Finite Group Databasebeta

← C5×#18462 #11941182

Subgroups — C5×#18462 #11941182

Order 1280.

1030 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3560C211yesmaximal, characteristic, complemented
2C5×#3217C211yesmaximal, characteristic, complemented
3C5×#3205C211yesmaximal, characteristic, complemented
4C5×#2818C211yesmaximal, characteristic, complemented
5C5×#1600C212yesmaximal, complemented
6C5×#1598C212yesmaximal, complemented
7C5×#1597C212yesmaximal, complemented
8C5×#1595C212yesmaximal, 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×#127C2211yescharacteristic, complemented
30C5×#529C2211yescharacteristic
31C2×C5×#126C2211yescharacteristic
32C5×#496—21no—
33C5×#493—21no—
34C5×#490—21no—
35C5×#486—21no—
36C5×#460—21no—
37C5×#459—21no—
38C5×#459—21no—
39C5×#459—21no—
40C5×#450C2212yescomplemented
41C5×#447C2212yes—
42C5×#447C2212yes—
43C5×#447C2212yescomplemented
44C5×#432C2211yescharacteristic, complemented
45C5×#431C2211yescharacteristic, complemented
46C5×#394—21no—
47C5×#394—21no—
48C5×#394C2212yescomplemented
49C5×#392—21no—
50C5×#392—21no—
51C5×#392C2212yes—
52C5×#383C2211yescharacteristic, complemented
53C5×#328C2212yescomplemented
54C5×#327C2212yes—
55C5×#327C2212yes—
56C5×#327C2212yescomplemented
57C5×#324C2212yescomplemented
58C5×#323C2212yes—
59#18462C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C2×C5×#41—21no—
62C22×C5×D4—21no—
63C22×C5×D4—22no—
64C22×C5×D4—21no—
65C22×C5×D4—21no—
66C22×C5×D4C2312yes—
67C2×C5×SD16—22no—
68C2×C5×D8—22no—
69C2×C5×D8—22no—
70C2×C5×D8—22no—
71C5×C4⋊Q8—21no—
72C5×C4⋊Q8D411yescharacteristic, complemented
73C5×#127—21no—
74C5×#127—21no—
75C5×#127—21no—
76C5×#127—21no—
77C5×#127D411yescharacteristic, complemented
78C5×#126—21no—
79C5×#126—21no—
80C5×#126—21no—
81C5×#126—21no—
82C5×#126—21no—
83C5×#126—21no—
84C5×#126—21no—
85C5×#126—21no—
86C5×#126—21no—
87C5×#125—21no—
88C5×#125—21no—
89C5×#125D411yescharacteristic, complemented
90C5×#124—21no—
91C5×#124—21no—
92C5×#124—21no—
93C5×#124—21no—
94C5×#124D411yescharacteristic, complemented
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×#123—21no—
105C5×#123—21no—
106C5×#123—21no—
107C5×C22⋊Q8—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⋊Q8C2311yescharacteristic
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×#121—21no—
125C5×#121—21no—
126C5×#121—21no—
127C5×#121C2311yescharacteristic
128C5×#121C2311yescharacteristic
129C5×#121C2311yescharacteristic
130C5×#120—21no—
131C5×#120—21no—
132C5×#120—21no—
133C5×#120—21no—
134C5×#120—21no—
135C4×C5×Q8D411yescharacteristic, complemented
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×D4—21no—
143C4×C5×D4—21no—
144C4×C5×D4D411yescharacteristic, complemented
145C4×C5×D4D411yescharacteristic, complemented
146C4×C5×D4D411yescharacteristic, complemented
147C5×#117—21no—
148C5×#117—21no—
149C2×C5×C4⋊C4—21no—
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⋊C4—22no—
157C2×C5×C22⋊C4—22no—
158C2×C5×C22⋊C4D411yescharacteristic
159C2×C5×C22⋊C4D411yescharacteristic
160C2×C5×C22⋊C4C2311yescharacteristic
161C2×C42×C5C2311yescharacteristic
162C5×C4⋊C8—21no—
163C5×C4⋊C8—21no—
164C5×#102—22no—
165C5×#102—22no—
166C5×#102—22no—
167C5×#102—22no—
168C5×C22⋊C8C2312yes—
169C5×C22⋊C8C2312yes—
170C5×#97—21no—
171C4×C5×C8—21no—
172C5×#95—21no—
173C5×#95—21no—
174C5×#95C2312yes—
175#3560C2×C511yescharacteristic, complemented
176#3217C2×C511yescharacteristic, complemented
177#3205C2×C511yescharacteristic, complemented
178#2818C2×C511yescharacteristic, complemented
