Finite Group Databasebeta

← C5×#25217 #11947937

Subgroups — C5×#25217 #11947937

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#484C211yesmaximal, characteristic, complemented
2C2×C5×#468C211yesmaximal, characteristic
3C5×#2501C211yesmaximal, characteristic
4C5×#2362C211yesmaximal, characteristic, complemented
5C5×#2083C211yesmaximal, characteristic, complemented
6C5×#2072C211yesmaximal, characteristic, complemented
7C5×#2067C211yesmaximal, characteristic, complemented
8C5×#2055C211yesmaximal, characteristic, complemented
9C5×#1947C211yesmaximal, characteristic, complemented
10C5×#1925C211yesmaximal, characteristic, complemented
11C5×#1880C211yesmaximal, characteristic, complemented
12C5×#1875C211yesmaximal, characteristic
13C5×#1851C211yesmaximal, characteristic, complemented
14C5×#1803C211yesmaximal, characteristic, complemented
15C5×#1736C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×#123—21no—
19C2×C5×#123—21no—
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C5×#117C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C5×#484—24no—
26C5×#468—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C5×#399—21no—
40C5×#399—21no—
41C5×#391C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#388—21no—
46C5×#388—21no—
47C5×#387—21no—
48C5×#384C2211yescharacteristic
49C5×#384C2211yescharacteristic
50C4×C5×C4⋊C4—21no—
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25217C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×D4—21no—
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5C2311yescharacteristic
67C2×C5×SD16—22no—
68C2×C5×SD16—22no—
69C2×C5×SD16—41no—
70C2×C5×M16—22no—
71C2×C5×M16—22no—
72C2×C5×M16—41no—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×#123—44no—
78C5×#123—44no—
79C5×C22⋊Q8—22no—
80C5×C22⋊Q8D414yes—
81C5×#121—22no—
82C5×#121—22no—
83C4×C5×Q8—22no—
84C4×C5×Q8—41no—
85C5×#117—22no—
86C5×#117—41no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
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—21no—
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
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⋊C4D411yescharacteristic
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C2×C42×C5C2311yescharacteristic
117C5×#107—22no—
118C5×#107—22no—
119C5×#107—22no—
120C5×C4⋊C8—22no—
121C5×C4⋊C8—41no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#103—22no—
125C5×#102—22no—
126C5×#102—22no—
127C5×#102—41no—
128C5×C22⋊C8—22no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95D411yescharacteristic
134C5×#95D411yescharacteristic
135C2×#484C2×C511yescharacteristic, complemented
136C2×#468C2×C511yescharacteristic
137#2501C2×C511yescharacteristic
138#2362C2×C511yescharacteristic, complemented
139#2083C2×C511yescharacteristic, complemented
140#2072C2×C511yescharacteristic, complemented
141#2067C2×C511yescharacteristic, complemented
142#2055C2×C511yescharacteristic, complemented
143#1947C2×C511yescharacteristic, complemented
144#1925C2×C511yescharacteristic, complemented
145#1880C2×C511yescharacteristic, complemented
146#1875C2×C511yescharacteristic
147#1851C2×C511yescharacteristic, complemented
148#1803C2×C511yescharacteristic, complemented
149#1736C2×C511yescharacteristic, complemented
150C24×C5—21no—
151C24×C5C2×D411yescharacteristic
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8C2×D412yes—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—42no—
165C2×C5×D4—42no—
166C2×C5×D4—42no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—42no—
179C22×C4×C5—42no—
180C22×C4×C5—42no—
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5#4112yes—
188C22×C4×C5C2411yescharacteristic
189C5×SD16—44no—
190C5×M16—44no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8#4112yes—
203C5×C4⋊C4—24no—
