Finite Group Databasebeta

← C5×#18471 #11941191

Subgroups — C5×#18471 #11941191

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3560C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3227C211yesmaximal, characteristic, complemented
4C5×#2821C211yesmaximal, characteristic, complemented
5C5×#1618C212yesmaximal, complemented
6C5×#1616C212yesmaximal, complemented
7C5×#1615C212yesmaximal, complemented
8C5×#1613C212yesmaximal, 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×#501—21no—
33C5×#498—21no—
34C5×#489—21no—
35C5×#486—21no—
36C5×#484C2212yescomplemented
37C5×#481C2212yes—
38C5×#481C2212yes—
39C5×#481C2212yescomplemented
40C5×#476—21no—
41C5×#476—21no—
42C5×#475—21no—
43C5×#474—21no—
44C5×#432C2211yescharacteristic, complemented
45C5×#431C2211yescharacteristic, complemented
46C5×#400C2212yescomplemented
47C5×#399C2212yes—
48C5×#398—21no—
49C5×#397—21no—
50C5×#395—21no—
51C5×#393—21no—
52C5×#383C2211yescharacteristic, complemented
53C5×#328C2212yescomplemented
54C5×#327C2212yes—
55C5×#327C2212yes—
56C5×#327C2212yescomplemented
57C5×#324C2212yescomplemented
58C5×#323C2212yes—
59#18471C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C2×C5×#41—21no—
62C22×C5×Q8—21no—
63C22×C5×D4—21no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8D411yescharacteristic
70C5×#127D411yescharacteristic
71C5×#126—21no—
72C5×#126—21no—
73C5×#126—21no—
74C5×#126—21no—
75C5×#126—21no—
76C5×#126—21no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#125—21no—
81C5×#125—21no—
82C5×#125D411yescharacteristic
83C5×#124—21no—
84C5×#124—21no—
85C5×#124—21no—
86C5×#124—21no—
87C5×#124D411yescharacteristic
88C5×#123—21no—
89C5×#123—21no—
90C5×#123—21no—
91C5×#123—21no—
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×C22⋊Q8—21no—
101C5×C22⋊Q8—21no—
102C5×C22⋊Q8—21no—
103C5×C22⋊Q8—21no—
104C5×C22⋊Q8—21no—
105C5×C22⋊Q8—21no—
106C5×C22⋊Q8—21no—
107C5×C22⋊Q8C2311yescharacteristic
108C5×#121—21no—
109C5×#121—21no—
110C5×#121—21no—
111C5×#121—21no—
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×#121C2311yescharacteristic
121C5×#121C2311yescharacteristic
122C5×#121C2311yescharacteristic
123C5×#120—21no—
124C5×#120—21no—
125C5×#120—21no—
126C5×#120—21no—
127C5×#120—21no—
128C4×C5×Q8D411yescharacteristic
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×D4—21no—
136C4×C5×D4—21no—
137C4×C5×D4D411yescharacteristic
138C4×C5×D4D411yescharacteristic
139C4×C5×D4D411yescharacteristic
140C5×#117—21no—
141C5×#117—21no—
142C2×C5×C4⋊C4—21no—
143C2×C5×C4⋊C4—21no—
144C2×C5×C4⋊C4—22no—
145C2×C5×C4⋊C4D411yescharacteristic
146C2×C5×C4⋊C4D411yescharacteristic
147C2×C5×C4⋊C4C2312yes—
148C2×C5×C4⋊C4C2311yescharacteristic
149C2×C5×C22⋊C4—21no—
150C2×C5×C22⋊C4—21no—
151C2×C5×C22⋊C4—22no—
152C2×C5×C22⋊C4D411yescharacteristic
153C2×C5×C22⋊C4D411yescharacteristic
154C2×C5×C22⋊C4C2311yescharacteristic
155C2×C42×C5C2311yescharacteristic
156C5×#107—22no—
157C5×#106—22no—
158C5×#106—22no—
159C5×#106—22no—
160C5×C4⋊C8—21no—
161C5×C4⋊C8—21no—
162C5×#103—22no—
163C5×#102—22no—
164C5×#102—22no—
