Finite Group Databasebeta

← C5×#24143 #11946863

Subgroups — C5×#24143 #11946863

Order 1280.

1156 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3505C211yesmaximal, characteristic
2C5×#2627C211yesmaximal, characteristic, complemented
3C5×#2618C211yesmaximal, characteristic, complemented
4C5×#2322C211yesmaximal, characteristic, complemented
5C5×#2044C212yesmaximal, complemented
6C5×#2022C212yesmaximal, complemented
7C5×#1996C211yesmaximal, characteristic, complemented
8C5×#1964C211yesmaximal, characteristic, complemented
9C5×#1890C212yesmaximal, complemented
10C5×#1867C212yesmaximal, complemented
11C5×#1799C211yesmaximal, characteristic, complemented
12C5×#553—22no—
13C5×#553—21no—
14C5×#552—21no—
15C5×#551—22no—
16C5×#548—21no—
17C5×#546—21no—
18C5×#539—21no—
19C5×#538—21no—
20C5×#534C2212yes—
21C5×#529—21no—
22C5×#525—21no—
23C2×C5×#123C2211yescharacteristic
24C2×C5×#123C2212yes—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C5×#518C2212yes—
28C2×C4×C5×D4C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C2×C5×#99C2212yes—
31C2×C5×#99C2212yes—
32C2×C5×#99C2212yes—
33C5×#400—21no—
34C5×#398—21no—
35C5×#398—22no—
36C5×#396—22no—
37C5×#395—21no—
38C5×#394—21no—
39C5×#389—21no—
40C5×#388—21no—
41C5×#387—21no—
42C5×#386C2211yescharacteristic
43C5×#386C2212yes—
44C5×#385—21no—
45C5×#385C2212yes—
46C5×#385C2211yescharacteristic
47C5×#381C2212yes—
48C5×#381C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C4×C5×C22⋊C4C2211yescharacteristic
52C5×#342C2212yes—
53C5×#342C2212yes—
54C5×#342C2212yes—
55#24143C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C22×C5×Q8D411yescharacteristic
58C22×C5×D4D411yescharacteristic
59C22×C5×D4C2311yescharacteristic
60C22×C5×D4C2312yes—
61C23×C4×C5D411yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C5×#126—22no—
66C5×#126—22no—
67C5×#126—22no—
68C5×#125—21no—
69C5×#125—22no—
70C5×#124—21no—
71C5×#124—22no—
72C5×#123—22no—
73C5×#123—22no—
74C5×#123—22no—
75C5×#123—22no—
76C5×#123—22no—
77C5×#123—22no—
78C5×#123—22no—
79C5×#123—24no—
80C5×#123—42no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—21no—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—21no—
87C5×#121—21no—
88C5×#121—22no—
89C5×#121—21no—
90C5×#121—21no—
91C5×#121—21no—
92C5×#121—21no—
93C5×#121—22no—
94C5×#121—22no—
95C5×#120—22no—
96C5×#120—22no—
97C4×C5×Q8—21no—
98C4×C5×D4—22no—
99C4×C5×D4—21no—
100C4×C5×D4—21no—
101C4×C5×D4—21no—
102C4×C5×D4—21no—
103C4×C5×D4—21no—
104C4×C5×D4—22no—
105C4×C5×D4—22no—
106C4×C5×D4—22no—
107C4×C5×D4—22no—
108C5×#117—21no—
109C5×#117—22no—
110C5×#117—22no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—22no—
118C2×C5×C4⋊C4—21no—
119C2×C5×C4⋊C4—21no—
120C2×C5×C4⋊C4—21no—
121C2×C5×C4⋊C4—21no—
122C2×C5×C4⋊C4—22no—
123C2×C5×C4⋊C4D411yescharacteristic
124C2×C5×C4⋊C4D411yescharacteristic
125C2×C5×C4⋊C4D412yes—
126C2×C5×C4⋊C4D411yescharacteristic
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4D411yescharacteristic
133C2×C5×C22⋊C4D412yes—
134C2×C5×C22⋊C4C2311yescharacteristic
135C2×C5×C22⋊C4C2312yes—
136C2×C5×C22⋊C4C2312yes—
137C2×C5×C22⋊C4C2311yescharacteristic
138C2×C5×C22⋊C4C2312yes—
139C2×C5×C22⋊C4C2311yescharacteristic
140C2×C42×C5—21no—
141C2×C42×C5D411yescharacteristic
142C5×#99—24no—
143C5×#99—42no—
144C5×#99—42no—
145C5×#95—21no—
146C5×#95—21no—
147C5×#95—21no—
148C5×#95—21no—
149C5×#95—21no—
150C5×#95—22no—
151C5×#95—22no—
152C5×#95—21no—
153C5×#95—22no—
154C5×#95—21no—
