Finite Group Databasebeta

← C5×#24174 #11946894

Subgroups — C5×#24174 #11946894

Order 1280.

1078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3512C211yesmaximal, characteristic, complemented
2C5×#3036C211yesmaximal, characteristic, complemented
3C4×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C5×#2566C211yesmaximal, characteristic, complemented
5C5×#2040C211yesmaximal, characteristic, complemented
6C5×#2039C211yesmaximal, characteristic, complemented
7C5×#2006C211yesmaximal, characteristic, complemented
8C5×#2006C211yesmaximal, characteristic, complemented
9C5×#1998C211yesmaximal, characteristic, complemented
10C5×#1980C211yesmaximal, characteristic, complemented
11C5×#1883C211yesmaximal, characteristic, complemented
12C5×#1883C211yesmaximal, characteristic, complemented
13C5×#1860C211yesmaximal, characteristic, complemented
14C5×#1859C211yesmaximal, characteristic, complemented
15C5×#1806C211yesmaximal, characteristic, complemented
16C2×C5×AGL(1,ℤ/8)C2211yescharacteristic
17C2×C5×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C5×AGL(1,ℤ/8)C2211yescharacteristic
19C5×#553—21no—
20C5×#553—21no—
21C5×#553—22no—
22C5×#553—22no—
23C5×#552—21no—
24C5×#552—21no—
25C5×#541—21no—
26C5×#540—21no—
27C5×#537C2211yescharacteristic
28C5×#537C2211yescharacteristic
29C5×#532C2211yescharacteristic
30C5×#529—21no—
31C5×#529—21no—
32C2×C5×#125C2211yescharacteristic
33C5×#520C2211yescharacteristic
34C5×#520C2211yescharacteristic
35C4×C5×#41C2211yescharacteristic
36C2×C4×C5×D4C2211yescharacteristic
37C5×#463—21no—
38C5×#463—21no—
39C5×#461—21no—
40C5×#459—21no—
41C5×#442—21no—
42C5×#440—21no—
43C4×C5×SD16—21no—
44C4×C5×D8—21no—
45C5×#428C2211yescharacteristic
46C5×#423C2211yescharacteristic
47C2×C5×#104C2211yescharacteristic
48C2×C5×#104C2211yescharacteristic
49C2×C5×#104C2211yescharacteristic
50C2×C5×#104C2211yescharacteristic
51C2×C5×#104C2211yescharacteristic
52C2×C5×#104C2211yescharacteristic
53C5×#418C2211yescharacteristic
54C5×#417C2211yescharacteristic
55C5×#417C2211yescharacteristic
56C5×#417C2211yescharacteristic
57C4×C5×M16C2211yescharacteristic
58C5×#396—22no—
59C5×#390C2211yescharacteristic
60C5×#390C2211yescharacteristic
61C5×#385—22no—
62C5×#384C2211yescharacteristic
63C5×#382C2211yescharacteristic
64C4×C5×C4⋊C4C2211yescharacteristic
65C5×#343C2211yescharacteristic
66C5×#343C2211yescharacteristic
67C5×#343C2211yescharacteristic
68C5×#343C2211yescharacteristic
69C5×#339C2211yescharacteristic
70C5×#339C2211yescharacteristic
71#24174C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41C2311yescharacteristic
73C2×C5×#41C2311yescharacteristic
74C2×C5×#41C2311yescharacteristic
75C22×C5×D4C2311yescharacteristic
76C23×C4×C5—21no—
77C5×AGL(1,ℤ/8)—22no—
78C5×AGL(1,ℤ/8)—22no—
79C5×AGL(1,ℤ/8)—22no—
80C5×AGL(1,ℤ/8)—22no—
81C5×AGL(1,ℤ/8)—41no—
