Finite Group Databasebeta

← C5×#22676 #11945396

Subgroups — C5×#22676 #11945396

Order 1280.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#442C211yesmaximal, characteristic
2C2×C5×#442C211yesmaximal, characteristic
3C2×C4×C5×D8C211yesmaximal, characteristic
4C5×#2349C211yesmaximal, characteristic, complemented
5C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
6C5×#1944C211yesmaximal, characteristic, complemented
7C5×#1941C211yesmaximal, characteristic, complemented
8C5×#1864C211yesmaximal, characteristic, complemented
9C5×#1864C211yesmaximal, characteristic, complemented
10C5×#1862C211yesmaximal, characteristic, complemented
11C5×#1862C211yesmaximal, characteristic, complemented
12C5×#1847C211yesmaximal, characteristic, complemented
13C5×#1804C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C5×#1771C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C22×C5×C4⋊C4—21no—
24C5×#442—24no—
25C5×#442C418yescomplemented
26C4×C5×D8—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×#106C2211yescharacteristic
32C2×C5×C4⋊C8C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
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×#389C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#385—21no—
47C5×#385—21no—
48C5×#385—21no—
49C5×#385—21no—
50C5×#384C2211yescharacteristic
51C5×#382C2211yescharacteristic
52C5×#380—21no—
53C5×#380—21no—
54C4×C5×C4⋊C4C2211yescharacteristic
55C2×C5×#95—21no—
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62#22676C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×D4C2311yescharacteristic
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C2×C5×D8C2×C414yes—
72C2×C5×D8D414yes—
73C2×C5×D8Q814yes—
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C4×C5×D4—22no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
84C4×C5×D4—41no—
85C4×C5×D4—41no—
86C4×C5×D4—41no—
87C4×C5×D4—41no—
88C4×C5×D4C2×C414yescomplemented
89C4×C5×D4C2×C414yescomplemented
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—44no—
97C2×C5×C4⋊C4D411yescharacteristic
98C2×C5×C4⋊C4D411yescharacteristic
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⋊C4—21no—
111C2×C42×C5C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C5×#107—22no—
115C5×#107—41no—
116C5×#106—22no—
117C5×#106—41no—
118C5×#106C2×C414yescomplemented
119C5×C4⋊C8—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102C2×C414yescomplemented
125C5×#102C2×C414yescomplemented
126C5×#97—22no—
127C5×#97C2×C414yescomplemented
128C4×C5×C8—22no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95D411yescharacteristic
136C5×#95D411yescharacteristic
137C2×#442C2×C511yescharacteristic
138C2×#442C2×C511yescharacteristic
139C2×C4×D8C2×C511yescharacteristic
140#2349C2×C511yescharacteristic, complemented
141D4×C4⋊C4C2×C511yescharacteristic, complemented
142#1944C2×C511yescharacteristic, complemented
143#1941C2×C511yescharacteristic, complemented
144#1864C2×C511yescharacteristic, complemented
145#1864C2×C511yescharacteristic, complemented
146#1862C2×C511yescharacteristic, complemented
147#1862C2×C511yescharacteristic, complemented
148#1847C2×C511yescharacteristic, complemented
149#1804C2×C511yescharacteristic, complemented
150#1802C2×C511yescharacteristic, complemented
151#1771C2×C511yescharacteristic, complemented
152C24×C5—21no—
153C24×C5—21no—
154C2×C5×D4—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4C22×C412yes—
161C2×C5×D4C22×C412yes—
162C2×C5×D4C2×D412yes—
163C2×C5×D4C2×D412yes—
164C2×C5×D4C2×Q812yes—
165C2×C5×D4C2×Q812yes—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—24no—
169C22×C4×C5—24no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5—42no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—42no—
180C22×C4×C5—42no—
181C22×C4×C5—42no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—81no—
185C22×C4×C5—81no—
186C22×C4×C5—81no—
187C22×C4×C5—81no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2411yescharacteristic
197C5×D8C4⋊C4116yescomplemented
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8C22×C412yes—
207C2×C5×C8C22×C412yes—
208C2×C5×C8C2×D412yes—
209C2×C5×C8C2×Q812yes—
210C5×C4⋊C4—22no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
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—41no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—81no—
