Finite Group Databasebeta

← C5×#22491 #11945211

Subgroups — C5×#22491 #11945211

Order 1280.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic
2C2×C5×#435C211yesmaximal, characteristic
3C5×D4×C4⋊C4C211yesmaximal, characteristic
4C5×#1992C211yesmaximal, characteristic, complemented
5C5×#1989C211yesmaximal, characteristic, complemented
6C5×#1894C211yesmaximal, characteristic, complemented
7C5×#1892C211yesmaximal, characteristic, complemented
8C5×#1872C211yesmaximal, characteristic, complemented
9C5×#1872C211yesmaximal, characteristic, complemented
10C5×#1825C211yesmaximal, characteristic, complemented
11C5×#1823C211yesmaximal, characteristic, complemented
12C5×#1803C211yesmaximal, characteristic, complemented
13C5×#1763C211yesmaximal, characteristic, complemented
14C5×#1736C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C5×#552—24no—
19C5×#552C418yescomplemented
20C2×C5×#126—21no—
21C2×C5×#125—21no—
22C2×C5×#125C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4—21no—
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117—21no—
30C2×C5×#117C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic
32C22×C5×C4⋊C4C2211yescharacteristic
33C22×C5×C4⋊C4C2211yescharacteristic
34C5×#435—24no—
35C2×C5×C4⋊C8C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×C22⋊C8C2211yescharacteristic
41C2×C5×C22⋊C8C2211yescharacteristic
42C2×C5×#97C2211yescharacteristic
43C5×#389—21no—
44C5×#385—21no—
45C5×#385—21no—
46C5×#384C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C4×C5×C4⋊C4C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62#22491C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4D411yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C2×C5×M16—22no—
71C2×C5×M16—22no—
72C2×C5×M16—41no—
73C22×C5×C8—22no—
74C22×C5×C8—22no—
75C22×C5×C8—41no—
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×#126—28no—
81C5×#125—28no—
82C5×#125—22no—
83C5×#125C2×C414yescomplemented
84C5×#123—28no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8C2×C414yescomplemented
88C5×C22⋊Q8C2×C414yescomplemented
89C4×C5×Q8—22no—
90C4×C5×Q8C2×C414yescomplemented
91C4×C5×D4—44no—
92C4×C5×D4C2×C414yes—
93C4×C5×D4D414yes—
94C5×#117—22no—
95C5×#117—28no—
96C5×#117C2×C414yescomplemented
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—41no—
111C2×C5×C4⋊C4—41no—
112C2×C5×C4⋊C4C2×C414yescomplemented
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×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
127C2×C5×C22⋊C4D411yescharacteristic
128C2×C42×C5—21no—
129C2×C42×C5—21no—
130C2×C42×C5—21no—
131C2×C42×C5C2311yescharacteristic
132C5×C4⋊C8—22no—
133C5×#103—22no—
134C5×#103—22no—
135C5×#103—41no—
136C5×#103—41no—
137C5×C22⋊C8—22no—
138C5×C22⋊C8—22no—
139C5×#97—22no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C2×#552C2×C511yescharacteristic
144C2×#435C2×C511yescharacteristic
145D4×C4⋊C4C2×C511yescharacteristic
146#1992C2×C511yescharacteristic, complemented
147#1989C2×C511yescharacteristic, complemented
148#1894C2×C511yescharacteristic, complemented
149#1892C2×C511yescharacteristic, complemented
150#1872C2×C511yescharacteristic, complemented
151#1872C2×C511yescharacteristic, complemented
152#1825C2×C511yescharacteristic, complemented
153#1823C2×C511yescharacteristic, complemented
154#1803C2×C511yescharacteristic, complemented
155#1763C2×C511yescharacteristic, complemented
