Finite Group Databasebeta

← C5×#18463 #11941183

Subgroups — C5×#18463 #11941183

Order 1280.

930 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3560C211yesmaximal, characteristic
2C5×#3218C211yesmaximal, characteristic, complemented
3C5×#3206C211yesmaximal, characteristic, complemented
4C5×#2821C211yesmaximal, characteristic, complemented
5C5×#1606C212yesmaximal, complemented
6C5×#1604C212yesmaximal, complemented
7C5×#1603C212yesmaximal, complemented
8C5×#1601C212yesmaximal, complemented
9C5×#1521C211yesmaximal, characteristic, complemented
10C5×#1514C211yesmaximal, characteristic, complemented
11C5×#1473C211yesmaximal, characteristic, complemented
12C5×#563—21no—
13C5×#560—21no—
14C5×#553—21no—
15C5×#553—21no—
16C5×#551—21no—
17C5×#547—21no—
18C5×#546—21no—
19C5×#546—21no—
20C5×#542—21no—
21C5×#539—21no—
22C5×#539C2211yescharacteristic
23C5×#538—21no—
24C5×#538—21no—
25C5×#538C2211yescharacteristic
26C5×#537C2211yescharacteristic
27C5×#534C2211yescharacteristic
28C5×#532C2211yescharacteristic
29C2×C5×C4⋊Q8C2211yescharacteristic, complemented
30C5×#529C2211yescharacteristic
31C2×C5×#126C2211yescharacteristic
32C5×#497—21no—
33C5×#492—21no—
34C5×#491—21no—
35C5×#487—21no—
36C5×#462—21no—
37C5×#461—21no—
38C5×#461—21no—
39C5×#461—21no—
40C5×#451C2212yescomplemented
41C5×#448C2212yes—
42C5×#448C2212yes—
43C5×#448C2212yescomplemented
44C5×#432C2211yescharacteristic, complemented
45C5×#431C2211yescharacteristic, complemented
46C5×#400—21no—
47C5×#399—21no—
48C5×#398—21no—
49C5×#397—21no—
50C5×#395C2212yescomplemented
51C5×#393C2212yes—
52C5×#383C2211yescharacteristic, complemented
53C5×#328C2212yescomplemented
54C5×#327C2212yes—
55C5×#327C2212yes—
56C5×#327C2212yescomplemented
57C5×#324C2212yescomplemented
58C5×#323C2212yes—
59#18463C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C2×C5×#41—21no—
62C22×C5×Q8C2312yes—
63C22×C5×D4—21no—
64C2×C5×Q16—22no—
65C2×C5×SD16—22no—
66C2×C5×SD16—22no—
67C2×C5×SD16—22no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8—21no—
72C5×C4⋊Q8—21no—
73C5×C4⋊Q8D411yescharacteristic
74C5×#127D411yescharacteristic
75C5×#126—21no—
76C5×#126—21no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#126—21no—
81C5×#126—21no—
82C5×#126—21no—
83C5×#126—21no—
84C5×#125—21no—
85C5×#125—21no—
86C5×#125D411yescharacteristic
87C5×#124—21no—
88C5×#124—21no—
89C5×#124—21no—
90C5×#124—21no—
91C5×#124D411yescharacteristic
92C5×#123—21no—
93C5×#123—21no—
94C5×#123—21no—
95C5×#123—21no—
96C5×#123—21no—
97C5×#123—21no—
98C5×#123—21no—
99C5×#123—21no—
100C5×#123—21no—
101C5×#123—21no—
102C5×#123—21no—
103C5×#123—21no—
104C5×C22⋊Q8—21no—
105C5×C22⋊Q8—21no—
106C5×C22⋊Q8—21no—
107C5×C22⋊Q8—21no—
108C5×C22⋊Q8—21no—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8C2311yescharacteristic
112C5×#121—21no—
113C5×#121—21no—
114C5×#121—21no—
115C5×#121—21no—
116C5×#121—21no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#121—21no—
120C5×#121—21no—
121C5×#121—21no—
122C5×#121—21no—
123C5×#121—21no—
124C5×#121C2311yescharacteristic
125C5×#121C2311yescharacteristic
126C5×#121C2311yescharacteristic
127C5×#120—21no—
128C5×#120—21no—
129C5×#120—21no—
130C5×#120—21no—
131C5×#120—21no—
132C4×C5×Q8D411yescharacteristic
133C4×C5×D4—21no—
134C4×C5×D4—21no—
135C4×C5×D4—21no—
136C4×C5×D4—21no—
137C4×C5×D4—21no—
138C4×C5×D4—21no—
139C4×C5×D4—21no—
140C4×C5×D4—21no—
141C4×C5×D4D411yescharacteristic
142C4×C5×D4D411yescharacteristic
143C4×C5×D4D411yescharacteristic
144C5×#117—21no—
145C5×#117—21no—
146C2×C5×C4⋊C4—21no—
147C2×C5×C4⋊C4—21no—
148C2×C5×C4⋊C4—21no—
149C2×C5×C4⋊C4—22no—
150C2×C5×C4⋊C4D411yescharacteristic