165C5×#102—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#3239C2×C511yescharacteristic, complemented
177#3227C2×C511yescharacteristic, complemented
178#2821C2×C511yescharacteristic, complemented
179#1618C2×C512yescomplemented
180#1616C2×C512yescomplemented
181#1615C2×C512yescomplemented
182#1613C2×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—41no—
193C2×C5×Q8—41no—
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
228C2×C5×C8—22no—
229C2×C5×C8—22no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
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—22no—
248C5×C4⋊C4—22no—
249C5×C4⋊C4—41no—
250C5×C4⋊C4—41no—
251C5×C4⋊C4—82no—
252C5×C4⋊C4C2×D411yescharacteristic
253C5×C4⋊C4C2×D411yescharacteristic
254C5×C4⋊C4C2×D411yescharacteristic
255C5×C4⋊C4C2×D411yescharacteristic
256C5×C22⋊C4—21no—
257C5×C22⋊C4—21no—
258C5×C22⋊C4—21no—
259C5×C22⋊C4—21no—
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—82no—
282C42×C5—21no—
283C42×C5—21no—
284C42×C5—21no—
285C42×C5C2×D411yescharacteristic
286C42×C5C2×D411yescharacteristic
287C42×C5C2×D411yescharacteristic
288C42×C5C2×D411yescharacteristic
289#563—21no—
290#560—21no—
291#553—21no—
292#553—21no—
293#551—21no—
294#547—21no—
295#546—21no—
296#546—21no—
297#542—21no—
298#539—21no—
299#539C22×C511yescharacteristic
300#538—21no—
301#538—21no—
302#538C22×C511yescharacteristic
303#537C22×C511yescharacteristic
304#534C22×C511yescharacteristic
305#532C22×C511yescharacteristic
306C2×C4⋊Q8C22×C511yescharacteristic, complemented
307#529C22×C511yescharacteristic
308C2×#126C22×C511yescharacteristic
309#501—21no—
310#498—21no—
311#489—21no—
312#486—21no—
313#484C22×C512yescomplemented
314#481C22×C512yes—
315#481C22×C512yes—
316#481C22×C512yescomplemented
317#476—21no—
318#476—21no—
319#475—21no—
320#474—21no—
321#432C22×C511yescharacteristic, complemented
322#431C22×C511yescharacteristic, complemented
323#400C22×C512yescomplemented
324#399C22×C512yes—
325#398—21no—
326#397—21no—
327#395—21no—
328#393—21no—
329#383C22×C511yescharacteristic, complemented
330#328C22×C512yescomplemented
331#327C22×C512yes—
332#327C22×C512yes—
333#327C22×C512yescomplemented
334#324C22×C512yescomplemented
335#323C22×C512yes—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—22no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—81no—
344C23×C5—81no—
345C23×C5—81no—
346C23×C5C22×D411yescharacteristic
347C5×Q8—41no—
348C5×Q8—81no—
349C5×Q8—82no—
350C5×Q8—82no—
351C5×Q8—81no—
352C5×D4—41no—
353C5×D4—41no—
354C5×D4—41no—
355C5×D4—42no—
356C5×D4—42no—
357C5×D4—42no—
358C5×D4—81no—
359C5×D4—81no—
360C5×D4—81no—
361C5×D4—81no—
362C5×D4—81no—
363C5×D4—81no—
364C5×D4—81no—
365C5×D4—81no—
366C5×D4—81no—
367C2×C4×C5—22no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—21no—
372C2×C4×C5—21no—
373C2×C4×C5—21no—
374C2×C4×C5—21no—
375C2×C4×C5—21no—
376C2×C4×C5—22no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
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—81no—
388C2×C4×C5—81no—
389C2×C4×C5—81no—
390C2×C4×C5—81no—
391C2×C4×C5—81no—
392C2×C4×C5—81no—
393C2×C4×C5—81no—
394C2×C4×C5—81no—
395C2×C4×C5#12011yescharacteristic
