Finite Group Databasebeta

← C5×#18638 #11941358

Subgroups — C5×#18638 #11941358

Order 1280.

956 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3520C211yesmaximal, characteristic, complemented
2C5×#3247C211yesmaximal, characteristic, complemented
3C5×#3131C211yesmaximal, characteristic, complemented
4C5×#3109C211yesmaximal, characteristic, complemented
5C5×#1638C211yesmaximal, characteristic, complemented
6C5×#1637C211yesmaximal, characteristic, complemented
7C5×#1635C211yesmaximal, characteristic, complemented
8C5×#1635C211yesmaximal, characteristic, complemented
9C5×#1628C211yesmaximal, characteristic, complemented
10C5×#1627C211yesmaximal, characteristic, complemented
11C5×#1625C211yesmaximal, characteristic, complemented
12C5×#1625C211yesmaximal, characteristic, complemented
13C5×#1552C211yesmaximal, characteristic, complemented
14C5×#1494C211yesmaximal, characteristic, complemented
15C2×C5×D4⋊C8C211yesmaximal, characteristic, complemented
16C5×#556C2211yescharacteristic
17C5×#554—21no—
18C5×#552—21no—
19C5×#551—22no—
20C5×D4×Q8C2211yescharacteristic
21C5×#548—21no—
22C5×#547C2211yescharacteristic
23C5×#547C2211yescharacteristic
24C5×#546—21no—
25C5×#542—21no—
26C5×#539—22no—
27C5×#533C2211yescharacteristic
28C5×#532C2211yescharacteristic
29C5×#529C2211yescharacteristic
30C5×#525—21no—
31C2×C5×C22⋊Q8—21no—
32C5×#520—21no—
33C2×C4×C5×D4C2211yescharacteristic
34C5×#488—22no—
35C5×#487C2211yescharacteristic, complemented
36C5×#487C2211yescharacteristic, complemented
37C5×#486C2211yescharacteristic, complemented
38C5×#486C2211yescharacteristic, complemented
39C5×#481—21no—
40C5×#478—21no—
41C5×#477C2211yescharacteristic, complemented
42C5×#476C2211yescharacteristic
43C5×#476C2211yescharacteristic
44C5×#476C2211yescharacteristic, complemented
45C5×#466—21no—
46C5×#465—21no—
47C5×#463—21no—
48C5×#460C2211yescharacteristic, complemented
49C5×#459C2211yescharacteristic
50C5×#459C2211yescharacteristic
51C5×#459C2211yescharacteristic, complemented
52C5×#447—21no—
53C5×#442—21no—
54C5×#442—21no—
55C5×#432C2211yescharacteristic
56C2×C5×C4⋊C8C2211yescharacteristic
57C5×#416—22no—
58C2×C4×C5×C8C2211yescharacteristic
59C5×#332C2211yescharacteristic, complemented
60C5×#332C2211yescharacteristic, complemented
61C5×#332C2211yescharacteristic, complemented
62C5×#332C2211yescharacteristic, complemented
63C5×Q8⋊C8C2211yescharacteristic, complemented
64C5×Q8⋊C8C2211yescharacteristic, complemented
65C5×D4⋊C8C2211yescharacteristic
66C5×D4⋊C8C2211yescharacteristic
67C5×D4⋊C8C2211yescharacteristic
68C5×D4⋊C8C2211yescharacteristic
69C5×D4⋊C8C2211yescharacteristic, complemented
70C5×D4⋊C8C2211yescharacteristic, complemented
71#18638C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41—21no—
73C2×C5×#41—21no—
74C2×C5×#41—21no—
75C22×C5×Q8—21no—
76C22×C5×D4D411yescharacteristic
77C23×C4×C5—21no—
78C2×C5×SD16—21no—
79C2×C5×D8—21no—
80C2×C5×D8—21no—
81C2×C5×D8—21no—
82C22×C5×C8—21no—
83C22×C5×C8—21no—
84C5×C4⋊Q8—21no—
85C5×C4⋊Q8C2311yescharacteristic
86C5×C4⋊Q8C2311yescharacteristic
87C5×C4⋊Q8C2311yescharacteristic
88C5×#127C2311yescharacteristic
89C5×#126—22no—
90C5×#126—22no—
91C5×#126—21no—
92C5×#125—22no—
93C5×#125D411yescharacteristic
94C5×#125D412yes—
95C5×#124—22no—
96C5×#124—21no—
97C5×#124—21no—
98C5×#124D411yescharacteristic
99C5×#123—22no—
100C5×#123—22no—
101C5×#123—21no—
102C5×#123—22no—
103C5×#123—22no—
104C5×C22⋊Q8—22no—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8—22no—