155C5×#95—22no—
156#3505C2×C511yescharacteristic
157#2627C2×C511yescharacteristic, complemented
158#2618C2×C511yescharacteristic, complemented
159#2322C2×C511yescharacteristic, complemented
160#2044C2×C512yescomplemented
161#2022C2×C512yescomplemented
162#1996C2×C511yescharacteristic, complemented
163#1964C2×C511yescharacteristic, complemented
164#1890C2×C512yescomplemented
165#1867C2×C512yescomplemented
166#1799C2×C511yescharacteristic, complemented
167C24×C5C2×D412yes—
168C24×C5C2×D411yescharacteristic
169C24×C5C2411yescharacteristic
170C5×#41—82no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—81no—
174C2×C5×D4—21no—
175C2×C5×D4—22no—
176C2×C5×D4—21no—
177C2×C5×D4—22no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4—22no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4—22no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—81no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—22no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—22no—
207C22×C4×C5—21no—
208C22×C4×C5—81no—
209C22×C4×C5—81no—
210C22×C4×C5—81no—
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5#4112yescomplemented
224C5×C4⋊C4—24no—
225C5×C4⋊C4—22no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—22no—
228C5×C4⋊C4—22no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—22no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—22no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—44no—
238C5×C4⋊C4—41no—
239C5×C4⋊C4—41no—
240C5×C4⋊C4—41no—
241C5×C4⋊C4—41no—
242C5×C4⋊C4—81no—
243C5×C4⋊C4—81no—
244C5×C4⋊C4—81no—
245C5×C4⋊C4—82no—
246C5×C22⋊C4—22no—
247C5×C22⋊C4—22no—
248C5×C22⋊C4—24no—
249C5×C22⋊C4—22no—
250C5×C22⋊C4—22no—
251C5×C22⋊C4—22no—
252C5×C22⋊C4—22no—
253C5×C22⋊C4—21no—
254C5×C22⋊C4—22no—
255C5×C22⋊C4—21no—
256C5×C22⋊C4—22no—
257C5×C22⋊C4—21no—
258C5×C22⋊C4—22no—
259C5×C22⋊C4—21no—
260C5×C22⋊C4—21no—
261C5×C22⋊C4—22no—
262C5×C22⋊C4—22no—
263C5×C22⋊C4—22no—
264C5×C22⋊C4—22no—
265C5×C22⋊C4—21no—
266C5×C22⋊C4—22no—
267C5×C22⋊C4—21no—
268C5×C22⋊C4—44no—
269C5×C22⋊C4—81no—
270C5×C22⋊C4—82no—
271C5×C22⋊C4#4112yescomplemented
272C42×C5—22no—
273C42×C5—22no—
274C42×C5—21no—
275C42×C5—21no—
276C42×C5—81no—
277#553—22no—
278#553—21no—
279#552—21no—
280#551—22no—
281#548—21no—
282#546—21no—
283#539—21no—
284#538—21no—
285#534C22×C512yes—
286#529—21no—
287#525—21no—
288C2×#123C22×C511yescharacteristic
289C2×#123C22×C512yes—
290C2×C22⋊Q8C22×C511yescharacteristic
291C2×#121C22×C511yescharacteristic
292#518C22×C512yes—
293C2×C4×D4C22×C511yescharacteristic
294C22×C4⋊C4C22×C511yescharacteristic
295C2×#99C22×C512yes—
296C2×#99C22×C512yes—
297C2×#99C22×C512yes—
298#400—21no—
299#398—21no—
300#398—22no—
301#396—22no—
302#395—21no—
303#394—21no—
304#389—21no—
305#388—21no—
306#387—21no—
307#386C22×C511yescharacteristic
308#386C22×C512yes—
309#385—21no—
310#385C22×C511yescharacteristic
311#385C22×C512yes—
312#381C22×C511yescharacteristic
313#381C22×C512yes—
314#380C22×C511yescharacteristic
315#380C22×C511yescharacteristic
316C4×C22⋊C4C22×C511yescharacteristic
317#342C22×C512yes—
318#342C22×C512yes—
319#342C22×C512yes—
320C23×C5—21no—
321C23×C5—22no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—42no—
331C23×C5—42no—
332C23×C5C22×D411yescharacteristic
333C23×C5C22×D411yescharacteristic
334C23×C5C22×D411yescharacteristic
335C23×C5C2×#4111yescharacteristic
336C23×C5C2×#4111yescharacteristic
337C23×C5H(5,𝔽2)11yescharacteristic
338C23×C52−1+411yescharacteristic