396C2×C4×C5#12011yescharacteristic
397C2×C4×C5#12011yescharacteristic
398C2×C4×C5#12011yescharacteristic
399C2×C4×C5C22×D411yescharacteristic
400C2×C4×C5C22×D411yescharacteristic
401C5×C8—42no—
402C5×C8—42no—
403C2×#41—21no—
404C2×#41—21no—
405C22×Q8—21no—
406C22×D4—21no—
407C4⋊Q8—21no—
408C4⋊Q8—21no—
409C4⋊Q8—21no—
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412C4⋊Q8C5×D411yescharacteristic
413#127C5×D411yescharacteristic
414#126—21no—
415#126—21no—
416#126—21no—
417#126—21no—
418#126—21no—
419#126—21no—
420#126—21no—
421#126—21no—
422#126—21no—
423#125—21no—
424#125—21no—
425#125C5×D411yescharacteristic
426#124—21no—
427#124—21no—
428#124—21no—
429#124—21no—
430#124C5×D411yescharacteristic
431#123—21no—
432#123—21no—
433#123—21no—
434#123—21no—
435#123—21no—
436#123—21no—
437#123—21no—
438#123—21no—
439#123—21no—
440#123—21no—
441#123—21no—
442#123—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8C23×C511yescharacteristic
451#121—21no—
452#121—21no—
453#121—21no—
454#121—21no—
455#121—21no—
456#121—21no—
457#121—21no—
458#121—21no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121C23×C511yescharacteristic
464#121C23×C511yescharacteristic
465#121C23×C511yescharacteristic
466#120—21no—
467#120—21no—
468#120—21no—
469#120—21no—
470#120—21no—
471C4×Q8C5×D411yescharacteristic
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4C5×D411yescharacteristic
481C4×D4C5×D411yescharacteristic
482C4×D4C5×D411yescharacteristic
483#117—21no—
484#117—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4C5×D411yescharacteristic
489C2×C4⋊C4C5×D411yescharacteristic
490C2×C4⋊C4C23×C512yes—
491C2×C4⋊C4C23×C511yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4C5×D411yescharacteristic
496C2×C22⋊C4C5×D411yescharacteristic
497C2×C22⋊C4C23×C511yescharacteristic
498C2×C42C23×C511yescharacteristic
499#107—22no—
500#106—22no—
501#106—22no—
502#106—22no—
503C4⋊C8—21no—
504C4⋊C8—21no—
505#103—22no—
506#102—22no—
507#102—22no—
508#102—22no—
509C22⋊C8C23×C512yes—
510C22⋊C8C23×C512yes—
511#97—21no—
512C4×C8—21no—
513#95—21no—
514#95—21no—
515#95—22no—
516#95—22no—
517#95C23×C512yes—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—41no—
521C22×C5—41no—
522C22×C5—41no—
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—41no—
532C22×C5—82no—
533C22×C5—162no—
534C22×C5C2×#12011yescharacteristic
535C22×C5#57712yes—
536C4×C5—21no—
537C4×C5—21no—
538C4×C5—21no—
539C4×C5—21no—
540C4×C5—21no—
541C4×C5—21no—
542C4×C5—41no—
543C4×C5—41no—
544C4×C5—41no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5—41no—
548C4×C5—41no—
549C4×C5—41no—
550C4×C5—82no—
551C4×C5—82no—
552C24—21no—
553C24C2×C5×D411yescharacteristic
554#41—82no—
555#41—82no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—82no—
561C2×Q8C2×C5×D411yescharacteristic
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—82no—
575C2×D4C2×C5×D411yescharacteristic
576C2×D4C2×C5×D411yescharacteristic
577C2×D4C2×C5×D411yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4C2×C5×D411yescharacteristic
589C22×C4C2×C5×D411yescharacteristic
