Finite Group Databasebeta

← C5×#18232 #11940952

Subgroups — C5×#18232 #11940952

Order 1280.

1002 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×#3534C211yesmaximal, characteristic
2C5×#3092C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic, complemented
4C5×#2623C211yesmaximal, characteristic, complemented
5C5×#1612C212yesmaximal, complemented
6C5×#1610C212yesmaximal, complemented
7C5×#1609C212yesmaximal, complemented
8C5×#1607C212yesmaximal, complemented
9C5×#1516C211yesmaximal, characteristic, complemented
10C5×#1510C211yesmaximal, characteristic, complemented
11C5×#1468C211yesmaximal, characteristic, complemented
12C5×#562—21no—
13C5×#560—21no—
14C5×#553—21no—
15C5×#551—21no—
16C5×#546—21no—
17C5×#546—21no—
18C5×#546—21no—
19C5×D42—21no—
20C5×#540—21no—
21C5×#539—21no—
22C5×#539C2211yescharacteristic
23C5×#538—21no—
24C5×#538C2211yescharacteristic
25C5×#537C2211yescharacteristic
26C5×#534—21no—
27C5×#534C2211yescharacteristic
28C5×#525C2211yescharacteristic
29C2×C5×#123C2211yescharacteristic
30C2×C5×#121C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic, complemented
32C5×#484—21no—
33C5×#483C2212yescomplemented
34C5×#481—21no—
35C5×#480—21no—
36C5×#480—21no—
37C5×#480C2212yes—
38C5×#480C2212yescomplemented
39C5×#480C2212yescomplemented
40C5×#428—21no—
41C2×C5×#107—21no—
42C5×#417—21no—
43C2×C5×#102—21no—
44C5×#407C2211yescharacteristic, complemented
45C2×C5×C22⋊C8C2211yescharacteristic, complemented
46C5×#400—21no—
47C5×#399—21no—
48C5×#398C2212yescomplemented
49C5×#397C2212yescomplemented
50C5×#386—21no—
51C5×#385—21no—
52C5×#381C2211yescharacteristic, complemented
53C5×#328C2212yescomplemented
54C5×#327C2212yes—
55C5×#327C2212yescomplemented
56C5×#327C2212yescomplemented
57C5×#324C2212yescomplemented
58C5×#323C2212yescomplemented
59#18232C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C2×C5×#41D411yescharacteristic
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4—21no—
65C22×C5×D4D411yescharacteristic
66C22×C5×D4D411yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C2×C5×M16—21no—
70C22×C5×C8—21no—
71C5×#127—21no—
72C5×#126—21no—
73C5×#126—21no—
74C5×#126—21no—
75C5×#126—21no—
76C5×#125—21no—
77C5×#125—21no—
78C5×#124—21no—
79C5×#124—21no—
80C5×#124—21no—
81C5×#123—21no—
82C5×#123—21no—
83C5×#123—21no—
84C5×#123—21no—
85C5×#123—21no—
86C5×#123—21no—
87C5×#123—21no—
88C5×#123—21no—
89C5×#123—21no—
90C5×#123—21no—
91C5×#123—21no—
92C5×#123—21no—
93C5×#123—21no—
94C5×#123—21no—
95C5×C22⋊Q8—21no—
96C5×C22⋊Q8—21no—
97C5×C22⋊Q8—21no—
98C5×C22⋊Q8—21no—
99C5×C22⋊Q8—21no—
100C5×C22⋊Q8D411yescharacteristic
101C5×C22⋊Q8C2311yescharacteristic
102C5×#121—21no—
103C5×#121—21no—
104C5×#121—21no—
105C5×#121—21no—
106C5×#121—21no—
107C5×#121—21no—
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×#121D411yescharacteristic
118C5×#121D411yescharacteristic
119C5×#121D411yescharacteristic
120C5×#121C2311yescharacteristic
121C5×#121C2311yescharacteristic
122C5×#121C2311yescharacteristic
123C5×#120—21no—
124C5×#120—21no—
125C5×#120—21no—
126C5×#120—21no—
127C5×#120—21no—
128C5×#120—21no—
129C5×#120—21no—
130C5×#120—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×D4—21no—
138C4×C5×D4—21no—
139C5×#117—21no—
140C5×#117D411yescharacteristic
141C2×C5×C4⋊C4—21no—
142C2×C5×C4⋊C4—21no—
143C2×C5×C4⋊C4—21no—
144C2×C5×C4⋊C4—21no—
145C2×C5×C4⋊C4—21no—
146C2×C5×C4⋊C4—22no—
147C2×C5×C4⋊C4D411yescharacteristic
148C2×C5×C4⋊C4D411yescharacteristic
149C2×C5×C4⋊C4C2312yes—
150C2×C5×C4⋊C4C2311yescharacteristic
151C2×C5×C22⋊C4—21no—
152C2×C5×C22⋊C4—21no—