179#1600C2×C512yescomplemented
180#1598C2×C512yescomplemented
181#1597C2×C512yescomplemented
182#1595C2×C512yescomplemented
183#1521C2×C511yescharacteristic, complemented
184#1514C2×C511yescharacteristic, complemented
185#1473C2×C511yescharacteristic, complemented
186C24×C5—21no—
187C24×C5—22no—
188C24×C5C2×D411yescharacteristic
189C5×#41—82no—
190C5×#41—82no—
191C2×C5×Q8—21no—
192C2×C5×Q8—21no—
193C2×C5×Q8C2×D411yescharacteristic
194C2×C5×D4—21no—
195C2×C5×D4—21no—
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—22no—
207C2×C5×D4—22no—
208C2×C5×D4—41no—
209C2×C5×D4—41no—
210C2×C5×D4—41no—
211C2×C5×D4—41no—
212C2×C5×D4—82no—
213C2×C5×D4—82no—
214C2×C5×D4—82no—
215C2×C5×D4—82no—
216C2×C5×D4—82no—
217C2×C5×D4—82no—
218C2×C5×D4—82no—
219C2×C5×D4C2×D411yescharacteristic
220C2×C5×D4C2×D411yescharacteristic
221C2×C5×D4C2×D411yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—22no—
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D411yescharacteristic
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2411yescharacteristic
237C5×SD16—82no—
238C5×D8—82no—
239C5×D8—82no—
240C5×D8—82no—
241C2×C5×C8—22no—
242C2×C5×C8—22no—
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—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
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×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—21no—
286C5×C22⋊C4—21no—
287C5×C22⋊C4—21no—
288C5×C22⋊C4—21no—
289C5×C22⋊C4—82no—
290C5×C22⋊C4—82no—
291C5×C22⋊C4—82no—
292C42×C5—21no—
293C42×C5—21no—
294C42×C5—21no—
295C42×C5C2×D411yescharacteristic
296C42×C5C2×D411yescharacteristic
297C42×C5C2×D411yescharacteristic
298C42×C5C2×D411yescharacteristic
299#563—21no—
300#560—21no—
301#553—21no—
302#553—21no—
303#551—21no—
304#547—21no—
305#546—21no—
306#546—21no—
307#542—21no—
308#539—21no—
309#539C22×C511yescharacteristic
310#538—21no—
311#538—21no—
312#538C22×C511yescharacteristic
313#537C22×C511yescharacteristic
314#534C22×C511yescharacteristic
315#532C22×C511yescharacteristic
316C2×#127C22×C511yescharacteristic, complemented
317#529C22×C511yescharacteristic
318C2×#126C22×C511yescharacteristic
319#496—21no—
320#493—21no—
321#490—21no—
322#486—21no—
323#460—21no—
324#459—21no—
325#459—21no—
326#459—21no—
327#450C22×C512yescomplemented
328#447C22×C512yes—
329#447C22×C512yes—
330#447C22×C512yescomplemented
331#432C22×C511yescharacteristic, complemented
332#431C22×C511yescharacteristic, complemented
333#394—21no—
334#394—21no—
335#394C22×C512yescomplemented
336#392—21no—
337#392—21no—
338#392C22×C512yes—
339#383C22×C511yescharacteristic, complemented
340#328C22×C512yescomplemented
341#327C22×C512yes—
342#327C22×C512yes—
343#327C22×C512yescomplemented
344#324C22×C512yescomplemented
345#323C22×C512yes—
346C23×C5—21no—
347C23×C5—21no—
348C23×C5—21no—
349C23×C5—21no—
350C23×C5—22no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—42no—
354C23×C5—42no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—81no—
361C23×C5—81no—
362C23×C5—81no—
363C23×C5C22×D411yescharacteristic
364C5×Q8—41no—
365C5×Q8—81no—
366C5×Q8—81no—
367C5×D4—41no—
368C5×D4—41no—
369C5×D4—41no—
370C5×D4—42no—
371C5×D4—42no—
372C5×D4—42no—
373C5×D4—42no—
374C5×D4—42no—
375C5×D4—42no—
376C5×D4—42no—
377C5×D4—81no—
378C5×D4—81no—
379C5×D4—82no—
380C5×D4—82no—
381C5×D4—82no—
382C5×D4—82no—
383C5×D4—81no—
384C5×D4—81no—
385C5×D4—81no—
386C5×D4—81no—
387C5×D4—81no—
388C5×D4—81no—
389C5×D4—81no—
390C5×D4—88no—
