114yes—
229C22×C4×C5#4112yes—
230C5×C4⋊C4—28no—
231C5×C4⋊C4—44no—
232C5×C4⋊C4—44no—
233C5×C22⋊C4—216no—
234C5×C22⋊C4—28no—
235C5×C22⋊C4—48no—
236C5×C22⋊C4—48no—
237C5×C22⋊C4—48no—
238C5×C22⋊C4—48no—
239C5×C22⋊C4—44no—
240C23×D4C22×C512yes—
241C23×D4C22×C511yescharacteristic
242C24×C4C22×C512yes—
243C24×C4C22×C511yescharacteristic
244C2×#121—28no—
245C2×#121—24no—
246C22×C4⋊C4C22×C511yescharacteristic
247C22×C4⋊C4C22×C511yescharacteristic
248C22×C4⋊C4C22×C511yescharacteristic
249C22×C22⋊C4C22×C512yes—
250C22×C22⋊C4C22×C511yescharacteristic
251C22×C22⋊C4C22×C512yes—
252C22×C22⋊C4C22×C512yes—
253C22×C22⋊C4C22×C512yes—
254C22×C22⋊C4C22×C512yes—
255C22×C22⋊C4C22×C511yescharacteristic
256#394—24no—
257#386—28no—
258#386—28no—
259#385—24no—
260C2×#95—24no—
261C2×#95C22×C511yescharacteristic
262C2×#95C22×C511yescharacteristic
263C2×#95C22×C512yes—
264C2×#95C22×C512yes—
265C2×#95C22×C512yes—
266C2×#95C22×C511yescharacteristic
267C2×#95C22×C512yes—
268C2×#95C22×C512yes—
269C2×#95C22×C511yescharacteristic
270C23×C5—22no—
271C23×C5—24no—
272C23×C5—24no—
273C23×C5—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—24no—
277C23×C5—24no—
278C23×C5—24no—
279C23×C5—22no—
280C23×C5—24no—
281C23×C5—24no—
282C23×C5—24no—
283C23×C5—22no—
284C23×C5—24no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—24no—
288C23×C5—24no—
289C23×C5—24no—
290C23×C5—24no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—24no—
294C23×C5—24no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5—42no—
298C23×C5—42no—
299C23×C5—42no—
300C23×C5—42no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5—42no—
304C23×C5—42no—
305C23×C5—42no—
306C23×C5—42no—
307C23×C5—42no—
308C23×C5—42no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5—42no—
312C23×C5—42no—
313C23×C5—42no—
314C23×C5—42no—
315C23×C5—42no—
316C23×C5—42no—
317C23×C5—42no—
318C23×C5—42no—
319C23×C5—42no—
320C23×C5—42no—
321C23×C5—42no—
322C23×C5—42no—
323C23×C5#12014yes—
324C23×C5#12114yes—
325C23×C5#12118yes—
326C23×C5#12318yes—
327C23×C5#12414yes—
328C23×C5C22×D411yescharacteristic
329C23×C5C22×D412yes—
330C23×C5C22×D411yescharacteristic
331C23×C5C22×D411yescharacteristic
332C23×C5C2×#4111yescharacteristic
333C23×C5C2×#4112yes—
334C23×C5C2×#4111yescharacteristic
335C23×C5C2×#4112yes—
336C23×C5H(5,𝔽2)12yes—
337C23×C5H(5,𝔽2)11yescharacteristic
338C23×C52−1+411yescharacteristic
339C5×D4—416no—
340C5×D4—432no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—24no—
344C2×C4×C5—24no—
345C2×C4×C5—22no—
346C2×C4×C5—24no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—24no—
351C2×C4×C5—24no—
352C2×C4×C5—24no—
353C2×C4×C5—24no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—24no—
357C2×C4×C5—24no—
358C2×C4×C5—24no—
359C2×C4×C5—24no—
360C2×C4×C5—24no—
361C2×C4×C5—22no—
362C2×C4×C5—416no—
363C2×C4×C5—432no—
364C2×C4×C5—41no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—42no—
368C2×C4×C5—42no—
369C2×C4×C5—42no—
370C2×C4×C5—42no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—42no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—42no—
392C2×C4×C5—42no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5#12114yes—
396C25C23×C512yes—