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
159C5×#107—22no—
160C5×#107—22no—
161C5×#107—22no—
162C5×#106—22no—
163C5×#103—22no—
164C5×#102—22no—
165C5×#102—22no—
166C5×#102—22no—
167C5×C22⋊C8—21no—
168C5×C22⋊C8—21no—
169C5×C22⋊C8C2312yes—
170C5×C22⋊C8C2312yes—
171C5×#95—21no—
172C5×#95—22no—
173C5×#95—22no—
174C5×#95C2312yes—
175#3534C2×C511yescharacteristic
176#3092C2×C511yescharacteristic, complemented
177C2×#480C2×C511yescharacteristic, complemented
178#2623C2×C511yescharacteristic, complemented
179#1612C2×C512yescomplemented
180#1610C2×C512yescomplemented
181#1609C2×C512yescomplemented
182#1607C2×C512yescomplemented
183#1516C2×C511yescharacteristic, complemented
184#1510C2×C511yescharacteristic, complemented
185#1468C2×C511yescharacteristic, complemented
186C24×C5—21no—
187C24×C5—21no—
188C24×C5C2×D411yescharacteristic
189C24×C5C2×D411yescharacteristic
190C5×#41—42no—
191C5×#41—82no—
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—21no—
207C2×C5×D4—21no—
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—21no—
211C2×C5×D4—42no—
212C2×C5×D4—42no—
213C2×C5×D4—82no—
214C2×C5×D4—82no—
215C2×C5×D4—82no—
216C2×C5×D4C2×D411yescharacteristic
217C2×C5×D4C2×D411yescharacteristic
218C2×C5×D4C2×D411yescharacteristic
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—42no—
229C22×C4×C5—41no—
230C22×C4×C5—41no—
231C22×C4×C5—82no—
232C22×C4×C5C2×D411yescharacteristic
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2×D411yescharacteristic
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2411yescharacteristic
241C5×M16—42no—
242C2×C5×C8—22no—
243C2×C5×C8—22no—
244C2×C5×C8—42no—
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—22no—
259C5×C4⋊C4—22no—
260C5×C4⋊C4—41no—
261C5×C4⋊C4—41no—
262C5×C4⋊C4—82no—
263C5×C4⋊C4C2×D411yescharacteristic
264C5×C4⋊C4C2×D411yescharacteristic
265C5×C4⋊C4C2×D411yescharacteristic
266C5×C4⋊C4C2×D411yescharacteristic
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—21no—
290C5×C22⋊C4—21no—
291C5×C22⋊C4—21no—
292C5×C22⋊C4—42no—
293C5×C22⋊C4—82no—
294C42×C5—21no—
295C42×C5—21no—
296C42×C5—21no—
297#562—21no—
298#560—21no—
299#553—21no—
300#551—21no—
301#546—21no—
302#546—21no—
303#546—21no—
304D42—21no—
305#540—21no—
306#539—21no—
307#539C22×C511yescharacteristic
308#538—21no—
309#538C22×C511yescharacteristic
310#537C22×C511yescharacteristic
311#534—21no—
312#534C22×C511yescharacteristic
313#525C22×C511yescharacteristic
314C2×#123C22×C511yescharacteristic
315C2×#121C22×C511yescharacteristic
316C22×C4⋊C4C22×C511yescharacteristic, complemented
317#484—21no—
318#483C22×C512yescomplemented
319#481—21no—
320#480—21no—
321#480—21no—
322#480C22×C512yes—
323#480C22×C512yescomplemented
324#480C22×C512yescomplemented
325#428—21no—
326C2×#107—21no—
327#417—21no—
328C2×#102—21no—
329#407C22×C511yescharacteristic, complemented
330C2×C22⋊C8C22×C511yescharacteristic, complemented
331#400—21no—
332#399—21no—
333#398C22×C512yescomplemented
334#397C22×C512yescomplemented
335#386—21no—
336#385—21no—
337#381C22×C511yescharacteristic, complemented
338#328C22×C512yescomplemented
339#327C22×C512yes—
340#327C22×C512yescomplemented
341#327C22×C512yescomplemented
342#324C22×C512yescomplemented
343#323C22×C512yescomplemented
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—21no—
347C23×C5—21no—
348C23×C5—21no—
349C23×C5—21no—
350C23×C5—22no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5—42no—
355C23×C5—81no—
356C23×C5—81no—
357C23×C5—81no—
358C23×C5—81no—
359C23×C5—81no—
360C23×C5#12011yescharacteristic
361C23×C5#12011yescharacteristic
362C23×C5C22×D411yescharacteristic
