Finite Group Databasebeta

← C5×#18252 #11940972

Subgroups — C5×#18252 #11940972

Order 1280.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3534C211yesmaximal, characteristic, complemented
2C5×#3006C211yesmaximal, characteristic, complemented
3C5×#3002C211yesmaximal, characteristic, complemented
4C5×#2430C211yesmaximal, characteristic, complemented
5C5×#1606C211yesmaximal, characteristic, complemented
6C5×#1604C211yesmaximal, characteristic, complemented
7C5×#1603C211yesmaximal, characteristic, complemented
8C5×#1601C211yesmaximal, characteristic, complemented
9C5×#1600C211yesmaximal, characteristic, complemented
10C5×#1598C211yesmaximal, characteristic, complemented
11C5×#1597C211yesmaximal, characteristic, complemented
12C5×#1595C211yesmaximal, characteristic, complemented
13C5×#1504C211yesmaximal, characteristic, complemented
14C2×C5×#327C211yesmaximal, characteristic, complemented
15C5×#1468C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic, complemented
17C2×C5×AGL(1,ℤ/8)—21no—
18C2×C5×#135—21no—
19C5×#562—21no—
20C5×#560—21no—
21C5×#553—21no—
22C5×#551—21no—
23C5×#546—21no—
24C5×#546—21no—
25C5×#546—21no—
26C5×D42—21no—
27C5×#540—21no—
28C5×#539—21no—
29C5×#539C2211yescharacteristic
30C5×#538—21no—
31C5×#538C2211yescharacteristic
32C5×#537C2211yescharacteristic
33C5×#534—21no—
34C5×#534C2211yescharacteristic
35C5×#525C2211yescharacteristic
36C2×C5×#123C2211yescharacteristic
37C2×C5×#121—21no—
38C2×C5×#121C2211yescharacteristic
39C5×#452—21no—
40C5×#451C2211yescharacteristic, complemented
41C5×#450C2211yescharacteristic, complemented
42C5×#449—21no—
43C5×#449—21no—
44C5×#449—21no—
45C5×#448C2211yescharacteristic
46C5×#448C2211yescharacteristic, complemented
47C5×#448C2211yescharacteristic, complemented
48C5×#447C2211yescharacteristic
49C5×#447C2211yescharacteristic, complemented
50C5×#447C2211yescharacteristic, complemented
51C5×#417—21no—
52C5×#416—21no—
53C5×#407C2211yescharacteristic, complemented
54C2×C5×C22⋊C8C2211yescharacteristic, complemented
55C5×#395C2211yescharacteristic, complemented
56C5×#394C2211yescharacteristic, complemented
57C5×#393C2211yescharacteristic, complemented
58C5×#392C2211yescharacteristic, complemented
59C5×#386—21no—
60C5×#386—21no—
61C5×#385—21no—
62C2×C5×#95C2211yescharacteristic, complemented
63C5×#328C2211yescharacteristic, complemented
64C5×#328C2211yescharacteristic, complemented
65C5×#327C2211yescharacteristic
66C5×#327C2211yescharacteristic
67C5×#327C2211yescharacteristic, complemented
68C5×#327C2211yescharacteristic, complemented
69C5×#327C2211yescharacteristic, complemented
70C5×#327C2211yescharacteristic, complemented
71C5×#324C2211yescharacteristic, complemented
72C5×#324C2211yescharacteristic, complemented
73C5×#323C2211yescharacteristic, complemented
74C5×#323C2211yescharacteristic, complemented
75#18252C511yesmaximal, characteristic, direct product factor, Sylow
76C2×C5×#41—21no—
77C2×C5×#41—21no—
78C2×C5×#41—21no—
79C2×C5×#41—21no—
80C2×C5×#41—21no—
81C2×C5×#41—44no—
82C2×C5×#41D411yescharacteristic, complemented
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4—21no—
