Finite Group Databasebeta

← C5×#24137 #11946857

Subgroups — C5×#24137 #11946857

Order 1280.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic, complemented
2C2×C5×#478C211yesmaximal, characteristic, complemented
3C2×C5×#440C211yesmaximal, characteristic, complemented
4C5×#2537C211yesmaximal, characteristic
5C5×#2036C211yesmaximal, characteristic, complemented
6C5×#2035C211yesmaximal, characteristic, complemented
7C5×#2000C211yesmaximal, characteristic, complemented
8C5×#2000C211yesmaximal, characteristic, complemented
9C5×#1992C211yesmaximal, characteristic, complemented
10C5×#1955C211yesmaximal, characteristic, complemented
11C5×#1875C211yesmaximal, characteristic, complemented
12C5×#1874C211yesmaximal, characteristic, complemented
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1852C211yesmaximal, characteristic, complemented
15C5×#1803C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C5×#552—24no—
18C5×#552—24no—
19C2×C5×#126—21no—
20C2×C5×#125—21no—
21C2×C5×#125C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C5×#121C2211yescharacteristic
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×C4×C5×D4C2211yescharacteristic
31C2×C5×#117—21no—
32C2×C5×#117C2211yescharacteristic
33C22×C5×C4⋊C4C2211yescharacteristic
34C5×#478—24no—
35C5×#440—24no—
36C2×C5×#107C2211yescharacteristic
37C2×C5×#107C2211yescharacteristic
38C2×C5×#106C2211yescharacteristic
39C2×C5×C4⋊C8C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#103C2211yescharacteristic
43C2×C5×#102C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×#102C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×#97C2211yescharacteristic
51C5×#394—21no—
52C5×#394—21no—
53C5×#384C2211yescharacteristic
54C5×#380—21no—
55C5×#380C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62C5×#340C2211yescharacteristic
63#24137C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8C2311yescharacteristic
65C22×C5×D4—21no—
66C22×C5×D4—21no—
67C22×C5×D4D411yescharacteristic
68C22×C5×D4C2311yescharacteristic
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C2×C5×SD16—22no—
74C2×C5×SD16—22no—
75C2×C5×SD16—22no—
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×#126—28no—
81C5×#125—28no—
82C5×#125—22no—
83C5×#125D414yescomplemented
84C5×#123—28no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—22no—
89C5×#121—22no—
90C5×#121—22no—
91C5×#121—41no—
92C5×#121—41no—
93C5×#121—44no—
94C4×C5×Q8—22no—
95C4×C5×Q8D414yescomplemented
96C4×C5×D4—22no—
97C4×C5×D4—22no—
98C4×C5×D4—22no—
99C4×C5×D4—22no—
100C5×#117—28no—
101C5×#117—22no—
102C5×#117—22no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—22no—
110C2×C5×C4⋊C4—22no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C4⋊C4C2311yescharacteristic
118C2×C5×C4⋊C4C2311yescharacteristic
119C2×C5×C4⋊C4C2311yescharacteristic
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4—21no—
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4D411yescharacteristic
129C2×C5×C22⋊C4D411yescharacteristic
130C2×C42×C5—21no—
131C2×C42×C5—21no—
132C2×C42×C5C2311yescharacteristic
133C5×#107—22no—
134C5×#107—22no—
135C5×#106—22no—
136C5×C4⋊C8—22no—
137C5×#103—22no—
138C5×#103—41no—
139C5×#103—41no—
140C5×#102—22no—
141C5×#102—22no—
142C5×#102—22no—
143C5×C22⋊C8—22no—
144C5×C22⋊C8—22no—
145C5×C22⋊C8—41no—
146C5×C22⋊C8—41no—
147C5×#97—22no—
148C5×#95—21no—
149C5×#95—21no—
150C2×#552C2×C511yescharacteristic, complemented
151C2×#478C2×C511yescharacteristic, complemented