82C5×AGL(1,ℤ/8)—41no—
83C2×C5×SD16—21no—
84C2×C5×SD16—21no—
85C2×C5×SD16—21no—
86C2×C5×D8—21no—
87C2×C5×D8—21no—
88C2×C5×D8—21no—
89C2×C5×M16C2311yescharacteristic
90C2×C5×M16C2311yescharacteristic
91C2×C5×M16C2311yescharacteristic
92C2×C5×M16C2311yescharacteristic
93C5×C4⋊Q8D411yescharacteristic
94C5×#127D411yescharacteristic
95C5×#126—22no—
96C5×#126—22no—
97C5×#126—22no—
98C5×#126—22no—
99C5×#125—22no—
100C5×#125—22no—
101C5×#125—21no—
102C5×#125—21no—
103C5×#125—21no—
104C5×#125—21no—
105C5×#124D411yescharacteristic
106C5×#124D411yescharacteristic
107C5×#123—22no—
108C5×#123—22no—
109C5×#123—22no—
110C5×#123—22no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×#121—22no—
116C5×#121—22no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#121—21no—
120C5×#121—21no—
121C5×#121—21no—
122C5×#121—21no—
123C5×#121—22no—
124C5×#121—22no—
125C4×C5×Q8—21no—
126C4×C5×Q8—21no—
127C4×C5×Q8D411yescharacteristic
128C4×C5×Q8D411yescharacteristic
129C4×C5×D4—22no—
130C4×C5×D4—22no—
131C4×C5×D4—21no—
132C4×C5×D4—21no—
133C4×C5×D4—21no—
134C4×C5×D4—21no—
135C4×C5×D4—22no—
136C4×C5×D4—22no—
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×D4D411yescharacteristic
144C4×C5×D4D411yescharacteristic
145C5×#117—22no—
146C5×#117—22no—
147C5×#117—21no—
148C5×#117—21no—
149C5×#117—21no—
150C5×#117C2311yescharacteristic
151C2×C5×C4⋊C4—21no—
152C2×C5×C4⋊C4—21no—
153C2×C5×C4⋊C4—21no—
154C2×C5×C4⋊C4—22no—
155C2×C5×C4⋊C4D412yes—
156C2×C5×C4⋊C4D412yes—
157C2×C5×C4⋊C4C2311yescharacteristic
158C2×C5×C4⋊C4C2311yescharacteristic
159C2×C5×C4⋊C4C2311yescharacteristic
160C2×C5×C22⋊C4—22no—
161C2×C5×C22⋊C4—21no—
162C2×C5×C22⋊C4—22no—
163C2×C42×C5—21no—
164C2×C42×C5C2311yescharacteristic
165C2×C42×C5C2311yescharacteristic
166C2×C42×C5C2311yescharacteristic
167C5×#107—21no—
168C5×#106—21no—
169C5×C4⋊C8—21no—
170C5×C4⋊C8—21no—
171C5×#104—22no—
172C5×#104—22no—
173C5×#104—41no—
174C5×#104—41no—
175C5×#104—41no—
176C5×#104—41no—
177C5×#103—21no—
178C5×#103—21no—
179C5×#103—21no—
180C5×#102—21no—
181C5×#102—21no—
182C5×#102—21no—
183C5×#102—21no—
184C5×#102—21no—
185C5×#97—21no—
186C4×C5×C8—21no—
187C5×#95—21no—
188C5×#95—22no—
189#3512C2×C511yescharacteristic, complemented
190#3036C2×C511yescharacteristic, complemented
191C4×AGL(1,ℤ/8)C2×C511yescharacteristic, complemented
192#2566C2×C511yescharacteristic, complemented
193#2040C2×C511yescharacteristic, complemented
194#2039C2×C511yescharacteristic, complemented
195#2006C2×C511yescharacteristic, complemented
196#2006C2×C511yescharacteristic, complemented
197#1998C2×C511yescharacteristic, complemented
198#1980C2×C511yescharacteristic, complemented
199#1883C2×C511yescharacteristic, complemented
200#1883C2×C511yescharacteristic, complemented
201#1860C2×C511yescharacteristic, complemented
202#1859C2×C511yescharacteristic, complemented
203#1806C2×C511yescharacteristic, complemented
