Finite Group Databasebeta

← C5×#11016 #11933736

Subgroups — C5×#11016 #11933736

Order 1280.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C22×C5×#104C211yesmaximal, characteristic, complemented
3C2×C5×#418C211yesmaximal, characteristic, complemented
4C5×#2311C211yesmaximal, characteristic, complemented
5C2×C5×#390C211yesmaximal, characteristic, complemented
6C2×C5×#343C211yesmaximal, characteristic, complemented
7C2×C5×#339C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C23×C5×D4C2211yescharacteristic
10C2×C5×AGL(1,ℤ/8)—22no—
11C2×C5×AGL(1,ℤ/8)—22no—
12C2×C5×AGL(1,ℤ/8)—22no—
13C2×C5×AGL(1,ℤ/8)—22no—
14C2×C5×AGL(1,ℤ/8)—22no—
15C2×C5×AGL(1,ℤ/8)C414yescomplemented
16C22×C5×SD16—21no—
17C22×C5×D8—21no—
18C22×C5×M16C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4—22no—
23C22×C42×C5C2211yescharacteristic
24C2×C5×#104—22no—
25C2×C5×#104—22no—
26C2×C5×#104—22no—
27C5×#418—22no—
28C5×#418—22no—
29C2×C5×#102—22no—
30C5×#391—21no—
31C5×#390—22no—
32C5×#390—21no—
33C5×#390—22no—
34C5×#386—22no—
35C5×#380—22no—
36C5×#343—22no—
37C5×#339—22no—
38#11016C511yesmaximal, characteristic, direct product factor, Sylow
39C25×C5—21no—
40C2×C5×#41—21no—
41C2×C5×#41—21no—
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41—21no—
50C2×C5×#41C2×C412yes—
51C2×C5×#41D412yes—
52C22×C5×Q8D411yescharacteristic
53C22×C5×D4—21no—
54C22×C5×D4—21no—
55C22×C5×D4—21no—
56C22×C5×D4—21no—
57C22×C5×D4—21no—
58C22×C5×D4—21no—
59C22×C5×D4—21no—
60C22×C5×D4—21no—
61C22×C5×D4—21no—
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4—21no—
65C22×C5×D4C2×C412yes—
66C22×C5×D4D411yescharacteristic
67C22×C5×D4D412yes—
68C22×C5×D4D412yes—
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C23×C4×C5D412yes—
72C23×C4×C5C2311yescharacteristic
73C5×AGL(1,ℤ/8)—28no—
74C5×AGL(1,ℤ/8)—28no—
75C5×AGL(1,ℤ/8)—28no—
76C5×AGL(1,ℤ/8)—28no—
77C2×C5×SD16—24no—
78C2×C5×SD16—24no—
79C2×C5×SD16—24no—
80C2×C5×D8—24no—
81C2×C5×D8—24no—
82C2×C5×D8—24no—
83C2×C5×M16—21no—
84C2×C5×M16—21no—
85C2×C5×M16—21no—
86C2×C5×M16—21no—
87C2×C5×M16—21no—
88C2×C5×M16—21no—
89C2×C5×M16—21no—
90C2×C5×M16—21no—
91C2×C5×M16C2×C412yes—
92C2×C5×M16D412yes—
93C2×C5×M16D412yes—
94C2×C5×M16D412yes—
95C22×C5×C8—21no—
96C22×C5×C8—21no—
97C5×#117—21no—
98C5×#117—21no—
99C5×#117—21no—
100C5×#117—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4D412yes—
108C2×C5×C22⋊C4—28no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4—48no—
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5—21no—
116C2×C42×C5—21no—
117C2×C42×C5—21no—
118C2×C42×C5D412yes—
119C5×#104—28no—
120C5×#102—28no—
121C5×#95—24no—
122C22×AGL(1,ℤ/8)C2×C511yescharacteristic
123C22×#104C2×C511yescharacteristic, complemented
124C2×#418C2×C511yescharacteristic, complemented
125#2311C2×C511yescharacteristic, complemented
126C2×#390C2×C511yescharacteristic, complemented
127C2×#343C2×C511yescharacteristic, complemented
128C2×#339C2×C511yescharacteristic, complemented
129C24×C5—22no—
130C24×C5—22no—
131C24×C5—21no—
132C24×C5—22no—
133C24×C5—44no—
134C24×C5—44no—
135C24×C5—41no—
136C24×C5—41no—
137C24×C5—41no—
138C24×C5—41no—
139C24×C5C2×D411yescharacteristic