151C2×C5×C4⋊C4D411yescharacteristic
152C2×C5×C4⋊C4C2311yescharacteristic
153C2×C5×C22⋊C4—21no—
154C2×C5×C22⋊C4—21no—
155C2×C5×C22⋊C4—22no—
156C2×C5×C22⋊C4D411yescharacteristic
157C2×C5×C22⋊C4D411yescharacteristic
158C2×C5×C22⋊C4C2311yescharacteristic
159C2×C42×C5C2311yescharacteristic
160C5×C4⋊C8—21no—
161C5×C4⋊C8—21no—
162C5×#103—22no—
163C5×#103—22no—
164C5×#103—22no—
165C5×#103—22no—
166C5×C22⋊C8C2312yes—
167C5×C22⋊C8C2312yes—
168C5×#97—21no—
169C4×C5×C8—21no—
170C5×#95—21no—
171C5×#95—21no—
172C5×#95—22no—
173C5×#95—22no—
174C5×#95C2312yes—
175#3560C2×C511yescharacteristic
176#3218C2×C511yescharacteristic, complemented
177#3206C2×C511yescharacteristic, complemented
178#2821C2×C511yescharacteristic, complemented
179#1606C2×C512yescomplemented
180#1604C2×C512yescomplemented
181#1603C2×C512yescomplemented
182#1601C2×C512yescomplemented
183#1521C2×C511yescharacteristic, complemented
184#1514C2×C511yescharacteristic, complemented
185#1473C2×C511yescharacteristic, complemented
186C24×C5—21no—
187C24×C5C2×D411yescharacteristic
188C5×#41—82no—
189C5×#41—82no—
190C2×C5×Q8—21no—
191C2×C5×Q8—21no—
192C2×C5×Q8—22no—
193C2×C5×Q8—22no—
194C2×C5×Q8—82no—
195C2×C5×Q8C2×D411yescharacteristic
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4—21no—
200C2×C5×D4—21no—
201C2×C5×D4—21no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—21no—
208C2×C5×D4—82no—
209C2×C5×D4C2×D411yescharacteristic
210C2×C5×D4C2×D411yescharacteristic
211C2×C5×D4C2×D411yescharacteristic
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2411yescharacteristic
228C5×Q16—82no—
229C5×SD16—82no—
230C5×SD16—82no—
231C5×SD16—82no—
232C2×C5×C8—22no—
233C2×C5×C8—22no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—41no—
252C5×C4⋊C4—41no—
253C5×C4⋊C4—41no—
254C5×C4⋊C4—41no—
255C5×C4⋊C4—82no—
256C5×C4⋊C4C2×D411yescharacteristic
257C5×C4⋊C4C2×D411yescharacteristic
258C5×C4⋊C4C2×D411yescharacteristic
259C5×C4⋊C4C2×D411yescharacteristic
260C5×C22⋊C4—21no—
261C5×C22⋊C4—21no—
262C5×C22⋊C4—21no—
263C5×C22⋊C4—21no—
264C5×C22⋊C4—21no—
265C5×C22⋊C4—21no—
266C5×C22⋊C4—21no—
267C5×C22⋊C4—21no—
268C5×C22⋊C4—21no—
269C5×C22⋊C4—21no—
270C5×C22⋊C4—21no—
271C5×C22⋊C4—21no—
272C5×C22⋊C4—21no—
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—21no—
282C5×C22⋊C4—21no—
283C5×C22⋊C4—21no—
284C5×C22⋊C4—21no—
285C5×C22⋊C4—82no—
286C42×C5—21no—
287C42×C5—21no—
288C42×C5—21no—
289C42×C5C2×D411yescharacteristic
290C42×C5C2×D411yescharacteristic
291C42×C5C2×D411yescharacteristic
292C42×C5C2×D411yescharacteristic
293#563—21no—
294#560—21no—
295#553—21no—
296#553—21no—
297#551—21no—
298#547—21no—
299#546—21no—
300#546—21no—
301#542—21no—
302#539—21no—
303#539C22×C511yescharacteristic
304#538—21no—
305#538—21no—
306#538C22×C511yescharacteristic
307#537C22×C511yescharacteristic
308#534C22×C511yescharacteristic
309#532C22×C511yescharacteristic
310C2×C4⋊Q8C22×C511yescharacteristic, complemented
311#529C22×C511yescharacteristic
312C2×#126C22×C511yescharacteristic
313#497—21no—
314#492—21no—
315#491—21no—
316#487—21no—
317#462—21no—
318#461—21no—
319#461—21no—
320#461—21no—
321#451C22×C512yescomplemented
322#448C22×C512yes—
323#448C22×C512yes—
324#448C22×C512yescomplemented
325#432C22×C511yescharacteristic, complemented
326#431C22×C511yescharacteristic, complemented
327#400—21no—
328#399—21no—
329#398—21no—
330#397—21no—
331#395C22×C512yescomplemented
332#393C22×C512yes—
333#383C22×C511yescharacteristic, complemented
334#328C22×C512yescomplemented
335#327C22×C512yes—
336#327C22×C512yes—
337#327C22×C512yescomplemented
338#324C22×C512yescomplemented
339#323C22×C512yes—
