Finite Group Databasebeta

← C5×#16501 #11939221

Subgroups — C5×#16501 #11939221

Order 1280.

2310 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#121C211yesmaximal, characteristic
2C2×C5×#398C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×C5×#394C212yesmaximal, complemented
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C5×#1445C211yesmaximal, characteristic, complemented
7C5×#1439C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×#1438C211yesmaximal, characteristic, complemented
10C5×#1438C212yesmaximal, complemented
11C5×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C5×D4C2212yes—
13C23×C5×D4C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C2×C5×#121—24no—
16C2×C5×#121—24no—
17C2×C5×#121—24no—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2212yes—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2212yes—
23C22×C5×C22⋊C4C2212yes—
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2212yes—
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2212yes—
29C22×C5×C22⋊C4C2212yes—
30C5×#398—24no—
31C5×#394—24no—
32C5×#394—28no—
33C5×#385—24no—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41C2×C5×#95C2212yes—
42#16501C511yesmaximal, 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—22no—
51C22×C5×D4—22no—
52C22×C5×D4—42no—
53C22×C5×D4—42no—
54C22×C5×D4—42no—
55C22×C5×D4—42no—
56C22×C5×D4D414yes—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—42no—
60C23×C4×C5—42no—
61C23×C4×C5D414yes—
62C23×C4×C5C2312yes—
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2312yes—
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2312yes—
70C23×C4×C5C2311yescharacteristic
71C5×#121—232no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—24no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—24no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—42no—
81C2×C5×C4⋊C4—42no—
82C2×C5×C4⋊C4D414yes—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—24no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—24no—
87C2×C5×C22⋊C4—24no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—24no—
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—42no—
98C2×C5×C22⋊C4—42no—
99C2×C5×C22⋊C4—42no—
100C2×C5×C22⋊C4—42no—
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—22no—
107C5×#95—22no—
108C5×#95—24no—
109C5×#95—22no—
110C5×#95—22no—
111C5×#95—24no—
112C5×#95—42no—
113C5×#95—42no—
114C22×#121C2×C511yescharacteristic
115C2×#398C2×C511yescharacteristic, complemented
116C2×#394C2×C511yescharacteristic, complemented
117C2×#394C2×C512yescomplemented
118C2×#385C2×C511yescharacteristic, complemented
119#1445C2×C511yescharacteristic, complemented
120#1439C2×C512yescomplemented
121#1439C2×C512yescomplemented
122#1438C2×C512yescomplemented
123#1438C2×C511yescharacteristic, complemented
124C22⋊#95C2×C511yescharacteristic, complemented
125C24×C5—21no—
126C24×C5—21no—
127C24×C5—22no—
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×C5—22no—
147C24×C5C2×D414yes—
148C24×C5C2×D412yes—
149C24×C5C2×D412yes—
150C24×C5#4112yes—
151C24×C5C2411yescharacteristic
152C2×C5×D4—216no—
153C2×C5×D4—28no—
154C2×C5×D4—48no—
155C2×C5×D4—48no—
156C2×C5×D4—48no—
157C2×C5×D4—44no—
158C2×C5×D4—44no—
159C2×C5×D4—48no—
160C2×C5×D4—48no—
161C2×C5×D4—48no—
162C2×C5×D4—48no—
163C2×C5×D4—48no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—21no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—21no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
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—28no—
193C22×C4×C5—21no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—21no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—21no—
209C22×C4×C5—22no—
210C22×C4×C5—44no—
211C22×C4×C5—44no—
212C22×C4×C5—48no—
213C22×C4×C5—48no—
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2×D414yes—
218C22×C4×C5C2×D412yes—
219C22×C4×C5C2×D412yes—
220C22×C4×C5C2×D412yes—
221C22×C4×C5#4114yes—
222C5×C4⋊C4—28no—
223C5×C4⋊C4—48no—
224C5×C4⋊C4—44no—
225C5×C4⋊C4—44no—
226C5×C22⋊C4—216no—
227C5×C22⋊C4—28no—
228C5×C22⋊C4—48no—
