Finite Group Databasebeta

← C5×#25916 #11948636

Subgroups — C5×#25916 #11948636

Order 1280.

1052 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#544C211yesmaximal, characteristic, complemented
2C2×C5×#489C211yesmaximal, characteristic, complemented
3C2×C5×#488C211yesmaximal, characteristic, complemented
4C5×#2620C211yesmaximal, characteristic
5C5×#2026C211yesmaximal, characteristic, complemented
6C5×#2025C211yesmaximal, characteristic, complemented
7C5×#2024C211yesmaximal, characteristic, complemented
8C5×#2023C211yesmaximal, characteristic, complemented
9C5×#1992C211yesmaximal, characteristic, complemented
10C5×#1990C211yesmaximal, characteristic, complemented
11C5×#1875C211yesmaximal, characteristic
12C5×#1874C211yesmaximal, characteristic
13C5×#1873C211yesmaximal, characteristic, complemented
14C5×#1872C211yesmaximal, characteristic, complemented
15C5×#1750C211yesmaximal, characteristic, complemented
16C5×#544—24no—
17C5×#544—24no—
18C2×C5×C4⋊Q8—21no—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#125—21no—
22C2×C5×#125C2211yescharacteristic
23C2×C5×#125C2211yescharacteristic
24C2×C5×#124C2211yescharacteristic
25C2×C5×C22⋊Q8—21no—
26C2×C5×C22⋊Q8—21no—
27C2×C5×C22⋊Q8C2211yescharacteristic
28C2×C5×#121C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C2×C5×#117C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic
32C5×#489—24no—
33C5×#488—24no—
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×#396—21no—
47C5×#396—21no—
48C5×#394—21no—
49C5×#394—21no—
50C5×#391C2211yescharacteristic
51C5×#390C2211yescharacteristic
52C5×#384C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#25916C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8—21no—
66C22×C5×Q8C2311yescharacteristic
67C22×C5×D4—21no—
68C22×C5×D4C2311yescharacteristic
69C23×C4×C5—21no—
70C23×C4×C5C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×C4⋊Q8—28no—
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8—22no—
78C5×C4⋊Q8—22no—
79C5×C4⋊Q8D414yescomplemented
80C5×#125—28no—
81C5×#125—22no—
82C5×#125—22no—
83C5×#125—22no—
84C5×#125D414yescomplemented
85C5×#124—22no—
86C5×#124—22no—
87C5×C22⋊Q8—28no—
88C5×C22⋊Q8—28no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×#121—22no—
92C5×#121—22no—
93C5×#117—22no—
94C5×#117—22no—
95C5×#117—22no—
96C5×#117—22no—
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—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⋊C4D411yescharacteristic
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C5×C22⋊C4D411yescharacteristic
126C2×C42×C5—21no—
127C2×C42×C5C2311yescharacteristic
128C2×C42×C5C2311yescharacteristic
129C5×#103—22no—
130C5×#103—22no—
131C5×#103—22no—
132C5×#103—22no—
133C5×#102—22no—
134C5×#102—22no—
135C5×#102—22no—
136C5×#102—22no—
137C5×C22⋊C8—22no—
138C5×C22⋊C8—22no—
139C5×#97—22no—
140C4×C5×C8—22no—
141C5×#95—21no—
142C5×#95—21no—
143C2×#544C2×C511yescharacteristic, complemented
144C2×#489C2×C511yescharacteristic, complemented
145C2×#488C2×C511yescharacteristic, complemented
146#2620C2×C511yescharacteristic
147#2026C2×C511yescharacteristic, complemented
148#2025C2×C511yescharacteristic, complemented
149#2024C2×C511yescharacteristic, complemented
150#2023C2×C511yescharacteristic, complemented
151#1992C2×C511yescharacteristic, complemented
152#1990C2×C511yescharacteristic, complemented
153#1875C2×C511yescharacteristic
154#1874C2×C511yescharacteristic
155#1873C2×C511yescharacteristic, complemented
156#1872C2×C511yescharacteristic, complemented
157#1750C2×C511yescharacteristic, complemented
158C24×C5—21no—
159C24×C5C2×D411yescharacteristic
160C2×C5×Q8—24no—
161C2×C5×Q8—24no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—81no—
169C2×C5×Q8—81no—
170C2×C5×Q8—81no—
171C2×C5×Q8—81no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4—42no—
179C2×C5×D4—81no—
180C2×C5×D4—81no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—24no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—81no—
194C22×C4×C5—81no—
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5#4112yes—
201C22×C4×C5#4112yes—
202C22×C4×C5C2411yescharacteristic
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—
214C2×C5×C8—21no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—24no—