140C5×#41—22no—
141C5×#41—22no—
142C5×#41—22no—
143C5×#41—22no—
144C5×#41—22no—
145C5×#41—22no—
146C5×#41—22no—
147C5×#41—22no—
148C5×#41—41no—
149C5×#41—41no—
150C5×#41—41no—
151C5×#41—41no—
152C5×#41—41no—
153C5×#41—41no—
154C5×#41—41no—
155C5×#41—41no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8C22⋊C412yescomplemented
162C2×C5×D4—22no—
163C2×C5×D4—22no—
164C2×C5×D4—22no—
165C2×C5×D4—22no—
166C2×C5×D4—22no—
167C2×C5×D4—22no—
168C2×C5×D4—22no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4—22no—
174C2×C5×D4—22no—
175C2×C5×D4—22no—
176C2×C5×D4—22no—
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—41no—
185C2×C5×D4—41no—
186C2×C5×D4—41no—
187C2×C5×D4—41no—
188C2×C5×D4—41no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4—41no—
192C2×C5×D4—41no—
193C2×C5×D4—41no—
194C2×C5×D4—41no—
195C2×C5×D4—41no—
196C2×C5×D4—41no—
197C2×C5×D4—41no—
198C2×C5×D4—41no—
199C2×C5×D4—41no—
200C2×C5×D4C22⋊C412yescomplemented
201C2×C5×D4C22⋊C414yescomplemented
202C22×C4×C5—24no—
203C22×C4×C5—22no—
204C22×C4×C5—21no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—42no—
212C22×C4×C5—41no—
213C22×C4×C5—41no—
214C22×C4×C5—41no—
215C22×C4×C5—41no—
216C22×C4×C5—41no—
217C22×C4×C5—41no—
218C22×C4×C5—44no—
219C22×C4×C5C22×C411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5#4111yescharacteristic
230C22×C4×C5#4111yescharacteristic
231C22×C4×C5#4111yescharacteristic
232C22×C4×C5#4111yescharacteristic
233C5×SD16—216no—
234C5×D8—216no—
235C5×M16—22no—
236C5×M16—22no—
237C5×M16—22no—
238C5×M16—22no—
239C5×M16—22no—
240C5×M16—41no—
241C5×M16—41no—
242C5×M16C22⋊C414yescomplemented
243C2×C5×C8—22no—
244C2×C5×C8—22no—
245C2×C5×C8—22no—
246C2×C5×C8—22no—
247C2×C5×C8—41no—
248C2×C5×C8—41no—
249C5×C4⋊C4—22no—
250C5×C4⋊C4—22no—
251C5×C4⋊C4—41no—
252C5×C4⋊C4—41no—
253C5×C4⋊C4—41no—
254C5×C4⋊C4—41no—
255C5×C22⋊C4—416no—
256C5×C22⋊C4—41no—
257C5×C22⋊C4—41no—
258C5×C22⋊C4—84no—
259C42×C5—22no—
260C42×C5—22no—
261C42×C5—41no—
262C42×C5—41no—
263C42×C5—41no—
264C42×C5—41no—
265C22×#41C22×C511yescharacteristic
266C23×D4C22×C511yescharacteristic
267C2×AGL(1,ℤ/8)—22no—
268C2×AGL(1,ℤ/8)—22no—
269C2×AGL(1,ℤ/8)—22no—
270C2×AGL(1,ℤ/8)—22no—
271C2×AGL(1,ℤ/8)—22no—
272C2×AGL(1,ℤ/8)C4×C514yescomplemented
273C22×SD16—21no—
274C22×D8—21no—
275C22×M16C22×C511yescharacteristic
276C22×M16C22×C511yescharacteristic
277C2×#117C22×C511yescharacteristic
278C22×C4⋊C4C22×C511yescharacteristic
279C22×C22⋊C4—22no—
280C22×C42C22×C511yescharacteristic
281C2×#104—22no—
282C2×#104—22no—
283C2×#104—22no—
284#418—22no—
285#418—22no—
286C2×#102—22no—
287#391—21no—
288#390—21no—
289#390—22no—
290#390—22no—
291#386—22no—
292#380—22no—
293#343—22no—
294#339—22no—
295C23×C5—22no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5—24no—
299C23×C5—44no—
300C23×C5—48no—
301C23×C5—44no—
302C23×C5—48no—
303C23×C5—42no—
304C23×C5—42no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—42no—
308C23×C5—42no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5—42no—
312C23×C5—42no—
313C23×C5—84no—
314C23×C5—82no—
315C23×C5—82no—
316C23×C5—84no—
317C23×C5—82no—
318C23×C5—82no—
319C23×C5C4×D411yescharacteristic
