Finite Group Databasebeta

← C5×#21871 #11944591

Subgroups — C5×#21871 #11944591

Order 1280.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic
2C2×C5×#433C211yesmaximal, characteristic, complemented
3C5×#2317C211yesmaximal, characteristic, complemented
4C5×#1993C211yesmaximal, characteristic, complemented
5C5×#1990C211yesmaximal, characteristic, complemented
6C5×#1959C211yesmaximal, characteristic, complemented
7C5×#1958C211yesmaximal, characteristic, complemented
8C5×#1875C211yesmaximal, characteristic
9C5×#1874C211yesmaximal, characteristic
10C5×#1873C211yesmaximal, characteristic, complemented
11C5×#1872C211yesmaximal, characteristic, complemented
12C5×#1805C211yesmaximal, characteristic, complemented
13C5×#1804C211yesmaximal, characteristic, complemented
14C5×#1803C211yesmaximal, characteristic, complemented
15C5×#1802C211yesmaximal, characteristic, complemented
16C5×#542—24no—
17C5×#542C418yescomplemented
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×#126—21no—
20C2×C5×#124—21no—
21C2×C5×#124C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#433—24no—
32C2×C5×C4⋊C8C2211yescharacteristic
33C2×C5×C4⋊C8C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×#102C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×C22⋊C8C2211yescharacteristic
43C2×C5×C22⋊C8C2211yescharacteristic
44C2×C5×#97C2211yescharacteristic
45C2×C4×C5×C8C2211yescharacteristic
46C5×#389—21no—
47C5×#389—21no—
48C5×#385—21no—
49C5×#385—21no—
50C5×#384C2211yescharacteristic
51C5×#384C2211yescharacteristic
52C5×#382C2211yescharacteristic
53C5×#382C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62#21871C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×Q8—21no—
64C22×C5×Q8C2311yescharacteristic
65C22×C5×D4—21no—
66C22×C5×D4C2311yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C5×C4⋊Q8—22no—
75C5×C4⋊Q8C2×C414yescomplemented
76C5×#126—28no—
77C5×#124—28no—
78C5×#124—22no—
79C5×#124C2×C414yescomplemented
80C5×#123—28no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—28no—
83C5×C22⋊Q8C2×C414yes—
84C5×#121—22no—
85C5×#121C2×C414yes—
86C4×C5×Q8—22no—
87C4×C5×Q8C2×C414yescomplemented
88C4×C5×D4—22no—
89C4×C5×D4C2×C414yescomplemented
90C5×#117—41no—
91C5×#117—41no—
92C5×#117C2×C414yes—
93C5×#117D414yes—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—41no—
103C2×C5×C4⋊C4—41no—
104C2×C5×C4⋊C4D411yescharacteristic
105C2×C5×C4⋊C4D411yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4D411yescharacteristic
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C42×C5—21no—
121C2×C42×C5—21no—
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124C5×C4⋊C8—22no—
125C5×C4⋊C8—22no—
126C5×#103—41no—
127C5×#103—41no—
128C5×#103—41no—
129C5×#103—41no—
130C5×#102—41no—
131C5×#102—41no—
132C5×#102—41no—
133C5×#102—41no—
134C5×C22⋊C8—22no—
135C5×C22⋊C8—22no—
136C5×#97—22no—
137C4×C5×C8—22no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C5×#95—21no—
142C2×#542C2×C511yescharacteristic
143C2×#433C2×C511yescharacteristic, complemented
144#2317C2×C511yescharacteristic, complemented
145#1993C2×C511yescharacteristic, complemented
146#1990C2×C511yescharacteristic, complemented
147#1959C2×C511yescharacteristic, complemented
148#1958C2×C511yescharacteristic, complemented
149#1875C2×C511yescharacteristic
150#1874C2×C511yescharacteristic
