Finite Group Databasebeta

← C5×#24126 #11946846

Subgroups — C5×#24126 #11946846

Order 1280.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#553C211yesmaximal, characteristic
2C2×C5×#479C211yesmaximal, characteristic, complemented
3C2×C4×C5×SD16C211yesmaximal, characteristic, complemented
4C5×#2536C211yesmaximal, characteristic, complemented
5C5×#2034C211yesmaximal, characteristic, complemented
6C5×#2033C211yesmaximal, characteristic, complemented
7C5×#2000C211yesmaximal, characteristic, complemented
8C5×#2000C211yesmaximal, characteristic, complemented
9C5×#1991C211yesmaximal, characteristic, complemented
10C5×#1954C211yesmaximal, characteristic, complemented
11C5×#1873C211yesmaximal, characteristic, complemented
12C5×#1872C211yesmaximal, characteristic, complemented
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1853C211yesmaximal, characteristic, complemented
15C5×#1804C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C5×#553—24no—
18C5×#553—24no—
19C2×C5×#126—21no—
20C2×C5×#125C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×#121—21no—
25C2×C5×#121C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C2×C4×C5×D4C2211yescharacteristic
31C2×C5×#117C2211yescharacteristic
32C22×C5×C4⋊C4C2211yescharacteristic
33C5×#479—24no—
34C4×C5×SD16—24no—
35C2×C5×#107C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×#106C2211yescharacteristic
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×#102C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C4×C5×C8C2211yescharacteristic
50C5×#398—21no—
51C5×#394—21no—
52C5×#388—21no—
53C5×#388—21no—
54C5×#382C2211yescharacteristic
55C5×#380C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62C5×#340C2211yescharacteristic
63#24126C511yesmaximal, 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—22no—
82C5×#125D414yes—
83C5×#123—28no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—41no—
87C5×C22⋊Q8—41no—
88C5×#121—28no—
89C5×#121—22no—
90C5×#121—22no—
91C5×#121—22no—
92C5×#121—22no—
93C4×C5×Q8—22no—
94C4×C5×Q8—22no—
95C4×C5×D4—28no—
96C4×C5×D4—22no—
97C4×C5×D4—22no—
98C4×C5×D4—22no—
99C4×C5×D4D414yes—
100C5×#117—22no—
101C5×#117—22no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
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⋊C4D411yescharacteristic
126C2×C5×C22⋊C4D411yescharacteristic
127C2×C42×C5—21no—
128C2×C42×C5—21no—
129C2×C42×C5C2311yescharacteristic
130C5×#107—22no—
131C5×#106—22no—
132C5×#106—22no—
133C5×C4⋊C8—22no—
134C5×#103—22no—
135C5×#103—22no—
136C5×#103—22no—
137C5×#102—22no—
138C5×#102—41no—
139C5×#102—41no—
140C5×C22⋊C8—22no—
141C5×C22⋊C8—22no—
142C5×C22⋊C8—41no—
143C5×C22⋊C8—41no—
144C4×C5×C8—22no—
145C5×#95—21no—
146C5×#95—21no—
147C5×#95—21no—
148C5×#95—21no—
149C2×#553C2×C511yescharacteristic
150C2×#479C2×C511yescharacteristic, complemented
151C2×C4×SD16C2×C511yescharacteristic, complemented
152#2536C2×C511yescharacteristic, complemented
153#2034C2×C511yescharacteristic, complemented
154#2033C2×C511yescharacteristic, complemented
155#2000C2×C511yescharacteristic, complemented
156#2000C2×C511yescharacteristic, complemented
157#1991C2×C511yescharacteristic, complemented
158#1954C2×C511yescharacteristic, complemented
159#1873C2×C511yescharacteristic, complemented
160#1872C2×C511yescharacteristic, complemented
161#1854C2×C511yescharacteristic, complemented
162#1853C2×C511yescharacteristic, complemented
163#1804C2×C511yescharacteristic, complemented
164C24×C5—21no—
165C24×C5C2×D411yescharacteristic
166C24×C5C2×D411yescharacteristic
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8#4112yes—
173C2×C5×D4—24no—
174C2×C5×D4—22no—
175C2×C5×D4—24no—
176C2×C5×D4—22no—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—41no—
183C2×C5×D4—42no—
184C2×C5×D4—42no—
185C2×C5×D4—81no—
186C2×C5×D4—81no—
187C2×C5×D4C2×D412yes—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—24no—
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—24no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—81no—
210C22×C4×C5—81no—
211C22×C4×C5—81no—
212C22×C4×C5—81no—
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2411yescharacteristic
218C5×SD16—28no—
219C2×C5×C8—21no—
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#4112yes—
231C5×C4⋊C4—24no—
232C5×C4⋊C4—24no—
233C5×C4⋊C4—24no—
234C5×C4⋊C4—22no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—42no—
245C5×C4⋊C4—42no—
246C5×C4⋊C4—42no—