339C5×Q8—42no—
340C5×Q8—81no—
341C5×D4—42no—
342C5×D4—42no—
343C5×D4—42no—
344C5×D4—41no—
345C5×D4—41no—
346C5×D4—41no—
347C5×D4—42no—
348C5×D4—41no—
349C5×D4—42no—
350C5×D4—81no—
351C5×D4—82no—
352C5×D4—82no—
353C2×C4×C5—21no—
354C2×C4×C5—22no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—42no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—42no—
382C2×C4×C5—41no—
383C2×C4×C5—42no—
384C2×C4×C5—41no—
385C2×C4×C5—42no—
386C2×C4×C5—41no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—41no—
391C2×C4×C5—42no—
392C2×C4×C5—41no—
393C2×C4×C5—42no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—42no—
397C2×C4×C5—42no—
398C2×C4×C5—81no—
399C2×C4×C5—82no—
400C2×C4×C5—82no—
401C2×C4×C5#12011yescharacteristic
402C2×C4×C5#12011yescharacteristic
403C2×C4×C5#12011yescharacteristic
404C2×C4×C5#12011yescharacteristic
405C2×#41—21no—
406C22×Q8C5×D411yescharacteristic
407C22×D4C5×D411yescharacteristic
408C22×D4C23×C511yescharacteristic
409C22×D4C23×C512yes—
410C23×C4C5×D411yescharacteristic
411C23×C4C23×C511yescharacteristic
412C23×C4C23×C511yescharacteristic
413C23×C4C23×C511yescharacteristic
414#126—22no—
415#126—22no—
416#126—22no—
417#125—21no—
418#125—22no—
419#124—21no—
420#124—22no—
421#123—22no—
422#123—22no—
423#123—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427#123—22no—
428#123—24no—
429#123—42no—
430C22⋊Q8—21no—
431C22⋊Q8—22no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C22⋊Q8—21no—
435C22⋊Q8—21no—
436#121—21no—
437#121—22no—
438#121—21no—
439#121—21no—
440#121—21no—
441#121—21no—
442#121—22no—
443#121—22no—
444#120—22no—
445#120—22no—
446C4×Q8—21no—
447C4×D4—22no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—22no—
457#117—21no—
458#117—22no—
459#117—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4C5×D411yescharacteristic
473C2×C4⋊C4C5×D411yescharacteristic
474C2×C4⋊C4C5×D412yes—
475C2×C4⋊C4C5×D411yescharacteristic
476C2×C22⋊C4—22no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4C5×D411yescharacteristic
482C2×C22⋊C4C5×D412yes—
483C2×C22⋊C4C23×C512yes—
484C2×C22⋊C4C23×C511yescharacteristic
485C2×C22⋊C4C23×C512yes—
486C2×C22⋊C4C23×C511yescharacteristic
487C2×C22⋊C4C23×C512yes—
488C2×C22⋊C4C23×C511yescharacteristic
489C2×C42—21no—
490C2×C42C5×D411yescharacteristic
491#99—24no—
492#99—42no—
493#99—42no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—22no—
500#95—22no—
501#95—21no—
502#95—22no—
503#95—21no—
504#95—22no—
505C22×C5—21no—
506C22×C5—21no—
507C22×C5—21no—
508C22×C5—21no—
509C22×C5—21no—
510C22×C5—21no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—42no—
516C22×C5—41no—
517C22×C5—42no—
518C22×C5—41no—
519C22×C5—42no—
520C22×C5—42no—
521C22×C5—41no—
522C22×C5—82no—
523C22×C5—81no—
524C22×C5—82no—
525C22×C5C2×#12011yescharacteristic
526C22×C5#52511yescharacteristic
527C22×C5#53711yescharacteristic
528C22×C5#54611yescharacteristic
529C22×C5#54711yescharacteristic
530C22×C5#54811yescharacteristic
531C22×C5#55011yescharacteristic
532C4×C5—21no—
533C4×C5—21no—
534C4×C5—21no—
535C4×C5—21no—
536C4×C5—42no—
537C4×C5—42no—
538C4×C5—41no—
539C4×C5—42no—
540C4×C5—41no—
541C4×C5—42no—
542C4×C5—41no—
543C4×C5—42no—
544C4×C5—82no—
545C4×C5—82no—
546C4×C5—81no—
547C4×C5—81no—
548C24C2×C5×D412yes—
549C24C2×C5×D411yescharacteristic
550C24C24×C511yescharacteristic
551#41—82no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—81no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×C5×D411yescharacteristic