229C5×C22⋊C4—48no—
230C5×C22⋊C4—48no—
231C5×C22⋊C4—48no—
232C5×C22⋊C4—44no—
233C5×C22⋊C4—48no—
234C23×D4C22×C512yes—
235C23×D4C22×C511yescharacteristic
236C24×C4C22×C511yescharacteristic
237C2×#121—24no—
238C2×#121—24no—
239C2×#121—24no—
240C22×C4⋊C4C22×C511yescharacteristic
241C22×C4⋊C4C22×C512yes—
242C22×C4⋊C4C22×C511yescharacteristic
243C22×C4⋊C4C22×C511yescharacteristic
244C22×C22⋊C4C22×C512yes—
245C22×C22⋊C4C22×C512yes—
246C22×C22⋊C4C22×C512yes—
247C22×C22⋊C4C22×C512yes—
248C22×C22⋊C4C22×C511yescharacteristic
249C22×C22⋊C4C22×C512yes—
250C22×C22⋊C4C22×C512yes—
251C22×C22⋊C4C22×C511yescharacteristic
252#398—24no—
253#394—24no—
254#394—28no—
255#385—24no—
256C2×#95C22×C511yescharacteristic
257C2×#95C22×C512yes—
258C2×#95C22×C511yescharacteristic
259C2×#95C22×C512yes—
260C2×#95C22×C511yescharacteristic
261C2×#95C22×C511yescharacteristic
262C2×#95C22×C512yes—
263C2×#95C22×C512yes—
264C23×C5—22no—
265C23×C5—22no—
266C23×C5—22no—
267C23×C5—22no—
268C23×C5—22no—
269C23×C5—22no—
270C23×C5—24no—
271C23×C5—24no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5—24no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—24no—
278C23×C5—24no—
279C23×C5—24no—
280C23×C5—24no—
281C23×C5—24no—
282C23×C5—24no—
283C23×C5—24no—
284C23×C5—24no—
285C23×C5—42no—
286C23×C5—42no—
287C23×C5—42no—
288C23×C5—42no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—42no—
292C23×C5—42no—
293C23×C5—42no—
294C23×C5—42no—
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#12114yes—
322C23×C5C22×D411yescharacteristic
323C23×C5C22×D411yescharacteristic
324C23×C5C22×D411yescharacteristic
325C23×C5C22×D411yescharacteristic
326C23×C5C2×#4111yescharacteristic
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C5H(5,𝔽2)11yescharacteristic
331C23×C5H(5,𝔽2)11yescharacteristic
332C23×C52−1+412yes—
333C5×D4—416no—
334C5×D4—432no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—24no—
338C2×C4×C5—24no—
339C2×C4×C5—22no—
340C2×C4×C5—24no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—24no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—24no—
349C2×C4×C5—24no—
350C2×C4×C5—24no—
351C2×C4×C5—24no—
352C2×C4×C5—24no—
353C2×C4×C5—416no—
354C2×C4×C5—41no—
355C2×C4×C5—42no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—42no—
359C2×C4×C5—41no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5—42no—
363C2×C4×C5—42no—
364C2×C4×C5—42no—
365C2×C4×C5—42no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
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—41no—
376C2×C4×C5—42no—
377C2×C4×C5—41no—
378C2×C4×C5—42no—
379C2×C4×C5—41no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5#12014yes—
389C25C23×C512yes—
390C25C23×C511yescharacteristic
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4C5×D414yes—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4C5×D414yes—
408C23×C4C23×C511yescharacteristic
409C23×C4C23×C511yescharacteristic
410C23×C4C23×C512yes—
411C23×C4C23×C511yescharacteristic
412C23×C4C23×C511yescharacteristic
413C23×C4C23×C511yescharacteristic
414C23×C4C23×C512yes—
415C23×C4C23×C512yes—
416C23×C4C23×C511yescharacteristic
417#121—232no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4C5×D414yes—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4C5×D414yescomplemented
452#95—22no—
453#95—22no—
454#95—24no—
455#95—22no—
456#95—22no—
457#95—24no—
458#95—42no—
459#95—42no—
460C22×C5—24no—
461C22×C5—24no—
462C22×C5—24no—
463C22×C5—42no—
464C22×C5—42no—
465C22×C5—42no—
466C22×C5—44no—
467C22×C5—44no—
468C22×C5—42no—
469C22×C5—44no—
470C22×C5—44no—
471C22×C5—44no—
472C22×C5—44no—
473C22×C5—44no—
474C22×C5—44no—
475C22×C5—44no—
476C22×C5—44no—
477C22×C5—44no—
478C22×C5—82no—
479C22×C5—82no—
480C22×C5—82no—
481C22×C5—82no—
482C22×C5—82no—
483C22×C5—82no—
484C22×C5—82no—
485C22×C5—82no—
486C22×C5C2×#12011yescharacteristic
487C22×C5C2×#12111yescharacteristic
488C22×C5#53211yescharacteristic
489C22×C5#53411yescharacteristic
490C22×C5#53411yescharacteristic
491C22×C5#53412yes—
492C22×C5#53511yescharacteristic
493C22×C5#53512yes—
494C22×C5#53611yescharacteristic