156#1736C2×C511yescharacteristic, complemented
157C2×#340C2×C511yescharacteristic, complemented
158C24×C5C2×D411yescharacteristic
159C24×C5C2×D411yescharacteristic
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C22×C412yes—
166C2×C5×D4—22no—
167C2×C5×D4—22no—
168C2×C5×D4C22⋊C414yes—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—24no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—42no—
189C22×C4×C5—42no—
190C22×C4×C5—42no—
191C22×C4×C5—42no—
192C22×C4×C5—81no—
193C22×C4×C5—81no—
194C22×C4×C5C22×C412yes—
195C22×C4×C5C22×C412yes—
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D412yes—
201C22×C4×C5C2×D412yes—
202C22×C4×C5C2411yescharacteristic
203C5×M16—44no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8—21no—
213C2×C5×C8—21no—
214C2×C5×C8—21no—
215C2×C5×C8—44no—
216C2×C5×C8#4112yes—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—24no—
221C5×C4⋊C4—24no—
222C5×C4⋊C4—24no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—42no—
234C5×C4⋊C4—42no—
235C5×C4⋊C4—42no—
236C5×C4⋊C4—81no—
237C5×C4⋊C4C22⋊C414yes—
238C5×C4⋊C4C22×C412yes—
239C5×C4⋊C4C22×C412yes—
240C5×C4⋊C4C22×C412yes—
241C5×C4⋊C4#4112yes—
242C5×C22⋊C4—24no—
243C5×C22⋊C4—24no—
244C5×C22⋊C4—24no—
245C5×C22⋊C4—42no—
246C5×C22⋊C4—42no—
247C5×C22⋊C4C22⋊C414yes—
248C5×C22⋊C4C22⋊C414yes—
249C42×C5—24no—
250C42×C5—24no—
251C42×C5—42no—
252C42×C5C22×C412yes—
253C42×C5C2×D412yes—
254C22×M16C22×C511yescharacteristic
255C23×C8C22×C511yescharacteristic
256#552—24no—
257#552C4×C518yescomplemented
258C2×#126—21no—
259C2×#125—21no—
260C2×#125C22×C511yescharacteristic
261C2×#123—21no—
262C2×C22⋊Q8C22×C511yescharacteristic
263C2×C22⋊Q8C22×C511yescharacteristic
264C2×C4×Q8C22×C511yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4C22×C511yescharacteristic
267C2×#117—21no—
268C2×#117C22×C511yescharacteristic
269C22×C4⋊C4C22×C511yescharacteristic
270C22×C4⋊C4C22×C511yescharacteristic
271C22×C4⋊C4C22×C511yescharacteristic
272#435—24no—
273C2×C4⋊C8C22×C511yescharacteristic
274C2×#103C22×C511yescharacteristic
275C2×#103C22×C511yescharacteristic
276C2×#103C22×C511yescharacteristic
277C2×#103C22×C511yescharacteristic
278C2×C22⋊C8C22×C511yescharacteristic
279C2×C22⋊C8C22×C511yescharacteristic
280C2×#97C22×C511yescharacteristic
281#389—21no—
282#385—21no—
283#385—21no—
284#384C22×C511yescharacteristic
285#380C22×C511yescharacteristic
286#380C22×C511yescharacteristic
287C4×C4⋊C4C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#340C22×C511yescharacteristic
290#340C22×C511yescharacteristic
291#340C22×C511yescharacteristic
292#340C22×C511yescharacteristic
293#340C22×C511yescharacteristic
294#340C22×C511yescharacteristic
295#340C22×C511yescharacteristic
296#340C22×C511yescharacteristic
297#340C22×C511yescharacteristic
298#340C22×C511yescharacteristic
299#340C22×C511yescharacteristic
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—21no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5C2×C22⋊C412yes—
311C23×C5C2×C22⋊C412yes—
312C23×C5AGL(1,ℤ/8)12yes—
313C23×C5#13712yes—
314C23×C5C22×D411yescharacteristic
315C5×Q8—22no—
316C5×Q8—22no—
317C5×Q8—41no—
318C5×Q8—41no—
319C5×D4—28no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—48no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—84no—
362C2×C4×C5—84no—
363C2×C4×C5C2×C22⋊C412yes—
364C2×C4×C5C2×C22⋊C412yes—