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—21no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—42no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4C2×D412yes—
222C5×C4⋊C4#4112yes—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—42no—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—42no—
237C42×C5—42no—
238C42×C5—42no—
239C22×SD16C22×C511yescharacteristic
240C22×M16C22×C511yescharacteristic
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8C22×C511yescharacteristic
244C2×#121C22×C511yescharacteristic
245C2×C4×Q8C22×C511yescharacteristic
246C2×#117C22×C511yescharacteristic
247C22×C4⋊C4C22×C511yescharacteristic
248#484—24no—
249#468—24no—
250C2×#107C22×C511yescharacteristic
251C2×#107C22×C511yescharacteristic
252C2×#107C22×C511yescharacteristic
253C2×C4⋊C8C22×C511yescharacteristic
254C2×C4⋊C8C22×C511yescharacteristic
255C2×#103C22×C511yescharacteristic
256C2×#103C22×C511yescharacteristic
257C2×#103C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×C22⋊C8C22×C511yescharacteristic
262#399—21no—
263#399—21no—
264#391C22×C511yescharacteristic
265#390C22×C511yescharacteristic
266#390C22×C511yescharacteristic
267#389C22×C511yescharacteristic
268#388—21no—
269#388—21no—
270#387—21no—
271#384C22×C511yescharacteristic
272#384C22×C511yescharacteristic
273C4×C4⋊C4—21no—
274C4×C4⋊C4C22×C511yescharacteristic
275C4×C22⋊C4C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#336C22×C511yescharacteristic
283#336C22×C511yescharacteristic
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5#12112yes—
298C23×C5C22×D411yescharacteristic
299C5×Q8—22no—
300C5×Q8—22no—
301C5×Q8—41no—
302C5×Q8—41no—
303C5×D4—41no—
304C5×D4—41no—
305C5×D4—41no—
306C5×D4—41no—
307C5×D4—84no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—22no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
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—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#12112yes—
347C2×C4×C5AGL(1,ℤ/8)12yes—
348C2×C4×C5AGL(1,ℤ/8)12yes—
349C2×C4×C5C22×D411yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5C2×#4111yescharacteristic
352C2×C4×C5C2×#4111yescharacteristic
353C2×C4×C5H(5,𝔽2)11yescharacteristic
354C2×C4×C52−1+411yescharacteristic
355C5×C8—22no—
356C5×C8—41no—
357C5×C8—41no—
358C5×C8—41no—
359C22×Q8C23×C511yescharacteristic
360C22×D4—21no—
361C22×D4C23×C511yescharacteristic
362C23×C4—21no—
363C23×C4C23×C511yescharacteristic
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—41no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—41no—
370C22×C8C23×C511yescharacteristic
371C22×C8C23×C511yescharacteristic
372C22×C8C23×C511yescharacteristic
373C22×C8C23×C511yescharacteristic
374#123—44no—
375#123—44no—
376C22⋊Q8—22no—
377C22⋊Q8C5×D414yes—
378#121—22no—
379#121—22no—
380C4×Q8—22no—
381C4×Q8—41no—
382#117—22no—
383#117—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C4⋊C4C23×C511yescharacteristic
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4C5×D411yescharacteristic
408C2×C22⋊C4C5×D411yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C511yescharacteristic
413C2×C42C23×C511yescharacteristic
414#107—22no—
415#107—22no—
416#107—22no—
417C4⋊C8—22no—
418C4⋊C8—41no—
419#103—22no—
420#103—22no—
421#103—22no—
422#102—22no—
423#102—22no—
424#102—41no—
425C22⋊C8—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95C5×D411yescharacteristic
431#95C5×D411yescharacteristic
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—22no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—81no—
440C22×C5—81no—
441C22×C5—81no—
442C22×C5—81no—
443C22×C5—81no—
444C22×C5—81no—
445C22×C5—81no—
446C22×C5C2×#12111yescharacteristic
447C22×C5#54611yescharacteristic
448C22×C5#54711yescharacteristic
449C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C5#57811yescharacteristic