107C5×C22⋊Q8—21no—
108C5×C22⋊Q8—21no—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—22no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8D411yescharacteristic
115C5×#121—22no—
116C5×#121—21no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#121—21no—
120C5×#121D411yescharacteristic
121C5×#120—22no—
122C4×C5×Q8—21no—
123C4×C5×Q8—21no—
124C4×C5×Q8—21no—
125C4×C5×Q8C2311yescharacteristic
126C4×C5×D4—22no—
127C4×C5×D4—22no—
128C4×C5×D4—22no—
129C4×C5×D4—21no—
130C4×C5×D4—21no—
131C4×C5×D4—21no—
132C4×C5×D4—21no—
133C4×C5×D4—21no—
134C4×C5×D4—21no—
135C4×C5×D4D411yescharacteristic
136C4×C5×D4D411yescharacteristic
137C4×C5×D4C2311yescharacteristic
138C4×C5×D4C2311yescharacteristic
139C4×C5×D4C2311yescharacteristic
140C5×#117—22no—
141C5×#117—21no—
142C5×#117—21no—
143C5×#117D412yes—
144C2×C5×C4⋊C4—22no—
145C2×C5×C4⋊C4—21no—
146C2×C5×C4⋊C4—21no—
147C2×C5×C4⋊C4D411yescharacteristic
148C2×C5×C22⋊C4—22no—
149C2×C5×C22⋊C4—21no—
150C2×C42×C5C2311yescharacteristic
151C5×#107—21no—
152C5×#106—21no—
153C5×#106—21no—
154C5×#106—21no—
155C5×C4⋊C8—21no—
156C5×C4⋊C8C2311yescharacteristic
157C5×C4⋊C8C2311yescharacteristic
158C5×C4⋊C8C2311yescharacteristic
159C5×C4⋊C8C2311yescharacteristic
160C5×#103—21no—
161C5×#103—22no—
162C5×#103—22no—
163C5×#102—21no—
164C5×#102—21no—
165C5×#102—21no—
166C5×#102—22no—
167C5×#102—22no—
168C5×#102—21no—
169C5×#102—21no—
170C5×#102—21no—
171C5×#102—21no—
172C5×C22⋊C8—21no—
173C5×#97—21no—
174C4×C5×C8—21no—
175C4×C5×C8C2311yescharacteristic
176C4×C5×C8C2311yescharacteristic
177#3520C2×C511yescharacteristic, complemented
178#3247C2×C511yescharacteristic, complemented
179#3131C2×C511yescharacteristic, complemented
180#3109C2×C511yescharacteristic, complemented
181#1638C2×C511yescharacteristic, complemented
182#1637C2×C511yescharacteristic, complemented
183#1635C2×C511yescharacteristic, complemented
184#1635C2×C511yescharacteristic, complemented
185#1628C2×C511yescharacteristic, complemented
186#1627C2×C511yescharacteristic, complemented
187#1625C2×C511yescharacteristic, complemented
188#1625C2×C511yescharacteristic, complemented
189#1552C2×C511yescharacteristic, complemented
190#1494C2×C511yescharacteristic, complemented
191C2×D4⋊C8C2×C511yescharacteristic, complemented
192C24×C5—21no—
193C5×#41—44no—
194C5×#41—42no—
195C5×#41—42no—
196C5×#41—81no—
197C5×#41—81no—
198C2×C5×Q8—22no—
199C2×C5×Q8—21no—
200C2×C5×Q8—21no—
201C2×C5×Q8—21no—
202C2×C5×Q8—81no—
203C2×C5×Q8—81no—
204C2×C5×Q8C2×D411yescharacteristic
205C2×C5×D4—22no—
206C2×C5×D4—22no—
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—21no—
210C2×C5×D4—21no—
211C2×C5×D4—21no—
212C2×C5×D4—21no—
213C2×C5×D4—41no—
214C2×C5×D4—41no—
215C2×C5×D4C2×D411yescharacteristic
216C2×C5×D4C2×D411yescharacteristic
217C2×C5×D4C2×D411yescharacteristic
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—41no—
228C22×C4×C5—81no—
229C22×C4×C5—81no—
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D411yescharacteristic
233C5×SD16—81no—
234C5×D8—42no—
235C5×D8—42no—
236C5×D8—81no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—21no—
243C2×C5×C8—42no—
244C2×C5×C8—81no—
245C5×C4⋊C4—22no—
246C5×C4⋊C4—22no—
247C5×C4⋊C4—22no—
248C5×C4⋊C4—22no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—22no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4C2×D411yescharacteristic
261C5×C4⋊C4C2×D411yescharacteristic
262C5×C4⋊C4C2×D411yescharacteristic
263C5×C4⋊C4C2×D411yescharacteristic
264C5×C4⋊C4C2×D412yes—