151#1873C2×C511yescharacteristic, complemented
152#1872C2×C511yescharacteristic, complemented
153#1805C2×C511yescharacteristic, complemented
154#1804C2×C511yescharacteristic, complemented
155#1803C2×C511yescharacteristic, complemented
156#1802C2×C511yescharacteristic, complemented
157C24×C5—21no—
158C24×C5C2×D411yescharacteristic
159C2×C5×Q8—24no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—81no—
166C2×C5×Q8—81no—
167C2×C5×Q8C22×C412yes—
168C2×C5×D4—24no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—81no—
175C2×C5×D4—81no—
176C2×C5×D4C22×C412yes—
177C22×C4×C5—21no—
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—24no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—42no—
190C22×C4×C5—81no—
191C22×C4×C5—81no—
192C22×C4×C5—81no—
193C22×C4×C5—81no—
194C22×C4×C5C22×C412yes—
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D412yes—
201C22×C4×C5C2411yescharacteristic
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×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8—21no—
213C2×C5×C8—21no—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4—81no—
229C5×C4⋊C4—81no—
230C5×C4⋊C4—81no—
231C5×C4⋊C4—81no—
232C5×C4⋊C4C22⋊C414yes—
233C5×C4⋊C4C22⋊C414yes—
234C5×C4⋊C4C22×C412yes—
235C5×C4⋊C4C22×C412yes—
236C5×C22⋊C4—24no—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—24no—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—24no—
241C5×C22⋊C4—42no—
242C5×C22⋊C4C22⋊C414yes—
243C5×C22⋊C4C22⋊C414yes—
244C42×C5—24no—
245C42×C5—42no—
246C42×C5C22×C412yes—
247C42×C5C22×C412yes—
248C42×C5C2×D412yes—
249C42×C5C2×D412yes—
250#542—24no—
251#542C4×C518yescomplemented
252C2×C4⋊Q8C22×C511yescharacteristic
253C2×#126—21no—
254C2×#124—21no—
255C2×#124C22×C511yescharacteristic
256C2×#123—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C22×C511yescharacteristic
259C2×#121C22×C511yescharacteristic
260C2×C4×Q8C22×C511yescharacteristic
261C2×C4×D4C22×C511yescharacteristic
262C2×#117C22×C511yescharacteristic
263C2×#117C22×C511yescharacteristic
264C22×C4⋊C4C22×C511yescharacteristic
265#433—24no—
266C2×C4⋊C8C22×C511yescharacteristic
267C2×C4⋊C8C22×C511yescharacteristic
268C2×#103C22×C511yescharacteristic
269C2×#103C22×C511yescharacteristic
270C2×#103C22×C511yescharacteristic
271C2×#103C22×C511yescharacteristic
272C2×#102C22×C511yescharacteristic
273C2×#102C22×C511yescharacteristic
274C2×#102C22×C511yescharacteristic
275C2×#102C22×C511yescharacteristic
276C2×C22⋊C8C22×C511yescharacteristic
277C2×C22⋊C8C22×C511yescharacteristic
278C2×#97C22×C511yescharacteristic
279C2×C4×C8C22×C511yescharacteristic
280#389—21no—
281#389—21no—
282#385—21no—
283#385—21no—
284#384C22×C511yescharacteristic
285#384C22×C511yescharacteristic
286#382C22×C511yescharacteristic
287#382C22×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
296C23×C5—21no—
297C23×C5—21no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—22no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5C2×C22⋊C412yes—
310C23×C5C22×D411yescharacteristic
311C5×Q8—22no—
312C5×Q8—22no—
313C5×Q8—41no—
314C5×Q8—41no—
315C5×Q8—84no—
316C5×D4—22no—
317C5×D4—22no—
318C5×D4—41no—
319C5×D4—41no—
320C5×D4—84no—
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—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
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—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—41no—
