Finite Group Databasebeta

← C5×#23011 #11945731

Subgroups — C5×#23011 #11945731

Order 1280.

1058 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#463C211yesmaximal, characteristic
2C2×C5×#440C211yesmaximal, characteristic, complemented
3C2×C4×C5×D8C211yesmaximal, characteristic
4C5×#2367C211yesmaximal, characteristic, complemented
5C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
6C5×#1959C211yesmaximal, characteristic, complemented
7C5×#1947C211yesmaximal, characteristic, complemented
8C5×#1936C211yesmaximal, characteristic, complemented
9C5×#1933C211yesmaximal, characteristic, complemented
10C5×#1879C211yesmaximal, characteristic
11C5×#1877C211yesmaximal, characteristic, complemented
12C5×#1863C211yesmaximal, characteristic, complemented
13C5×#1862C211yesmaximal, characteristic, complemented
14C5×#1771C211yesmaximal, characteristic, complemented
15C5×#1762C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C2×C5×#124C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C2×C4×C5×D4C2211yescharacteristic
24C22×C5×C4⋊C4—21no—
25C5×#463C418yescomplemented
26C5×#440—24no—
27C4×C5×D8—24no—
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×#97C2211yescharacteristic
40C2×C5×#97C2211yescharacteristic
41C2×C4×C5×C8C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#388—21no—
47C5×#388—21no—
48C5×#385—21no—
49C5×#385—21no—
50C5×#385—21no—
51C5×#384C2211yescharacteristic
52C5×#380—21no—
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C4⋊C4C2211yescharacteristic
55C4×C5×C22⋊C4—21no—
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62#23011C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4C2311yescharacteristic
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C2×C5×SD16—22no—
71C2×C5×SD16—22no—
72C2×C5×SD16C2×C414yescomplemented
73C2×C5×D8—22no—
74C2×C5×D8—22no—
75C2×C5×D8C2×C414yes—
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×#124—22no—
81C5×#124C2×C414yescomplemented
82C4×C5×Q8—22no—
83C4×C5×Q8—41no—
84C4×C5×D4—22no—
85C4×C5×D4—22no—
86C4×C5×D4—22no—
87C4×C5×D4—22no—
88C4×C5×D4—41no—
89C4×C5×D4—41no—
90C4×C5×D4—41no—
91C4×C5×D4C2×C414yescomplemented
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—44no—
98C2×C5×C4⋊C4D411yescharacteristic
99C2×C5×C4⋊C4D411yescharacteristic
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⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C2×C42×C5C2311yescharacteristic
117C2×C42×C5C2311yescharacteristic
118C5×#107—22no—
119C5×#107—22no—
120C5×C4⋊C8C2×C414yescomplemented
121C5×#103—22no—
122C5×#103—41no—
123C5×#103C2×C414yescomplemented
124C5×#102—22no—
125C5×#102—22no—
126C5×#102—41no—
127C5×#102C2×C414yescomplemented
128C5×#102D414yes—
129C5×#97—22no—
130C5×#97—22no—
131C4×C5×C8—22no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95D411yescharacteristic
138C5×#95D411yescharacteristic
139C2×#463C2×C511yescharacteristic
140C2×#440C2×C511yescharacteristic, complemented
141C2×C4×D8C2×C511yescharacteristic
142#2367C2×C511yescharacteristic, complemented
143D4×C4⋊C4C2×C511yescharacteristic, complemented
144#1959C2×C511yescharacteristic, complemented
145#1947C2×C511yescharacteristic, complemented
146#1936C2×C511yescharacteristic, complemented
147#1933C2×C511yescharacteristic, complemented
148#1879C2×C511yescharacteristic
149#1877C2×C511yescharacteristic, complemented
150#1863C2×C511yescharacteristic, complemented
151#1862C2×C511yescharacteristic, complemented
152#1771C2×C511yescharacteristic, complemented
153#1762C2×C511yescharacteristic, complemented
154C24×C5—21no—
155C24×C5—21no—
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—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4C22×C412yes—
171C2×C5×D4C22×C412yes—
172C2×C5×D4C2×D412yes—
173C2×C5×D4#4112yes—
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—42no—
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—42no—
189C22×C4×C5—81no—
190C22×C4×C5—81no—
191C22×C4×C5—81no—
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2411yescharacteristic
199C5×SD16—28no—
200C5×D8—28no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
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×C8—21no—
210C2×C5×C8C22×C412yes—
211C2×C5×C8C22×C412yes—
212C2×C5×C8C2×D412yes—
213C5×C4⋊C4—22no—
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—41no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—42no—