365C2×C4×C5C2×C22⋊C412yes—
366C2×C4×C5C2×C22⋊C412yes—
367C2×C4×C5C23×C411yescharacteristic
368C2×C4×C5C22×D411yescharacteristic
369C2×C4×C5C2×#4111yescharacteristic
370C2×C4×C5C2×#4111yescharacteristic
371C2×C4×C5H(5,𝔽2)11yescharacteristic
372C2×C4×C52−1+411yescharacteristic
373C5×C8—22no—
374C5×C8—41no—
375C5×C8—41no—
376C5×C8—41no—
377C22×Q8C23×C511yescharacteristic
378C22×D4C5×D411yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4C23×C511yescharacteristic
383C23×C4C23×C511yescharacteristic
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—41no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—41no—
390C22×C8C23×C511yescharacteristic
391C22×C8C23×C511yescharacteristic
392C22×C8C23×C511yescharacteristic
393C22×C8C23×C511yescharacteristic
394#126—28no—
395#125—28no—
396#125—22no—
397#125C2×C4×C514yescomplemented
398#123—28no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8C2×C4×C514yescomplemented
402C22⋊Q8C2×C4×C514yescomplemented
403C4×Q8—22no—
404C4×Q8C2×C4×C514yescomplemented
405C4×D4—44no—
406C4×D4C2×C4×C514yes—
407C4×D4C5×D414yes—
408#117—22no—
409#117—28no—
410#117C2×C4×C514yescomplemented
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4C2×C4×C514yescomplemented
427C2×C4⋊C4C5×D411yescharacteristic
428C2×C4⋊C4C23×C511yescharacteristic
429C2×C4⋊C4C23×C511yescharacteristic
430C2×C4⋊C4C23×C511yescharacteristic
431C2×C4⋊C4C23×C511yescharacteristic
432C2×C4⋊C4C23×C511yescharacteristic
433C2×C4⋊C4C23×C511yescharacteristic
434C2×C4⋊C4C23×C511yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4C5×D411yescharacteristic
441C2×C22⋊C4C5×D411yescharacteristic
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42C23×C511yescharacteristic
446C4⋊C8—22no—
447#103—22no—
448#103—22no—
449#103—41no—
450#103—41no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453#97—22no—
454#95—21no—
455#95—21no—
456#95—21no—
457C22×C5—22no—
458C22×C5—22no—
459C22×C5—22no—
460C22×C5—22no—
461C22×C5—22no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5—22no—
466C22×C5—41no—
467C22×C5—41no—
468C22×C5—41no—
469C22×C5—41no—
470C22×C5#41714yes—
471C22×C5C22×C22⋊C411yescharacteristic
472C22×C5#54611yescharacteristic
473C22×C5#54711yescharacteristic
474C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
475C22×C5C2×#13711yescharacteristic
476C22×C5#57711yescharacteristic
477C22×C5#57811yescharacteristic
478C4×C5—22no—
479C4×C5—22no—
480C4×C5—22no—
481C4×C5—22no—
482C4×C5—42no—
483C4×C5—42no—
484C4×C5—42no—
485C4×C5—42no—
486C4×C5—42no—
487C4×C5—81no—
488C4×C5—81no—
489C4×C5—81no—
490C4×C5C4×#4111yescharacteristic
491C4×C5#52011yescharacteristic
492C4×C5#54611yescharacteristic
493C4×C5#54711yescharacteristic
494C24C2×C5×D411yescharacteristic
495C24C2×C5×D411yescharacteristic
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C22×C4×C512yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4C5×C22⋊C414yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C22×C4×C512yes—
531C22×C4C22×C4×C512yes—
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D411yescharacteristic
534C22×C4C2×C5×D411yescharacteristic
535C22×C4C2×C5×D411yescharacteristic
536C22×C4C2×C5×D412yes—
537C22×C4C2×C5×D412yes—
538C22×C4C24×C511yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8C5×#4112yes—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4C5×C22⋊C414yes—