86C22×C5×D4—21no—
87C22×C5×D4—21no—
88C22×C5×D4—21no—
89C22×C5×D4D411yescharacteristic
90C22×C5×D4D411yescharacteristic, complemented
91C22×C5×D4C2311yescharacteristic
92C23×C4×C5—21no—
93C23×C4×C5—21no—
94C23×C4×C5C2311yescharacteristic
95C5×AGL(1,ℤ/8)—44no—
96C5×#135—44no—
97C2×C5×Q16—21no—
98C2×C5×SD16—21no—
99C2×C5×SD16—21no—
100C2×C5×SD16—21no—
101C2×C5×SD16—21no—
102C2×C5×D8—21no—
103C2×C5×D8—21no—
104C2×C5×D8—21no—
105C2×C5×M16—21no—
106C22×C5×C8—21no—
107C5×#127—21no—
108C5×#126—21no—
109C5×#126—21no—
110C5×#126—21no—
111C5×#126—21no—
112C5×#125—21no—
113C5×#125—21no—
114C5×#124—21no—
115C5×#124—21no—
116C5×#124—21no—
117C5×#123—21no—
118C5×#123—21no—
119C5×#123—21no—
120C5×#123—21no—
121C5×#123—21no—
122C5×#123—21no—
123C5×#123—21no—
124C5×#123—21no—
125C5×#123—21no—
126C5×#123—21no—
127C5×#123—21no—
128C5×#123—21no—
129C5×#123—21no—
130C5×#123—21no—
131C5×C22⋊Q8—21no—
132C5×C22⋊Q8—21no—
133C5×C22⋊Q8—21no—
134C5×C22⋊Q8—21no—
135C5×C22⋊Q8—21no—
136C5×C22⋊Q8D411yescharacteristic, complemented
137C5×C22⋊Q8C2311yescharacteristic
138C5×#121—21no—
139C5×#121—21no—
140C5×#121—21no—
141C5×#121—21no—
142C5×#121—21no—
143C5×#121—21no—
144C5×#121—21no—
145C5×#121—21no—
146C5×#121—21no—
147C5×#121—21no—
148C5×#121—21no—
149C5×#121—21no—
150C5×#121—21no—
151C5×#121—21no—
152C5×#121—21no—
153C5×#121—44no—
154C5×#121D411yescharacteristic, complemented
155C5×#121D411yescharacteristic, complemented
156C5×#121D411yescharacteristic, complemented
157C5×#121C2311yescharacteristic
158C5×#121C2311yescharacteristic
159C5×#121C2311yescharacteristic
160C5×#120—21no—
161C5×#120—21no—
162C5×#120—21no—
163C5×#120—21no—
164C5×#120—21no—
165C5×#120—21no—
166C5×#120—21no—
167C5×#120—21no—
168C4×C5×D4—21no—
169C4×C5×D4—21no—
170C4×C5×D4—21no—
171C4×C5×D4—21no—
172C4×C5×D4—21no—
173C4×C5×D4—21no—
174C4×C5×D4—21no—
175C4×C5×D4—21no—
176C5×#117—21no—
177C5×#117D411yescharacteristic, complemented
178C2×C5×C4⋊C4—21no—
179C2×C5×C4⋊C4D411yescharacteristic
180C2×C5×C4⋊C4D411yescharacteristic, complemented
181C2×C5×C4⋊C4C2311yescharacteristic
182C2×C5×C22⋊C4—21no—
183C2×C5×C22⋊C4—21no—
184C2×C5×C22⋊C4—21no—
185C2×C5×C22⋊C4—21no—
186C2×C5×C22⋊C4—21no—
187C2×C5×C22⋊C4—21no—
188C2×C5×C22⋊C4—21no—
189C2×C5×C22⋊C4D411yescharacteristic
190C2×C5×C22⋊C4D411yescharacteristic
191C2×C5×C22⋊C4C2311yescharacteristic
192C5×#103—21no—
193C5×#103—21no—
194C5×#103—21no—
195C5×#103—21no—
196C5×#102—21no—
197C5×#102—21no—
198C5×#102—21no—
199C5×#102—21no—
200C5×C22⋊C8—21no—
201C5×C22⋊C8—21no—
202C5×C22⋊C8C2311yescharacteristic
203C5×C22⋊C8C2311yescharacteristic
204C5×C22⋊C8C2311yescharacteristic
205C5×C22⋊C8C2311yescharacteristic
206C5×#95—21no—
207C5×#95—21no—
208C5×#95—21no—
209C5×#95C2311yescharacteristic
210C5×#95C2311yescharacteristic
211#3534C2×C511yescharacteristic, complemented
212#3006C2×C511yescharacteristic, complemented
213#3002C2×C511yescharacteristic, complemented
214#2430C2×C511yescharacteristic, complemented
215#1606C2×C511yescharacteristic, complemented
216#1604C2×C511yescharacteristic, complemented
217#1603C2×C511yescharacteristic, complemented