152C2×#440C2×C511yescharacteristic, complemented
153#2537C2×C511yescharacteristic
154#2036C2×C511yescharacteristic, complemented
155#2035C2×C511yescharacteristic, complemented
156#2000C2×C511yescharacteristic, complemented
157#2000C2×C511yescharacteristic, complemented
158#1992C2×C511yescharacteristic, complemented
159#1955C2×C511yescharacteristic, complemented
160#1875C2×C511yescharacteristic, complemented
161#1874C2×C511yescharacteristic, complemented
162#1854C2×C511yescharacteristic, complemented
163#1852C2×C511yescharacteristic, complemented
164#1803C2×C511yescharacteristic, complemented
165C24×C5—21no—
166C24×C5C2×D411yescharacteristic
167C24×C5C2×D411yescharacteristic
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8C2×D412yes—
174C2×C5×D4—22no—
175C2×C5×D4—22no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4—41no—
182C2×C5×D4—42no—
183C2×C5×D4—42no—
184C2×C5×D4—42no—
185C2×C5×D4—42no—
186C2×C5×D4—81no—
187C2×C5×D4—81no—
188C2×C5×D4#4112yes—
189C22×C4×C5—24no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—42no—
210C22×C4×C5—42no—
211C22×C4×C5—42no—
212C22×C4×C5—42no—
213C22×C4×C5—42no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2411yescharacteristic
219C5×SD16—28no—
220C2×C5×C8—21no—
221C2×C5×C8—21no—
222C2×C5×C8—21no—
223C2×C5×C8—21no—
224C2×C5×C8—21no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8—21no—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C2×C5×C8#4112yes—
232C5×C4⋊C4—24no—
233C5×C4⋊C4—24no—
234C5×C4⋊C4—24no—
235C5×C4⋊C4—24no—
236C5×C4⋊C4—24no—
237C5×C4⋊C4—24no—
238C5×C4⋊C4—22no—
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—21no—
248C5×C4⋊C4—42no—
249C5×C4⋊C4—81no—
250C5×C4⋊C4C2×D412yes—
251C5×C4⋊C4C2×D412yes—
252C5×C4⋊C4C2×D412yes—
253C5×C22⋊C4—24no—
254C5×C22⋊C4—24no—
255C5×C22⋊C4—24no—
256C5×C22⋊C4—22no—
257C5×C22⋊C4—22no—
258C5×C22⋊C4—42no—
259C5×C22⋊C4—42no—
260C5×C22⋊C4—42no—
261C5×C22⋊C4—42no—
262C5×C22⋊C4—42no—
263C42×C5—24no—
264C42×C5—24no—
265C42×C5C2×D412yes—
266C42×C5C2×D412yes—
267C22×SD16C22×C511yescharacteristic
268#552—24no—
269#552—24no—
270C2×#126—21no—
271C2×#125—21no—
272C2×#125C22×C511yescharacteristic
273C2×#123—21no—
274C2×C22⋊Q8C22×C511yescharacteristic
275C2×C22⋊Q8C22×C511yescharacteristic
276C2×#121—21no—
277C2×#121C22×C511yescharacteristic
278C2×#121C22×C511yescharacteristic
279C2×C4×Q8C22×C511yescharacteristic
280C2×C4×D4C22×C511yescharacteristic
281C2×C4×D4C22×C511yescharacteristic
282C2×#117—21no—
283C2×#117C22×C511yescharacteristic
284C22×C4⋊C4C22×C511yescharacteristic
285#478—24no—
286#440—24no—
287C2×#107C22×C511yescharacteristic
288C2×#107C22×C511yescharacteristic
289C2×#106C22×C511yescharacteristic
290C2×C4⋊C8C22×C511yescharacteristic
291C2×#103C22×C511yescharacteristic
292C2×#103C22×C511yescharacteristic
293C2×#103C22×C511yescharacteristic
294C2×#102C22×C511yescharacteristic
295C2×#102C22×C511yescharacteristic
296C2×#102C22×C511yescharacteristic
297C2×C22⋊C8C22×C511yescharacteristic
298C2×C22⋊C8C22×C511yescharacteristic
299C2×C22⋊C8C22×C511yescharacteristic
300C2×C22⋊C8C22×C511yescharacteristic
301C2×#97C22×C511yescharacteristic
302#394—21no—
303#394—21no—
304#384C22×C511yescharacteristic
305#380—21no—
306#380C22×C511yescharacteristic
307#380C22×C511yescharacteristic
308#340C22×C511yescharacteristic
309#340C22×C511yescharacteristic
310#340C22×C511yescharacteristic
311#340C22×C511yescharacteristic
312#340C22×C511yescharacteristic
313#340C22×C511yescharacteristic