204C24×C5—21no—
205C5×#41—21no—
206C5×#41—21no—
207C5×#41—21no—
208C5×#41—21no—
209C5×#41—21no—
210C5×#41—21no—
211C5×#41—21no—
212C5×#41—21no—
213C5×#41—21no—
214C5×#41—21no—
215C5×#41—21no—
216C5×#41—21no—
217C2×C5×Q8C2×D411yescharacteristic
218C2×C5×Q8C2×D411yescharacteristic
219C2×C5×Q8C2×D411yescharacteristic
220C2×C5×D4—21no—
221C2×C5×D4—21no—
222C2×C5×D4—21no—
223C2×C5×D4—22no—
224C2×C5×D4—22no—
225C2×C5×D4—21no—
226C2×C5×D4—21no—
227C2×C5×D4—21no—
228C2×C5×D4—21no—
229C2×C5×D4—21no—
230C2×C5×D4—21no—
231C2×C5×D4—21no—
232C2×C5×D4C2×D411yescharacteristic
233C2×C5×D4C2×D411yescharacteristic
234C2×C5×D4C2×D411yescharacteristic
235C2×C5×D4#4112yes—
236C22×C4×C5—21no—
237C22×C4×C5—22no—
238C22×C4×C5—22no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—41no—
247C22×C4×C5—41no—
248C22×C4×C5—82no—
249C22×C4×C5C2×D412yes—
250C22×C4×C5C2×D412yes—
251C22×C4×C5C2×D411yescharacteristic
252C22×C4×C5C2×D411yescharacteristic
253C22×C4×C5C2411yescharacteristic
254C5×SD16—24no—
255C5×SD16—42no—
256C5×SD16—42no—
257C5×D8—24no—
258C5×D8—42no—
259C5×D8—42no—
260C5×M16—21no—
261C5×M16—21no—
262C5×M16—21no—
263C5×M16—21no—
264C5×M16—21no—
265C5×M16—21no—
266C5×M16—21no—
267C5×M16#4112yes—
268C2×C5×C8—21no—
269C2×C5×C8—21no—
270C2×C5×C8—21no—
271C2×C5×C8—21no—
272C5×C4⋊C4—22no—
273C5×C4⋊C4—22no—
274C5×C4⋊C4—22no—
275C5×C4⋊C4—22no—
276C5×C4⋊C4—22no—
277C5×C4⋊C4—22no—
278C5×C4⋊C4—22no—
279C5×C4⋊C4—22no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4—21no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—42no—
291C5×C4⋊C4—82no—
292C5×C4⋊C4C2×D411yescharacteristic
293C5×C4⋊C4C2×D411yescharacteristic
294C5×C22⋊C4—22no—
295C5×C22⋊C4—22no—
296C5×C22⋊C4—22no—
297C5×C22⋊C4—22no—
298C5×C22⋊C4—22no—
299C5×C22⋊C4—22no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C5×C22⋊C4—21no—
305C5×C22⋊C4—21no—
306C5×C22⋊C4—21no—
307C5×C22⋊C4—44no—
308C5×C22⋊C4—41no—
309C5×C22⋊C4—41no—
310C5×C22⋊C4—82no—
311C42×C5—22no—
312C42×C5—22no—
313C42×C5—21no—
314C42×C5—21no—
315C42×C5—21no—
316C42×C5—21no—
317C42×C5—21no—
318C42×C5—21no—
319C42×C5—21no—
320C42×C5C2×D411yescharacteristic
321C42×C5C2×D411yescharacteristic
322C42×C5C2×D411yescharacteristic
323C42×C5C2×D411yescharacteristic
324C2×AGL(1,ℤ/8)C22×C511yescharacteristic
325C2×AGL(1,ℤ/8)C22×C511yescharacteristic
326C2×AGL(1,ℤ/8)C22×C511yescharacteristic
327#553—21no—
328#553—21no—
329#553—22no—
330#553—22no—
331#552—21no—
332#552—21no—
333#541—21no—
334#540—21no—
335#537C22×C511yescharacteristic
336#537C22×C511yescharacteristic
337#532C22×C511yescharacteristic
338#529—21no—
339#529—21no—
340C2×#125C22×C511yescharacteristic
341#520C22×C511yescharacteristic
342#520C22×C511yescharacteristic
343C4×#41C22×C511yescharacteristic
344C2×C4×D4C22×C511yescharacteristic
345#463—21no—
346#463—21no—
347#461—21no—
348#459—21no—