590C22×C4C2×C5×D411yescharacteristic
591C22×C4C2×C5×D411yescharacteristic
592C22×C4C2×C5×D411yescharacteristic
593C22×C4C24×C511yescharacteristic
594C2×C8—22no—
595C2×C8—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—82no—
618C4⋊C4C2×C5×D411yescharacteristic
619C4⋊C4C2×C5×D411yescharacteristic
620C4⋊C4C2×C5×D411yescharacteristic
621C4⋊C4C2×C5×D411yescharacteristic
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
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—82no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42C2×C5×D411yescharacteristic
652C42C2×C5×D411yescharacteristic
653C42C2×C5×D411yescharacteristic
654C42C2×C5×D411yescharacteristic
655C2×C5—22no—
656C2×C5—81no—
657C2×C5—81no—
658C2×C5—81no—
659C2×C5—81no—
660C2×C5#300911yescharacteristic
661C2×C5#302111yescharacteristic
662C2×C5#302811yescharacteristic
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23C22×C5×D411yescharacteristic
674Q8—41no—
675Q8—81no—
676Q8—82no—
677Q8—82no—
678Q8—81no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—81no—
686D4—81no—
687D4—81no—
688D4—81no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4C5×#12011yescharacteristic
723C2×C4C5×#12011yescharacteristic
724C2×C4C5×#12011yescharacteristic
725C2×C4C5×#12011yescharacteristic
726C2×C4C22×C5×D411yescharacteristic
727C2×C4C22×C5×D411yescharacteristic
728C8—42no—
729C8—42no—
730C5#1847111yescharacteristic, direct product factor, Sylow
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—82no—
746C22—162no—
747C22C2×C5×#12011yescharacteristic
748C22C5×#57712yes—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—82no—
764C4—82no—
765C2—22no—
766C2—81no—
767C2—81no—
768C2—81no—
769C2—81no—
770C2C5×#300911yescharacteristic
771C2C5×#302111yescharacteristic
772C2C5×#302811yescharacteristic
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×#3239C2semidirect
3. C5×#3227C2semidirect
4. C5×#2821C2semidirect
5. C5×#1618C2semidirect
6. C5×#1616C2semidirect
7. C5×#1615C2semidirect
8. C5×#1613C2semidirect
9. C5×#1521C2semidirect
10. C5×#1514C2semidirect
11. C5×#1473C2semidirect
29. C2×C5×C4⋊Q8C22semidirect
36. C5×#484C22semidirect
39. C5×#481C22semidirect
44. C5×#432C22semidirect
45. C5×#431C22semidirect
46. C5×#400C22semidirect
52. C5×#383C22semidirect
53. C5×#328C22semidirect
56. C5×#327C22semidirect
57. C5×#324C22semidirect
59. #18471C5direct (N × H)
176. #3239C2×C5semidirect
177. #3227C2×C5semidirect
178. #2821C2×C5semidirect
179. #1618C2×C5semidirect
180. #1616C2×C5semidirect
181. #1615C2×C5semidirect
182. #1613C2×C5semidirect
183. #1521C2×C5semidirect
184. #1514C2×C5semidirect
185. #1473C2×C5semidirect
306. C2×C4⋊Q8C22×C5semidirect
313. #484C22×C5semidirect
316. #481C22×C5semidirect
321. #432C22×C5semidirect
322. #431C22×C5semidirect
323. #400C22×C5semidirect
329. #383C22×C5semidirect
330. #328C22×C5semidirect
333. #327C22×C5semidirect
334. #324C22×C5semidirect
730. C5#18471direct (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×#32392
C5×#32272
C5×#28212
C5×#16182
C5×#16162
C5×#16152
C5×#16132
C5×#15212
C5×#15142
C5×#14732
#184715