574C4⋊C4C22×C4×C512yes—
575C4⋊C4C22×C4×C512yes—
576C4⋊C4C22×C4×C512yes—
577C4⋊C4C5×#4112yes—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4C5×C22⋊C414yes—
584C22⋊C4C5×C22⋊C414yes—
585C42—24no—
586C42—24no—
587C42—42no—
588C42C22×C4×C512yes—
589C42C2×C5×D412yes—
590C2×C5—24no—
591C2×C5—42no—
592C2×C5#233911yescharacteristic
593C2×C5C2×#41711yescharacteristic
594C2×C5#289811yescharacteristic
595C2×C5#331011yescharacteristic
596C2×C5#331211yescharacteristic
597C2×C5#334311yescharacteristic
598C2×C5#334411yescharacteristic
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×C5×C22⋊C412yes—
610C23C2×C5×C22⋊C412yes—
611C23C5×AGL(1,ℤ/8)12yes—
612C23C5×#13712yes—
613C23C22×C5×D411yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618D4—28no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4C2×C5×C22⋊C412yes—
663C2×C4C2×C5×C22⋊C412yes—
664C2×C4C2×C5×C22⋊C412yes—
665C2×C4C2×C5×C22⋊C412yes—
666C2×C4C23×C4×C511yescharacteristic
667C2×C4C22×C5×D411yescharacteristic
668C2×C4C2×C5×#4111yescharacteristic
669C2×C4C2×C5×#4111yescharacteristic
670C2×C4C5×H(5,𝔽2)11yescharacteristic
671C2×C4C5×2−1+411yescharacteristic
672C8—22no—
673C8—41no—
674C8—41no—
675C8—41no—
676C5#2249111yescharacteristic, direct product factor, Sylow
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C5×#41714yes—
691C22C22×C5×C22⋊C411yescharacteristic
692C22C5×#54611yescharacteristic
693C22C5×#54711yescharacteristic
694C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
695C22C2×C5×#13711yescharacteristic
696C22C5×#57711yescharacteristic
697C22C5×#57811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C4×C5×#4111yescharacteristic
711C4C5×#52011yescharacteristic
712C4C5×#54611yescharacteristic
713C4C5×#54711yescharacteristic
714C2—24no—
715C2—42no—
716C2C5×#233911yescharacteristic
717C2C2×C5×#41711yescharacteristic
718C2C5×#289811yescharacteristic
719C2C5×#331011yescharacteristic
720C2C5×#331211yescharacteristic
721C2C5×#334311yescharacteristic
722C2C5×#334411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×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
4. C5×#1992C2semidirect
5. C5×#1989C2semidirect
6. C5×#1894C2semidirect
7. C5×#1892C2semidirect
8. C5×#1872C2semidirect
9. C5×#1872C2semidirect
10. C5×#1825C2semidirect
11. C5×#1823C2semidirect
12. C5×#1803C2semidirect
13. C5×#1763C2semidirect
14. C5×#1736C2semidirect
15. C2×C5×#340C2semidirect
19. C5×#552C4semidirect
62. #22491C5direct (N × H)
83. C5×#125C2×C4semidirect
87. C5×C22⋊Q8C2×C4semidirect
88. C5×C22⋊Q8C2×C4semidirect
90. C4×C5×Q8C2×C4semidirect
96. C5×#117C2×C4semidirect
112. C2×C5×C4⋊C4C2×C4semidirect
146. #1992C2×C5semidirect
147. #1989C2×C5semidirect
148. #1894C2×C5semidirect
149. #1892C2×C5semidirect
150. #1872C2×C5semidirect
151. #1872C2×C5semidirect
152. #1825C2×C5semidirect
153. #1823C2×C5semidirect
154. #1803C2×C5semidirect
155. #1763C2×C5semidirect
156. #1736C2×C5semidirect
157. C2×#340C2×C5semidirect
257. #552C4×C5semidirect
397. #125C2×C4×C5semidirect
401. C22⋊Q8C2×C4×C5semidirect
402. C22⋊Q8C2×C4×C5semidirect
404. C4×Q8C2×C4×C5semidirect
410. #117C2×C4×C5semidirect
426. C2×C4⋊C4C2×C4×C5semidirect
676. C5#22491direct (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×#4352
C5×D4×C4⋊C42
C5×#19922
C5×#19892
C5×#18942
C5×#18922
C5×#18722
C5×#18252
C5×#18232
C5×#18032
C5×#17632
C5×#17362
C2×C5×#3402
#224915