349#442—21no—
350#440—21no—
351C4×SD16—21no—
352C4×D8—21no—
353#428C22×C511yescharacteristic
354#423C22×C511yescharacteristic
355C2×#104C22×C511yescharacteristic
356C2×#104C22×C511yescharacteristic
357C2×#104C22×C511yescharacteristic
358C2×#104C22×C511yescharacteristic
359C2×#104C22×C511yescharacteristic
360C2×#104C22×C511yescharacteristic
361#418C22×C511yescharacteristic
362#417C22×C511yescharacteristic
363#417C22×C511yescharacteristic
364#417C22×C511yescharacteristic
365C4×M16C22×C511yescharacteristic
366#396—22no—
367#390C22×C511yescharacteristic
368#390C22×C511yescharacteristic
369#385—22no—
370#384C22×C511yescharacteristic
371#382C22×C511yescharacteristic
372C4×C4⋊C4C22×C511yescharacteristic
373#343C22×C511yescharacteristic
374#343C22×C511yescharacteristic
375#343C22×C511yescharacteristic
376#343C22×C511yescharacteristic
377#339C22×C511yescharacteristic
378#339C22×C511yescharacteristic
379C23×C5—21no—
380C23×C5—21no—
381C23×C5—21no—
382C23×C5—22no—
383C23×C5—42no—
384C23×C5—42no—
385C23×C5—41no—
386C23×C5—41no—
387C23×C5C22×D411yescharacteristic
388C5×Q8—21no—
389C5×Q8—21no—
390C5×Q8—21no—
391C5×Q8—21no—
392C5×Q8—21no—
393C5×Q8—21no—
394C5×D4—21no—
395C5×D4—22no—
396C5×D4—21no—
397C5×D4—22no—
398C5×D4—21no—
399C5×D4—21no—
400C5×D4—21no—
401C5×D4—21no—
402C5×D4—41no—
403C5×D4—41no—
404C5×D4—41no—
405C5×D4—41no—
406C5×D4—41no—
407C5×D4—41no—
408C5×D4—41no—
409C5×D4—41no—
410C5×D4—81no—
411C5×D4—81no—
412C5×D4—82no—
413C5×D4—82no—
414C2×C4×C5—22no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—42no—
433C2×C4×C5—42no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—42no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—81no—
440C2×C4×C5—81no—
441C2×C4×C5—82no—
442C2×C4×C5—82no—
443C2×C4×C5—82no—
444C2×C4×C5—82no—
445C2×C4×C5#12011yescharacteristic
446C2×C4×C5#12011yescharacteristic
447C2×C4×C5#12011yescharacteristic
448C2×C4×C5#12011yescharacteristic
449C2×C4×C5C22×D411yescharacteristic
450C2×C4×C5C22×D411yescharacteristic
451C2×C4×C5C2×#4111yescharacteristic
452C2×C4×C5C2×#4111yescharacteristic
453C2×C4×C5H(5,𝔽2)11yescharacteristic
454C2×C4×C52−1+411yescharacteristic
455C5×C8—22no—
456C5×C8—41no—
457C5×C8—41no—
458C5×C8—41no—
459C2×#41C23×C511yescharacteristic
460C2×#41C23×C511yescharacteristic
461C2×#41C23×C511yescharacteristic
462C22×D4C23×C511yescharacteristic
463C23×C4—21no—
464AGL(1,ℤ/8)—22no—
465AGL(1,ℤ/8)—22no—
466AGL(1,ℤ/8)—22no—
467AGL(1,ℤ/8)—22no—
468AGL(1,ℤ/8)—41no—
469AGL(1,ℤ/8)—41no—
470C2×SD16—21no—
471C2×SD16—21no—
472C2×SD16—21no—
473C2×D8—21no—
474C2×D8—21no—
475C2×D8—21no—
476C2×M16C23×C511yescharacteristic
477C2×M16C23×C511yescharacteristic
478C2×M16C23×C511yescharacteristic
479C2×M16C23×C511yescharacteristic
480C4⋊Q8C5×D411yescharacteristic
481#127C5×D411yescharacteristic
482#126—22no—
483#126—22no—
484#126—22no—
485#126—22no—