391C2×C4×C5—22no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—22no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—42no—
406C2×C4×C5—42no—
407C2×C4×C5—42no—
408C2×C4×C5—81no—
409C2×C4×C5—81no—
410C2×C4×C5—81no—
411C2×C4×C5—81no—
412C2×C4×C5—81no—
413C2×C4×C5—81no—
414C2×C4×C5—81no—
415C2×C4×C5—81no—
416C2×C4×C5#12011yescharacteristic
417C2×C4×C5#12011yescharacteristic
418C2×C4×C5#12011yescharacteristic
419C2×C4×C5#12011yescharacteristic
420C2×C4×C5C22×D411yescharacteristic
421C2×C4×C5C22×D411yescharacteristic
422C5×C8—42no—
423C5×C8—42no—
424C2×#41—21no—
425C2×#41—21no—
426C22×D4—21no—
427C22×D4—22no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4C23×C512yes—
431C2×SD16—22no—
432C2×D8—22no—
433C2×D8—22no—
434C2×D8—22no—
435C4⋊Q8—21no—
436C4⋊Q8C5×D411yescharacteristic, complemented
437#127—21no—
438#127—21no—
439#127—21no—
440#127—21no—
441#127C5×D411yescharacteristic, complemented
442#126—21no—
443#126—21no—
444#126—21no—
445#126—21no—
446#126—21no—
447#126—21no—
448#126—21no—
449#126—21no—
450#126—21no—
451#125—21no—
452#125—21no—
453#125C5×D411yescharacteristic, complemented
454#124—21no—
455#124—21no—
456#124—21no—
457#124—21no—
458#124C5×D411yescharacteristic, complemented
459#123—21no—
460#123—21no—
461#123—21no—
462#123—21no—
463#123—21no—
464#123—21no—
465#123—21no—
466#123—21no—
467#123—21no—
468#123—21no—
469#123—21no—
470#123—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8C23×C511yescharacteristic
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121C23×C511yescharacteristic
492#121C23×C511yescharacteristic
493#121C23×C511yescharacteristic
494#120—21no—
495#120—21no—
496#120—21no—
497#120—21no—
498#120—21no—
499C4×Q8C5×D411yescharacteristic, complemented
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4C5×D411yescharacteristic, complemented
509C4×D4C5×D411yescharacteristic, complemented
510C4×D4C5×D411yescharacteristic, complemented
511#117—21no—
512#117—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4C5×D411yescharacteristic
515C2×C4⋊C4C5×D411yescharacteristic
516C2×C4⋊C4C23×C511yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4C5×D411yescharacteristic
523C2×C22⋊C4C5×D411yescharacteristic
524C2×C22⋊C4C23×C511yescharacteristic
525C2×C42C23×C511yescharacteristic
526C4⋊C8—21no—
527C4⋊C8—21no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532C22⋊C8C23×C512yes—
533C22⋊C8C23×C512yes—
534#97—21no—
535C4×C8—21no—
536#95—21no—
537#95—21no—
538#95C23×C512yes—
539C22×C5—21no—
540C22×C5—21no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—41no—
546C22×C5—41no—
547C22×C5—41no—
548C22×C5—41no—
549C22×C5—41no—
550C22×C5—41no—
551C22×C5—41no—
552C22×C5—41no—
553C22×C5—82no—
554C22×C5—82no—
555C22×C5—82no—
556C22×C5—82no—
557C22×C5—82no—
558C22×C5—82no—
559C22×C5—82no—
560C22×C5—82no—
561C22×C5—162no—
562C22×C5C2×#12011yescharacteristic
563C22×C5#57612yes—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—21no—
567C4×C5—21no—
568C4×C5—21no—
569C4×C5—21no—
570C4×C5—41no—
571C4×C5—41no—
572C4×C5—41no—
573C4×C5—41no—
574C4×C5—41no—
575C4×C5—41no—
576C4×C5—41no—
577C4×C5—41no—
578C4×C5—82no—
579C24—21no—
580C24—22no—
581C24C2×C5×D411yescharacteristic
582#41—82no—
583#41—82no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×C5×D411yescharacteristic
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4C2×C5×D411yescharacteristic
613C2×D4C2×C5×D411yescharacteristic
614C2×D4C2×C5×D411yescharacteristic
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4C2×C5×D411yescharacteristic
625C22×C4C2×C5×D411yescharacteristic