221C5×C4⋊C4—24no—
222C5×C4⋊C4—22no—
223C5×C4⋊C4—22no—
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—42no—
233C5×C4⋊C4—81no—
234C5×C4⋊C4—81no—
235C5×C4⋊C4C2×D412yes—
236C5×C4⋊C4C2×D412yes—
237C5×C4⋊C4C2×D412yes—
238C5×C4⋊C4C2×D412yes—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—22no—
241C5×C22⋊C4—22no—
242C5×C22⋊C4—42no—
243C5×C22⋊C4—42no—
244C5×C22⋊C4—42no—
245C5×C22⋊C4—42no—
246C5×C22⋊C4—81no—
247C5×C22⋊C4—81no—
248C42×C5—24no—
249C42×C5—21no—
250C42×C5—21no—
251C42×C5C2×D412yes—
252C42×C5C2×D412yes—
253#544—24no—
254#544—24no—
255C2×C4⋊Q8—21no—
256C2×C4⋊Q8C22×C511yescharacteristic
257C2×C4⋊Q8C22×C511yescharacteristic
258C2×#125—21no—
259C2×#125C22×C511yescharacteristic
260C2×#125C22×C511yescharacteristic
261C2×#124C22×C511yescharacteristic
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—21no—
264C2×C22⋊Q8C22×C511yescharacteristic
265C2×#121C22×C511yescharacteristic
266C2×#117C22×C511yescharacteristic
267C2×#117C22×C511yescharacteristic
268C22×C4⋊C4C22×C511yescharacteristic
269#489—24no—
270#488—24no—
271C2×#103C22×C511yescharacteristic
272C2×#103C22×C511yescharacteristic
273C2×#103C22×C511yescharacteristic
274C2×#103C22×C511yescharacteristic
275C2×#102C22×C511yescharacteristic
276C2×#102C22×C511yescharacteristic
277C2×#102C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×C22⋊C8C22×C511yescharacteristic
280C2×C22⋊C8C22×C511yescharacteristic
281C2×#97C22×C511yescharacteristic
282C2×C4×C8C22×C511yescharacteristic
283#396—21no—
284#396—21no—
285#394—21no—
286#394—21no—
287#391C22×C511yescharacteristic
288#390C22×C511yescharacteristic
289#384C22×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#336C22×C511yescharacteristic
299#336C22×C511yescharacteristic
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—21no—
305C23×C5—21no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5—41no—
312C23×C5—41no—
313C23×C5#12412yes—
314C23×C5C22×D411yescharacteristic
315C5×Q8—41no—
316C5×Q8—41no—
317C5×Q8—41no—
318C5×Q8—41no—
319C5×Q8—84no—
320C5×Q8—84no—
321C5×D4—41no—
322C5×D4—41no—
323C5×D4—41no—
324C5×D4—41no—
325C5×D4—84no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—21no—
337C2×C4×C5—22no—
338C2×C4×C5—21no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
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—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—84no—
364C2×C4×C5#12012yes—
365C2×C4×C5#12012yes—
366C2×C4×C5#12412yes—
367C2×C4×C5C22×D411yescharacteristic
368C2×C4×C5C22×D411yescharacteristic
369C2×C4×C5C2×#4111yescharacteristic
370C2×C4×C5C2×#4111yescharacteristic
371C2×C4×C52−1+411yescharacteristic
372C2×C4×C52−1+411yescharacteristic
373C5×C8—41no—
374C5×C8—41no—
375C5×C8—41no—
376C5×C8—41no—
377C22×Q8—21no—
378C22×Q8—21no—
379C22×Q8C23×C511yescharacteristic
380C22×D4—21no—
381C22×D4C23×C511yescharacteristic
382C23×C4—21no—
383C23×C4C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386C22×C8C23×C511yescharacteristic
387C22×C8C23×C511yescharacteristic
388C4⋊Q8—28no—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8C5×D414yescomplemented
393#125—28no—
394#125—22no—
395#125—22no—
396#125—22no—
397#125C5×D414yescomplemented
398#124—22no—
399#124—22no—
400C22⋊Q8—28no—
401C22⋊Q8—28no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404#121—22no—
405#121—22no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C5×D411yescharacteristic
423C2×C4⋊C4C5×D411yescharacteristic
424C2×C4⋊C4C23×C511yescharacteristic
425C2×C4⋊C4C23×C511yescharacteristic
426C2×C4⋊C4C23×C511yescharacteristic
427C2×C4⋊C4C23×C511yescharacteristic
428C2×C4⋊C4C23×C511yescharacteristic
429C2×C4⋊C4C23×C511yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4C5×D411yescharacteristic
438C2×C22⋊C4C5×D411yescharacteristic
439C2×C42—21no—
440C2×C42C23×C511yescharacteristic
441C2×C42C23×C511yescharacteristic
442#103—22no—
443#103—22no—
444#103—22no—
445#103—22no—
446#102—22no—
447#102—22no—
448#102—22no—
449#102—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452#97—22no—
453C4×C8—22no—
454#95—21no—
455#95—21no—
456C22×C5—22no—
457C22×C5—22no—
458C22×C5—22no—
459C22×C5—41no—
460C22×C5—41no—
461C22×C5—41no—
462C22×C5—41no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5—81no—