486#125—22no—
487#125—22no—
488#125—21no—
489#125—21no—
490#125—21no—
491#125—21no—
492#124C5×D411yescharacteristic
493#124C5×D411yescharacteristic
494#123—22no—
495#123—22no—
496#123—22no—
497#123—22no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512C4×Q8—21no—
513C4×Q8—21no—
514C4×Q8C5×D411yescharacteristic
515C4×Q8C5×D411yescharacteristic
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4C5×D411yescharacteristic
531C4×D4C5×D411yescharacteristic
532#117—22no—
533#117—22no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117C23×C511yescharacteristic
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4C5×D412yes—
543C2×C4⋊C4C5×D412yes—
544C2×C4⋊C4C23×C511yescharacteristic
545C2×C4⋊C4C23×C511yescharacteristic
546C2×C4⋊C4C23×C511yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C42—21no—
551C2×C42C23×C511yescharacteristic
552C2×C42C23×C511yescharacteristic
553C2×C42C23×C511yescharacteristic
554#107—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558#104—22no—
559#104—22no—
560#104—41no—
561#104—41no—
562#104—41no—
563#104—41no—
564#103—21no—
565#103—21no—
566#103—21no—
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#97—21no—
573C4×C8—21no—
574#95—21no—
575#95—22no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—44no—
579C22×C5—41no—
580C22×C5—41no—
581C22×C5—41no—
582C22×C5—42no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—82no—
590C22×C5—81no—
591C22×C5—81no—
592C22×C5C2×#12011yescharacteristic
593C22×C5#54811yescharacteristic
594C22×C5#55011yescharacteristic
595C4×C5—21no—
596C4×C5—21no—
597C4×C5—21no—
598C4×C5—21no—
599C4×C5—42no—
600C4×C5—41no—
601C4×C5—41no—
602C4×C5—41no—
603C4×C5—42no—
604C4×C5—41no—
605C4×C5—42no—
606C4×C5—41no—
607C4×C5—81no—
608C4×C5—81no—
609C4×C5#52511yescharacteristic
610C4×C5#53711yescharacteristic
611C4×C5#54611yescharacteristic
612C4×C5#54711yescharacteristic
613C24—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—21no—
625#41—21no—
626C2×Q8C2×C5×D411yescharacteristic
627C2×Q8C2×C5×D411yescharacteristic
628C2×Q8C2×C5×D411yescharacteristic
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4C2×C5×D411yescharacteristic
642C2×D4C2×C5×D411yescharacteristic
643C2×D4C2×C5×D411yescharacteristic
644C2×D4C5×#4112yes—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—82no—
658C22×C4C2×C5×D412yes—
659C22×C4C2×C5×D412yes—
660C22×C4C2×C5×D411yescharacteristic
661C22×C4C2×C5×D411yescharacteristic
662C22×C4C24×C511yescharacteristic
663SD16—24no—
664SD16—42no—
665SD16—42no—
666D8—24no—
667D8—42no—
668D8—42no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16C5×#4112yes—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4—82no—
701C4⋊C4C2×C5×D411yescharacteristic
702C4⋊C4C2×C5×D411yescharacteristic
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—44no—
717C22⋊C4—41no—
718C22⋊C4—41no—