320C23×C5#12011yescharacteristic
321C23×C5#12011yescharacteristic
322C23×C5#12111yescharacteristic
323C23×C5#12111yescharacteristic
324C23×C5#12111yescharacteristic
325C23×C5#12711yescharacteristic
326C5×Q8—22no—
327C5×Q8—22no—
328C5×Q8—41no—
329C5×Q8—41no—
330C5×D4—22no—
331C5×D4—24no—
332C5×D4—24no—
333C5×D4—22no—
334C5×D4—42no—
335C5×D4—42no—
336C5×D4—42no—
337C5×D4—42no—
338C5×D4—42no—
339C5×D4—42no—
340C5×D4—42no—
341C5×D4—42no—
342C5×D4—42no—
343C5×D4—42no—
344C5×D4—41no—
345C5×D4—41no—
346C2×C4×C5—24no—
347C2×C4×C5—22no—
348C2×C4×C5—44no—
349C2×C4×C5—42no—
350C2×C4×C5—44no—
351C2×C4×C5—42no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—42no—
355C2×C4×C5—42no—
356C2×C4×C5—42no—
357C2×C4×C5—42no—
358C2×C4×C5—44no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5—44no—
363C2×C4×C5—42no—
364C2×C4×C5—82no—
365C2×C4×C5C2×C22⋊C411yescharacteristic
366C2×C4×C5C2×C22⋊C411yescharacteristic
367C2×C4×C5C2×C22⋊C411yescharacteristic
368C2×C4×C5C4×D411yescharacteristic
369C2×C4×C5C4×D411yescharacteristic
370C2×C4×C5C4×D411yescharacteristic
371C2×C4×C5#12011yescharacteristic
372C2×C4×C5#12011yescharacteristic
373C2×C4×C5#12011yescharacteristic
374C2×C4×C5#12011yescharacteristic
375C2×C4×C5#12011yescharacteristic
376C2×C4×C5#12011yescharacteristic
377C2×C4×C5#12111yescharacteristic
378C2×C4×C5#12111yescharacteristic
379C2×C4×C5#12111yescharacteristic
380C2×C4×C5#12111yescharacteristic
381C2×C4×C5#12111yescharacteristic
382C2×C4×C5#12111yescharacteristic
383C2×C4×C5#12111yescharacteristic
384C2×C4×C5#12111yescharacteristic
385C2×C4×C5#12111yescharacteristic
386C2×C4×C5#12311yescharacteristic
387C2×C4×C5#12311yescharacteristic
388C2×C4×C5#12311yescharacteristic
389C2×C4×C5#12311yescharacteristic
390C2×C4×C5#12411yescharacteristic
391C2×C4×C5#12411yescharacteristic
392C2×C4×C5#12711yescharacteristic
393C5×C8—24no—
394C5×C8—42no—
395C25—21no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41—21no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41C2×C4×C512yes—
407C2×#41C5×D412yes—
408C22×Q8C5×D411yescharacteristic
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—21no—
420C22×D4—21no—
421C22×D4C2×C4×C512yes—
422C22×D4C5×D411yescharacteristic
423C22×D4C5×D412yes—
424C22×D4C5×D412yes—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C5×D412yes—
428C23×C4C23×C511yescharacteristic
429AGL(1,ℤ/8)—28no—
430AGL(1,ℤ/8)—28no—
431AGL(1,ℤ/8)—28no—
432AGL(1,ℤ/8)—28no—
433C2×SD16—24no—
434C2×SD16—24no—
435C2×SD16—24no—
436C2×D8—24no—
437C2×D8—24no—
438C2×D8—24no—
439C2×M16—21no—
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16C2×C4×C512yes—
448C2×M16C5×D412yes—
449C2×M16C5×D412yes—
450C2×M16C5×D412yes—
451C22×C8—21no—
452C22×C8—21no—
453#117—21no—
454#117—21no—
455#117—21no—
456#117—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4C5×D412yes—
464C2×C22⋊C4—28no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—48no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C5×D412yes—
475#104—28no—
476#102—28no—
477#95—24no—
478C22×C5—22no—
479C22×C5—22no—
480C22×C5—21no—
481C22×C5—21no—
482C22×C5—21no—
483C22×C5—21no—
484C22×C5—22no—
485C22×C5—22no—
486C22×C5—48no—