218#1601C2×C511yescharacteristic, complemented
219#1600C2×C511yescharacteristic, complemented
220#1598C2×C511yescharacteristic, complemented
221#1597C2×C511yescharacteristic, complemented
222#1595C2×C511yescharacteristic, complemented
223#1504C2×C511yescharacteristic, complemented
224C2×#327C2×C511yescharacteristic, complemented
225#1468C2×C511yescharacteristic, complemented
226C24×C5—21no—
227C24×C5—21no—
228C24×C5—21no—
229C24×C5C2×D411yescharacteristic
230C24×C5C2×D411yescharacteristic
231C5×#41—24no—
232C5×#41—24no—
233C5×#41—42no—
234C5×#41—42no—
235C5×#41—42no—
236C5×#41—42no—
237C5×#41—42no—
238C5×#41—42no—
239C5×#41—42no—
240C5×#41—81no—
241C5×#41—81no—
242C2×C5×Q8—21no—
243C2×C5×Q8—21no—
244C2×C5×Q8—21no—
245C2×C5×Q8—42no—
246C2×C5×Q8C2×D411yescharacteristic
247C2×C5×D4—24no—
248C2×C5×D4—21no—
249C2×C5×D4—21no—
250C2×C5×D4—21no—
251C2×C5×D4—21no—
252C2×C5×D4—21no—
253C2×C5×D4—21no—
254C2×C5×D4—21no—
255C2×C5×D4—21no—
256C2×C5×D4—21no—
257C2×C5×D4—21no—
258C2×C5×D4—21no—
259C2×C5×D4—21no—
260C2×C5×D4—21no—
261C2×C5×D4—21no—
262C2×C5×D4—21no—
263C2×C5×D4—21no—
264C2×C5×D4—21no—
265C2×C5×D4—21no—
266C2×C5×D4—21no—
267C2×C5×D4—42no—
268C2×C5×D4—42no—
269C2×C5×D4—42no—
270C2×C5×D4—42no—
271C2×C5×D4—41no—
272C2×C5×D4—41no—
273C2×C5×D4—42no—
274C2×C5×D4—42no—
275C2×C5×D4—81no—
276C2×C5×D4—81no—
277C2×C5×D4—81no—
278C2×C5×D4—81no—
279C2×C5×D4—81no—
280C2×C5×D4—82no—
281C2×C5×D4C2×D411yescharacteristic
282C2×C5×D4C2×D411yescharacteristic
283C2×C5×D4C2×D411yescharacteristic
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—21no—
290C22×C4×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—21no—
293C22×C4×C5—21no—
294C22×C4×C5—42no—
295C22×C4×C5—42no—
296C22×C4×C5—42no—
297C22×C4×C5—42no—
298C22×C4×C5—41no—
299C22×C4×C5—41no—
300C22×C4×C5—42no—
301C22×C4×C5—81no—
302C22×C4×C5C2×D411yescharacteristic
303C22×C4×C5C2×D411yescharacteristic
304C22×C4×C5C2×D411yescharacteristic
305C22×C4×C5C2×D411yescharacteristic
306C22×C4×C5C2×D411yescharacteristic
307C22×C4×C5C2×D411yescharacteristic
308C22×C4×C5C2×D411yescharacteristic
309C22×C4×C5C2×D411yescharacteristic
310C22×C4×C5C2411yescharacteristic
311C5×Q16—42no—
312C5×SD16—42no—
313C5×SD16—42no—
314C5×SD16—42no—
315C5×SD16—42no—
316C5×D8—42no—
317C5×D8—42no—
318C5×D8—42no—
319C5×M16—42no—
320C2×C5×C8—21no—
321C2×C5×C8—21no—
322C2×C5×C8—21no—
323C2×C5×C8—21no—
324C2×C5×C8—42no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4—21no—
327C5×C4⋊C4—21no—
328C5×C4⋊C4—21no—
329C5×C4⋊C4—21no—
330C5×C4⋊C4—21no—
331C5×C4⋊C4—21no—
332C5×C4⋊C4—21no—
333C5×C4⋊C4—21no—
334C5×C4⋊C4—21no—
335C5×C4⋊C4—21no—
336C5×C4⋊C4—21no—
337C5×C4⋊C4—21no—
338C5×C4⋊C4—42no—
339C5×C4⋊C4C2×D411yescharacteristic
340C5×C4⋊C4C2×D411yescharacteristic
341C5×C4⋊C4C2×D411yescharacteristic
342C5×C4⋊C4C2×D411yescharacteristic
343C5×C22⋊C4—21no—
344C5×C22⋊C4—21no—
345C5×C22⋊C4—21no—
346C5×C22⋊C4—21no—
347C5×C22⋊C4—21no—
348C5×C22⋊C4—21no—
349C5×C22⋊C4—21no—
350C5×C22⋊C4—21no—
351C5×C22⋊C4—21no—
352C5×C22⋊C4—21no—
353C5×C22⋊C4—21no—
354C5×C22⋊C4—21no—
355C5×C22⋊C4—21no—
356C5×C22⋊C4—21no—
357C5×C22⋊C4—21no—
358C5×C22⋊C4—21no—
359C5×C22⋊C4—21no—