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—22no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5AGL(1,ℤ/8)12yes—
335C23×C5C22×D411yescharacteristic
336C5×Q8—22no—
337C5×Q8—22no—
338C5×Q8—41no—
339C5×Q8—41no—
340C5×D4—22no—
341C5×D4—22no—
342C5×D4—44no—
343C5×D4—41no—
344C5×D4—41no—
345C5×D4—84no—
346C5×D4—84no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—21no—
356C2×C4×C5—22no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—48no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—84no—
388C2×C4×C5#12012yes—
389C2×C4×C5#12012yes—
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C22×D411yescharacteristic
392C2×C4×C5C2×#4111yescharacteristic
393C2×C4×C5C2×#4111yescharacteristic
394C2×C4×C5H(5,𝔽2)11yescharacteristic
395C2×C4×C52−1+411yescharacteristic
396C5×C8—22no—
397C5×C8—41no—
398C5×C8—41no—
399C5×C8—41no—
400C22×Q8C23×C511yescharacteristic
401C22×D4—21no—
402C22×D4—21no—
403C22×D4C5×D411yescharacteristic
404C22×D4C23×C511yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4C23×C511yescharacteristic
408C23×C4C23×C511yescharacteristic
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—22no—
412C22×C8C23×C511yescharacteristic
413C22×C8C23×C511yescharacteristic
414C22×C8C23×C511yescharacteristic
415C22×C8C23×C511yescharacteristic
416#126—28no—
417#125—28no—
418#125—22no—
419#125C5×D414yescomplemented
420#123—28no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425#121—22no—
426#121—22no—
427#121—41no—
428#121—41no—
429#121—44no—
430C4×Q8—22no—
431C4×Q8C5×D414yescomplemented
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436#117—28no—
437#117—22no—
438#117—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C5×D411yescharacteristic
450C2×C4⋊C4C23×C511yescharacteristic
451C2×C4⋊C4C23×C511yescharacteristic
452C2×C4⋊C4C23×C511yescharacteristic
453C2×C4⋊C4C23×C511yescharacteristic
454C2×C4⋊C4C23×C511yescharacteristic
455C2×C4⋊C4C23×C511yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4C5×D411yescharacteristic
465C2×C22⋊C4C5×D411yescharacteristic
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C511yescharacteristic
469#107—22no—
470#107—22no—
471#106—22no—
472C4⋊C8—22no—
473#103—22no—
474#103—41no—
475#103—41no—
476#102—22no—
477#102—22no—
478#102—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483#97—22no—
484#95—21no—
485#95—21no—
486C22×C5—22no—
487C22×C5—22no—
488C22×C5—22no—
489C22×C5—41no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5—41no—
496C22×C5—42no—
497C22×C5—41no—
498C22×C5—41no—
499C22×C5—41no—
500C22×C5—42no—
501C22×C5—41no—
502C22×C5—42no—
503C22×C5—81no—
504C22×C5—81no—
505C22×C5—81no—
506C22×C5—81no—
507C22×C5C2×#12011yescharacteristic
508C22×C5#54611yescharacteristic
509C22×C5#54711yescharacteristic
510C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
511C22×C5#57511yescharacteristic
512C22×C5#57711yescharacteristic
513C22×C5#57811yescharacteristic
514C4×C5—22no—
515C4×C5—22no—
516C4×C5—41no—
517C4×C5—41no—
518C4×C5—42no—
519C4×C5—42no—
520C4×C5—42no—
521C4×C5—42no—
522C4×C5—81no—
523C4×C5—81no—
524C4×C5—81no—
525C4×C5#52511yescharacteristic
526C4×C5#53711yescharacteristic
527C4×C5#54811yescharacteristic
528C4×C5#55011yescharacteristic
529C24—21no—
530C24C2×C5×D411yescharacteristic
531C24C2×C5×D411yescharacteristic
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8C2×C5×D412yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—41no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4C5×#4112yes—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4C2×C5×D411yescharacteristic