265C5×C4⋊C4C2×D412yes—
266C5×C22⋊C4—22no—
267C5×C22⋊C4—22no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—22no—
270C5×C22⋊C4—22no—
271C5×C22⋊C4—21no—
272C5×C22⋊C4—22no—
273C5×C22⋊C4—21no—
274C5×C22⋊C4—21no—
275C5×C22⋊C4—21no—
276C5×C22⋊C4—21no—
277C5×C22⋊C4—21no—
278C5×C22⋊C4—21no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—21no—
281C5×C22⋊C4—41no—
282C5×C22⋊C4—41no—
283C42×C5—22no—
284C42×C5—22no—
285C42×C5—21no—
286C42×C5C2×D411yescharacteristic
287C42×C5C2×D411yescharacteristic
288C42×C5C2×D411yescharacteristic
289C42×C5C2411yescharacteristic
290#556C22×C511yescharacteristic
291#554—21no—
292#552—21no—
293#551—22no—
294D4×Q8C22×C511yescharacteristic
295#548—21no—
296#547C22×C511yescharacteristic
297#547C22×C511yescharacteristic
298#546—21no—
299#542—21no—
300#539—22no—
301#533C22×C511yescharacteristic
302#532C22×C511yescharacteristic
303#529C22×C511yescharacteristic
304#525—21no—
305C2×C22⋊Q8—21no—
306#520—21no—
307C2×C4×D4C22×C511yescharacteristic
308#488—22no—
309#487C22×C511yescharacteristic, complemented
310#487C22×C511yescharacteristic, complemented
311#486C22×C511yescharacteristic, complemented
312#486C22×C511yescharacteristic, complemented
313#481—21no—
314#478—21no—
315#477C22×C511yescharacteristic, complemented
316#476C22×C511yescharacteristic
317#476C22×C511yescharacteristic
318#476C22×C511yescharacteristic, complemented
319#466—21no—
320#465—21no—
321#463—21no—
322#460C22×C511yescharacteristic, complemented
323#459C22×C511yescharacteristic
324#459C22×C511yescharacteristic
325#459C22×C511yescharacteristic, complemented
326#447—21no—
327#442—21no—
328#442—21no—
329#432C22×C511yescharacteristic
330C2×C4⋊C8C22×C511yescharacteristic
331#416—22no—
332C2×C4×C8C22×C511yescharacteristic
333#332C22×C511yescharacteristic, complemented
334#332C22×C511yescharacteristic, complemented
335#332C22×C511yescharacteristic, complemented
336#332C22×C511yescharacteristic, complemented
337Q8⋊C8C22×C511yescharacteristic, complemented
338Q8⋊C8C22×C511yescharacteristic, complemented
339D4⋊C8C22×C511yescharacteristic
340D4⋊C8C22×C511yescharacteristic
341D4⋊C8C22×C511yescharacteristic
342D4⋊C8C22×C511yescharacteristic
343D4⋊C8C22×C511yescharacteristic, complemented
344D4⋊C8C22×C511yescharacteristic, complemented
345C23×C5—21no—
346C23×C5—21no—
347C23×C5—21no—
348C23×C5—42no—
349C23×C5—42no—
350C23×C5—41no—
351C23×C5—81no—
352C23×C5#12011yescharacteristic
353C5×Q8—21no—
354C5×Q8—21no—
355C5×Q8—42no—
356C5×Q8—41no—
357C5×Q8—41no—
358C5×Q8—41no—
359C5×Q8—41no—
360C5×Q8—82no—
361C5×D4—21no—
362C5×D4—21no—
363C5×D4—21no—
364C5×D4—21no—
365C5×D4—21no—
366C5×D4—42no—
367C5×D4—42no—
368C5×D4—44no—
369C5×D4—42no—
370C5×D4—41no—
371C5×D4—41no—
372C5×D4—41no—
373C5×D4—41no—
374C5×D4—82no—
375C5×D4—82no—
376C5×D4#13512yes—
377C2×C4×C5—22no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—22no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—22no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—44no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—81no—
398C2×C4×C5—81no—
399C2×C4×C5—82no—
400C2×C4×C5—81no—
401C2×C4×C5—82no—
402C2×C4×C5—82no—
403C2×C4×C5#12011yescharacteristic
404C2×C4×C5#12011yescharacteristic
405C2×C4×C5#12011yescharacteristic
406C2×C4×C5C22×D411yescharacteristic
407C2×C4×C5C22×D411yescharacteristic
408C2×C4×C5C22×D411yescharacteristic
409C5×C8—41no—
410C5×C8—41no—
411C5×C8—41no—
412C5×C8—41no—
413C5×C8—41no—
414C5×C8—41no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C22×Q8—21no—
