Finite Group Databasebeta

← C5×#24100 #11946820

Subgroups — C5×#24100 #11946820

Order 1280.

1300 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#547C211yesmaximal, characteristic
2C2×C5×#482C211yesmaximal, characteristic, complemented
3C2×C5×#428C211yesmaximal, characteristic, complemented
4C5×#2485C211yesmaximal, characteristic, complemented
5C5×#2058C211yesmaximal, characteristic, complemented
6C5×#2057C211yesmaximal, characteristic, complemented
7C5×#2034C211yesmaximal, characteristic, complemented
8C5×#2033C211yesmaximal, characteristic, complemented
9C5×#1895C211yesmaximal, characteristic, complemented
10C5×#1870C211yesmaximal, characteristic, complemented
11C5×#1864C211yesmaximal, characteristic, complemented
12C5×#1862C211yesmaximal, characteristic, complemented
13C5×#1853C211yesmaximal, characteristic, complemented
14C5×#1852C211yesmaximal, characteristic, complemented
15C5×#1824C211yesmaximal, characteristic, complemented
16C22×C5×#41—21no—
17C22×C5×M16C2211yescharacteristic
18C5×#547—24no—
19C5×#547—24no—
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×#121C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#482—24no—
32C5×#428—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#107C2211yescharacteristic
35C2×C5×#107C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×#106C2211yescharacteristic
38C2×C5×#106C2211yescharacteristic
39C2×C5×#102C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×C22⋊C8C2211yescharacteristic
44C2×C5×C22⋊C8C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C5×#397—21no—
47C5×#394—21no—
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#388—21no—
51C5×#387—21no—
52C5×#380C2211yescharacteristic
53C5×#380C2211yescharacteristic
54C5×#380C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24100C511yesmaximal, characteristic, direct product factor, Sylow
64C2×C5×#41—28no—
65C2×C5×#41—44no—
66C2×C5×#41—44no—
67C22×C5×Q8—21no—
68C22×C5×D4—21no—
69C22×C5×D4—21no—
70C22×C5×D4D411yescharacteristic
71C22×C5×D4C2311yescharacteristic
72C23×C4×C5—21no—
73C23×C4×C5—21no—
74C23×C4×C5—21no—
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C2×C5×M16—22no—
78C2×C5×M16—22no—
79C2×C5×M16—22no—
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C22×C5×C8C2311yescharacteristic
84C5×C4⋊Q8—22no—
85C5×C4⋊Q8—22no—
86C5×#123—28no—
87C5×#123—28no—
88C5×C22⋊Q8—28no—
89C5×#121—22no—
90C5×#121—22no—
91C5×#121—22no—
92C5×#121D414yes—
93C4×C5×D4—22no—
94C4×C5×D4—22no—
95C4×C5×D4—22no—
96C4×C5×D4—22no—
97C5×#117—22no—
98C5×#117—22no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4D411yescharacteristic
108C2×C5×C4⋊C4D414yes—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
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⋊C4D411yescharacteristic
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C42×C5—21no—
126C2×C42×C5C2311yescharacteristic
127C5×#107—22no—
128C5×#107—22no—
129C5×#107—22no—
130C5×#106—22no—
131C5×#106—22no—
132C5×#106—22no—
133C5×#102—22no—
134C5×#102—22no—
135C5×#102—22no—
136C5×#102—22no—
137C5×C22⋊C8—22no—
138C5×C22⋊C8—22no—
139C5×C22⋊C8—22no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C5×#95—21no—
144C5×#95—21no—
145C2×#547C2×C511yescharacteristic
146C2×#482C2×C511yescharacteristic, complemented
147C2×#428C2×C511yescharacteristic, complemented
148#2485C2×C511yescharacteristic, complemented
149#2058C2×C511yescharacteristic, complemented
150#2057C2×C511yescharacteristic, complemented
