Finite Group Databasebeta

← C5×#19055 #11941775

Subgroups — C5×#19055 #11941775

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3545C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3218C211yesmaximal, characteristic, complemented
4C2×C5×#489C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1662C212yesmaximal, complemented
7C5×#1661C212yesmaximal, complemented
8C5×#1659C212yesmaximal, complemented
9C5×#1533C211yesmaximal, characteristic, complemented
10C5×#1532C211yesmaximal, characteristic, complemented
11C5×#1532C211yesmaximal, characteristic, complemented
12C5×#563C2211yescharacteristic
13C5×#562C2211yescharacteristic
14C5×#562C2211yescharacteristic
15C5×H(3,𝔽4)C2211yescharacteristic
16C5×#555—21no—
17C5×#551—21no—
18C5×#551—21no—
19C5×#551—21no—
20C5×#546—21no—
21C5×#546—21no—
22C5×#542—21no—
23C5×#542—21no—
24C5×#538—21no—
25C5×#538—21no—
26C5×#536—21no—
27C5×#534—21no—
28C2×C5×C4⋊Q8C2211yescharacteristic, complemented
29C5×#529C2211yescharacteristic
30C5×#529C2211yescharacteristic
31C2×C5×#124C2211yescharacteristic
32C5×#501C2212yescomplemented
33C5×#497C2212yescomplemented
34C5×#491C2212yescomplemented
35C5×#489—21no—
36C5×#489—21no—
37C5×#489C2212yes—
38C5×#489C2212yescomplemented
39C5×#489C2212yescomplemented
40C5×#484—21no—
41C5×#481—21no—
42C5×#475—21no—
43C5×#474—21no—
44C5×#462—21no—
45C5×#461—21no—
46C5×#451—21no—
47C5×#448—21no—
48C5×#432C2211yescharacteristic, complemented
49C5×#432C2211yescharacteristic, complemented
50C2×C5×#103—21no—
51C2×C5×#102—21no—
52C2×C5×#97C2211yescharacteristic, complemented
53C5×#330C2212yescomplemented
54C5×#330C2212yescomplemented
55C5×#329C2212yes—
56C5×#329C2212yescomplemented
57C5×#329C2212yescomplemented
58C5×#329C2212yescomplemented
59#19055C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C22×C5×Q8—21no—
62C22×C5×Q8D411yescharacteristic
63C22×C5×D4—21no—
64C22×C5×D4D411yescharacteristic
65C2×C5×Q16—22no—
66C2×C5×SD16—22no—
67C22×C5×C8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8—21no—
72C5×C4⋊Q8—21no—
73C5×C4⋊Q8C2312yes—
74C5×#126—21no—
75C5×#126—21no—
76C5×#126—21no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#125C2311yescharacteristic
81C5×#125C2311yescharacteristic
82C5×#124—21no—
83C5×#124—21no—
84C5×#124—21no—
85C5×#124—21no—
86C5×#124—21no—
87C5×#124—21no—
88C5×#124—21no—
89C5×#124—21no—
90C5×#124D411yescharacteristic
91C5×#124D411yescharacteristic
92C5×#124C2311yescharacteristic
93C5×#124C2311yescharacteristic
94C5×#124C2311yescharacteristic
95C5×#124C2311yescharacteristic
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×#123—21no—
105C5×#123—21no—
106C5×#123—21no—
107C5×#123—21no—
108C5×C22⋊Q8—21no—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8D411yescharacteristic
117C5×C22⋊Q8D411yescharacteristic
118C5×#121—21no—
119C5×#121—21no—
120C5×#121—21no—
121C5×#121—21no—
122C5×#121—21no—
123C5×#121—21no—
124C5×#121—21no—
125C5×#121—21no—
126C5×#121D411yescharacteristic
127C5×#121D411yescharacteristic
128C5×#120—21no—
129C5×#120—21no—
130C5×#120—21no—
131C5×#120—21no—
132C5×#120—21no—
133C5×#120—21no—
134C4×C5×Q8D411yescharacteristic
135C4×C5×Q8D411yescharacteristic
136C4×C5×D4—21no—
137C4×C5×D4—21no—
138C4×C5×D4—21no—
139C4×C5×D4—21no—
140C4×C5×D4—21no—
141C4×C5×D4—21no—
142C4×C5×D4D411yescharacteristic
143C4×C5×D4D411yescharacteristic
144C5×#117—21no—
145C5×#117—21no—
146C5×#117—21no—
147C5×#117—21no—
148C5×#117—21no—
149C2×C5×C4⋊C4—21no—
150C2×C5×C4⋊C4—21no—
151C2×C5×C22⋊C4—21no—