419C22×D4C5×D411yescharacteristic
420C23×C4—21no—
421C2×SD16—21no—
422C2×D8—21no—
423C2×D8—21no—
424C2×D8—21no—
425C22×C8—21no—
426C22×C8—21no—
427C4⋊Q8—21no—
428C4⋊Q8C23×C511yescharacteristic
429C4⋊Q8C23×C511yescharacteristic
430C4⋊Q8C23×C511yescharacteristic
431#127C23×C511yescharacteristic
432#126—22no—
433#126—22no—
434#126—21no—
435#125—22no—
436#125C5×D411yescharacteristic
437#125C5×D412yes—
438#124—22no—
439#124—21no—
440#124—21no—
441#124C5×D411yescharacteristic
442#123—22no—
443#123—22no—
444#123—21no—
445#123—22no—
446#123—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—22no—
456C22⋊Q8—21no—
457C22⋊Q8C5×D411yescharacteristic
458#121—22no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121C5×D411yescharacteristic
464#120—22no—
465C4×Q8—21no—
466C4×Q8—21no—
467C4×Q8—21no—
468C4×Q8C23×C511yescharacteristic
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4C5×D411yescharacteristic
479C4×D4C5×D411yescharacteristic
480C4×D4C23×C511yescharacteristic
481C4×D4C23×C511yescharacteristic
482C4×D4C23×C511yescharacteristic
483#117—22no—
484#117—21no—
485#117—21no—
486#117C5×D412yes—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C5×D411yescharacteristic
491C2×C22⋊C4—22no—
492C2×C22⋊C4—21no—
493C2×C42C23×C511yescharacteristic
494#107—21no—
495#106—21no—
496#106—21no—
497#106—21no—
498C4⋊C8—21no—
499C4⋊C8C23×C511yescharacteristic
500C4⋊C8C23×C511yescharacteristic
501C4⋊C8C23×C511yescharacteristic
502C4⋊C8C23×C511yescharacteristic
503#103—21no—
504#103—22no—
505#103—22no—
506#102—21no—
507#102—21no—
508#102—21no—
509#102—22no—
510#102—22no—
511#102—21no—
512#102—21no—
513#102—21no—
514#102—21no—
515C22⋊C8—21no—
516#97—21no—
517C4×C8—21no—
518C4×C8C23×C511yescharacteristic
519C4×C8C23×C511yescharacteristic
520C22×C5—21no—
521C22×C5—21no—
522C22×C5—22no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5—41no—
528C22×C5—41no—
529C22×C5—41no—
530C22×C5—41no—
531C22×C5—84no—
532C22×C5—81no—
533C22×C5—81no—
534C22×C5—81no—
535C22×C5#45412yes—
536C22×C5C2×#12011yescharacteristic
537C4×C5—21no—
538C4×C5—21no—
539C4×C5—21no—
540C4×C5—21no—
541C4×C5—41no—
542C4×C5—42no—
543C4×C5—41no—
544C4×C5—41no—
545C4×C5—42no—
546C4×C5—41no—
547C4×C5—41no—
548C4×C5—81no—
549C4×C5C2×#13511yescharacteristic
550C4×C5#57511yescharacteristic
551C4×C5#57611yescharacteristic
552C4×C5#57711yescharacteristic
553C24—21no—
554#41—44no—
555#41—42no—
556#41—42no—
557#41—81no—
558#41—81no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—81no—
564C2×Q8—81no—
565C2×Q8C2×C5×D411yescharacteristic
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4C2×C5×D411yescharacteristic
577C2×D4C2×C5×D411yescharacteristic
578C2×D4C2×C5×D411yescharacteristic
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4C2×C5×D411yescharacteristic
592C22×C4C2×C5×D411yescharacteristic
593C22×C4C2×C5×D411yescharacteristic
594SD16—81no—
595D8—42no—
596D8—42no—
597D8—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C2×C8—81no—
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—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4C2×C5×D412yes—
622C4⋊C4C2×C5×D412yes—
623C4⋊C4C2×C5×D411yescharacteristic
624C4⋊C4C2×C5×D411yescharacteristic
625C4⋊C4C2×C5×D411yescharacteristic
626C4⋊C4C2×C5×D411yescharacteristic
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42C2×C5×D411yescharacteristic
648C42C2×C5×D411yescharacteristic
649C42C2×C5×D411yescharacteristic
650C42C24×C511yescharacteristic
651C2×C5—22no—