227C5×C4⋊C4—81no—
228C5×C4⋊C4C22×C412yes—
229C5×C4⋊C4C2×D412yes—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—24no—
232C5×C22⋊C4—24no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
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—81no—
244C42×C5C22×C412yes—
245C42×C5#4112yes—
246C22×SD16C22×C511yescharacteristic
247C22×D8C22×C511yescharacteristic
248C2×#124C22×C511yescharacteristic
249C2×C4×Q8C22×C511yescharacteristic
250C2×C4×D4C22×C511yescharacteristic
251C2×C4×D4C22×C511yescharacteristic
252C2×C4×D4C22×C511yescharacteristic
253C2×C4×D4C22×C511yescharacteristic
254C22×C4⋊C4—21no—
255#463C4×C518yescomplemented
256#440—24no—
257C4×D8—24no—
258C2×#107C22×C511yescharacteristic
259C2×#107C22×C511yescharacteristic
260C2×C4⋊C8C22×C511yescharacteristic
261C2×#103C22×C511yescharacteristic
262C2×#103C22×C511yescharacteristic
263C2×#103C22×C511yescharacteristic
264C2×#102C22×C511yescharacteristic
265C2×#102C22×C511yescharacteristic
266C2×#102C22×C511yescharacteristic
267C2×#102C22×C511yescharacteristic
268C2×#102C22×C511yescharacteristic
269C2×#97C22×C511yescharacteristic
270C2×#97C22×C511yescharacteristic
271C2×C4×C8C22×C511yescharacteristic
272#391C22×C511yescharacteristic
273#390C22×C511yescharacteristic
274#389C22×C511yescharacteristic
275#389C22×C511yescharacteristic
276#388—21no—
277#388—21no—
278#385—21no—
279#385—21no—
280#385—21no—
281#384C22×C511yescharacteristic
282#380—21no—
283C4×C4⋊C4C22×C511yescharacteristic
284C4×C4⋊C4C22×C511yescharacteristic
285C4×C22⋊C4—21no—
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#340C22×C511yescharacteristic
290#336C22×C511yescharacteristic
291#336C22×C511yescharacteristic
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5C22×D411yescharacteristic
307C5×Q8—22no—
308C5×Q8—22no—
309C5×Q8—41no—
310C5×Q8—41no—
311C5×D4—22no—
312C5×D4—22no—
313C5×D4—22no—
314C5×D4—22no—
315C5×D4—22no—
316C5×D4—41no—
317C5×D4—41no—
318C5×D4C4×D414yes—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
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—48no—
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—84no—
354C2×C4×C5—84no—
355C2×C4×C5—84no—
356C2×C4×C5C4×D412yes—
357C2×C4×C5C4×D412yes—
358C2×C4×C5AGL(1,ℤ/8)12yes—
359C2×C4×C5C23×C411yescharacteristic
360C2×C4×C5C22×D411yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C2×C4×C5C2×#4111yescharacteristic
363C2×C4×C5H(5,𝔽2)11yescharacteristic
364C2×C4×C52−1+411yescharacteristic
365C5×C8—22no—
366C5×C8—22no—
367C5×C8—22no—
368C5×C8—41no—
369C22×Q8C23×C511yescharacteristic
370C22×D4C23×C511yescharacteristic
371C22×D4C23×C511yescharacteristic
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—21no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16C2×C4×C514yescomplemented
379C2×D8—22no—
380C2×D8—22no—
381C2×D8C2×C4×C514yes—
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386#124—22no—
387#124C2×C4×C514yescomplemented
388C4×Q8—22no—
389C4×Q8—41no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—41no—
395C4×D4—41no—
396C4×D4—41no—
397C4×D4C2×C4×C514yescomplemented
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4C5×D411yescharacteristic
405C2×C4⋊C4C5×D411yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
407C2×C4⋊C4C23×C511yescharacteristic
408C2×C4⋊C4C23×C511yescharacteristic
409C2×C4⋊C4C23×C511yescharacteristic
410C2×C4⋊C4C23×C511yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42C23×C511yescharacteristic
422C2×C42C23×C511yescharacteristic
423C2×C42C23×C511yescharacteristic
424#107—22no—
425#107—22no—
426C4⋊C8C2×C4×C514yescomplemented
427#103—22no—
428#103—41no—
429#103C2×C4×C514yescomplemented
430#102—22no—
431#102—22no—
432#102—41no—
433#102C2×C4×C514yescomplemented
434#102C5×D414yes—
435#97—22no—
436#97—22no—
437C4×C8—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95C5×D411yescharacteristic
444#95C5×D411yescharacteristic
445C22×C5—24no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—42no—
451C22×C5—42no—
452C22×C5—42no—
453C22×C5—42no—
454C22×C5—42no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5C2×C4×D411yescharacteristic
460C22×C5D4211yescharacteristic
461C22×C5#54811yescharacteristic
462C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
463C22×C5#57511yescharacteristic
464C22×C5#57611yescharacteristic