719C22⋊C4—82no—
720C42—22no—
721C42—22no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42C2×C5×D411yescharacteristic
730C42C2×C5×D411yescharacteristic
731C42C2×C5×D411yescharacteristic
732C42C2×C5×D411yescharacteristic
733C2×C5—21no—
734C2×C5—21no—
735C2×C5—81no—
736C2×C5—81no—
737C2×C5—81no—
738C2×C5—82no—
739C2×C5#240711yescharacteristic
740C2×C5#301811yescharacteristic
741C2×C5#302111yescharacteristic
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23C22×C5×D411yescharacteristic
751Q8—21no—
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757D4—21no—
758D4—22no—
759D4—21no—
760D4—22no—
761D4—21no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—81no—
774D4—81no—
775D4—82no—
776D4—82no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4C5×#12011yescharacteristic
809C2×C4C5×#12011yescharacteristic
810C2×C4C5×#12011yescharacteristic
811C2×C4C5×#12011yescharacteristic
812C2×C4C22×C5×D411yescharacteristic
813C2×C4C22×C5×D411yescharacteristic
814C2×C4C2×C5×#4111yescharacteristic
815C2×C4C2×C5×#4111yescharacteristic
816C2×C4C5×H(5,𝔽2)11yescharacteristic
817C2×C4C5×2−1+411yescharacteristic
818C8—22no—
819C8—41no—
820C8—41no—
821C8—41no—
822C5#2417411yescharacteristic, direct product factor, Sylow
823C22—21no—
824C22—21no—
825C22—44no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—81no—
839C22C2×C5×#12011yescharacteristic
840C22C5×#54811yescharacteristic
841C22C5×#55011yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C5×#52511yescharacteristic
857C4C5×#53711yescharacteristic
858C4C5×#54611yescharacteristic
859C4C5×#54711yescharacteristic
860C2—21no—
861C2—21no—
862C2—82no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2C5×#240711yescharacteristic
867C2C5×#301811yescharacteristic
868C2C5×#302111yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3512C2semidirect
2. C5×#3036C2semidirect
3. C4×C5×AGL(1,ℤ/8)C2semidirect
4. C5×#2566C2semidirect
5. C5×#2040C2semidirect
6. C5×#2039C2semidirect
7. C5×#2006C2semidirect
8. C5×#2006C2semidirect
9. C5×#1998C2semidirect
10. C5×#1980C2semidirect
11. C5×#1883C2semidirect
12. C5×#1883C2semidirect
13. C5×#1860C2semidirect
14. C5×#1859C2semidirect
15. C5×#1806C2semidirect
71. #24174C5direct (N × H)
189. #3512C2×C5semidirect
190. #3036C2×C5semidirect
191. C4×AGL(1,ℤ/8)C2×C5semidirect
192. #2566C2×C5semidirect
193. #2040C2×C5semidirect
194. #2039C2×C5semidirect
195. #2006C2×C5semidirect
196. #2006C2×C5semidirect
197. #1998C2×C5semidirect
198. #1980C2×C5semidirect
199. #1883C2×C5semidirect
200. #1883C2×C5semidirect
201. #1860C2×C5semidirect
202. #1859C2×C5semidirect
203. #1806C2×C5semidirect
822. C5#24174direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35122
C5×#30362
C4×C5×AGL(1,ℤ/8)2
C5×#25662
C5×#20402
C5×#20392
C5×#20062
C5×#19982
C5×#19802
C5×#18832
C5×#18602
C5×#18592
C5×#18062
#241745