467C22×C5—81no—
468C22×C5—81no—
469C22×C5—81no—
470C22×C5C2×#12011yescharacteristic
471C22×C5C2×#12411yescharacteristic
472C22×C5#53611yescharacteristic
473C22×C5#57611yescharacteristic
474C22×C5#57711yescharacteristic
475C22×C5#57711yescharacteristic
476C22×C5#57811yescharacteristic
477C4×C5—22no—
478C4×C5—22no—
479C4×C5—22no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—42no—
483C4×C5—42no—
484C4×C5—41no—
485C4×C5—42no—
486C4×C5—81no—
487C4×C5—81no—
488C4×C5—81no—
489C4×C5#54811yescharacteristic
490C4×C5#54811yescharacteristic
491C4×C5#54811yescharacteristic
492C4×C5#54811yescharacteristic
493C24—21no—
494C24C2×C5×D411yescharacteristic
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—81no—
504C2×Q8—81no—
505C2×Q8—81no—
506C2×Q8—81no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—81no—
515C2×D4—81no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D411yescharacteristic
534C22×C4C2×C5×D411yescharacteristic
535C22×C4C5×#4112yes—
536C22×C4C5×#4112yes—
537C22×C4C24×C511yescharacteristic
538C2×C8—21no—
539C2×C8—21no—
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—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—22no—
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—42no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4C2×C5×D412yes—
571C4⋊C4C2×C5×D412yes—
572C4⋊C4C2×C5×D412yes—
573C4⋊C4C2×C5×D412yes—
574C22⋊C4—24no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C42—24no—
584C42—21no—
585C42—21no—
586C42C2×C5×D412yes—
587C42C2×C5×D412yes—
588C2×C5—42no—
589C2×C5—161no—
590C2×C5#243611yescharacteristic
591C2×C5#301211yescharacteristic
592C2×C5#301311yescharacteristic
593C2×C5#313611yescharacteristic
594C2×C5#313711yescharacteristic
595C2×C5#324311yescharacteristic
596C2×C5#324411yescharacteristic
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C5×#12412yes—
611C23C22×C5×D411yescharacteristic
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—84no—
617Q8—84no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—84no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
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×C4C5×#12012yes—
662C2×C4C5×#12012yes—
663C2×C4C5×#12412yes—
664C2×C4C22×C5×D411yescharacteristic
665C2×C4C22×C5×D411yescharacteristic
666C2×C4C2×C5×#4111yescharacteristic
667C2×C4C2×C5×#4111yescharacteristic
668C2×C4C5×2−1+411yescharacteristic
669C2×C4C5×2−1+411yescharacteristic
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C5#2591611yescharacteristic, direct product factor, Sylow
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C5×#12011yescharacteristic
690C22C2×C5×#12411yescharacteristic
691C22C5×#53611yescharacteristic
692C22C5×#57611yescharacteristic
693C22C5×#57711yescharacteristic
694C22C5×#57711yescharacteristic
695C22C5×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C5×#54811yescharacteristic
709C4C5×#54811yescharacteristic
710C4C5×#54811yescharacteristic
711C4C5×#54811yescharacteristic
712C2—42no—
713C2—161no—
714C2C5×#243611yescharacteristic
715C2C5×#301211yescharacteristic
716C2C5×#301311yescharacteristic
717C2C5×#313611yescharacteristic
718C2C5×#313711yescharacteristic
719C2C5×#324311yescharacteristic
720C2C5×#324411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#544C2semidirect
2. C2×C5×#489C2semidirect
3. C2×C5×#488C2semidirect
5. C5×#2026C2semidirect
6. C5×#2025C2semidirect
7. C5×#2024C2semidirect
8. C5×#2023C2semidirect
9. C5×#1992C2semidirect
10. C5×#1990C2semidirect
13. C5×#1873C2semidirect
14. C5×#1872C2semidirect
15. C5×#1750C2semidirect
63. #25916C5direct (N × H)
79. C5×C4⋊Q8D4semidirect
84. C5×#125D4semidirect
143. C2×#544C2×C5semidirect
144. C2×#489C2×C5semidirect
145. C2×#488C2×C5semidirect
147. #2026C2×C5semidirect
148. #2025C2×C5semidirect
149. #2024C2×C5semidirect
150. #2023C2×C5semidirect
151. #1992C2×C5semidirect
152. #1990C2×C5semidirect
155. #1873C2×C5semidirect
156. #1872C2×C5semidirect
157. #1750C2×C5semidirect
392. C4⋊Q8C5×D4semidirect
397. #125C5×D4semidirect
674. C5#25916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5442
C2×C5×#4892
C2×C5×#4882
C5×#26202
C5×#20262
C5×#20252
C5×#20242
C5×#20232
C5×#19922
C5×#19902
C5×#18752
C5×#18742
C5×#18732
C5×#18722
C5×#17502
#259165