Finite Group Databasebeta

← C5×#23032 #11945752

Subgroups — C5×#23032 #11945752

Order 1280.

1054 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#465C211yesmaximal, characteristic
2C2×C5×#440C211yesmaximal, characteristic, complemented
3C22×C5×#107C211yesmaximal, characteristic, complemented
4C5×#2361C211yesmaximal, characteristic
5C5×#2360C211yesmaximal, characteristic, complemented
6C5×#1973C211yesmaximal, characteristic, complemented
7C5×#1944C211yesmaximal, characteristic, complemented
8C5×#1928C211yesmaximal, characteristic, complemented
9C5×#1925C211yesmaximal, characteristic, complemented
10C5×#1874C211yesmaximal, characteristic
11C5×#1872C211yesmaximal, characteristic, complemented
12C5×#1863C211yesmaximal, characteristic, complemented
13C5×#1862C211yesmaximal, characteristic, complemented
14C5×#1776C211yesmaximal, characteristic, complemented
15C5×#1752C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×D4—21no—
22C2×C4×C5×D4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C5×#465C418yescomplemented
26C5×#440—24no—
27C2×C5×#107—24no—
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
30C2×C5×#107C2211yescharacteristic
31C2×C5×#107C2211yescharacteristic
32C2×C5×#106C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×#97C2211yescharacteristic
41C2×C5×#97C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#389—21no—
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#388—21no—
48C5×#387—21no—
49C5×#386—21no—
50C5×#385—21no—
51C5×#385—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C22⋊C4—21no—
55C4×C5×C22⋊C4C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62#23032C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4—21no—
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5C2311yescharacteristic
70C2×C5×SD16—22no—
71C2×C5×SD16—22no—
72C2×C5×SD16C2×C414yescomplemented
73C22×C5×C8—22no—
74C22×C5×C8—22no—
75C22×C5×C8C2×C414yescomplemented
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8C2×C414yescomplemented
82C5×#121—22no—
83C5×#121C2×C414yes—
84C4×C5×Q8—22no—
85C4×C5×Q8—41no—
86C4×C5×D4—22no—
87C4×C5×D4—41no—
88C4×C5×D4—44no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—41no—
98C2×C5×C4⋊C4—41no—
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C2×C42×C5C2311yescharacteristic
117C5×#107—22no—
118C5×#107—22no—
119C5×#107—22no—
120C5×#107D414yescomplemented
121C5×#106C2×C414yescomplemented
122C5×#103—22no—
123C5×#103—41no—
124C5×#103C2×C414yescomplemented
125C5×#102—22no—
126C5×#102—41no—
127C5×#102C2×C414yescomplemented
128C5×C22⋊C8—22no—
129C5×#97—22no—
130C5×#97—22no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95D411yescharacteristic
138C5×#95D411yescharacteristic
139C2×#465C2×C511yescharacteristic
140C2×#440C2×C511yescharacteristic, complemented
141C22×#107C2×C511yescharacteristic, complemented
142#2361C2×C511yescharacteristic
143#2360C2×C511yescharacteristic, complemented
144#1973C2×C511yescharacteristic, complemented
145#1944C2×C511yescharacteristic, complemented
146#1928C2×C511yescharacteristic, complemented
147#1925C2×C511yescharacteristic, complemented
148#1874C2×C511yescharacteristic
149#1872C2×C511yescharacteristic, complemented
150#1863C2×C511yescharacteristic, complemented
151#1862C2×C511yescharacteristic, complemented
152#1776C2×C511yescharacteristic, complemented
153#1752C2×C511yescharacteristic, complemented
154C24×C5—21no—
155C24×C5C2×D411yescharacteristic
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8C22×C412yes—
162C2×C5×D4—24no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—42no—
169C2×C5×D4—42no—
170C2×C5×D4C22×C412yes—
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—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—42no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5—81no—
191C22×C4×C5C22×C412yes—
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5#4112yes—
198C22×C4×C5C2411yescharacteristic
199C5×SD16—28no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—28no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8C22×C412yes—
210C2×C5×C8C22×C412yes—
211C2×C5×C8C2×D412yes—
212C2×C5×C8#4112yes—
213C5×C4⋊C4—24no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—81no—
227C5×C4⋊C4C22×C412yes—
228C5×C4⋊C4C22×C412yes—
229C5×C4⋊C4C2×D412yes—
230C5×C4⋊C4C2×D412yes—