397C25C23×C511yescharacteristic
398C22×D4—24no—
399C22×D4—24no—
400C22×D4—24no—
401C22×D4—24no—
402C22×D4—24no—
403C22×D4—24no—
404C22×D4—24no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—42no—
409C22×D4C5×D418yes—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—22no—
414C23×C4—24no—
415C23×C4—22no—
416C23×C4—24no—
417C23×C4—24no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4C5×D414yes—
422C23×C4C23×C511yescharacteristic
423C23×C4C23×C511yescharacteristic
424C23×C4C23×C511yescharacteristic
425C23×C4C23×C511yescharacteristic
426C23×C4C23×C511yescharacteristic
427C23×C4C23×C512yes—
428C23×C4C23×C512yes—
429C23×C4C23×C512yes—
430C23×C4C23×C511yescharacteristic
431#121—232no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—42no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4C5×D414yescomplemented
459#95—24no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95C5×D414yescomplemented
468C22×C5—24no—
469C22×C5—24no—
470C22×C5—24no—
471C22×C5—24no—
472C22×C5—28no—
473C22×C5—28no—
474C22×C5—24no—
475C22×C5—28no—
476C22×C5—28no—
477C22×C5—24no—
478C22×C5—44no—
479C22×C5—44no—
480C22×C5—44no—
481C22×C5—44no—
482C22×C5—44no—
483C22×C5—44no—
484C22×C5—44no—
485C22×C5—82no—
486C22×C5—82no—
487C22×C5—82no—
488C22×C5—82no—
489C22×C5—82no—
490C22×C5—82no—
491C22×C5—82no—
492C22×C5—82no—
493C22×C5#39418yescomplemented
494C22×C5C2×#12011yescharacteristic
495C22×C5C2×#12111yescharacteristic
496C22×C5C2×#12111yescharacteristic
497C22×C5C2×#12112yes—
498C22×C5C2×#12312yes—
499C22×C5#52512yes—
500C22×C5C2×#12411yescharacteristic
501C22×C5#52912yes—
502C22×C5#53211yescharacteristic
503C22×C5#53411yescharacteristic
504C22×C5#53711yescharacteristic
505C22×C5#53812yes—
506C22×C5#53912yes—
507C22×C5D4212yes—
508C22×C5D4211yescharacteristic
509C22×C5#54612yes—
510C22×C5#54612yes—
511C22×C5#54612yes—
512C22×C5#54711yescharacteristic
513C22×C5#54712yes—
514C22×C5#54811yescharacteristic
515C22×C5#55311yescharacteristic
516C22×C5#55312yes—
517C4×C5—24no—
518C4×C5—44no—
519C4×C5—42no—
520C4×C5—42no—
521C4×C5—44no—
522C4×C5—44no—
523C4×C5—42no—
524C4×C5—81no—
525C4×C5—81no—
526C24—21no—
527C24—21no—
528C24—22no—
529C24—22no—
530C24—21no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C5×D414yes—
547C24C2×C5×D414yes—
548C24C2×C5×D412yes—
549C24C2×C5×D412yes—
550C24C5×#4112yes—
551C24C5×#4114yes—
552C24C24×C511yescharacteristic
553C2×D4—28no—
554C2×D4—216no—
555C2×D4—216no—
556C2×D4—216no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—44no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—44no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—216no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—28no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4C2×C5×D412yes—
622C22×C4C2×C5×D412yes—
623C22×C4C2×C5×D414yes—
624C22×C4C2×C5×D414yes—
625C22×C4C2×C5×D412yes—
626C22×C4C2×C5×D412yes—
627C22×C4C2×C5×D412yes—
628C22×C4C5×#4114yes—
629C22×C4C5×#4112yes—
630C4⋊C4—28no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C22⋊C4—216no—
634C22⋊C4—28no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—44no—
640C2×C5—28no—
641C2×C5—84no—
642C2×C5C2×#39411yescharacteristic
643C2×C5#241011yescharacteristic