363C5×Q8—41no—
364C5×Q8—81no—
365C5×D4—41no—
366C5×D4—41no—
367C5×D4—41no—
368C5×D4—42no—
369C5×D4—42no—
370C5×D4—42no—
371C5×D4—42no—
372C5×D4—42no—
373C5×D4—81no—
374C5×D4—81no—
375C5×D4—81no—
376C5×D4—81no—
377C5×D4—81no—
378C5×D4—81no—
379C5×D4—81no—
380C5×D4—81no—
381C5×D4—81no—
382C5×D4—81no—
383C5×D4—81no—
384C5×D4—81no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—22no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—42no—
403C2×C4×C5—42no—
404C2×C4×C5—42no—
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—82no—
416C2×C4×C5—82no—
417C2×C4×C5#12011yescharacteristic
418C2×C4×C5#12011yescharacteristic
419C2×C4×C5C22×D411yescharacteristic
420C2×C4×C5C22×D411yescharacteristic
421C5×C8—42no—
422C5×C8—42no—
423C2×#41—21no—
424C2×#41C5×D411yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C5×D411yescharacteristic
429C22×D4C5×D411yescharacteristic
430C23×C4—21no—
431C23×C4C23×C511yescharacteristic
432C2×M16—21no—
433C22×C8—21no—
434#127—21no—
435#126—21no—
436#126—21no—
437#126—21no—
438#126—21no—
439#125—21no—
440#125—21no—
441#124—21no—
442#124—21no—
443#124—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—
453#123—21no—
454#123—21no—
455#123—21no—
456#123—21no—
457#123—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8C5×D411yescharacteristic
464C22⋊Q8C23×C511yescharacteristic
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#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121C5×D411yescharacteristic
481#121C5×D411yescharacteristic
482#121C5×D411yescharacteristic
483#121C23×C511yescharacteristic
484#121C23×C511yescharacteristic
485#121C23×C511yescharacteristic
486#120—21no—
487#120—21no—
488#120—21no—
489#120—21no—
490#120—21no—
491#120—21no—
492#120—21no—
493#120—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502#117—21no—
503#117C5×D411yescharacteristic
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4C5×D411yescharacteristic
511C2×C4⋊C4C5×D411yescharacteristic
512C2×C4⋊C4C23×C512yes—
513C2×C4⋊C4C23×C511yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4C5×D411yescharacteristic
520C2×C22⋊C4C5×D411yescharacteristic
521C2×C22⋊C4C23×C511yescharacteristic
522#107—22no—
523#107—22no—
524#107—22no—
525#106—22no—
526#103—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530C22⋊C8—21no—
531C22⋊C8—21no—
532C22⋊C8C23×C512yes—
533C22⋊C8C23×C512yes—
534#95—21no—
535#95—22no—
536#95—22no—
537#95C23×C512yes—
538C22×C5—21no—
539C22×C5—21no—
540C22×C5—21no—
541C22×C5—21no—
542C22×C5—21no—
543C22×C5—21no—
544C22×C5—21no—
545C22×C5—44no—
546C22×C5—41no—
547C22×C5—41no—
548C22×C5—41no—
549C22×C5—41no—
550C22×C5—41no—
551C22×C5—41no—
552C22×C5—41no—
553C22×C5—41no—
554C22×C5—41no—
555C22×C5—41no—
556C22×C5—41no—
557C22×C5—41no—
558C22×C5—82no—
559C22×C5—162no—
560C22×C5—162no—
561C22×C5#45812yes—
562C22×C5C2×#12011yescharacteristic
563C22×C5#57612yes—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—21no—
567C4×C5—21no—
568C4×C5—41no—
569C4×C5—41no—
570C4×C5—41no—
571C4×C5—41no—
572C4×C5—41no—
573C4×C5—41no—
574C4×C5—41no—
575C4×C5—41no—
576C4×C5—82no—
577C4×C5—82no—
578C24—21no—
579C24—21no—
580C24C2×C5×D411yescharacteristic
581C24C2×C5×D411yescharacteristic
582#41—42no—
583#41—82no—
584C2×Q8—21no—
585C2×Q8C2×C5×D411yescharacteristic
586C2×D4—21no—
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—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4C2×C5×D411yescharacteristic
609C2×D4C2×C5×D411yescharacteristic
610C2×D4C2×C5×D411yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—42no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—82no—