340C23×C5—21no—
341C23×C5—21no—
342C23×C5—21no—
343C23×C5—21no—
344C23×C5—22no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—81no—
348C23×C5—81no—
349C23×C5—81no—
350C23×C5C22×D411yescharacteristic
351C5×Q8—41no—
352C5×Q8—42no—
353C5×Q8—42no—
354C5×Q8—42no—
355C5×Q8—42no—
356C5×Q8—81no—
357C5×Q8—81no—
358C5×D4—41no—
359C5×D4—41no—
360C5×D4—41no—
361C5×D4—42no—
362C5×D4—42no—
363C5×D4—42no—
364C5×D4—81no—
365C5×D4—81no—
366C5×D4—81no—
367C5×D4—81no—
368C5×D4—81no—
369C5×D4—81no—
370C5×D4—81no—
371C5×D4—81no—
372C5×D4—81no—
373C2×C4×C5—22no—
374C2×C4×C5—21no—
375C2×C4×C5—21no—
376C2×C4×C5—21no—
377C2×C4×C5—21no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—22no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5—42no—
392C2×C4×C5—42no—
393C2×C4×C5—81no—
394C2×C4×C5—81no—
395C2×C4×C5—81no—
396C2×C4×C5—81no—
397C2×C4×C5—81no—
398C2×C4×C5—81no—
399C2×C4×C5—81no—
400C2×C4×C5—81no—
401C2×C4×C5#12011yescharacteristic
402C2×C4×C5#12011yescharacteristic
403C2×C4×C5#12011yescharacteristic
404C2×C4×C5#12011yescharacteristic
405C2×C4×C5C22×D411yescharacteristic
406C2×C4×C5C22×D411yescharacteristic
407C5×C8—42no—
408C5×C8—42no—
409C2×#41—21no—
410C2×#41—21no—
411C22×Q8C23×C512yes—
412C22×D4—21no—
413C2×Q16—22no—
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16—22no—
417C4⋊Q8—21no—
418C4⋊Q8—21no—
419C4⋊Q8—21no—
420C4⋊Q8—21no—
421C4⋊Q8—21no—
422C4⋊Q8C5×D411yescharacteristic
423#127C5×D411yescharacteristic
424#126—21no—
425#126—21no—
426#126—21no—
427#126—21no—
428#126—21no—
429#126—21no—
430#126—21no—
431#126—21no—
432#126—21no—
433#125—21no—
434#125—21no—
435#125C5×D411yescharacteristic
436#124—21no—
437#124—21no—
438#124—21no—
439#124—21no—
440#124C5×D411yescharacteristic
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—21no—
446#123—21no—
447#123—21no—
448#123—21no—
449#123—21no—
450#123—21no—
451#123—21no—
452#123—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8C23×C511yescharacteristic
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121C23×C511yescharacteristic
474#121C23×C511yescharacteristic
475#121C23×C511yescharacteristic
476#120—21no—
477#120—21no—
478#120—21no—
479#120—21no—
480#120—21no—
481C4×Q8C5×D411yescharacteristic
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4C5×D411yescharacteristic
491C4×D4C5×D411yescharacteristic
492C4×D4C5×D411yescharacteristic
493#117—21no—
494#117—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4C5×D411yescharacteristic
500C2×C4⋊C4C5×D411yescharacteristic
501C2×C4⋊C4C23×C511yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4C5×D411yescharacteristic
506C2×C22⋊C4C5×D411yescharacteristic
507C2×C22⋊C4C23×C511yescharacteristic
508C2×C42C23×C511yescharacteristic
509C4⋊C8—21no—
510C4⋊C8—21no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515C22⋊C8C23×C512yes—
516C22⋊C8C23×C512yes—
517#97—21no—
518C4×C8—21no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95C23×C512yes—
524C22×C5—21no—
525C22×C5—21no—
526C22×C5—41no—
527C22×C5—41no—
528C22×C5—41no—
529C22×C5—41no—
530C22×C5—41no—
531C22×C5—41no—
532C22×C5—41no—
533C22×C5—41no—
534C22×C5—41no—
535C22×C5—41no—
536C22×C5—41no—
537C22×C5—41no—
538C22×C5—82no—
539C22×C5—162no—
540C22×C5C2×#12011yescharacteristic
541C22×C5#57712yes—
542C4×C5—21no—
543C4×C5—21no—
544C4×C5—21no—
545C4×C5—21no—
546C4×C5—21no—
547C4×C5—21no—
548C4×C5—41no—
549C4×C5—41no—
550C4×C5—41no—
551C4×C5—41no—
552C4×C5—41no—
553C4×C5—41no—
554C4×C5—41no—
555C4×C5—41no—
556C4×C5—82no—
557C4×C5—82no—
558C24—21no—
559C24C2×C5×D411yescharacteristic
560#41—82no—
561#41—82no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—82no—