152C2×C5×C22⋊C4—21no—
153C2×C5×C22⋊C4—21no—
154C2×C5×C22⋊C4—21no—
155C2×C5×C22⋊C4—21no—
156C2×C42×C5C2311yescharacteristic
157C5×#107—22no—
158C5×#106—22no—
159C5×C4⋊C8—21no—
160C5×C4⋊C8—21no—
161C5×#103—22no—
162C5×#103—22no—
163C5×#103—22no—
164C5×#103—22no—
165C5×#103—22no—
166C5×#102—22no—
167C5×#102—22no—
168C5×#102—22no—
169C5×C22⋊C8—21no—
170C5×C22⋊C8—21no—
171C5×#97—21no—
172C5×#97C2312yes—
173C5×#97C2312yes—
174C5×#97C2312yes—
175#3545C2×C511yescharacteristic
176#3239C2×C511yescharacteristic, complemented
177#3218C2×C511yescharacteristic, complemented
178C2×#489C2×C511yescharacteristic, complemented
179#1664C2×C512yescomplemented
180#1662C2×C512yescomplemented
181#1661C2×C512yescomplemented
182#1659C2×C512yescomplemented
183#1533C2×C511yescharacteristic, complemented
184#1532C2×C511yescharacteristic, complemented
185#1532C2×C511yescharacteristic, complemented
186C24×C5—21no—
187C24×C5—21no—
188C5×#41—82no—
189C2×C5×Q8—21no—
190C2×C5×Q8—21no—
191C2×C5×Q8—22no—
192C2×C5×Q8—42no—
193C2×C5×Q8—41no—
194C2×C5×Q8—82no—
195C2×C5×Q8C2×D411yescharacteristic
196C2×C5×Q8C2×D411yescharacteristic
197C2×C5×Q8C2×D411yescharacteristic
198C2×C5×Q8C2×D411yescharacteristic
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—21no—
209C2×C5×D4—42no—
210C2×C5×D4—82no—
211C2×C5×D4C2×D411yescharacteristic
212C2×C5×D4C2×D411yescharacteristic
213C2×C5×D4C2×D411yescharacteristic
214C2×C5×D4C2×D411yescharacteristic
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—41no—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C5×Q16—82no—
228C5×SD16—82no—
229C2×C5×C8—22no—
230C2×C5×C8—22no—
231C2×C5×C8—22no—
232C2×C5×C8—42no—
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⋊C4C2×D411yescharacteristic
252C5×C4⋊C4C2×D411yescharacteristic
253C5×C4⋊C4C2×D411yescharacteristic
254C5×C4⋊C4C2×D411yescharacteristic
255C5×C22⋊C4—21no—
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—21no—
282C5×C22⋊C4—21no—
283C42×C5—21no—
284C42×C5—21no—
285C42×C5—21no—
286C42×C5—21no—
287C42×C5C2×D411yescharacteristic
288C42×C5C2×D411yescharacteristic
289C42×C5C2×D411yescharacteristic
290C42×C5C2411yescharacteristic
291#563C22×C511yescharacteristic
292#562C22×C511yescharacteristic
293#562C22×C511yescharacteristic
294H(3,𝔽4)C22×C511yescharacteristic
295#555—21no—
296#551—21no—
297#551—21no—
298#551—21no—
299#546—21no—
300#546—21no—
301#542—21no—
302#542—21no—
303#538—21no—
304#538—21no—
305#536—21no—
306#534—21no—
307C2×C4⋊Q8C22×C511yescharacteristic, complemented
308#529C22×C511yescharacteristic
309#529C22×C511yescharacteristic
310C2×#124C22×C511yescharacteristic
311#501C22×C512yescomplemented
312#497C22×C512yescomplemented
313#491C22×C512yescomplemented
314#489—21no—
315#489—21no—
316#489C22×C512yes—
317#489C22×C512yescomplemented
318#489C22×C512yescomplemented
319#484—21no—
320#481—21no—
321#475—21no—
322#474—21no—
323#462—21no—
324#461—21no—
325#451—21no—
326#448—21no—
327#432C22×C511yescharacteristic, complemented
328#432C22×C511yescharacteristic, complemented
329C2×#103—21no—
330C2×#102—21no—
331C2×#97C22×C511yescharacteristic, complemented
332#330C22×C512yescomplemented
333#330C22×C512yescomplemented
334#329C22×C512yes—
335#329C22×C512yescomplemented
336#329C22×C512yescomplemented
337#329C22×C512yescomplemented
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—21no—
341C23×C5—21no—
342C23×C5—42no—
343C23×C5—81no—
344C23×C5—81no—
345C23×C5—81no—
346C23×C5—81no—
347C23×C5—81no—