151#2034C2×C511yescharacteristic, complemented
152#2033C2×C511yescharacteristic, complemented
153#1895C2×C511yescharacteristic, complemented
154#1870C2×C511yescharacteristic, complemented
155#1864C2×C511yescharacteristic, complemented
156#1862C2×C511yescharacteristic, complemented
157#1853C2×C511yescharacteristic, complemented
158#1852C2×C511yescharacteristic, complemented
159#1824C2×C511yescharacteristic, complemented
160C24×C5—21no—
161C24×C5C2×D411yescharacteristic
162C24×C5C2×D411yescharacteristic
163C5×#41—432no—
164C2×C5×Q8—24no—
165C2×C5×Q8—42no—
166C2×C5×Q8—42no—
167C2×C5×D4—22no—
168C2×C5×D4—22no—
169C2×C5×D4—24no—
170C2×C5×D4—24no—
171C2×C5×D4—22no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—42no—
178C2×C5×D4—42no—
179C2×C5×D4—42no—
180C2×C5×D4—42no—
181C2×C5×D4C2×D412yes—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—24no—
187C22×C4×C5—24no—
188C22×C4×C5—24no—
189C22×C4×C5—21no—
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—42no—
203C22×C4×C5—42no—
204C22×C4×C5—42no—
205C22×C4×C5—42no—
206C22×C4×C5—42no—
207C22×C4×C5—42no—
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D412yes—
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2411yescharacteristic
215C5×M16—28no—
216C2×C5×C8—21no—
217C2×C5×C8—21no—
218C2×C5×C8—21no—
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#4112yescomplemented
227C2×C5×C8#4112yescomplemented
228C5×C4⋊C4—24no—
229C5×C4⋊C4—24no—
230C5×C4⋊C4—24no—
231C5×C4⋊C4—22no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
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—42no—
244C5×C4⋊C4—81no—
245C5×C4⋊C4C2×D412yes—
246C5×C4⋊C4C2×D412yes—
247C5×C4⋊C4C2×D412yes—
248C5×C22⋊C4—24no—
249C5×C22⋊C4—24no—
250C5×C22⋊C4—22no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—22no—
253C5×C22⋊C4—42no—
254C5×C22⋊C4—42no—
255C5×C22⋊C4—81no—
256C5×C22⋊C4—81no—
257C42×C5—21no—
258C42×C5—21no—
259C42×C5—42no—
260C22×#41—21no—
261C22×M16C22×C511yescharacteristic
262#547—24no—
263#547—24no—
264C2×C4⋊Q8C22×C511yescharacteristic
265C2×#123—21no—
266C2×#123—21no—
267C2×C22⋊Q8—21no—
268C2×#121C22×C511yescharacteristic
269C2×#121C22×C511yescharacteristic
270C2×C4×D4C22×C511yescharacteristic
271C2×C4×D4C22×C511yescharacteristic
272C2×#117C22×C511yescharacteristic
273C22×C4⋊C4C22×C511yescharacteristic
274C22×C4⋊C4C22×C511yescharacteristic
275#482—24no—
276#428—24no—
277C2×#107C22×C511yescharacteristic
278C2×#107C22×C511yescharacteristic
279C2×#107C22×C511yescharacteristic
280C2×#106C22×C511yescharacteristic
281C2×#106C22×C511yescharacteristic
282C2×#106C22×C511yescharacteristic
283C2×#102C22×C511yescharacteristic
284C2×#102C22×C511yescharacteristic
285C2×#102C22×C511yescharacteristic
286C2×#102C22×C511yescharacteristic
287C2×C22⋊C8C22×C511yescharacteristic
288C2×C22⋊C8C22×C511yescharacteristic
289C2×C22⋊C8C22×C511yescharacteristic
290#397—21no—
291#394—21no—
292#389C22×C511yescharacteristic
293#389C22×C511yescharacteristic
294#388—21no—
295#387—21no—
296#380C22×C511yescharacteristic
297#380C22×C511yescharacteristic
298#380C22×C511yescharacteristic
299#340C22×C511yescharacteristic
300#340C22×C511yescharacteristic
301#340C22×C511yescharacteristic
302#340C22×C511yescharacteristic
303#340C22×C511yescharacteristic
304#340C22×C511yescharacteristic
305#336C22×C511yescharacteristic
306#336C22×C511yescharacteristic
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—22no—
320C23×C5—41no—