360C5×C22⋊C4—21no—
361C5×C22⋊C4—21no—
362C5×C22⋊C4—21no—
363C5×C22⋊C4—21no—
364C5×C22⋊C4—21no—
365C5×C22⋊C4—21no—
366C5×C22⋊C4—21no—
367C5×C22⋊C4—21no—
368C5×C22⋊C4—42no—
369C5×C22⋊C4—42no—
370C5×C22⋊C4—42no—
371C5×C22⋊C4—81no—
372C42×C5—21no—
373C42×C5—21no—
374C42×C5—21no—
375C22×#41C22×C511yescharacteristic, complemented
376C2×AGL(1,ℤ/8)—21no—
377C2×#135—21no—
378#562—21no—
379#560—21no—
380#553—21no—
381#551—21no—
382#546—21no—
383#546—21no—
384#546—21no—
385D42—21no—
386#540—21no—
387#539—21no—
388#539C22×C511yescharacteristic
389#538—21no—
390#538C22×C511yescharacteristic
391#537C22×C511yescharacteristic
392#534—21no—
393#534C22×C511yescharacteristic
394#525C22×C511yescharacteristic
395C2×#123C22×C511yescharacteristic
396C2×#121—21no—
397C2×#121C22×C511yescharacteristic
398#452—21no—
399#451C22×C511yescharacteristic, complemented
400#450C22×C511yescharacteristic, complemented
401#449—21no—
402#449—21no—
403#449—21no—
404#448C22×C511yescharacteristic
405#448C22×C511yescharacteristic, complemented
406#448C22×C511yescharacteristic, complemented
407#447C22×C511yescharacteristic
408#447C22×C511yescharacteristic, complemented
409#447C22×C511yescharacteristic, complemented
410#417—21no—
411#416—21no—
412#407C22×C511yescharacteristic, complemented
413C2×C22⋊C8C22×C511yescharacteristic, complemented
414#395C22×C511yescharacteristic, complemented
415#394C22×C511yescharacteristic, complemented
416#393C22×C511yescharacteristic, complemented
417#392C22×C511yescharacteristic, complemented
418#386—21no—
419#386—21no—
420#385—21no—
421C2×#95C22×C511yescharacteristic, complemented
422#328C22×C511yescharacteristic, complemented
423#328C22×C511yescharacteristic, complemented
424#327C22×C511yescharacteristic
425#327C22×C511yescharacteristic
426#327C22×C511yescharacteristic, complemented
427#327C22×C511yescharacteristic, complemented
428#327C22×C511yescharacteristic, complemented
429#327C22×C511yescharacteristic, complemented
430#324C22×C511yescharacteristic, complemented
431#324C22×C511yescharacteristic, complemented
432#323C22×C511yescharacteristic, complemented
433#323C22×C511yescharacteristic, complemented
434C23×C5—21no—
435C23×C5—21no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—21no—
441C23×C5—21no—
442C23×C5—21no—
443C23×C5—21no—
444C23×C5—41no—
445C23×C5—41no—
446C23×C5—41no—
447C23×C5—41no—
448C23×C5—41no—
449C23×C5—41no—
450C23×C5—41no—
451C23×C5—41no—
452C23×C5—41no—
453C23×C5—42no—
454C23×C5—81no—
455C23×C5—81no—
456C23×C5—81no—
457C23×C5—81no—
458C23×C5—81no—
459C23×C5#12011yescharacteristic
460C23×C5#12011yescharacteristic
461C23×C5C22×D411yescharacteristic
462C5×Q8—22no—
463C5×Q8—22no—
464C5×Q8—41no—
465C5×Q8—41no—
466C5×Q8—41no—
467C5×Q8—81no—
468C5×D4—22no—
469C5×D4—22no—
470C5×D4—41no—
471C5×D4—41no—
472C5×D4—41no—
473C5×D4—41no—
474C5×D4—41no—
475C5×D4—44no—
476C5×D4—41no—
477C5×D4—41no—
478C5×D4—41no—
479C5×D4—41no—
480C5×D4—41no—
481C5×D4—41no—
482C5×D4—44no—
483C5×D4—42no—
484C5×D4—42no—
485C5×D4—81no—
486C5×D4—81no—
487C5×D4—81no—
488C5×D4—81no—
489C5×D4—81no—
490C5×D4—81no—
491C5×D4—81no—
492C5×D4—81no—