355C2×C4×C5—41no—
356C2×C4×C5—84no—
357C2×C4×C5—84no—
358C2×C4×C5C2×C22⋊C412yes—
359C2×C4×C5C2×C22⋊C412yes—
360C2×C4×C5C2×C22⋊C412yes—
361C2×C4×C5C2×C22⋊C412yes—
362C2×C4×C5C2×C22⋊C412yes—
363C2×C4×C5C23×C411yescharacteristic
364C2×C4×C5C22×D411yescharacteristic
365C2×C4×C5H(5,𝔽2)11yescharacteristic
366C2×C4×C5H(5,𝔽2)11yescharacteristic
367C2×C4×C52−1+411yescharacteristic
368C2×C4×C52−1+411yescharacteristic
369C5×C8—41no—
370C5×C8—41no—
371C5×C8—41no—
372C5×C8—41no—
373C22×Q8—21no—
374C22×Q8C23×C511yescharacteristic
375C22×D4—21no—
376C22×D4C23×C511yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C23×C4C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C22×C8C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C4⋊Q8—22no—
385C4⋊Q8C2×C4×C514yescomplemented
386#126—28no—
387#124—28no—
388#124—22no—
389#124C2×C4×C514yescomplemented
390#123—28no—
391C22⋊Q8—22no—
392C22⋊Q8—28no—
393C22⋊Q8C2×C4×C514yes—
394#121—22no—
395#121C2×C4×C514yes—
396C4×Q8—22no—
397C4×Q8C2×C4×C514yescomplemented
398C4×D4—22no—
399C4×D4C2×C4×C514yescomplemented
400#117—41no—
401#117—41no—
402#117C2×C4×C514yes—
403#117C5×D414yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4C5×D411yescharacteristic
415C2×C4⋊C4C5×D411yescharacteristic
416C2×C4⋊C4C23×C511yescharacteristic
417C2×C4⋊C4C23×C511yescharacteristic
418C2×C4⋊C4C23×C511yescharacteristic
419C2×C4⋊C4C23×C511yescharacteristic
420C2×C4⋊C4C23×C511yescharacteristic
421C2×C4⋊C4C23×C511yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4C5×D411yescharacteristic
429C2×C22⋊C4C5×D411yescharacteristic
430C2×C42—21no—
431C2×C42—21no—
432C2×C42C23×C511yescharacteristic
433C2×C42C23×C511yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—22no—
436#103—41no—
437#103—41no—
438#103—41no—
439#103—41no—
440#102—41no—
441#102—41no—
442#102—41no—
443#102—41no—
444C22⋊C8—22no—
445C22⋊C8—22no—
446#97—22no—
447C4×C8—22no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—42no—
460C22×C5—42no—
461C22×C5—42no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5C22×C22⋊C411yescharacteristic
467C22×C5#53511yescharacteristic
468C22×C5#53611yescharacteristic
469C22×C5#57611yescharacteristic
470C22×C5#57711yescharacteristic
471C22×C5#57711yescharacteristic
472C22×C5#57811yescharacteristic
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—22no—
476C4×C5—22no—
477C4×C5—22no—
478C4×C5—42no—
479C4×C5—42no—
480C4×C5—42no—
481C4×C5—81no—
482C4×C5—81no—
483C4×C5—81no—
484C4×C5—81no—
485C4×C5#52011yescharacteristic
486C4×C5#52011yescharacteristic
487C4×C5#53711yescharacteristic
488C4×C5#53711yescharacteristic
489C24—21no—
490C24C2×C5×D411yescharacteristic
491C2×Q8—24no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8C22×C4×C512yes—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4C22×C4×C512yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C22×C4×C512yes—
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D411yescharacteristic
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D412yes—
533C22×C4C24×C511yescharacteristic
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4C5×C22⋊C414yes—
565C4⋊C4C5×C22⋊C414yes—
566C4⋊C4C22×C4×C512yes—
567C4⋊C4C22×C4×C512yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—42no—
574C22⋊C4C5×C22⋊C414yes—
575C22⋊C4C5×C22⋊C414yes—
576C42—24no—