321C23×C5—41no—
322C23×C5—41no—
323C23×C5—41no—
324C23×C5—41no—
325C23×C5—41no—
326C23×C5#12012yes—
327C23×C5AGL(1,ℤ/8)12yes—
328C23×C5C22×D411yescharacteristic
329C5×Q8—48no—
330C5×D4—28no—
331C5×D4—22no—
332C5×D4—22no—
333C5×D4—48no—
334C5×D4—48no—
335C5×D4—41no—
336C5×D4—41no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—48no—
355C2×C4×C5—48no—
356C2×C4×C5—48no—
357C2×C4×C5—41no—
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#12012yes—
380C2×C4×C5AGL(1,ℤ/8)12yes—
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C22×D411yescharacteristic
383C2×C4×C5C2×#4111yescharacteristic
384C2×C4×C5C2×#4111yescharacteristic
385C2×C4×C52−1+411yescharacteristic
386C2×C4×C52−1+411yescharacteristic
387C5×C8—22no—
388C5×C8—22no—
389C5×C8—41no—
390C5×C8—41no—
391C2×#41—28no—
392C2×#41—44no—
393C2×#41—44no—
394C22×Q8—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4C5×D411yescharacteristic
398C22×D4C23×C511yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C23×C511yescharacteristic
403C23×C4C23×C511yescharacteristic
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C22×C8C23×C511yescharacteristic
408C22×C8C23×C511yescharacteristic
409C22×C8C23×C511yescharacteristic
410C22×C8C23×C511yescharacteristic
411C4⋊Q8—22no—
412C4⋊Q8—22no—
413#123—28no—
414#123—28no—
415C22⋊Q8—28no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121C5×D414yes—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424#117—22no—
425#117—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4C5×D411yescharacteristic
435C2×C4⋊C4C5×D414yes—
436C2×C4⋊C4C23×C511yescharacteristic
437C2×C4⋊C4C23×C511yescharacteristic
438C2×C4⋊C4C23×C511yescharacteristic
439C2×C4⋊C4C23×C511yescharacteristic
440C2×C4⋊C4C23×C511yescharacteristic
441C2×C4⋊C4C23×C511yescharacteristic
442C2×C4⋊C4C23×C511yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4C5×D411yescharacteristic
451C2×C22⋊C4C5×D411yescharacteristic
452C2×C42—21no—
453C2×C42C23×C511yescharacteristic
454#107—22no—
455#107—22no—
456#107—22no—
457#106—22no—
458#106—22no—
459#106—22no—
460#102—22no—
461#102—22no—
462#102—22no—
463#102—22no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5—22no—
475C22×C5—22no—
476C22×C5—22no—
477C22×C5—22no—
478C22×C5—41no—
479C22×C5—41no—
480C22×C5—41no—
481C22×C5—41no—
482C22×C5—41no—
483C22×C5—41no—
484C22×C5—41no—
485C22×C5—41no—
486C22×C5—42no—
487C22×C5—42no—
488C22×C5—42no—
489C22×C5—81no—
490C22×C5—81no—
491C22×C5—81no—
492C22×C5—81no—
493C22×C5C2×#12011yescharacteristic
494C22×C5#54711yescharacteristic
495C22×C5#54711yescharacteristic
496C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
497C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
498C22×C5#57711yescharacteristic
499C22×C5#57811yescharacteristic
500C4×C5—22no—
501C4×C5—22no—
502C4×C5—41no—
503C4×C5—42no—
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—41no—
507C4×C5—81no—
508C4×C5—81no—
509C4×C5—81no—
510C4×C5—81no—
511C4×C5#52511yescharacteristic
512C4×C5#53611yescharacteristic
513C4×C5#54711yescharacteristic
514C4×C5#54711yescharacteristic
515C24—21no—
516C24C2×C5×D411yescharacteristic
517C24C2×C5×D411yescharacteristic
518#41—432no—
519C2×Q8—24no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4C2×C5×D412yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4C2×C5×D411yescharacteristic
564C22×C4C2×C5×D411yescharacteristic
565C22×C4C2×C5×D411yescharacteristic
566C22×C4C2×C5×D412yes—
567C22×C4C2×C5×D412yes—
