Finite Group Databasebeta

← C5×#22711 #11945431

Subgroups — C5×#22711 #11945431

Order 1280.

970 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#435C211yesmaximal, characteristic
2C5×#2352C211yesmaximal, characteristic
3C5×D4×C4⋊C4C211yesmaximal, characteristic
4C5×#1949C211yesmaximal, characteristic, complemented
5C5×#1948C211yesmaximal, characteristic, complemented
6C5×#1854C211yesmaximal, characteristic, complemented
7C5×#1853C211yesmaximal, characteristic, complemented
8C5×#1853C211yesmaximal, characteristic, complemented
9C5×#1852C211yesmaximal, characteristic, complemented
10C5×#1836C211yesmaximal, characteristic, complemented
11C5×#1809C211yesmaximal, characteristic, complemented
12C5×#1807C211yesmaximal, characteristic, complemented
13C5×#1776C211yesmaximal, characteristic, complemented
14C5×#1736C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C4×C5×D4—21no—
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#435C418yescomplemented
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C2×C5×#97C2211yescharacteristic
35C5×#389—21no—
36C5×#388—21no—
37C5×#387—21no—
38C5×#386—21no—
39C5×#385—21no—
40C5×#385—21no—
41C5×#384C2211yescharacteristic
42C5×#382C2211yescharacteristic
43C5×#380C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C5×#380C2211yescharacteristic
47C4×C5×C4⋊C4C2211yescharacteristic
48C4×C5×C4⋊C4C2211yescharacteristic
49C4×C5×C22⋊C4—21no—
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60#22711C511yesmaximal, characteristic, direct product factor, Sylow
61C22×C5×D4D411yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C2×C5×M16—41no—
68C2×C5×M16—41no—
69C2×C5×M16C2×C414yescomplemented
70C22×C5×C8—41no—
71C22×C5×C8—41no—
72C22×C5×C8C2×C414yescomplemented
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C4×C5×D4—44no—
78C4×C5×D4C2×C414yes—
79C4×C5×D4Q814yes—
80C5×#117—22no—
81C5×#117—41no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C5×C22⋊C4D411yescharacteristic
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5—21no—
112C2×C42×C5C2311yescharacteristic
113C5×#107—22no—
114C5×#107—41no—
115C5×#106—22no—
116C5×#106—41no—
117C5×#106—41no—
118C5×#106—41no—
119C5×C4⋊C8C2×C414yescomplemented
120C5×C22⋊C8C2×C414yescomplemented
121C5×C22⋊C8C2×C414yescomplemented
122C5×#97C2×C414yescomplemented
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C2×#435C2×C511yescharacteristic
132#2352C2×C511yescharacteristic
133D4×C4⋊C4C2×C511yescharacteristic
134#1949C2×C511yescharacteristic, complemented
135#1948C2×C511yescharacteristic, complemented
136#1854C2×C511yescharacteristic, complemented
137#1853C2×C511yescharacteristic, complemented
138#1853C2×C511yescharacteristic, complemented
139#1852C2×C511yescharacteristic, complemented
140#1836C2×C511yescharacteristic, complemented
141#1809C2×C511yescharacteristic, complemented
142#1807C2×C511yescharacteristic, complemented
143#1776C2×C511yescharacteristic, complemented
144#1736C2×C511yescharacteristic, complemented
145C2×#340C2×C511yescharacteristic, complemented
146C24×C5C2×D411yescharacteristic
147C24×C5C2×D411yescharacteristic
148C2×C5×D4—22no—
149C2×C5×D4—22no—
150C2×C5×D4C4⋊C414yes—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—42no—
168C22×C4×C5—42no—
169C22×C4×C5—42no—
170C22×C4×C5—42no—
171C22×C4×C5—42no—
172C22×C4×C5—42no—
173C22×C4×C5—81no—
174C22×C4×C5—81no—
175C22×C4×C5—81no—
176C22×C4×C5C22×C412yes—
177C22×C4×C5C22×C412yes—
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×Q812yes—
183C22×C4×C5C2×Q812yes—
184C22×C4×C5C2411yescharacteristic
185C5×M16—44no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—44no—
195C2×C5×C8C22×C412yes—
196C2×C5×C8C22×C412yes—
197C2×C5×C8C22×C412yes—
198C2×C5×C8C22×C412yes—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4C4⋊C414yes—
219C5×C4⋊C4#4112yes—
220C5×C4⋊C4#4112yes—