493C5×D4—81no—
494C5×D4—81no—
495C5×D4—81no—
496C5×D4—81no—
497C5×D4—84no—
498C2×C4×C5—22no—
499C2×C4×C5—22no—
500C2×C4×C5—22no—
501C2×C4×C5—22no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—41no—
513C2×C4×C5—41no—
514C2×C4×C5—41no—
515C2×C4×C5—41no—
516C2×C4×C5—44no—
517C2×C4×C5—44no—
518C2×C4×C5—41no—
519C2×C4×C5—41no—
520C2×C4×C5—41no—
521C2×C4×C5—41no—
522C2×C4×C5—41no—
523C2×C4×C5—41no—
524C2×C4×C5—41no—
525C2×C4×C5—41no—
526C2×C4×C5—41no—
527C2×C4×C5—81no—
528C2×C4×C5—81no—
529C2×C4×C5—81no—
530C2×C4×C5—81no—
531C2×C4×C5—81no—
532C2×C4×C5—81no—
533C2×C4×C5—81no—
534C2×C4×C5—84no—
535C2×C4×C5#12011yescharacteristic
536C2×C4×C5#12011yescharacteristic
537C2×C4×C5C22×D411yescharacteristic
538C2×C4×C5C22×D411yescharacteristic
539C5×C8—41no—
540C5×C8—41no—
541C5×C8—41no—
542C5×C8—41no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—44no—
549C2×#41C5×D411yescharacteristic, complemented
550C22×Q8C23×C511yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4C5×D411yescharacteristic
557C22×D4C5×D411yescharacteristic, complemented
558C22×D4C23×C511yescharacteristic
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C23×C511yescharacteristic
562AGL(1,ℤ/8)—44no—
563#135—44no—
564C2×Q16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×D8—21no—
570C2×D8—21no—
571C2×D8—21no—
572C2×M16—21no—
573C22×C8—21no—
574#127—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#125—21no—
580#125—21no—
581#124—21no—
582#124—21no—
583#124—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8C5×D411yescharacteristic, complemented
604C22⋊Q8C23×C511yescharacteristic
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—44no—
621#121C5×D411yescharacteristic, complemented
622#121C5×D411yescharacteristic, complemented
623#121C5×D411yescharacteristic, complemented
624#121C23×C511yescharacteristic
625#121C23×C511yescharacteristic
626#121C23×C511yescharacteristic
627#120—21no—
628#120—21no—
629#120—21no—
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117C5×D411yescharacteristic, complemented
645C2×C4⋊C4—21no—
646C2×C4⋊C4C5×D411yescharacteristic
647C2×C4⋊C4C5×D411yescharacteristic, complemented
648C2×C4⋊C4C23×C511yescharacteristic
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4C5×D411yescharacteristic
657C2×C22⋊C4C5×D411yescharacteristic
658C2×C22⋊C4C23×C511yescharacteristic
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#102—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8C23×C511yescharacteristic
670C22⋊C8C23×C511yescharacteristic
671C22⋊C8C23×C511yescharacteristic
672C22⋊C8C23×C511yescharacteristic
673#95—21no—
674#95—21no—
675#95—21no—
676#95C23×C511yescharacteristic
677#95C23×C511yescharacteristic
678C22×C5—21no—
679C22×C5—21no—
680C22×C5—21no—
681C22×C5—21no—
682C22×C5—21no—
683C22×C5—21no—
684C22×C5—21no—
685C22×C5—42no—
686C22×C5—42no—
687C22×C5—42no—
688C22×C5—42no—
689C22×C5—41no—
690C22×C5—41no—
691C22×C5—41no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—41no—
697C22×C5—42no—
698C22×C5—41no—
699C22×C5—41no—
700C22×C5—41no—
701C22×C5—41no—
702C22×C5—81no—
703C22×C5—81no—
704C22×C5—81no—
705C22×C5—81no—