626C22×C4C2×C5×D411yescharacteristic
627C22×C4C2×C5×D411yescharacteristic
628C22×C4C2×C5×D411yescharacteristic
629C22×C4C24×C511yescharacteristic
630SD16—82no—
631D8—82no—
632D8—82no—
633D8—82no—
634C2×C8—22no—
635C2×C8—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4C2×C5×D411yescharacteristic
654C4⋊C4C2×C5×D411yescharacteristic
655C4⋊C4C2×C5×D411yescharacteristic
656C4⋊C4C2×C5×D411yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42C2×C5×D411yescharacteristic
689C42C2×C5×D411yescharacteristic
690C42C2×C5×D411yescharacteristic
691C42C2×C5×D411yescharacteristic
692C2×C5—22no—
693C2×C5—81no—
694C2×C5—81no—
695C2×C5—81no—
696C2×C5—81no—
697C2×C5—162no—
698C2×C5#300811yescharacteristic
699C2×C5#302111yescharacteristic
700C2×C5#302711yescharacteristic
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23C22×C5×D411yescharacteristic
719Q8—41no—
720Q8—81no—
721Q8—81no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—81no—
733D4—81no—
734D4—82no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—88no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4C5×#12011yescharacteristic
772C2×C4C5×#12011yescharacteristic
773C2×C4C5×#12011yescharacteristic
774C2×C4C5×#12011yescharacteristic
775C2×C4C22×C5×D411yescharacteristic
776C2×C4C22×C5×D411yescharacteristic
777C8—42no—
778C8—42no—
779C5#1846211yescharacteristic, direct product factor, Sylow
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—162no—
803C22C2×C5×#12011yescharacteristic
804C22C5×#57612yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—82no—
820C2—22no—
821C2—81no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—162no—
826C2C5×#300811yescharacteristic
827C2C5×#302111yescharacteristic
828C2C5×#302711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
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
1. C5×#3560C2semidirect
2. C5×#3217C2semidirect
3. C5×#3205C2semidirect
4. C5×#2818C2semidirect
5. C5×#1600C2semidirect
6. C5×#1598C2semidirect
7. C5×#1597C2semidirect
8. C5×#1595C2semidirect
9. C5×#1521C2semidirect
10. C5×#1514C2semidirect
11. C5×#1473C2semidirect
29. C2×C5×#127C22semidirect
40. C5×#450C22semidirect
43. C5×#447C22semidirect
44. C5×#432C22semidirect
45. C5×#431C22semidirect
48. C5×#394C22semidirect
52. C5×#383C22semidirect
53. C5×#328C22semidirect
56. C5×#327C22semidirect
57. C5×#324C22semidirect
59. #18462C5direct (N × H)
72. C5×C4⋊Q8D4semidirect
77. C5×#127D4semidirect
89. C5×#125D4semidirect
94. C5×#124D4semidirect
135. C4×C5×Q8D4semidirect
144. C4×C5×D4D4semidirect
145. C4×C5×D4D4semidirect
146. C4×C5×D4D4semidirect
175. #3560C2×C5semidirect
176. #3217C2×C5semidirect
177. #3205C2×C5semidirect
178. #2818C2×C5semidirect
179. #1600C2×C5semidirect
180. #1598C2×C5semidirect
181. #1597C2×C5semidirect
182. #1595C2×C5semidirect
183. #1521C2×C5semidirect
184. #1514C2×C5semidirect
185. #1473C2×C5semidirect
316. C2×#127C22×C5semidirect
327. #450C22×C5semidirect
330. #447C22×C5semidirect
331. #432C22×C5semidirect
332. #431C22×C5semidirect
335. #394C22×C5semidirect
339. #383C22×C5semidirect
340. #328C22×C5semidirect
343. #327C22×C5semidirect
344. #324C22×C5semidirect
436. C4⋊Q8C5×D4semidirect
441. #127C5×D4semidirect
453. #125C5×D4semidirect
458. #124C5×D4semidirect
499. C4×Q8C5×D4semidirect
508. C4×D4C5×D4semidirect
509. C4×D4C5×D4semidirect
510. C4×D4C5×D4semidirect
779. C5#18462direct (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×#32172
C5×#32052
C5×#28182
C5×#16002
C5×#15982
C5×#15972
C5×#15952
C5×#15212
C5×#15142
C5×#14732
#184625