226C5×C4⋊C4—81no—
227C5×C4⋊C4—81no—
228C5×C4⋊C4C22×C412yes—
229C5×C4⋊C4C22×C412yes—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—24no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4—42no—
236C42×C5—21no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5C22×C412yes—
241C42×C5#4112yes—
242C22×D8C22×C511yescharacteristic
243C2×C4×D4C22×C511yescharacteristic
244C2×C4×D4C22×C511yescharacteristic
245C2×C4×D4C22×C511yescharacteristic
246C2×C4×D4C22×C511yescharacteristic
247C2×C4×D4C22×C511yescharacteristic
248C2×C4×D4C22×C511yescharacteristic
249C22×C4⋊C4—21no—
250#442—24no—
251#442C4×C518yescomplemented
252C4×D8—24no—
253C2×#107C22×C511yescharacteristic
254C2×#107C22×C511yescharacteristic
255C2×#106C22×C511yescharacteristic
256C2×#106C22×C511yescharacteristic
257C2×#106C22×C511yescharacteristic
258C2×C4⋊C8C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×#102C22×C511yescharacteristic
263C2×#102C22×C511yescharacteristic
264C2×#102C22×C511yescharacteristic
265C2×#97C22×C511yescharacteristic
266C2×#97C22×C511yescharacteristic
267C2×C4×C8C22×C511yescharacteristic
268#389C22×C511yescharacteristic
269#389C22×C511yescharacteristic
270#389C22×C511yescharacteristic
271#389C22×C511yescharacteristic
272#385—21no—
273#385—21no—
274#385—21no—
275#385—21no—
276#384C22×C511yescharacteristic
277#382C22×C511yescharacteristic
278#380—21no—
279#380—21no—
280C4×C4⋊C4C22×C511yescharacteristic
281C2×#95—21no—
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#336C22×C511yescharacteristic
287#336C22×C511yescharacteristic
288C23×C5—22no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5C22×D411yescharacteristic
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—22no—
306C5×D4—22no—
307C5×D4—22no—
308C5×D4—22no—
309C5×D4C2×C4⋊C414yes—
310C5×D4C2×C4⋊C414yescomplemented
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
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—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—48no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
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—84no—
346C2×C4×C5—84no—
347C2×C4×C5—84no—
348C2×C4×C5—84no—
349C2×C4×C5—84no—
350C2×C4×C5C4×D412yes—
351C2×C4×C5C4×D412yes—
352C2×C4×C5AGL(1,ℤ/8)12yes—
353C2×C4×C5C23×C411yescharacteristic
354C2×C4×C5C22×D411yescharacteristic
355C2×C4×C5C22×Q811yescharacteristic
356C2×C4×C5C2×#4111yescharacteristic
357C2×C4×C5H(5,𝔽2)11yescharacteristic
358C2×C4×C52−1+411yescharacteristic
359C5×C8—22no—
360C5×C8—41no—
361C5×C8—41no—
362C5×C8C2×C4⋊C414yescomplemented
363C22×D4C23×C511yescharacteristic
364C22×D4C23×C511yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C2×D8C2×C4×C514yes—
372C2×D8C5×D414yes—
373C2×D8C5×Q814yes—
374C22×C8C23×C511yescharacteristic
375C22×C8C23×C511yescharacteristic
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—41no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—41no—
388C4×D4C2×C4×C514yescomplemented
389C4×D4C2×C4×C514yescomplemented
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4C5×D411yescharacteristic
398C2×C4⋊C4C5×D411yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42C23×C511yescharacteristic
412C2×C42C23×C511yescharacteristic
413C2×C42C23×C511yescharacteristic
414#107—22no—
415#107—41no—
416#106—22no—
417#106—41no—
418#106C2×C4×C514yescomplemented
419C4⋊C8—22no—
420#102—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#102C2×C4×C514yescomplemented
425#102C2×C4×C514yescomplemented
426#97—22no—
427#97C2×C4×C514yescomplemented
428C4×C8—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95C5×D411yescharacteristic
436#95C5×D411yescharacteristic
437C22×C5—24no—
438C22×C5—24no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—42no—
451C22×C5C2×C4×D411yescharacteristic
452C22×C5D4211yescharacteristic
453C22×C5D4×Q811yescharacteristic
454C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C5#57511yescharacteristic
456C22×C5#57611yescharacteristic
457C22×C5#57711yescharacteristic
458C4×C5—22no—
459C4×C5—22no—
460C4×C5—22no—
461C4×C5—42no—
462C4×C5—42no—
463C4×C5—41no—
464C4×C5—41no—
465C4×C5—41no—
466C4×C5—81no—
467C4×C5—81no—
468C4×C5—81no—
469C4×C5—81no—
470C4×C5C22×C4⋊C411yescharacteristic