706C22×C5—81no—
707C22×C5—81no—
708C22×C5—162no—
709C22×C5—162no—
710C22×C5B(4,𝔽2)12yes—
711C22×C5C2×#12011yescharacteristic
712C22×C5#57611yescharacteristic
713C22×C5#57711yescharacteristic
714C4×C5—21no—
715C4×C5—21no—
716C4×C5—21no—
717C4×C5—21no—
718C4×C5—42no—
719C4×C5—41no—
720C4×C5—41no—
721C4×C5—41no—
722C4×C5—41no—
723C4×C5—41no—
724C4×C5—41no—
725C4×C5—42no—
726C4×C5—41no—
727C4×C5—41no—
728C4×C5—81no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24C2×C5×D411yescharacteristic
733C24C2×C5×D411yescharacteristic
734#41—24no—
735#41—24no—
736#41—42no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—42no—
743#41—81no—
744#41—81no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—42no—
749C2×Q8C2×C5×D411yescharacteristic
750C2×D4—24no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—41no—
775C2×D4—41no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—81no—
779C2×D4—81no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—82no—
784C2×D4C2×C5×D411yescharacteristic
785C2×D4C2×C5×D411yescharacteristic
786C2×D4C2×C5×D411yescharacteristic
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—42no—
804C22×C4—81no—
805C22×C4C2×C5×D411yescharacteristic
806C22×C4C2×C5×D411yescharacteristic
807C22×C4C2×C5×D411yescharacteristic
808C22×C4C2×C5×D411yescharacteristic
809C22×C4C2×C5×D411yescharacteristic
810C22×C4C2×C5×D411yescharacteristic
811C22×C4C2×C5×D411yescharacteristic
812C22×C4C2×C5×D411yescharacteristic
813C22×C4C24×C511yescharacteristic
814Q16—42no—
815SD16—42no—
816SD16—42no—
817SD16—42no—
818SD16—42no—
819D8—42no—
820D8—42no—
821D8—42no—
822M16—42no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—42no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—42no—
842C4⋊C4C2×C5×D411yescharacteristic
843C4⋊C4C2×C5×D411yescharacteristic
844C4⋊C4C2×C5×D411yescharacteristic
845C4⋊C4C2×C5×D411yescharacteristic
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—81no—
875C42—21no—
876C42—21no—
877C42—21no—
878C2×C5—21no—
879C2×C5—21no—
880C2×C5—22no—
881C2×C5—41no—
882C2×C5—82no—
883C2×C5—81no—
884C2×C5—81no—
885C2×C5—81no—
886C2×C5—81no—
887C2×C5#301211yescharacteristic
888C2×C5#301811yescharacteristic
889C2×C5C2×B(4,𝔽2)11yescharacteristic
890C23—22no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—42no—
910C23—81no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23C5×#12011yescharacteristic
916C23C5×#12011yescharacteristic
917C23C22×C5×D411yescharacteristic
918Q8—22no—
919Q8—22no—
920Q8—41no—
921Q8—41no—
922Q8—41no—
923Q8—81no—
924D4—22no—
925D4—22no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—44no—
932D4—44no—
933D4—42no—
934D4—42no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—84no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—44no—
973C2×C4—44no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—81no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—84no—
991C2×C4C5×#12011yescharacteristic
992C2×C4C5×#12011yescharacteristic
993C2×C4C22×C5×D411yescharacteristic
994C2×C4C22×C5×D411yescharacteristic
995C8—41no—
996C8—41no—
997C8—41no—
998C8—41no—