577C42—42no—
578C42C22×C4×C512yes—
579C42C22×C4×C512yes—
580C42C2×C5×D412yes—
581C42C2×C5×D412yes—
582C2×C5—42no—
583C2×C5—82no—
584C2×C5#231111yescharacteristic
585C2×C5#289711yescharacteristic
586C2×C5#289811yescharacteristic
587C2×C5#322411yescharacteristic
588C2×C5#322511yescharacteristic
589C2×C5#324311yescharacteristic
590C2×C5#324411yescharacteristic
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—22no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C2×C5×C22⋊C412yes—
605C23C22×C5×D411yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—41no—
609Q8—41no—
610Q8—84no—
611D4—22no—
612D4—22no—
613D4—41no—
614D4—41no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
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—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
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—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4—84no—
653C2×C4C2×C5×C22⋊C412yes—
654C2×C4C2×C5×C22⋊C412yes—
655C2×C4C2×C5×C22⋊C412yes—
656C2×C4C2×C5×C22⋊C412yes—
657C2×C4C2×C5×C22⋊C412yes—
658C2×C4C23×C4×C511yescharacteristic
659C2×C4C22×C5×D411yescharacteristic
660C2×C4C5×H(5,𝔽2)11yescharacteristic
661C2×C4C5×H(5,𝔽2)11yescharacteristic
662C2×C4C5×2−1+411yescharacteristic
663C2×C4C5×2−1+411yescharacteristic
664C8—41no—
665C8—41no—
666C8—41no—
667C8—41no—
668C5#2187111yescharacteristic, direct product factor, Sylow
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C5×C22⋊C411yescharacteristic
684C22C5×#53511yescharacteristic
685C22C5×#53611yescharacteristic
686C22C5×#57611yescharacteristic
687C22C5×#57711yescharacteristic
688C22C5×#57711yescharacteristic
689C22C5×#57811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C5×#52011yescharacteristic
703C4C5×#52011yescharacteristic
704C4C5×#53711yescharacteristic
705C4C5×#53711yescharacteristic
706C2—42no—
707C2—82no—
708C2C5×#231111yescharacteristic
709C2C5×#289711yescharacteristic
710C2C5×#289811yescharacteristic
711C2C5×#322411yescharacteristic
712C2C5×#322511yescharacteristic
713C2C5×#324311yescharacteristic
714C2C5×#324411yescharacteristic
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 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#433C2semidirect
3. C5×#2317C2semidirect
4. C5×#1993C2semidirect
5. C5×#1990C2semidirect
6. C5×#1959C2semidirect
7. C5×#1958C2semidirect
10. C5×#1873C2semidirect
11. C5×#1872C2semidirect
12. C5×#1805C2semidirect
13. C5×#1804C2semidirect
14. C5×#1803C2semidirect
15. C5×#1802C2semidirect
17. C5×#542C4semidirect
62. #21871C5direct (N × H)
75. C5×C4⋊Q8C2×C4semidirect
79. C5×#124C2×C4semidirect
87. C4×C5×Q8C2×C4semidirect
89. C4×C5×D4C2×C4semidirect
143. C2×#433C2×C5semidirect
144. #2317C2×C5semidirect
145. #1993C2×C5semidirect
146. #1990C2×C5semidirect
147. #1959C2×C5semidirect
148. #1958C2×C5semidirect
151. #1873C2×C5semidirect
152. #1872C2×C5semidirect
153. #1805C2×C5semidirect
154. #1804C2×C5semidirect
155. #1803C2×C5semidirect
156. #1802C2×C5semidirect
251. #542C4×C5semidirect
385. C4⋊Q8C2×C4×C5semidirect
389. #124C2×C4×C5semidirect
397. C4×Q8C2×C4×C5semidirect
399. C4×D4C2×C4×C5semidirect
668. C5#21871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×C5×#4332
C5×#23172
C5×#19932
C5×#19902
C5×#19592
C5×#19582
C5×#18752
C5×#18742
C5×#18732
C5×#18722
C5×#18052
C5×#18042
C5×#18032
C5×#18022
#218715