487C22×C5—44no—
488C22×C5—42no—
489C22×C5—44no—
490C22×C5—84no—
491C22×C5—84no—
492C22×C5—84no—
493C22×C5—84no—
494C22×C5—81no—
495C22×C5—82no—
496C22×C5—81no—
497C22×C5—82no—
498C22×C5—82no—
499C22×C5—84no—
500C22×C5#38611yescharacteristic
501C22×C5#38611yescharacteristic
502C22×C5#39011yescharacteristic
503C22×C5#39211yescharacteristic
504C22×C5#39211yescharacteristic
505C22×C5#39211yescharacteristic
506C22×C5#39411yescharacteristic
507C22×C5#45312yes—
508C22×C5#45412yes—
509C4×C5—44no—
510C4×C5—42no—
511C4×C5—82no—
512C4×C5—82no—
513C4×C5#37911yescharacteristic
514C4×C5#38611yescharacteristic
515C4×C5#38611yescharacteristic
516C4×C5#39011yescharacteristic
517C4×C5#39211yescharacteristic
518C4×C5#39411yescharacteristic
519C4×C5#39411yescharacteristic
520C4×C5#39411yescharacteristic
521C24—22no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—44no—
526C24—44no—
527C24—41no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24C2×C5×D411yescharacteristic
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C5×C22⋊C412yescomplemented
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4C5×C22⋊C412yescomplemented
593C2×D4C5×C22⋊C414yescomplemented
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—42no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—44no—
611C22×C4C22×C4×C511yescharacteristic
612C22×C4C2×C5×D411yescharacteristic
613C22×C4C2×C5×D411yescharacteristic
614C22×C4C2×C5×D411yescharacteristic
615C22×C4C2×C5×D411yescharacteristic
616C22×C4C2×C5×D411yescharacteristic
617C22×C4C2×C5×D411yescharacteristic
618C22×C4C2×C5×D411yescharacteristic
619C22×C4C2×C5×D411yescharacteristic
620C22×C4C2×C5×D411yescharacteristic
621C22×C4C5×#4111yescharacteristic
622C22×C4C5×#4111yescharacteristic
623C22×C4C5×#4111yescharacteristic
624C22×C4C5×#4111yescharacteristic
625SD16—216no—
626D8—216no—
627M16—22no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—41no—
633M16—41no—
634M16C5×C22⋊C414yescomplemented
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—41no—
640C2×C8—41no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C22⋊C4—416no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C22⋊C4—84no—
651C42—22no—
652C42—22no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C2×C5—21no—
658C2×C5—21no—
659C2×C5—21no—
660C2×C5—21no—
661C2×C5—82no—
662C2×C5—84no—
663C2×C5#143811yescharacteristic
664C2×C5#188312yes—
665C2×C5#200211yescharacteristic
666C2×C5#200311yescharacteristic
667C2×C5#200612yes—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—44no—
673C23—48no—
674C23—44no—
675C23—48no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—84no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23—82no—
691C23—82no—
692C23C4×C5×D411yescharacteristic
693C23C5×#12011yescharacteristic
694C23C5×#12011yescharacteristic
695C23C5×#12111yescharacteristic
696C23C5×#12111yescharacteristic
697C23C5×#12111yescharacteristic
698C23C5×#12711yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—41no—
702Q8—41no—
703D4—22no—
704D4—24no—
705D4—24no—
706D4—22no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—41no—
718D4—41no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—82no—