568C22×C4C2×C5×D411yescharacteristic
569C22×C4C24×C511yescharacteristic
570M16—28no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8C5×#4112yescomplemented
582C2×C8C5×#4112yescomplemented
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4C2×C5×D412yes—
601C4⋊C4C2×C5×D412yes—
602C4⋊C4C2×C5×D412yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—22no—
606C22⋊C4—24no—
607C22⋊C4—22no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—42no—
615C2×C5—42no—
616C2×C5—42no—
617C2×C5—82no—
618C2×C5#240611yescharacteristic
619C2×C5#300311yescharacteristic
620C2×C5#301311yescharacteristic
621C2×C5#334311yescharacteristic
622C2×C5#334511yescharacteristic
623C2×C5#335311yescharacteristic
624C2×C5#335411yescharacteristic
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C5×#12012yes—
645C23C5×AGL(1,ℤ/8)12yes—
646C23C22×C5×D411yescharacteristic
647Q8—48no—
648D4—28no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—48no—
653D4—41no—
654D4—41no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—48no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
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×C4C5×#12012yes—
698C2×C4C5×AGL(1,ℤ/8)12yes—
699C2×C4C22×C5×D411yescharacteristic
700C2×C4C22×C5×D411yescharacteristic
701C2×C4C2×C5×#4111yescharacteristic
702C2×C4C2×C5×#4111yescharacteristic
703C2×C4C5×2−1+411yescharacteristic
704C2×C4C5×2−1+411yescharacteristic
705C8—22no—
706C8—22no—
707C8—41no—
708C8—41no—
709C5#2410011yescharacteristic, direct product factor, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C5×#12011yescharacteristic
732C22C5×#54711yescharacteristic
733C22C5×#54711yescharacteristic
734C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
735C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
736C22C5×#57711yescharacteristic
737C22C5×#57811yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C5×#52511yescharacteristic
750C4C5×#53611yescharacteristic
751C4C5×#54711yescharacteristic
752C4C5×#54711yescharacteristic
753C2—42no—
754C2—42no—
755C2—82no—
756C2C5×#240611yescharacteristic
757C2C5×#300311yescharacteristic
758C2C5×#301311yescharacteristic
759C2C5×#334311yescharacteristic
760C2C5×#334511yescharacteristic
761C2C5×#335311yescharacteristic
762C2C5×#335411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#547C2
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×#482C2semidirect
3. C2×C5×#428C2semidirect
4. C5×#2485C2semidirect
5. C5×#2058C2semidirect
6. C5×#2057C2semidirect
7. C5×#2034C2semidirect
8. C5×#2033C2semidirect
9. C5×#1895C2semidirect
10. C5×#1870C2semidirect
11. C5×#1864C2semidirect
12. C5×#1862C2semidirect
13. C5×#1853C2semidirect
14. C5×#1852C2semidirect
15. C5×#1824C2semidirect
63. #24100C5direct (N × H)
146. C2×#482C2×C5semidirect
147. C2×#428C2×C5semidirect
148. #2485C2×C5semidirect
149. #2058C2×C5semidirect
150. #2057C2×C5semidirect
151. #2034C2×C5semidirect
152. #2033C2×C5semidirect
153. #1895C2×C5semidirect
154. #1870C2×C5semidirect
155. #1864C2×C5semidirect
156. #1862C2×C5semidirect
157. #1853C2×C5semidirect
158. #1852C2×C5semidirect
159. #1824C2×C5semidirect
226. C2×C5×C8#41semidirect
227. C2×C5×C8#41semidirect
581. C2×C8C5×#41semidirect
582. C2×C8C5×#41semidirect
709. C5#24100direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5472
C2×C5×#4822
C2×C5×#4282
C5×#24852
C5×#20582
C5×#20572
C5×#20342
C5×#20332
C5×#18952
C5×#18702
C5×#18642
C5×#18622
C5×#18532
C5×#18522
C5×#18242
#241005