348C23×C5#12011yescharacteristic
349C5×Q8—41no—
350C5×Q8—41no—
351C5×Q8—41no—
352C5×Q8—41no—
353C5×Q8—42no—
354C5×Q8—42no—
355C5×Q8—81no—
356C5×Q8—82no—
357C5×Q8—81no—
358C5×D4—41no—
359C5×D4—41no—
360C5×D4—41no—
361C5×D4—41no—
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—
372C2×C4×C5—22no—
373C2×C4×C5—21no—
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—41no—
382C2×C4×C5—41no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—81no—
386C2×C4×C5—81no—
387C2×C4×C5—81no—
388C2×C4×C5—81no—
389C2×C4×C5—81no—
390C2×C4×C5—81no—
391C2×C4×C5—81no—
392C2×C4×C5—82no—
393C2×C4×C5#12011yescharacteristic
394C2×C4×C5#12011yescharacteristic
395C2×C4×C5#12011yescharacteristic
396C2×C4×C5C22×D411yescharacteristic
397C2×C4×C5C22×D411yescharacteristic
398C2×C4×C5C22×D411yescharacteristic
399C5×C8—42no—
400C5×C8—42no—
401C5×C8—42no—
402C2×#41—21no—
403C22×Q8—21no—
404C22×Q8C5×D411yescharacteristic
405C22×D4—21no—
406C22×D4C5×D411yescharacteristic
407C2×Q16—22no—
408C2×SD16—22no—
409C22×C8—21no—
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414C4⋊Q8—21no—
415C4⋊Q8C23×C512yes—
416#126—21no—
417#126—21no—
418#126—21no—
419#126—21no—
420#126—21no—
421#126—21no—
422#125C23×C511yescharacteristic
423#125C23×C511yescharacteristic
424#124—21no—
425#124—21no—
426#124—21no—
427#124—21no—
428#124—21no—
429#124—21no—
430#124—21no—
431#124—21no—
432#124C5×D411yescharacteristic
433#124C5×D411yescharacteristic
434#124C23×C511yescharacteristic
435#124C23×C511yescharacteristic
436#124C23×C511yescharacteristic
437#124C23×C511yescharacteristic
438#123—21no—
439#123—21no—
440#123—21no—
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—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8C5×D411yescharacteristic
459C22⋊Q8C5×D411yescharacteristic
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121C5×D411yescharacteristic
469#121C5×D411yescharacteristic
470#120—21no—
471#120—21no—
472#120—21no—
473#120—21no—
474#120—21no—
475#120—21no—
476C4×Q8C5×D411yescharacteristic
477C4×Q8C5×D411yescharacteristic
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4C5×D411yescharacteristic
485C4×D4C5×D411yescharacteristic
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C42C23×C511yescharacteristic
499#107—22no—
500#106—22no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#102—22no—
509#102—22no—
510#102—22no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513#97—21no—
514#97C23×C512yes—
515#97C23×C512yes—
516#97C23×C512yes—
517C22×C5—21no—
518C22×C5—21no—
519C22×C5—41no—
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—162no—
532C22×C5—162no—
533C22×C5#45512yes—
534C22×C5C2×#12011yescharacteristic
535C4×C5—21no—
536C4×C5—21no—
537C4×C5—21no—
538C4×C5—21no—
539C4×C5—21no—
540C4×C5—21no—
541C4×C5—41no—
542C4×C5—41no—
543C4×C5—41no—
544C4×C5—41no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5—41no—
548C4×C5—41no—
549C4×C5—82no—
550C24—21no—
551C24—21no—
552#41—82no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—42no—
557C2×Q8—41no—
558C2×Q8—82no—
559C2×Q8C2×C5×D411yescharacteristic
560C2×Q8C2×C5×D411yescharacteristic
561C2×Q8C2×C5×D411yescharacteristic
562C2×Q8C2×C5×D411yescharacteristic
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—42no—
574C2×D4—82no—
575C2×D4C2×C5×D411yescharacteristic
576C2×D4C2×C5×D411yescharacteristic
577C2×D4C2×C5×D411yescharacteristic
578C2×D4C2×C5×D411yescharacteristic
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4C2×C5×D411yescharacteristic