221C5×C22⋊C4—42no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—81no—
226C5×C22⋊C4C4⋊C414yes—
227C5×C22⋊C4C4⋊C414yes—
228C42×C5—42no—
229C42×C5—42no—
230C42×C5—81no—
231C42×C5C22×C412yes—
232C42×C5C2×Q812yes—
233C22×M16C22×C511yescharacteristic
234C23×C8C22×C511yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4C22×C511yescharacteristic
237C2×#117C22×C511yescharacteristic
238C22×C4⋊C4C22×C511yescharacteristic
239C22×C4⋊C4C22×C511yescharacteristic
240C22×C4⋊C4C22×C511yescharacteristic
241#435C4×C518yescomplemented
242C2×#107C22×C511yescharacteristic
243C2×#107C22×C511yescharacteristic
244C2×#106C22×C511yescharacteristic
245C2×#106C22×C511yescharacteristic
246C2×#106C22×C511yescharacteristic
247C2×#106C22×C511yescharacteristic
248C2×C4⋊C8C22×C511yescharacteristic
249C2×C22⋊C8C22×C511yescharacteristic
250C2×C22⋊C8C22×C511yescharacteristic
251C2×#97C22×C511yescharacteristic
252#389—21no—
253#388—21no—
254#387—21no—
255#386—21no—
256#385—21no—
257#385—21no—
258#384C22×C511yescharacteristic
259#382C22×C511yescharacteristic
260#380C22×C511yescharacteristic
261#380C22×C511yescharacteristic
262#380C22×C511yescharacteristic
263#380C22×C511yescharacteristic
264C4×C4⋊C4C22×C511yescharacteristic
265C4×C4⋊C4C22×C511yescharacteristic
266C4×C22⋊C4—21no—
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277C23×C5—21no—
278C23×C5—21no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5C2×C4⋊C412yes—
288C23×C5C2×C4⋊C412yes—
289C23×C5AGL(1,ℤ/8)12yes—
290C23×C5#13712yes—
291C23×C5C22×D411yescharacteristic
292C5×D4—28no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—84no—
334C2×C4×C5—84no—
335C2×C4×C5—84no—
336C2×C4×C5C2×C4⋊C412yes—
337C2×C4×C5C2×C4⋊C412yes—
338C2×C4×C5C2×C4⋊C412yes—
339C2×C4×C5C2×C4⋊C412yes—
340C2×C4×C5C23×C411yescharacteristic
341C2×C4×C5C22×Q811yescharacteristic
342C2×C4×C5C2×#4111yescharacteristic
343C2×C4×C5C2×#4111yescharacteristic
344C2×C4×C5H(5,𝔽2)11yescharacteristic
345C2×C4×C5H(5,𝔽2)11yescharacteristic
346C5×C8—22no—
347C5×C8—22no—
348C5×C8—22no—
349C5×C8—22no—
350C22×D4C5×D411yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4C23×C511yescharacteristic
355C23×C4C23×C511yescharacteristic
356C2×M16—41no—
357C2×M16—41no—
358C2×M16C2×C4×C514yescomplemented
359C22×C8—41no—
360C22×C8—41no—
361C22×C8C2×C4×C514yescomplemented
362C22×C8C23×C511yescharacteristic
363C22×C8C23×C511yescharacteristic
364C22×C8C23×C511yescharacteristic
365C22×C8C23×C511yescharacteristic
366C4×D4—44no—
367C4×D4C2×C4×C514yes—
368C4×D4C5×Q814yes—
369#117—22no—
370#117—41no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4C5×D411yescharacteristic
383C2×C4⋊C4C23×C511yescharacteristic
384C2×C4⋊C4C23×C511yescharacteristic
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4C5×D411yescharacteristic
397C2×C22⋊C4C5×D411yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C511yescharacteristic
402#107—22no—
403#107—41no—
404#106—22no—
405#106—41no—
406#106—41no—
407#106—41no—
408C4⋊C8C2×C4×C514yescomplemented
409C22⋊C8C2×C4×C514yescomplemented
410C22⋊C8C2×C4×C514yescomplemented
411#97C2×C4×C514yescomplemented
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420C22×C5—22no—
421C22×C5—22no—
422C22×C5—22no—
423C22×C5—22no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5#42814yes—
434C22×C5C22×C4⋊C411yescharacteristic
435C22×C5#54611yescharacteristic
436C22×C5#54611yescharacteristic
437C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
438C22×C5C2×#13711yescharacteristic
439C22×C5#57711yescharacteristic
440C22×C5#57711yescharacteristic
441C4×C5—22no—
442C4×C5—22no—
443C4×C5—22no—
444C4×C5—22no—
445C4×C5—42no—
446C4×C5—42no—
447C4×C5—81no—
448C4×C5—81no—
449C4×C5—81no—
450C4×C5—81no—
451C4×C5—81no—
452C4×C5—81no—
453C4×C5C4×#4111yescharacteristic
454C4×C5#51811yescharacteristic
455C4×C5#55411yescharacteristic
456C4×C5#55411yescharacteristic
457C24C2×C5×D411yescharacteristic