231C5×C22⋊C4—24no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4—24no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—42no—
237C5×C22⋊C4—81no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—42no—
243C42×C5—42no—
244C42×C5—81no—
245C22×SD16C22×C511yescharacteristic
246C23×C8C22×C511yescharacteristic
247C2×C22⋊Q8C22×C511yescharacteristic
248C2×#121C22×C511yescharacteristic
249C2×C4×Q8C22×C511yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4C22×C511yescharacteristic
252C22×C4⋊C4C22×C511yescharacteristic
253C22×C4⋊C4C22×C511yescharacteristic
254#465C4×C518yescomplemented
255#440—24no—
256C2×#107—24no—
257C2×#107C22×C511yescharacteristic
258C2×#107C22×C511yescharacteristic
259C2×#107C22×C511yescharacteristic
260C2×#107C22×C511yescharacteristic
261C2×#106C22×C511yescharacteristic
262C2×#103C22×C511yescharacteristic
263C2×#103C22×C511yescharacteristic
264C2×#103C22×C511yescharacteristic
265C2×#102C22×C511yescharacteristic
266C2×#102C22×C511yescharacteristic
267C2×#102C22×C511yescharacteristic
268C2×C22⋊C8C22×C511yescharacteristic
269C2×#97C22×C511yescharacteristic
270C2×#97C22×C511yescharacteristic
271#391C22×C511yescharacteristic
272#390C22×C511yescharacteristic
273#389—21no—
274#389C22×C511yescharacteristic
275#389C22×C511yescharacteristic
276#388—21no—
277#387—21no—
278#386—21no—
279#385—21no—
280#385—21no—
281C4×C4⋊C4C22×C511yescharacteristic
282C4×C4⋊C4C22×C511yescharacteristic
283C4×C22⋊C4—21no—
284C4×C22⋊C4C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#336C22×C511yescharacteristic
290#336C22×C511yescharacteristic
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5—22no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5C4×D412yes—
303C23×C5AGL(1,ℤ/8)12yes—
304C23×C5#13712yes—
305C23×C5C22×D411yescharacteristic
306C5×Q8—22no—
307C5×Q8—22no—
308C5×Q8—41no—
309C5×Q8—41no—
310C5×D4—22no—
311C5×D4—22no—
312C5×D4—48no—
313C5×D4—41no—
314C5×D4—41no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
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—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—84no—
355C2×C4×C5—84no—
356C2×C4×C5—84no—
357C2×C4×C5C4×D412yes—
358C2×C4×C5C23×C411yescharacteristic
359C2×C4×C5C22×D411yescharacteristic
360C2×C4×C5C2×#4111yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C2×C4×C5H(5,𝔽2)11yescharacteristic
363C2×C4×C52−1+411yescharacteristic
364C5×C8—22no—
365C5×C8—41no—
366C5×C8—41no—
367C5×C8C4×D414yescomplemented
368C22×Q8C23×C511yescharacteristic
369C22×D4—21no—
370C22×D4C23×C511yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4C23×C511yescharacteristic
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16C2×C4×C514yescomplemented
378C22×C8—22no—
379C22×C8—22no—
380C22×C8C2×C4×C514yescomplemented
381C22×C8C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22⋊Q8—22no—
386C22⋊Q8C2×C4×C514yescomplemented
387#121—22no—
388#121C2×C4×C514yes—
389C4×Q8—22no—
390C4×Q8—41no—
391C4×D4—22no—
392C4×D4—41no—
393C4×D4—44no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
407C2×C4⋊C4C23×C511yescharacteristic
408C2×C4⋊C4C23×C511yescharacteristic
409C2×C4⋊C4C23×C511yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4C5×D411yescharacteristic
416C2×C22⋊C4C5×D411yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42C23×C511yescharacteristic
421C2×C42C23×C511yescharacteristic
422#107—22no—
423#107—22no—
424#107—22no—
425#107C5×D414yescomplemented
426#106C2×C4×C514yescomplemented
427#103—22no—
428#103—41no—
429#103C2×C4×C514yescomplemented
430#102—22no—
431#102—41no—
432#102C2×C4×C514yescomplemented
433C22⋊C8—22no—
434#97—22no—
435#97—22no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95C5×D411yescharacteristic
443#95C5×D411yescharacteristic
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—22no—
450C22×C5—42no—
451C22×C5—42no—
452C22×C5—42no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5#44014yescomplemented
458C22×C5C2×C4×D411yescharacteristic
459C22×C5D4211yescharacteristic
460C22×C5#54711yescharacteristic
461C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C5C2×#13711yescharacteristic
463C22×C5#57611yescharacteristic
464C22×C5#57811yescharacteristic
465C4×C5—22no—
466C4×C5—41no—
467C4×C5—41no—
468C4×C5—42no—
469C4×C5—42no—
470C4×C5—42no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—42no—