589C22×C4C2×C5×D411yescharacteristic
590C22×C4C2×C5×D411yescharacteristic
591Q16—82no—
592SD16—82no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—42no—
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—22no—
612C4⋊C4—22no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4C2×C5×D411yescharacteristic
616C4⋊C4C2×C5×D411yescharacteristic
617C4⋊C4C2×C5×D411yescharacteristic
618C4⋊C4C2×C5×D411yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
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—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42C2×C5×D411yescharacteristic
652C42C2×C5×D411yescharacteristic
653C42C2×C5×D411yescharacteristic
654C42C24×C511yescharacteristic
655C2×C5—22no—
656C2×C5—81no—
657C2×C5—81no—
658C2×C5—81no—
659C2×C5—81no—
660C2×C5C2×#45511yescharacteristic
661C2×C5#302111yescharacteristic
662C2×C5#302211yescharacteristic
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—42no—
668C23—81no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23C5×#12011yescharacteristic
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—42no—
679Q8—42no—
680Q8—81no—
681Q8—82no—
682Q8—81no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—42no—
688D4—42no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4C5×#12011yescharacteristic
719C2×C4C5×#12011yescharacteristic
720C2×C4C5×#12011yescharacteristic
721C2×C4C22×C5×D411yescharacteristic
722C2×C4C22×C5×D411yescharacteristic
723C2×C4C22×C5×D411yescharacteristic
724C8—42no—
725C8—42no—
726C8—42no—
727C5#1905511yescharacteristic, direct product factor, Sylow
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—162no—
743C22—162no—
744C22C5×#45512yes—
745C22C2×C5×#12011yescharacteristic
746C4—21no—
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—82no—
761C2—22no—
762C2—81no—
763C2—81no—
764C2—81no—
765C2—81no—
766C2C2×C5×#45511yescharacteristic
767C2C5×#302111yescharacteristic
768C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3545C2
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
2. C5×#3239C2semidirect
3. C5×#3218C2semidirect
4. C2×C5×#489C2semidirect
5. C5×#1664C2semidirect
6. C5×#1662C2semidirect
7. C5×#1661C2semidirect
8. C5×#1659C2semidirect
9. C5×#1533C2semidirect
10. C5×#1532C2semidirect
11. C5×#1532C2semidirect
28. C2×C5×C4⋊Q8C22semidirect
32. C5×#501C22semidirect
33. C5×#497C22semidirect
34. C5×#491C22semidirect
38. C5×#489C22semidirect
39. C5×#489C22semidirect
48. C5×#432C22semidirect
49. C5×#432C22semidirect
52. C2×C5×#97C22semidirect
53. C5×#330C22semidirect
54. C5×#330C22semidirect
56. C5×#329C22semidirect
57. C5×#329C22semidirect
58. C5×#329C22semidirect
59. #19055C5direct (N × H)
176. #3239C2×C5semidirect
177. #3218C2×C5semidirect
178. C2×#489C2×C5semidirect
179. #1664C2×C5semidirect
180. #1662C2×C5semidirect
181. #1661C2×C5semidirect
182. #1659C2×C5semidirect
183. #1533C2×C5semidirect
184. #1532C2×C5semidirect
185. #1532C2×C5semidirect
307. C2×C4⋊Q8C22×C5semidirect
311. #501C22×C5semidirect
312. #497C22×C5semidirect
313. #491C22×C5semidirect
317. #489C22×C5semidirect
318. #489C22×C5semidirect
327. #432C22×C5semidirect
328. #432C22×C5semidirect
331. C2×#97C22×C5semidirect
332. #330C22×C5semidirect
333. #330C22×C5semidirect
335. #329C22×C5semidirect
336. #329C22×C5semidirect
337. #329C22×C5semidirect
727. C5#19055direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35452
C5×#32392
C5×#32182
C2×C5×#4892
C5×#16642
C5×#16622
C5×#16612
C5×#16592
C5×#15332
C5×#15322
#190555