593C22×C4C2×C5×D412yes—
594C22×C4C2×C5×D411yescharacteristic
595C22×C4C2×C5×D412yes—
596C22×C4C2×C5×D411yescharacteristic
597C22×C4C2×C5×D412yes—
598C22×C4C2×C5×D411yescharacteristic
599C22×C4C2×C5×D411yescharacteristic
600C22×C4C2×C5×D411yescharacteristic
601C22×C4C2×C5×D411yescharacteristic
602C22×C4C2×C5×D411yescharacteristic
603C22×C4C2×C5×D411yescharacteristic
604C22×C4C5×#4112yescomplemented
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—44no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4—81no—
625C4⋊C4—81no—
626C4⋊C4—82no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—21no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—21no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—44no—
650C22⋊C4—81no—
651C22⋊C4—82no—
652C22⋊C4C5×#4112yescomplemented
653C42—22no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—81no—
658C2×C5—21no—
659C2×C5—21no—
660C2×C5—21no—
661C2×C5—21no—
662C2×C5—21no—
663C2×C5—21no—
664C2×C5—81no—
665C2×C5—82no—
666C2×C5#240711yescharacteristic
667C2×C5#302611yescharacteristic
668C2×C5#302811yescharacteristic
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23C22×C5×D411yescharacteristic
682C23C22×C5×D411yescharacteristic
683C23C22×C5×D411yescharacteristic
684C23C2×C5×#4111yescharacteristic
685C23C2×C5×#4111yescharacteristic
686C23C5×H(5,𝔽2)11yescharacteristic
687C23C5×2−1+411yescharacteristic
688Q8—42no—
689Q8—81no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—42no—
697D4—42no—
698D4—41no—
699D4—81no—
700D4—82no—
701D4—82no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—81no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4C5×#12011yescharacteristic
751C2×C4C5×#12011yescharacteristic
752C2×C4C5×#12011yescharacteristic
753C2×C4C5×#12011yescharacteristic
754C5#2414311yescharacteristic, direct product factor, Sylow
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—82no—
773C22—81no—
774C22—82no—
775C22C2×C5×#12011yescharacteristic
776C22C5×#52511yescharacteristic
777C22C5×#53711yescharacteristic
778C22C5×#54611yescharacteristic
779C22C5×#54711yescharacteristic
780C22C5×#54811yescharacteristic
781C22C5×#55011yescharacteristic
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—42no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—41no—
793C4—42no—
794C4—82no—
795C4—82no—
796C4—81no—
797C4—81no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—81no—
805C2—82no—
806C2C5×#240711yescharacteristic
807C2C5×#302611yescharacteristic
808C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
prime radicalC5×#3505C2
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
2. C5×#2627C2semidirect
3. C5×#2618C2semidirect
4. C5×#2322C2semidirect
5. C5×#2044C2semidirect
6. C5×#2022C2semidirect
7. C5×#1996C2semidirect
8. C5×#1964C2semidirect
9. C5×#1890C2semidirect
10. C5×#1867C2semidirect
11. C5×#1799C2semidirect
55. #24143C5direct (N × H)
157. #2627C2×C5semidirect
158. #2618C2×C5semidirect
159. #2322C2×C5semidirect
160. #2044C2×C5semidirect
161. #2022C2×C5semidirect
162. #1996C2×C5semidirect
163. #1964C2×C5semidirect
164. #1890C2×C5semidirect
165. #1867C2×C5semidirect
166. #1799C2×C5semidirect
223. C22×C4×C5#41semidirect
271. C5×C22⋊C4#41semidirect
604. C22×C4C5×#41semidirect
652. C22⋊C4C5×#41semidirect
754. C5#24143direct (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×#26272
C5×#26182
C5×#23222
C5×#20442
C5×#20222
C5×#19962
C5×#19642
C5×#18902
C5×#18672
C5×#17992
#241435