247C5×C4⋊C4C2×D412yes—
248C5×C4⋊C4C2×D412yes—
249C5×C4⋊C4C2×D412yes—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—24no—
253C5×C22⋊C4—24no—
254C5×C22⋊C4—22no—
255C5×C22⋊C4—22no—
256C5×C22⋊C4—42no—
257C5×C22⋊C4—42no—
258C5×C22⋊C4—42no—
259C5×C22⋊C4—42no—
260C42×C5—24no—
261C42×C5—42no—
262C42×C5C2×D412yes—
263C42×C5C2×D412yes—
264C22×SD16C22×C511yescharacteristic
265#553—24no—
266#553—24no—
267C2×#126—21no—
268C2×#125C22×C511yescharacteristic
269C2×#123—21no—
270C2×C22⋊Q8C22×C511yescharacteristic
271C2×C22⋊Q8C22×C511yescharacteristic
272C2×#121—21no—
273C2×#121C22×C511yescharacteristic
274C2×#121C22×C511yescharacteristic
275C2×C4×Q8C22×C511yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C22×C511yescharacteristic
278C2×C4×D4C22×C511yescharacteristic
279C2×#117C22×C511yescharacteristic
280C22×C4⋊C4C22×C511yescharacteristic
281#479—24no—
282C4×SD16—24no—
283C2×#107C22×C511yescharacteristic
284C2×#106C22×C511yescharacteristic
285C2×#106C22×C511yescharacteristic
286C2×C4⋊C8C22×C511yescharacteristic
287C2×#103C22×C511yescharacteristic
288C2×#103C22×C511yescharacteristic
289C2×#103C22×C511yescharacteristic
290C2×#102C22×C511yescharacteristic
291C2×#102C22×C511yescharacteristic
292C2×#102C22×C511yescharacteristic
293C2×C22⋊C8C22×C511yescharacteristic
294C2×C22⋊C8C22×C511yescharacteristic
295C2×C22⋊C8C22×C511yescharacteristic
296C2×C22⋊C8C22×C511yescharacteristic
297C2×C4×C8C22×C511yescharacteristic
298#398—21no—
299#394—21no—
300#388—21no—
301#388—21no—
302#382C22×C511yescharacteristic
303#380C22×C511yescharacteristic
304#380C22×C511yescharacteristic
305#340C22×C511yescharacteristic
306#340C22×C511yescharacteristic
307#340C22×C511yescharacteristic
308#340C22×C511yescharacteristic
309#340C22×C511yescharacteristic
310#340C22×C511yescharacteristic
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—22no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5#13512yes—
332C23×C5C22×D411yescharacteristic
333C5×Q8—22no—
334C5×Q8—22no—
335C5×Q8—41no—
336C5×Q8—41no—
337C5×D4—22no—
338C5×D4—22no—
339C5×D4—44no—
340C5×D4—48no—
341C5×D4—41no—
342C5×D4—41no—
343C5×D4—84no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—21no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
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—84no—
384C2×C4×C5—84no—
385C2×C4×C5#12012yes—
386C2×C4×C5#12012yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C22×D411yescharacteristic
389C2×C4×C5C2×#4111yescharacteristic
390C2×C4×C5C2×#4111yescharacteristic
391C2×C4×C5H(5,𝔽2)11yescharacteristic
392C2×C4×C52−1+411yescharacteristic
393C5×C8—22no—
394C5×C8—41no—
395C5×C8—41no—
396C5×C8—41no—
397C22×Q8C23×C511yescharacteristic
398C22×D4—21no—
399C22×D4—21no—
400C22×D4C5×D411yescharacteristic
401C22×D4C23×C511yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4C23×C511yescharacteristic
405C23×C4C23×C511yescharacteristic
406C2×SD16—22no—
407C2×SD16—22no—
408C2×SD16—22no—
409C22×C8C23×C511yescharacteristic
410C22×C8C23×C511yescharacteristic
411C22×C8C23×C511yescharacteristic
412C22×C8C23×C511yescharacteristic
413#126—28no—
414#125—22no—
415#125C5×D414yes—
416#123—28no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—41no—
420C22⋊Q8—41no—
421#121—28no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×D4—28no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4C5×D414yes—
433#117—22no—
434#117—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4C5×D411yescharacteristic
444C2×C4⋊C4C23×C511yescharacteristic
445C2×C4⋊C4C23×C511yescharacteristic
446C2×C4⋊C4C23×C511yescharacteristic
447C2×C4⋊C4C23×C511yescharacteristic
448C2×C4⋊C4C23×C511yescharacteristic
449C2×C4⋊C4C23×C511yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4C5×D411yescharacteristic
459C2×C22⋊C4C5×D411yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C511yescharacteristic
463#107—22no—
464#106—22no—
465#106—22no—
466C4⋊C8—22no—
467#103—22no—
468#103—22no—
469#103—22no—
470#102—22no—
471#102—41no—
472#102—41no—
473C22⋊C8—22no—
474C22⋊C8—22no—
475C22⋊C8—41no—
476C22⋊C8—41no—
477C4×C8—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482C22×C5—22no—
483C22×C5—22no—
484C22×C5—22no—
485C22×C5—41no—
486C22×C5—41no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—42no—
493C22×C5—41no—
494C22×C5—42no—
495C22×C5—42no—
496C22×C5—41no—
497C22×C5—41no—
498C22×C5—41no—
499C22×C5—81no—
500C22×C5—81no—
501C22×C5—81no—
502C22×C5—81no—