652C2×C5—42no—
653C2×C5—81no—
654C2×C5—81no—
655C2×C5—161no—
656C2×C5#300211yescharacteristic
657C2×C5#301211yescharacteristic
658C2×C5C2×#45411yescharacteristic
659C23—21no—
660C23—21no—
661C23—21no—
662C23—42no—
663C23—42no—
664C23—41no—
665C23—81no—
666C23C5×#12011yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—42no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—82no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—42no—
681D4—42no—
682D4—44no—
683D4—42no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—82no—
689D4—82no—
690D4C5×#13512yes—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—44no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—82no—
714C2×C4—81no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4C5×#12011yescharacteristic
718C2×C4C5×#12011yescharacteristic
719C2×C4C5×#12011yescharacteristic
720C2×C4C22×C5×D411yescharacteristic
721C2×C4C22×C5×D411yescharacteristic
722C2×C4C22×C5×D411yescharacteristic
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C8—41no—
729C5#1863811yescharacteristic, direct product factor, Sylow
730C22—21no—
731C22—21no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—84no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C5×#45412yes—
746C22C2×C5×#12011yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4C2×C5×#13511yescharacteristic
760C4C5×#57511yescharacteristic
761C4C5×#57611yescharacteristic
762C4C5×#57711yescharacteristic
763C2—22no—
764C2—42no—
765C2—81no—
766C2—81no—
767C2—161no—
768C2C5×#300211yescharacteristic
769C2C5×#301211yescharacteristic
770C2C2×C5×#45411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3520C2semidirect
2. C5×#3247C2semidirect
3. C5×#3131C2semidirect
4. C5×#3109C2semidirect
5. C5×#1638C2semidirect
6. C5×#1637C2semidirect
7. C5×#1635C2semidirect
8. C5×#1635C2semidirect
9. C5×#1628C2semidirect
10. C5×#1627C2semidirect
11. C5×#1625C2semidirect
12. C5×#1625C2semidirect
13. C5×#1552C2semidirect
14. C5×#1494C2semidirect
15. C2×C5×D4⋊C8C2semidirect
35. C5×#487C22semidirect
36. C5×#487C22semidirect
37. C5×#486C22semidirect
38. C5×#486C22semidirect
41. C5×#477C22semidirect
44. C5×#476C22semidirect
48. C5×#460C22semidirect
51. C5×#459C22semidirect
59. C5×#332C22semidirect
60. C5×#332C22semidirect
61. C5×#332C22semidirect
62. C5×#332C22semidirect
63. C5×Q8⋊C8C22semidirect
64. C5×Q8⋊C8C22semidirect
69. C5×D4⋊C8C22semidirect
70. C5×D4⋊C8C22semidirect
71. #18638C5direct (N × H)
177. #3520C2×C5semidirect
178. #3247C2×C5semidirect
179. #3131C2×C5semidirect
180. #3109C2×C5semidirect
181. #1638C2×C5semidirect
182. #1637C2×C5semidirect
183. #1635C2×C5semidirect
184. #1635C2×C5semidirect
185. #1628C2×C5semidirect
186. #1627C2×C5semidirect
187. #1625C2×C5semidirect
188. #1625C2×C5semidirect
189. #1552C2×C5semidirect
190. #1494C2×C5semidirect
191. C2×D4⋊C8C2×C5semidirect
309. #487C22×C5semidirect
310. #487C22×C5semidirect
311. #486C22×C5semidirect
312. #486C22×C5semidirect
315. #477C22×C5semidirect
318. #476C22×C5semidirect
322. #460C22×C5semidirect
325. #459C22×C5semidirect
333. #332C22×C5semidirect
334. #332C22×C5semidirect
335. #332C22×C5semidirect
336. #332C22×C5semidirect
337. Q8⋊C8C22×C5semidirect
338. Q8⋊C8C22×C5semidirect
343. D4⋊C8C22×C5semidirect
344. D4⋊C8C22×C5semidirect
729. C5#18638direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35202
C5×#32472
C5×#31312
C5×#31092
C5×#16382
C5×#16372
C5×#16352
C5×#16282
C5×#16272
C5×#16252
C5×#15522
C5×#14942
C2×C5×D4⋊C82
#186385