495C22×C5#53712yes—
496C22×C5#53812yes—
497C22×C5#53912yes—
498C22×C5#54012yes—
499C22×C5D4211yescharacteristic
500C22×C5D4211yescharacteristic
501C22×C5#54611yescharacteristic
502C22×C5#54611yescharacteristic
503C22×C5#54612yes—
504C22×C5#54712yes—
505C22×C5#54812yes—
506C22×C5#55312yes—
507C22×C5#56212yes—
508C22×C5#56212yes—
509C4×C5—24no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—44no—
513C4×C5—44no—
514C4×C5—42no—
515C4×C5—81no—
516C4×C5—81no—
517C4×C5—82no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24C2×C5×D414yes—
541C24C2×C5×D412yes—
542C24C2×C5×D412yes—
543C24C5×#4112yes—
544C24C24×C511yescharacteristic
545C2×D4—216no—
546C2×D4—28no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4C2×C5×D412yes—
608C22×C4C2×C5×D412yes—
609C22×C4C2×C5×D414yes—
610C22×C4C2×C5×D412yes—
611C22×C4C2×C5×D412yes—
612C22×C4C2×C5×D412yes—
613C22×C4C2×C5×D412yes—
614C22×C4C5×#4114yes—
615C4⋊C4—28no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C22⋊C4—216no—
620C22⋊C4—28no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—44no—
626C22⋊C4—48no—
627C2×C5—44no—
628C2×C5—84no—
629C2×C5#240811yescharacteristic
630C2×C5#243211yescharacteristic
631C2×C5#254311yescharacteristic
632C2×C5#261311yescharacteristic
633C2×C5#261811yescharacteristic
634C2×C5#266111yescharacteristic
635C2×C5#267112yes—
636C2×C5#267612yes—
637C2×C5#270812yes—
638C2×C5#271112yes—
639C2×C5#281611yescharacteristic
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
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—
697C23C5×#12114yes—
698C23C22×C5×D411yescharacteristic
699C23C22×C5×D411yescharacteristic
700C23C22×C5×D411yescharacteristic
701C23C22×C5×D411yescharacteristic
702C23C2×C5×#4111yescharacteristic
703C23C2×C5×#4112yes—
704C23C5×H(5,𝔽2)12yes—
705C23C5×H(5,𝔽2)12yes—
706C23C5×H(5,𝔽2)11yescharacteristic
707C23C5×H(5,𝔽2)11yescharacteristic
708C23C5×2−1+412yes—
709D4—416no—
710D4—432no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—416no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4C5×#12014yes—
765C5#1650111yescharacteristic, direct product factor, Sylow
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C2×C5×#12011yescharacteristic
793C22C2×C5×#12111yescharacteristic
794C22C5×#53211yescharacteristic
795C22C5×#53411yescharacteristic
796C22C5×#53411yescharacteristic
797C22C5×#53412yes—
798C22C5×#53511yescharacteristic
799C22C5×#53512yes—
800C22C5×#53611yescharacteristic
801C22C5×#53712yes—
802C22C5×#53812yes—
803C22C5×#53912yes—
804C22C5×#54012yes—
805C22C5×D4211yescharacteristic
806C22C5×D4211yescharacteristic
807C22C5×#54612yes—
808C22C5×#54611yescharacteristic
809C22C5×#54611yescharacteristic
810C22C5×#54712yes—
811C22C5×#54812yes—
812C22C5×#55312yes—
813C22C5×#56212yes—
814C22C5×#56212yes—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—44no—
819C4—42no—
820C4—44no—
821C4—81no—
822C4—81no—
823C4—82no—
824C2—44no—
825C2—84no—
826C2C5×#240811yescharacteristic
827C2C5×#243211yescharacteristic
828C2C5×#254311yescharacteristic
829C2C5×#261311yescharacteristic
830C2C5×#261811yescharacteristic
831C2C5×#266111yescharacteristic
832C2C5×#267112yes—
833C2C5×#267612yes—
834C2C5×#270812yes—
835C2C5×#271112yes—
836C2C5×#281611yescharacteristic
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×#398C2semidirect
3. C2×C5×#394C2semidirect
4. C2×C5×#394C2semidirect
5. C2×C5×#385C2semidirect
6. C5×#1445C2semidirect
7. C5×#1439C2semidirect
8. C5×#1439C2semidirect
9. C5×#1438C2semidirect
10. C5×#1438C2semidirect
11. C5×C22⋊#95C2semidirect
42. #16501C5direct (N × H)
105. C2×C5×C22⋊C4D4semidirect
115. C2×#398C2×C5semidirect
116. C2×#394C2×C5semidirect
117. C2×#394C2×C5semidirect
118. C2×#385C2×C5semidirect
119. #1445C2×C5semidirect
120. #1439C2×C5semidirect
121. #1439C2×C5semidirect
122. #1438C2×C5semidirect
123. #1438C2×C5semidirect
124. C22⋊#95C2×C5semidirect
451. C2×C22⋊C4C5×D4semidirect
765. C5#16501direct (N × H)

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×#3982
C2×C5×#3942
C2×C5×#3852
C5×#14452
C5×#14392
C5×#14382
C5×C22⋊#952
#165015