458C24C2×C5×D411yescharacteristic
459C2×D4—22no—
460C2×D4—22no—
461C2×D4C5×C4⋊C414yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4C22×C4×C512yes—
488C22×C4C22×C4×C512yes—
489C22×C4C2×C5×D411yescharacteristic
490C22×C4C2×C5×D411yescharacteristic
491C22×C4C2×C5×D411yescharacteristic
492C22×C4C2×C5×D411yescharacteristic
493C22×C4C2×C5×Q812yes—
494C22×C4C2×C5×Q812yes—
495C22×C4C24×C511yescharacteristic
496M16—44no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—44no—
506C2×C8C22×C4×C512yes—
507C2×C8C22×C4×C512yes—
508C2×C8C22×C4×C512yes—
509C2×C8C22×C4×C512yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—81no—
529C4⋊C4C5×C4⋊C414yes—
530C4⋊C4C5×#4112yes—
531C4⋊C4C5×#4112yes—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4C5×C4⋊C414yes—
538C22⋊C4C5×C4⋊C414yes—
539C42—42no—
540C42—42no—
541C42—81no—
542C42C22×C4×C512yes—
543C42C2×C5×Q812yes—
544C2×C5—24no—
545C2×C5—42no—
546C2×C5#234911yescharacteristic
547C2×C5C2×#42811yescharacteristic
548C2×C5#291211yescharacteristic
549C2×C5#330611yescharacteristic
550C2×C5#331011yescharacteristic
551C2×C5#331611yescharacteristic
552C2×C5#332011yescharacteristic
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C2×C5×C4⋊C412yes—
564C23C2×C5×C4⋊C412yes—
565C23C5×AGL(1,ℤ/8)12yes—
566C23C5×#13712yes—
567C23C22×C5×D411yescharacteristic
568D4—28no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4C2×C5×C4⋊C412yes—
613C2×C4C2×C5×C4⋊C412yes—
614C2×C4C2×C5×C4⋊C412yes—
615C2×C4C2×C5×C4⋊C412yes—
616C2×C4C23×C4×C511yescharacteristic
617C2×C4C22×C5×Q811yescharacteristic
618C2×C4C2×C5×#4111yescharacteristic
619C2×C4C2×C5×#4111yescharacteristic
620C2×C4C5×H(5,𝔽2)11yescharacteristic
621C2×C4C5×H(5,𝔽2)11yescharacteristic
622C8—22no—
623C8—22no—
624C8—22no—
625C8—22no—
626C5#2271111yescharacteristic, direct product factor, Sylow
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22C5×#42814yes—
641C22C22×C5×C4⋊C411yescharacteristic
642C22C5×#54611yescharacteristic
643C22C5×#54611yescharacteristic
644C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
645C22C2×C5×#13711yescharacteristic
646C22C5×#57711yescharacteristic
647C22C5×#57711yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4C4×C5×#4111yescharacteristic
661C4C5×#51811yescharacteristic
662C4C5×#55411yescharacteristic
663C4C5×#55411yescharacteristic
664C2—24no—
665C2—42no—
666C2C5×#234911yescharacteristic
667C2C2×C5×#42811yescharacteristic
668C2C5×#291211yescharacteristic
669C2C5×#330611yescharacteristic
670C2C5×#331011yescharacteristic
671C2C5×#331611yescharacteristic
672C2C5×#332011yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1949C2semidirect
5. C5×#1948C2semidirect
6. C5×#1854C2semidirect
7. C5×#1853C2semidirect
8. C5×#1853C2semidirect
9. C5×#1852C2semidirect
10. C5×#1836C2semidirect
11. C5×#1809C2semidirect
12. C5×#1807C2semidirect
13. C5×#1776C2semidirect
14. C5×#1736C2semidirect
15. C2×C5×#340C2semidirect
24. C5×#435C4semidirect
60. #22711C5direct (N × H)
69. C2×C5×M16C2×C4semidirect
72. C22×C5×C8C2×C4semidirect
119. C5×C4⋊C8C2×C4semidirect
120. C5×C22⋊C8C2×C4semidirect
121. C5×C22⋊C8C2×C4semidirect
122. C5×#97C2×C4semidirect
134. #1949C2×C5semidirect
135. #1948C2×C5semidirect
136. #1854C2×C5semidirect
137. #1853C2×C5semidirect
138. #1853C2×C5semidirect
139. #1852C2×C5semidirect
140. #1836C2×C5semidirect
141. #1809C2×C5semidirect
142. #1807C2×C5semidirect
143. #1776C2×C5semidirect
144. #1736C2×C5semidirect
145. C2×#340C2×C5semidirect
241. #435C4×C5semidirect
358. C2×M16C2×C4×C5semidirect
361. C22×C8C2×C4×C5semidirect
408. C4⋊C8C2×C4×C5semidirect
409. C22⋊C8C2×C4×C5semidirect
410. C22⋊C8C2×C4×C5semidirect
411. #97C2×C4×C5semidirect
626. C5#22711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4352
C5×#23522
C5×D4×C4⋊C42
C5×#19492
C5×#19482
C5×#18542
C5×#18532
C5×#18522
C5×#18362
C5×#18092
C5×#18072
C5×#17762
C5×#17362
C2×C5×#3402
#227115