624C22×C4C2×C5×D411yescharacteristic
625C22×C4C2×C5×D411yescharacteristic
626C22×C4C2×C5×D411yescharacteristic
627C22×C4C2×C5×D411yescharacteristic
628C22×C4C2×C5×D411yescharacteristic
629C22×C4C2×C5×D411yescharacteristic
630C22×C4C2×C5×D411yescharacteristic
631C22×C4C2×C5×D411yescharacteristic
632C22×C4C24×C511yescharacteristic
633M16—42no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—42no—
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—22no—
651C4⋊C4—22no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—82no—
655C4⋊C4C2×C5×D411yescharacteristic
656C4⋊C4C2×C5×D411yescharacteristic
657C4⋊C4C2×C5×D411yescharacteristic
658C4⋊C4C2×C5×D411yescharacteristic
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—21no—
683C22⋊C4—21no—
684C22⋊C4—42no—
685C22⋊C4—82no—
686C42—21no—
687C42—21no—
688C42—21no—
689C2×C5—22no—
690C2×C5—22no—
691C2×C5—41no—
692C2×C5—81no—
693C2×C5—81no—
694C2×C5—81no—
695C2×C5—81no—
696C2×C5#300811yescharacteristic
697C2×C5#302211yescharacteristic
698C2×C5C2×#45811yescharacteristic
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23C5×#12011yescharacteristic
716C23C5×#12011yescharacteristic
717C23C22×C5×D411yescharacteristic
718Q8—41no—
719Q8—81no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
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—82no—
771C2×C4—82no—
772C2×C4C5×#12011yescharacteristic
773C2×C4C5×#12011yescharacteristic
774C2×C4C22×C5×D411yescharacteristic
775C2×C4C22×C5×D411yescharacteristic
776C8—42no—
777C8—42no—
778C5#1823211yescharacteristic, direct product factor, Sylow
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—44no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—82no—
800C22—162no—
801C22—162no—
802C22C5×#45812yes—
803C22C2×C5×#12011yescharacteristic
804C22C5×#57612yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—82no—
818C4—82no—
819C2—22no—
820C2—22no—
821C2—41no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—81no—
826C2C5×#300811yescharacteristic
827C2C5×#302211yescharacteristic
828C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3092C2semidirect
3. C2×C5×#480C2semidirect
4. C5×#2623C2semidirect
5. C5×#1612C2semidirect
6. C5×#1610C2semidirect
7. C5×#1609C2semidirect
8. C5×#1607C2semidirect
9. C5×#1516C2semidirect
10. C5×#1510C2semidirect
11. C5×#1468C2semidirect
31. C22×C5×C4⋊C4C22semidirect
33. C5×#483C22semidirect
38. C5×#480C22semidirect
39. C5×#480C22semidirect
44. C5×#407C22semidirect
45. C2×C5×C22⋊C8C22semidirect
48. C5×#398C22semidirect
49. C5×#397C22semidirect
52. C5×#381C22semidirect
53. C5×#328C22semidirect
55. C5×#327C22semidirect
56. C5×#327C22semidirect
57. C5×#324C22semidirect
58. C5×#323C22semidirect
59. #18232C5direct (N × H)
176. #3092C2×C5semidirect
177. C2×#480C2×C5semidirect
178. #2623C2×C5semidirect
179. #1612C2×C5semidirect
180. #1610C2×C5semidirect
181. #1609C2×C5semidirect
182. #1607C2×C5semidirect
183. #1516C2×C5semidirect
184. #1510C2×C5semidirect
185. #1468C2×C5semidirect
316. C22×C4⋊C4C22×C5semidirect
318. #483C22×C5semidirect
323. #480C22×C5semidirect
324. #480C22×C5semidirect
329. #407C22×C5semidirect
330. C2×C22⋊C8C22×C5semidirect
333. #398C22×C5semidirect
334. #397C22×C5semidirect
337. #381C22×C5semidirect
338. #328C22×C5semidirect
340. #327C22×C5semidirect
341. #327C22×C5semidirect
342. #324C22×C5semidirect
343. #323C22×C5semidirect
778. C5#18232direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35342
C5×#30922
C2×C5×#4802
C5×#26232
C5×#16122
C5×#16102
C5×#16092
C5×#16072
C5×#15162
C5×#15102
C5×#14682
#182325