465C22×C5#57811yescharacteristic
466C4×C5—22no—
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—42no—
470C4×C5—42no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—41no—
474C4×C5—41no—
475C4×C5—81no—
476C4×C5—81no—
477C4×C5—81no—
478C4×C5C2×C4×D411yescharacteristic
479C4×C5#52011yescharacteristic
480C4×C5#54711yescharacteristic
481C4×C5#55311yescharacteristic
482C24—21no—
483C24—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C22×C4×C512yes—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4C22×C4×C512yes—
499C2×D4C22×C4×C512yes—
500C2×D4C2×C5×D412yes—
501C2×D4C5×#4112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
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—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C24×C511yescharacteristic
527SD16—28no—
528D8—28no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8C22×C4×C512yes—
539C2×C8C22×C4×C512yes—
540C2×C8C2×C5×D412yes—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—41no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—81no—
556C4⋊C4C22×C4×C512yes—
557C4⋊C4C2×C5×D412yes—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—81no—
572C42C22×C4×C512yes—
573C42C5×#4112yes—
574C2×C5—44no—
575C2×C5—82no—
576C2×C5#236111yescharacteristic
577C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
578C2×C5#295111yescharacteristic
579C2×C5#326411yescharacteristic
580C2×C5#326911yescharacteristic
581C2×C5#336711yescharacteristic
582C2×C5#337011yescharacteristic
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C22×C5×D411yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602D4—22no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—41no—
608D4—41no—
609D4C4×C5×D414yes—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—48no—
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×C4C4×C5×D412yes—
649C2×C4C5×AGL(1,ℤ/8)12yes—
650C2×C4C23×C4×C511yescharacteristic
651C2×C4C22×C5×D411yescharacteristic
652C2×C4C2×C5×#4111yescharacteristic
653C2×C4C2×C5×#4111yescharacteristic
654C2×C4C5×H(5,𝔽2)11yescharacteristic
655C2×C4C5×2−1+411yescharacteristic
656C8—22no—
657C8—22no—
658C8—22no—
659C8—41no—
660C5#2301111yescharacteristic, direct product factor, Sylow
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C4×C5×D411yescharacteristic
676C22C5×D4211yescharacteristic
677C22C5×#54811yescharacteristic
678C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
679C22C5×#57511yescharacteristic
680C22C5×#57611yescharacteristic
681C22C5×#57811yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—42no—
687C4—41no—
688C4—41no—
689C4—42no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4C2×C4×C5×D411yescharacteristic
695C4C5×#52011yescharacteristic
696C4C5×#54711yescharacteristic
697C4C5×#55311yescharacteristic
698C2—44no—
699C2—82no—
700C2C5×#236111yescharacteristic
701C2C4×C5×AGL(1,ℤ/8)11yescharacteristic
702C2C5×#295111yescharacteristic
703C2C5×#326411yescharacteristic
704C2C5×#326911yescharacteristic
705C2C5×#336711yescharacteristic
706C2C5×#337011yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#440C2semidirect
4. C5×#2367C2semidirect
5. C5×D4×C4⋊C4C2semidirect
6. C5×#1959C2semidirect
7. C5×#1947C2semidirect
8. C5×#1936C2semidirect
9. C5×#1933C2semidirect
11. C5×#1877C2semidirect
12. C5×#1863C2semidirect
13. C5×#1862C2semidirect
14. C5×#1771C2semidirect
15. C5×#1762C2semidirect
25. C5×#463C4semidirect
62. #23011C5direct (N × H)
72. C2×C5×SD16C2×C4semidirect
81. C5×#124C2×C4semidirect
91. C4×C5×D4C2×C4semidirect
120. C5×C4⋊C8C2×C4semidirect
123. C5×#103C2×C4semidirect
127. C5×#102C2×C4semidirect
140. C2×#440C2×C5semidirect
142. #2367C2×C5semidirect
143. D4×C4⋊C4C2×C5semidirect
144. #1959C2×C5semidirect
145. #1947C2×C5semidirect
146. #1936C2×C5semidirect
147. #1933C2×C5semidirect
149. #1877C2×C5semidirect
150. #1863C2×C5semidirect
151. #1862C2×C5semidirect
152. #1771C2×C5semidirect
153. #1762C2×C5semidirect
255. #463C4×C5semidirect
378. C2×SD16C2×C4×C5semidirect
387. #124C2×C4×C5semidirect
397. C4×D4C2×C4×C5semidirect
426. C4⋊C8C2×C4×C5semidirect
429. #103C2×C4×C5semidirect
433. #102C2×C4×C5semidirect
660. C5#23011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4632
C2×C5×#4402
C2×C4×C5×D82
C5×#23672
C5×D4×C4⋊C42
C5×#19592
C5×#19472
C5×#19362
C5×#19332
C5×#18792
C5×#18772
C5×#18632
C5×#18622
C5×#17712
C5×#17622
#230115