567C2×Q8C2×C5×D411yescharacteristic
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—82no—
581C2×D4C2×C5×D411yescharacteristic
582C2×D4C2×C5×D411yescharacteristic
583C2×D4C2×C5×D411yescharacteristic
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4C2×C5×D411yescharacteristic
595C22×C4C2×C5×D411yescharacteristic
596C22×C4C2×C5×D411yescharacteristic
597C22×C4C2×C5×D411yescharacteristic
598C22×C4C2×C5×D411yescharacteristic
599C22×C4C24×C511yescharacteristic
600Q16—82no—
601SD16—82no—
602SD16—82no—
603SD16—82no—
604C2×C8—22no—
605C2×C8—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—82no—
628C4⋊C4C2×C5×D411yescharacteristic
629C4⋊C4C2×C5×D411yescharacteristic
630C4⋊C4C2×C5×D411yescharacteristic
631C4⋊C4C2×C5×D411yescharacteristic
632C22⋊C4—21no—
633C22⋊C4—21no—
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—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—82no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42C2×C5×D411yescharacteristic
662C42C2×C5×D411yescharacteristic
663C42C2×C5×D411yescharacteristic
664C42C2×C5×D411yescharacteristic
665C2×C5—22no—
666C2×C5—81no—
667C2×C5—81no—
668C2×C5—81no—
669C2×C5—81no—
670C2×C5#300911yescharacteristic
671C2×C5#302211yescharacteristic
672C2×C5#302711yescharacteristic
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23C22×C5×D411yescharacteristic
684Q8—41no—
685Q8—42no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—81no—
690Q8—81no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—81no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705D4—81no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4C5×#12011yescharacteristic
735C2×C4C5×#12011yescharacteristic
736C2×C4C5×#12011yescharacteristic
737C2×C4C5×#12011yescharacteristic
738C2×C4C22×C5×D411yescharacteristic
739C2×C4C22×C5×D411yescharacteristic
740C8—42no—
741C8—42no—
742C5#1846311yescharacteristic, direct product factor, Sylow
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—82no—
758C22—162no—
759C22C2×C5×#12011yescharacteristic
760C22C5×#57712yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C2—22no—
778C2—81no—
779C2—81no—
780C2—81no—
781C2—81no—
782C2C5×#300911yescharacteristic
783C2C5×#302211yescharacteristic
784C2C5×#302711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3560C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3218C2semidirect
3. C5×#3206C2semidirect
4. C5×#2821C2semidirect
5. C5×#1606C2semidirect
6. C5×#1604C2semidirect
7. C5×#1603C2semidirect
8. C5×#1601C2semidirect
9. C5×#1521C2semidirect
10. C5×#1514C2semidirect
11. C5×#1473C2semidirect
29. C2×C5×C4⋊Q8C22semidirect
40. C5×#451C22semidirect
43. C5×#448C22semidirect
44. C5×#432C22semidirect
45. C5×#431C22semidirect
50. C5×#395C22semidirect
52. C5×#383C22semidirect
53. C5×#328C22semidirect
56. C5×#327C22semidirect
57. C5×#324C22semidirect
59. #18463C5direct (N × H)
176. #3218C2×C5semidirect
177. #3206C2×C5semidirect
178. #2821C2×C5semidirect
179. #1606C2×C5semidirect
180. #1604C2×C5semidirect
181. #1603C2×C5semidirect
182. #1601C2×C5semidirect
183. #1521C2×C5semidirect
184. #1514C2×C5semidirect
185. #1473C2×C5semidirect
310. C2×C4⋊Q8C22×C5semidirect
321. #451C22×C5semidirect
324. #448C22×C5semidirect
325. #432C22×C5semidirect
326. #431C22×C5semidirect
331. #395C22×C5semidirect
333. #383C22×C5semidirect
334. #328C22×C5semidirect
337. #327C22×C5semidirect
338. #324C22×C5semidirect
742. C5#18463direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35602
C5×#32182
C5×#32062
C5×#28212
C5×#16062
C5×#16042
C5×#16032
C5×#16012
C5×#15212
C5×#15142
C5×#14732
#184635