474C4×C5—41no—
475C4×C5—81no—
476C4×C5—81no—
477C4×C5C2×C4×D411yescharacteristic
478C4×C5#52011yescharacteristic
479C4×C5#54811yescharacteristic
480C4×C5#55311yescharacteristic
481C24—21no—
482C24C2×C5×D411yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8C22×C4×C512yes—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C22×C4×C512yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4C22×C4×C512yes—
519C22×C4C2×C5×D411yescharacteristic
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C5×#4112yes—
525C22×C4C24×C511yescharacteristic
526SD16—28no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—28no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C22×C4×C512yes—
537C2×C8C22×C4×C512yes—
538C2×C8C2×C5×D412yes—
539C2×C8C5×#4112yes—
540C4⋊C4—24no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4C22×C4×C512yes—
555C4⋊C4C22×C4×C512yes—
556C4⋊C4C2×C5×D412yes—
557C4⋊C4C2×C5×D412yes—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—24no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—42no—
571C42—81no—
572C2×C5—24no—
573C2×C5—82no—
574C2×C5#236111yescharacteristic
575C2×C5C2×#44011yescharacteristic
576C2×C5#295111yescharacteristic
577C2×C5#326411yescharacteristic
578C2×C5#327011yescharacteristic
579C2×C5#334311yescharacteristic
580C2×C5#334611yescharacteristic
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C4×C5×D412yes—
593C23C5×AGL(1,ℤ/8)12yes—
594C23C5×#13712yes—
595C23C22×C5×D411yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4—41no—
604D4—41no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
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—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4C4×C5×D412yes—
648C2×C4C23×C4×C511yescharacteristic
649C2×C4C22×C5×D411yescharacteristic
650C2×C4C2×C5×#4111yescharacteristic
651C2×C4C2×C5×#4111yescharacteristic
652C2×C4C5×H(5,𝔽2)11yescharacteristic
653C2×C4C5×2−1+411yescharacteristic
654C8—22no—
655C8—41no—
656C8—41no—
657C8C4×C5×D414yescomplemented
658C5#2303211yescharacteristic, direct product factor, Sylow
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22C5×#44014yescomplemented
673C22C2×C4×C5×D411yescharacteristic
674C22C5×D4211yescharacteristic
675C22C5×#54711yescharacteristic
676C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
677C22C2×C5×#13711yescharacteristic
678C22C5×#57611yescharacteristic
679C22C5×#57811yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C2×C4×C5×D411yescharacteristic
693C4C5×#52011yescharacteristic
694C4C5×#54811yescharacteristic
695C4C5×#55311yescharacteristic
696C2—24no—
697C2—82no—
698C2C5×#236111yescharacteristic
699C2C2×C5×#44011yescharacteristic
700C2C5×#295111yescharacteristic
701C2C5×#326411yescharacteristic
702C2C5×#327011yescharacteristic
703C2C5×#334311yescharacteristic
704C2C5×#334611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#440C2semidirect
3. C22×C5×#107C2semidirect
5. C5×#2360C2semidirect
6. C5×#1973C2semidirect
7. C5×#1944C2semidirect
8. C5×#1928C2semidirect
9. C5×#1925C2semidirect
11. C5×#1872C2semidirect
12. C5×#1863C2semidirect
13. C5×#1862C2semidirect
14. C5×#1776C2semidirect
15. C5×#1752C2semidirect
25. C5×#465C4semidirect
62. #23032C5direct (N × H)
72. C2×C5×SD16C2×C4semidirect
75. C22×C5×C8C2×C4semidirect
81. C5×C22⋊Q8C2×C4semidirect
120. C5×#107D4semidirect
121. C5×#106C2×C4semidirect
124. C5×#103C2×C4semidirect
127. C5×#102C2×C4semidirect
140. C2×#440C2×C5semidirect
141. C22×#107C2×C5semidirect
143. #2360C2×C5semidirect
144. #1973C2×C5semidirect
145. #1944C2×C5semidirect
146. #1928C2×C5semidirect
147. #1925C2×C5semidirect
149. #1872C2×C5semidirect
150. #1863C2×C5semidirect
151. #1862C2×C5semidirect
152. #1776C2×C5semidirect
153. #1752C2×C5semidirect
254. #465C4×C5semidirect
367. C5×C8C4×D4semidirect
377. C2×SD16C2×C4×C5semidirect
380. C22×C8C2×C4×C5semidirect
386. C22⋊Q8C2×C4×C5semidirect
425. #107C5×D4semidirect
426. #106C2×C4×C5semidirect
429. #103C2×C4×C5semidirect
432. #102C2×C4×C5semidirect
457. C22×C5#440semidirect
657. C8C4×C5×D4semidirect
658. C5#23032direct (N × H)
672. C22C5×#440semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4652
C2×C5×#4402
C22×C5×#1072
C5×#23612
C5×#23602
C5×#19732
C5×#19442
C5×#19282
C5×#19252
C5×#18742
C5×#18722
C5×#18632
C5×#18622
C5×#17762
C5×#17522
#230325