503C22×C5C2×#12011yescharacteristic
504C22×C5#54611yescharacteristic
505C22×C5#54711yescharacteristic
506C22×C5C2×#13511yescharacteristic
507C22×C5#57511yescharacteristic
508C22×C5#57711yescharacteristic
509C22×C5#57711yescharacteristic
510C4×C5—22no—
511C4×C5—22no—
512C4×C5—41no—
513C4×C5—41no—
514C4×C5—42no—
515C4×C5—42no—
516C4×C5—42no—
517C4×C5—42no—
518C4×C5—81no—
519C4×C5—81no—
520C4×C5—81no—
521C4×C5#52511yescharacteristic
522C4×C5#53711yescharacteristic
523C4×C5#54811yescharacteristic
524C4×C5#55011yescharacteristic
525C24—21no—
526C24C2×C5×D411yescharacteristic
527C24C2×C5×D411yescharacteristic
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C5×#4112yes—
534C2×D4—24no—
535C2×D4—22no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—41no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4C2×C5×D412yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
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—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—81no—
571C22×C4—81no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4C2×C5×D411yescharacteristic
575C22×C4C2×C5×D411yescharacteristic
576C22×C4C2×C5×D411yescharacteristic
577C22×C4C2×C5×D411yescharacteristic
578C22×C4C24×C511yescharacteristic
579SD16—28no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8C5×#4112yes—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4C2×C5×D412yes—
609C4⋊C4C2×C5×D412yes—
610C4⋊C4C2×C5×D412yes—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C42—24no—
622C42—42no—
623C42C2×C5×D412yes—
624C42C2×C5×D412yes—
625C2×C5—42no—
626C2×C5—81no—
627C2×C5—82no—
628C2×C5#240711yescharacteristic
629C2×C5#300211yescharacteristic
630C2×C5#300911yescharacteristic
631C2×C5#330111yescharacteristic
632C2×C5#332611yescharacteristic
633C2×C5#333711yescharacteristic
634C2×C5#335111yescharacteristic
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C5×#13512yes—
656C23C22×C5×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—44no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—84no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
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—84no—
708C2×C4—84no—
709C2×C4C5×#12012yes—
710C2×C4C5×#12012yes—
711C2×C4C22×C5×D411yescharacteristic
712C2×C4C22×C5×D411yescharacteristic
713C2×C4C2×C5×#4111yescharacteristic
714C2×C4C2×C5×#4111yescharacteristic
715C2×C4C5×H(5,𝔽2)11yescharacteristic
716C2×C4C5×2−1+411yescharacteristic
717C8—22no—
718C8—41no—
719C8—41no—
720C8—41no—
721C5#2412611yescharacteristic, direct product factor, Sylow
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×C5×#12011yescharacteristic
744C22C5×#54611yescharacteristic
745C22C5×#54711yescharacteristic
746C22C2×C5×#13511yescharacteristic
747C22C5×#57511yescharacteristic
748C22C5×#57711yescharacteristic
749C22C5×#57711yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—41no—
756C4—41no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C5×#52511yescharacteristic
762C4C5×#53711yescharacteristic
763C4C5×#54811yescharacteristic
764C4C5×#55011yescharacteristic
765C2—42no—
766C2—81no—
767C2—82no—
768C2C5×#240711yescharacteristic
769C2C5×#300211yescharacteristic
770C2C5×#300911yescharacteristic
771C2C5×#330111yescharacteristic
772C2C5×#332611yescharacteristic
773C2C5×#333711yescharacteristic
774C2C5×#335111yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#553C2
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
2. C2×C5×#479C2semidirect
3. C2×C4×C5×SD16C2semidirect
4. C5×#2536C2semidirect
5. C5×#2034C2semidirect
6. C5×#2033C2semidirect
7. C5×#2000C2semidirect
8. C5×#2000C2semidirect
9. C5×#1991C2semidirect
10. C5×#1954C2semidirect
11. C5×#1873C2semidirect
12. C5×#1872C2semidirect
13. C5×#1854C2semidirect
14. C5×#1853C2semidirect
15. C5×#1804C2semidirect
63. #24126C5direct (N × H)
150. C2×#479C2×C5semidirect
151. C2×C4×SD16C2×C5semidirect
152. #2536C2×C5semidirect
153. #2034C2×C5semidirect
154. #2033C2×C5semidirect
155. #2000C2×C5semidirect
156. #2000C2×C5semidirect
157. #1991C2×C5semidirect
158. #1954C2×C5semidirect
159. #1873C2×C5semidirect
160. #1872C2×C5semidirect
161. #1854C2×C5semidirect
162. #1853C2×C5semidirect
163. #1804C2×C5semidirect
721. C5#24126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5532
C2×C5×#4792
C2×C4×C5×SD162
C5×#25362
C5×#20342
C5×#20332
C5×#20002
C5×#19912
C5×#19542
C5×#18732
C5×#18722
C5×#18542
C5×#18532
C5×#18042
#241265