738C2×C4C2×C5×C22⋊C411yescharacteristic
739C2×C4C2×C5×C22⋊C411yescharacteristic
740C2×C4C2×C5×C22⋊C411yescharacteristic
741C2×C4C4×C5×D411yescharacteristic
742C2×C4C4×C5×D411yescharacteristic
743C2×C4C4×C5×D411yescharacteristic
744C2×C4C5×#12011yescharacteristic
745C2×C4C5×#12011yescharacteristic
746C2×C4C5×#12011yescharacteristic
747C2×C4C5×#12011yescharacteristic
748C2×C4C5×#12011yescharacteristic
749C2×C4C5×#12011yescharacteristic
750C2×C4C5×#12111yescharacteristic
751C2×C4C5×#12111yescharacteristic
752C2×C4C5×#12111yescharacteristic
753C2×C4C5×#12111yescharacteristic
754C2×C4C5×#12111yescharacteristic
755C2×C4C5×#12111yescharacteristic
756C2×C4C5×#12111yescharacteristic
757C2×C4C5×#12111yescharacteristic
758C2×C4C5×#12111yescharacteristic
759C2×C4C5×#12311yescharacteristic
760C2×C4C5×#12311yescharacteristic
761C2×C4C5×#12311yescharacteristic
762C2×C4C5×#12311yescharacteristic
763C2×C4C5×#12411yescharacteristic
764C2×C4C5×#12411yescharacteristic
765C2×C4C5×#12711yescharacteristic
766C8—24no—
767C8—42no—
768C5#1101611yescharacteristic, direct product factor, Sylow
769C22—22no—
770C22—22no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—48no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—84no—
782C22—84no—
783C22—84no—
784C22—84no—
785C22—82no—
786C22—81no—
787C22—82no—
788C22—81no—
789C22—84no—
790C22—82no—
791C22C5×#38611yescharacteristic
792C22C5×#38611yescharacteristic
793C22C5×#39011yescharacteristic
794C22C5×#39211yescharacteristic
795C22C5×#39211yescharacteristic
796C22C5×#39211yescharacteristic
797C22C5×#39411yescharacteristic
798C22C5×#45312yes—
799C22C5×#45412yes—
800C4—44no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4C5×#37911yescharacteristic
805C4C5×#38611yescharacteristic
806C4C5×#38611yescharacteristic
807C4C5×#39011yescharacteristic
808C4C5×#39211yescharacteristic
809C4C5×#39411yescharacteristic
810C4C5×#39411yescharacteristic
811C4C5×#39411yescharacteristic
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—84no—
817C2—82no—
818C2C5×#143811yescharacteristic
819C2C5×#188312yes—
820C2C5×#200211yescharacteristic
821C2C5×#200311yescharacteristic
822C2C5×#200612yes—
subgroupG/H
center, socleC23×C5#120
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×AGL(1,ℤ/8)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C5×#104C2semidirect
3. C2×C5×#418C2semidirect
4. C5×#2311C2semidirect
5. C2×C5×#390C2semidirect
6. C2×C5×#343C2semidirect
7. C2×C5×#339C2semidirect
15. C2×C5×AGL(1,ℤ/8)C4semidirect
38. #11016C5direct (N × H)
123. C22×#104C2×C5semidirect
124. C2×#418C2×C5semidirect
125. #2311C2×C5semidirect
126. C2×#390C2×C5semidirect
127. C2×#343C2×C5semidirect
128. C2×#339C2×C5semidirect
161. C2×C5×Q8C22⋊C4semidirect
200. C2×C5×D4C22⋊C4semidirect
201. C2×C5×D4C22⋊C4semidirect
242. C5×M16C22⋊C4semidirect
272. C2×AGL(1,ℤ/8)C4×C5semidirect
553. C2×Q8C5×C22⋊C4semidirect
592. C2×D4C5×C22⋊C4semidirect
593. C2×D4C5×C22⋊C4semidirect
634. M16C5×C22⋊C4semidirect
768. C5#11016direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×AGL(1,ℤ/8)2
C22×C5×#1042
C2×C5×#4182
C5×#23112
C2×C5×#3902
C2×C5×#3432
C2×C5×#3392
#110165