644C2×C5#241611yescharacteristic
645C2×C5#242412yes—
646C2×C5#242512yes—
647C2×C5#243011yescharacteristic
648C2×C5#244312yes—
649C2×C5#244412yes—
650C2×C5#254311yescharacteristic
651C2×C5#263911yescharacteristic
652C2×C5#285011yescharacteristic
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23C5×#12014yes—
707C23C5×#12114yes—
708C23C5×#12118yes—
709C23C5×#12318yes—
710C23C5×#12414yes—
711C23C22×C5×D411yescharacteristic
712C23C22×C5×D412yes—
713C23C22×C5×D411yescharacteristic
714C23C22×C5×D411yescharacteristic
715C23C2×C5×#4111yescharacteristic
716C23C2×C5×#4112yes—
717C23C2×C5×#4111yescharacteristic
718C23C2×C5×#4112yes—
719C23C5×H(5,𝔽2)12yes—
720C23C5×H(5,𝔽2)11yescharacteristic
721C23C5×2−1+411yescharacteristic
722D4—416no—
723D4—432no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—416no—
746C2×C4—432no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4C5×#12114yes—
779C5#1474711yescharacteristic, direct product factor, Sylow
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—28no—
789C22—28no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22C5×#39418yescomplemented
806C22C2×C5×#12011yescharacteristic
807C22C2×C5×#12111yescharacteristic
808C22C2×C5×#12111yescharacteristic
809C22C2×C5×#12112yes—
810C22C2×C5×#12312yes—
811C22C5×#52512yes—
812C22C2×C5×#12411yescharacteristic
813C22C5×#52912yes—
814C22C5×#53211yescharacteristic
815C22C5×#53411yescharacteristic
816C22C5×#53711yescharacteristic
817C22C5×#53812yes—
818C22C5×#53912yes—
819C22C5×D4212yes—
820C22C5×D4211yescharacteristic
821C22C5×#54612yes—
822C22C5×#54612yes—
823C22C5×#54612yes—
824C22C5×#54711yescharacteristic
825C22C5×#54712yes—
826C22C5×#54811yescharacteristic
827C22C5×#55312yes—
828C22C5×#55311yescharacteristic
829C4—24no—
830C4—42no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—44no—
836C4—81no—
837C4—81no—
838C2—28no—
839C2—84no—
840C2C2×C5×#39411yescharacteristic
841C2C5×#241011yescharacteristic
842C2C5×#241611yescharacteristic
843C2C5×#242412yes—
844C2C5×#242512yes—
845C2C5×#243011yescharacteristic
846C2C5×#244312yes—
847C2C5×#244412yes—
848C2C5×#254311yescharacteristic
849C2C5×#263911yescharacteristic
850C2C5×#285011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC22×C5×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#394C2semidirect
3. C2×C5×#386C2semidirect
4. C2×C5×#386C2semidirect
5. C2×C5×#385C2semidirect
6. C22×C5×#95C2semidirect
7. C5×#1442C2semidirect
8. C5×#1441C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
11. C5×#1438C2semidirect
42. #14747C5direct (N × H)
105. C2×C5×C22⋊C4D4semidirect
114. C5×#95D4semidirect
116. C2×#394C2×C5semidirect
117. C2×#386C2×C5semidirect
118. C2×#386C2×C5semidirect
119. C2×#385C2×C5semidirect
120. C22×#95C2×C5semidirect
121. #1442C2×C5semidirect
122. #1441C2×C5semidirect
123. #1440C2×C5semidirect
124. #1439C2×C5semidirect
125. #1438C2×C5semidirect
458. C2×C22⋊C4C5×D4semidirect
467. #95C5×D4semidirect
493. C22×C5#394semidirect
779. C5#14747direct (N × H)
805. C22C5×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#1212
C2×C5×#3942
C2×C5×#3862
C2×C5×#3852
C22×C5×#952
C5×#14422
C5×#14412
C5×#14402
C5×#14392
C5×#14382
#147475