999C5#1825211yescharacteristic, direct product factor, Sylow
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C5×B(4,𝔽2)12yes—
1033C22C2×C5×#12011yescharacteristic
1034C22C5×#57611yescharacteristic
1035C22C5×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C5×#301211yescharacteristic
1061C2C5×#301811yescharacteristic
1062C2C2×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
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
1. C5×#3534C2semidirect
2. C5×#3006C2semidirect
3. C5×#3002C2semidirect
4. C5×#2430C2semidirect
5. C5×#1606C2semidirect
6. C5×#1604C2semidirect
7. C5×#1603C2semidirect
8. C5×#1601C2semidirect
9. C5×#1600C2semidirect
10. C5×#1598C2semidirect
11. C5×#1597C2semidirect
12. C5×#1595C2semidirect
13. C5×#1504C2semidirect
14. C2×C5×#327C2semidirect
15. C5×#1468C2semidirect
16. C22×C5×#41C22semidirect
40. C5×#451C22semidirect
41. C5×#450C22semidirect
46. C5×#448C22semidirect
47. C5×#448C22semidirect
49. C5×#447C22semidirect
50. C5×#447C22semidirect
53. C5×#407C22semidirect
54. C2×C5×C22⋊C8C22semidirect
55. C5×#395C22semidirect
56. C5×#394C22semidirect
57. C5×#393C22semidirect
58. C5×#392C22semidirect
62. C2×C5×#95C22semidirect
63. C5×#328C22semidirect
64. C5×#328C22semidirect
67. C5×#327C22semidirect
68. C5×#327C22semidirect
69. C5×#327C22semidirect
70. C5×#327C22semidirect
71. C5×#324C22semidirect
72. C5×#324C22semidirect
73. C5×#323C22semidirect
74. C5×#323C22semidirect
75. #18252C5direct (N × H)
82. C2×C5×#41D4semidirect
90. C22×C5×D4D4semidirect
136. C5×C22⋊Q8D4semidirect
154. C5×#121D4semidirect
155. C5×#121D4semidirect
156. C5×#121D4semidirect
177. C5×#117D4semidirect
180. C2×C5×C4⋊C4D4semidirect
211. #3534C2×C5semidirect
212. #3006C2×C5semidirect
213. #3002C2×C5semidirect
214. #2430C2×C5semidirect
215. #1606C2×C5semidirect
216. #1604C2×C5semidirect
217. #1603C2×C5semidirect
218. #1601C2×C5semidirect
219. #1600C2×C5semidirect
220. #1598C2×C5semidirect
221. #1597C2×C5semidirect
222. #1595C2×C5semidirect
223. #1504C2×C5semidirect
224. C2×#327C2×C5semidirect
225. #1468C2×C5semidirect
375. C22×#41C22×C5semidirect
399. #451C22×C5semidirect
400. #450C22×C5semidirect
405. #448C22×C5semidirect
406. #448C22×C5semidirect
408. #447C22×C5semidirect
409. #447C22×C5semidirect
412. #407C22×C5semidirect
413. C2×C22⋊C8C22×C5semidirect
414. #395C22×C5semidirect
415. #394C22×C5semidirect
416. #393C22×C5semidirect
417. #392C22×C5semidirect
421. C2×#95C22×C5semidirect
422. #328C22×C5semidirect
423. #328C22×C5semidirect
426. #327C22×C5semidirect
427. #327C22×C5semidirect
428. #327C22×C5semidirect
429. #327C22×C5semidirect
430. #324C22×C5semidirect
431. #324C22×C5semidirect
432. #323C22×C5semidirect
433. #323C22×C5semidirect
549. C2×#41C5×D4semidirect
557. C22×D4C5×D4semidirect
603. C22⋊Q8C5×D4semidirect
621. #121C5×D4semidirect
622. #121C5×D4semidirect
623. #121C5×D4semidirect
644. #117C5×D4semidirect
647. C2×C4⋊C4C5×D4semidirect
999. C5#18252direct (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×#30062
C5×#30022
C5×#24302
C5×#16062
C5×#16042
C5×#16032
C5×#16012
C5×#16002
C5×#15982
C5×#15972
C5×#15952
C5×#15042
C2×C5×#3272
C5×#14682
#182525