471C4×C5#52011yescharacteristic
472C4×C5#54711yescharacteristic
473C4×C5#55411yescharacteristic
474C24—21no—
475C24—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4C22×C4×C512yes—
483C2×D4C22×C4×C512yes—
484C2×D4C2×C5×D412yes—
485C2×D4C2×C5×D412yes—
486C2×D4C2×C5×Q812yes—
487C2×D4C2×C5×Q812yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4C2×C5×D411yescharacteristic
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C2×C5×D411yescharacteristic
515C22×C4C2×C5×D411yescharacteristic
516C22×C4C2×C5×D411yescharacteristic
517C22×C4C2×C5×D411yescharacteristic
518C22×C4C24×C511yescharacteristic
519D8C5×C4⋊C4116yescomplemented
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C22×C4×C512yes—
529C2×C8C22×C4×C512yes—
530C2×C8C2×C5×D412yes—
531C2×C8C2×C5×Q812yes—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—41no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4C22×C4×C512yes—
551C4⋊C4C22×C4×C512yes—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42C22×C4×C512yes—
563C42C5×#4112yes—
564C2×C5—44no—
565C2×C5—44no—
566C2×C5D4×C4⋊C411yescharacteristic
567C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
568C2×C5#294611yescharacteristic
569C2×C5#326411yescharacteristic
570C2×C5#326711yescharacteristic
571C2×C5#338411yescharacteristic
572C2×C5#338911yescharacteristic
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C22×C5×D411yescharacteristic
588D4—22no—
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4C2×C5×C4⋊C414yes—
595D4C2×C5×C4⋊C414yescomplemented
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—48no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4C4×C5×D412yes—
636C2×C4C4×C5×D412yes—
637C2×C4C5×AGL(1,ℤ/8)12yes—
638C2×C4C23×C4×C511yescharacteristic
639C2×C4C22×C5×D411yescharacteristic
640C2×C4C22×C5×Q811yescharacteristic
641C2×C4C2×C5×#4111yescharacteristic
642C2×C4C5×H(5,𝔽2)11yescharacteristic
643C2×C4C5×2−1+411yescharacteristic
644C8—22no—
645C8—41no—
646C8—41no—
647C8C2×C5×C4⋊C414yescomplemented
648C5#2267611yescharacteristic, direct product factor, Sylow
649C22—24no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C2×C4×C5×D411yescharacteristic
664C22C5×D4211yescharacteristic
665C22C5×D4×Q811yescharacteristic
666C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
667C22C5×#57511yescharacteristic
668C22C5×#57611yescharacteristic
669C22C5×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C22×C5×C4⋊C411yescharacteristic
683C4C5×#52011yescharacteristic
684C4C5×#54711yescharacteristic
685C4C5×#55411yescharacteristic
686C2—44no—
687C2—44no—
688C2C5×D4×C4⋊C411yescharacteristic
689C2C4×C5×AGL(1,ℤ/8)11yescharacteristic
690C2C5×#294611yescharacteristic
691C2C5×#326411yescharacteristic
692C2C5×#326711yescharacteristic
693C2C5×#338411yescharacteristic
694C2C5×#338911yescharacteristic
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
4. C5×#2349C2semidirect
5. C5×D4×C4⋊C4C2semidirect
6. C5×#1944C2semidirect
7. C5×#1941C2semidirect
8. C5×#1864C2semidirect
9. C5×#1864C2semidirect
10. C5×#1862C2semidirect
11. C5×#1862C2semidirect
12. C5×#1847C2semidirect
13. C5×#1804C2semidirect
14. C5×#1802C2semidirect
15. C5×#1771C2semidirect
25. C5×#442C4semidirect
62. #22676C5direct (N × H)
88. C4×C5×D4C2×C4semidirect
89. C4×C5×D4C2×C4semidirect
118. C5×#106C2×C4semidirect
124. C5×#102C2×C4semidirect
125. C5×#102C2×C4semidirect
127. C5×#97C2×C4semidirect
140. #2349C2×C5semidirect
141. D4×C4⋊C4C2×C5semidirect
142. #1944C2×C5semidirect
143. #1941C2×C5semidirect
144. #1864C2×C5semidirect
145. #1864C2×C5semidirect
146. #1862C2×C5semidirect
147. #1862C2×C5semidirect
148. #1847C2×C5semidirect
149. #1804C2×C5semidirect
150. #1802C2×C5semidirect
151. #1771C2×C5semidirect
197. C5×D8C4⋊C4semidirect
251. #442C4×C5semidirect
310. C5×D4C2×C4⋊C4semidirect
362. C5×C8C2×C4⋊C4semidirect
388. C4×D4C2×C4×C5semidirect
389. C4×D4C2×C4×C5semidirect
418. #106C2×C4×C5semidirect
424. #102C2×C4×C5semidirect
425. #102C2×C4×C5semidirect
427. #97C2×C4×C5semidirect
519. D8C5×C4⋊C4semidirect
595. D4C2×C5×C4⋊C4semidirect
647. C8C2×C5×C4⋊C4semidirect
648. C5#22676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4422
C2×C4×C5×D82
C5×#23492
C5×D4×C4⋊C42
C5×#19442
C5×#19412
C5×#18642
C5×#18622
C5×#18472
C5×#18042
C5×#18022
C5×#17712
#226765