579C22×C4C2×C5×D411yescharacteristic
580C22×C4C2×C5×D411yescharacteristic
581C22×C4C2×C5×D411yescharacteristic
582C22×C4C24×C511yescharacteristic
583SD16—28no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8C5×#4112yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—22no—
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—21no—
612C4⋊C4—42no—
613C4⋊C4—81no—
614C4⋊C4C2×C5×D412yes—
615C4⋊C4C2×C5×D412yes—
616C4⋊C4C2×C5×D412yes—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C42—24no—
628C42—24no—
629C42C2×C5×D412yes—
630C42C2×C5×D412yes—
631C2×C5—42no—
632C2×C5—81no—
633C2×C5—82no—
634C2×C5#240711yescharacteristic
635C2×C5#300611yescharacteristic
636C2×C5#301311yescharacteristic
637C2×C5#331011yescharacteristic
638C2×C5#331511yescharacteristic
639C2×C5#334311yescharacteristic
640C2×C5#334811yescharacteristic
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C5×AGL(1,ℤ/8)12yes—
662C23C22×C5×D411yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667D4—22no—
668D4—22no—
669D4—44no—
670D4—41no—
671D4—41no—
672D4—84no—
673D4—84no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—84no—
715C2×C4C5×#12012yes—
716C2×C4C5×#12012yes—
717C2×C4C22×C5×D411yescharacteristic
718C2×C4C22×C5×D411yescharacteristic
719C2×C4C2×C5×#4111yescharacteristic
720C2×C4C2×C5×#4111yescharacteristic
721C2×C4C5×H(5,𝔽2)11yescharacteristic
722C2×C4C5×2−1+411yescharacteristic
723C8—22no—
724C8—41no—
725C8—41no—
726C8—41no—
727C5#2413711yescharacteristic, direct product factor, Sylow
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C2×C5×#12011yescharacteristic
750C22C5×#54611yescharacteristic
751C22C5×#54711yescharacteristic
752C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
753C22C5×#57511yescharacteristic
754C22C5×#57711yescharacteristic
755C22C5×#57811yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4C5×#52511yescharacteristic
768C4C5×#53711yescharacteristic
769C4C5×#54811yescharacteristic
770C4C5×#55011yescharacteristic
771C2—42no—
772C2—81no—
773C2—82no—
774C2C5×#240711yescharacteristic
775C2C5×#300611yescharacteristic
776C2C5×#301311yescharacteristic
777C2C5×#331011yescharacteristic
778C2C5×#331511yescharacteristic
779C2C5×#334311yescharacteristic
780C2C5×#334811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#552C2semidirect
2. C2×C5×#478C2semidirect
3. C2×C5×#440C2semidirect
5. C5×#2036C2semidirect
6. C5×#2035C2semidirect
7. C5×#2000C2semidirect
8. C5×#2000C2semidirect
9. C5×#1992C2semidirect
10. C5×#1955C2semidirect
11. C5×#1875C2semidirect
12. C5×#1874C2semidirect
13. C5×#1854C2semidirect
14. C5×#1852C2semidirect
15. C5×#1803C2semidirect
63. #24137C5direct (N × H)
83. C5×#125D4semidirect
95. C4×C5×Q8D4semidirect
150. C2×#552C2×C5semidirect
151. C2×#478C2×C5semidirect
152. C2×#440C2×C5semidirect
154. #2036C2×C5semidirect
155. #2035C2×C5semidirect
156. #2000C2×C5semidirect
157. #2000C2×C5semidirect
158. #1992C2×C5semidirect
159. #1955C2×C5semidirect
160. #1875C2×C5semidirect
161. #1874C2×C5semidirect
162. #1854C2×C5semidirect
163. #1852C2×C5semidirect
164. #1803C2×C5semidirect
419. #125C5×D4semidirect
431. C4×Q8C5×D4semidirect
727. C5#24137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×C5×#4782
C2×C5×#4402
C5×#25372
C5×#20362
C5×#20352
C5×#20002
C5×#19922
C5×#19552
C5×#18752
C5×#18742
C5×#18542
C5×#18522
C5×#18032
#241375