452C22×C5#57811yescharacteristic
453C4×C5—22no—
454C4×C5—22no—
455C4×C5—22no—
456C4×C5—41no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5—42no—
460C4×C5—42no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5#52911yescharacteristic
466C4×C5#53911yescharacteristic
467C4×C5#54611yescharacteristic
468C4×C5#54711yescharacteristic
469C24—21no—
470C24C2×C5×D411yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8C2×C5×D412yes—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4C2×C5×D411yescharacteristic
501C22×C4C2×C5×D411yescharacteristic
502C22×C4C2×C5×D411yescharacteristic
503C22×C4C2×C5×D412yes—
504C22×C4C2×C5×D411yescharacteristic
505C22×C4C2×C5×D411yescharacteristic
506C22×C4C5×#4112yes—
507C22×C4C24×C511yescharacteristic
508SD16—44no—
509M16—44no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8C5×#4112yes—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4C2×C5×D412yes—
541C4⋊C4C5×#4112yes—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—42no—
557C42—42no—
558C2×C5—42no—
559C2×C5—161no—
560C2×C5#242511yescharacteristic
561C2×C5#303811yescharacteristic
562C2×C5#304411yescharacteristic
563C2×C5#330811yescharacteristic
564C2×C5#333011yescharacteristic
565C2×C5#334311yescharacteristic
566C2×C5#335311yescharacteristic
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23C5×#12112yes—
581C23C22×C5×D411yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—41no—
585Q8—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—84no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
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—84no—
629C2×C4C5×#12112yes—
630C2×C4C5×AGL(1,ℤ/8)12yes—
631C2×C4C5×AGL(1,ℤ/8)12yes—
632C2×C4C22×C5×D411yescharacteristic
633C2×C4C2×C5×#4111yescharacteristic
634C2×C4C2×C5×#4111yescharacteristic
635C2×C4C2×C5×#4111yescharacteristic
636C2×C4C5×H(5,𝔽2)11yescharacteristic
637C2×C4C5×2−1+411yescharacteristic
638C8—22no—
639C8—41no—
640C8—41no—
641C8—41no—
642C5#2521711yescharacteristic, direct product factor, Sylow
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22C2×C5×#12111yescharacteristic
658C22C5×#54611yescharacteristic
659C22C5×#54711yescharacteristic
660C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
661C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
662C22C5×#57811yescharacteristic
663C22C5×#57811yescharacteristic
664C4—22no—
665C4—22no—
666C4—22no—
667C4—42no—
668C4—41no—
669C4—42no—
670C4—41no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4C5×#52911yescharacteristic
677C4C5×#53911yescharacteristic
678C4C5×#54611yescharacteristic
679C4C5×#54711yescharacteristic
680C2—42no—
681C2—161no—
682C2C5×#242511yescharacteristic
683C2C5×#303811yescharacteristic
684C2C5×#304411yescharacteristic
685C2C5×#330811yescharacteristic
686C2C5×#333011yescharacteristic
687C2C5×#334311yescharacteristic
688C2C5×#335311yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#484C2semidirect
4. C5×#2362C2semidirect
5. C5×#2083C2semidirect
6. C5×#2072C2semidirect
7. C5×#2067C2semidirect
8. C5×#2055C2semidirect
9. C5×#1947C2semidirect
10. C5×#1925C2semidirect
11. C5×#1880C2semidirect
13. C5×#1851C2semidirect
14. C5×#1803C2semidirect
15. C5×#1736C2semidirect
61. #25217C5direct (N × H)
135. C2×#484C2×C5semidirect
138. #2362C2×C5semidirect
139. #2083C2×C5semidirect
140. #2072C2×C5semidirect
141. #2067C2×C5semidirect
142. #2055C2×C5semidirect
143. #1947C2×C5semidirect
144. #1925C2×C5semidirect
145. #1880C2×C5semidirect
147. #1851C2×C5semidirect
148. #1803C2×C5semidirect
149. #1736C2×C5semidirect
642. C5#25217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4842
C2×C5×#4682
C5×#25012
C5×#23622
C5×#20832
C5×#20722
C5×#20672
C5×#20552
C5×#19472
C5×#19252
C5×#18802
C5×#18752
C5×#18512
C5×#18032
C5×#17362
#252175