Finite Group Databasebeta

← C5×#24979 #11947699

Subgroups — C5×#24979 #11947699

Order 1280.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2536C211yesmaximal, characteristic
2C5×D4×C4⋊C4C211yesmaximal, characteristic
3C5×#2077C211yesmaximal, characteristic, complemented
4C5×#2075C211yesmaximal, characteristic, complemented
5C5×#2036C211yesmaximal, characteristic, complemented
6C5×#2035C211yesmaximal, characteristic, complemented
7C5×#1955C211yesmaximal, characteristic
8C5×#1949C211yesmaximal, characteristic, complemented
9C5×#1872C211yesmaximal, characteristic, complemented
10C5×#1872C211yesmaximal, characteristic, complemented
11C5×#1836C211yesmaximal, characteristic, complemented
12C5×#1824C211yesmaximal, characteristic, complemented
13C5×#1823C211yesmaximal, characteristic, complemented
14C5×#1803C211yesmaximal, characteristic, complemented
15C5×#1763C211yesmaximal, characteristic, complemented
16C2×C5×C22⋊Q8C2211yescharacteristic
17C2×C5×C22⋊Q8C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×D4—21no—
20C2×C4×C5×D4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C2×C5×#97C2211yescharacteristic
35C5×#398—21no—
36C5×#394—21no—
37C5×#389—21no—
38C5×#388—21no—
39C5×#388—21no—
40C5×#385—21no—
41C5×#385—21no—
42C5×#384C2211yescharacteristic
43C5×#382C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C5×#380C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C4×C5×C4⋊C4C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59#24979C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4D411yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C5×C22⋊Q8—22no—
71C5×C22⋊Q8—22no—
72C5×C22⋊Q8—41no—
73C5×C22⋊Q8—41no—
74C4×C5×Q8—22no—
75C4×C5×Q8—22no—
76C4×C5×D4—22no—
77C4×C5×D4—22no—
78C4×C5×D4—44no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4D411yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C42×C5—21no—
107C2×C42×C5—21no—
108C2×C42×C5C2311yescharacteristic
109C5×#107—41no—
110C5×#106—41no—
111C5×C4⋊C8—22no—
112C5×#103—22no—
113C5×#103—22no—
114C5×#103—41no—
115C5×#103—41no—
116C5×C22⋊C8—41no—
117C5×C22⋊C8—41no—
118C5×C22⋊C8—41no—
119C5×C22⋊C8—41no—
120C5×#97—22no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128#2536C2×C511yescharacteristic
129D4×C4⋊C4C2×C511yescharacteristic
130#2077C2×C511yescharacteristic, complemented
131#2075C2×C511yescharacteristic, complemented
132#2036C2×C511yescharacteristic, complemented
133#2035C2×C511yescharacteristic, complemented
134#1955C2×C511yescharacteristic
135#1949C2×C511yescharacteristic, complemented
136#1872C2×C511yescharacteristic, complemented
137#1872C2×C511yescharacteristic, complemented
138#1836C2×C511yescharacteristic, complemented
139#1824C2×C511yescharacteristic, complemented
140#1823C2×C511yescharacteristic, complemented
141#1803C2×C511yescharacteristic, complemented
142#1763C2×C511yescharacteristic, complemented
143C24×C5C2×D411yescharacteristic
144C24×C5C2×D411yescharacteristic
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8#4112yes—
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4—22no—
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—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—42no—
175C22×C4×C5—42no—
176C22×C4×C5—42no—
177C22×C4×C5—42no—
178C22×C4×C5—81no—
179C22×C4×C5—81no—
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2411yescharacteristic
185C2×C5×C8—21no—
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—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—21no—
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—42no—
212C5×C4⋊C4—42no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4#4112yes—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—42no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C42×C5—42no—
228C42×C5—42no—
229C42×C5#4112yes—
230C42×C5#4112yes—
231C2×C22⋊Q8C22×C511yescharacteristic
232C2×C22⋊Q8C22×C511yescharacteristic
233C2×C4×Q8C22×C511yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C22×C511yescharacteristic
236C22×C4⋊C4C22×C511yescharacteristic
237C22×C4⋊C4C22×C511yescharacteristic
238C2×#107C22×C511yescharacteristic
239C2×#106C22×C511yescharacteristic
240C2×C4⋊C8C22×C511yescharacteristic
241C2×#103C22×C511yescharacteristic
242C2×#103C22×C511yescharacteristic
243C2×#103C22×C511yescharacteristic
244C2×#103C22×C511yescharacteristic
245C2×C22⋊C8C22×C511yescharacteristic
246C2×C22⋊C8C22×C511yescharacteristic
247C2×C22⋊C8C22×C511yescharacteristic
248C2×C22⋊C8C22×C511yescharacteristic
249C2×#97C22×C511yescharacteristic
250#398—21no—
251#394—21no—
252#389—21no—
253#388—21no—
254#388—21no—
255#385—21no—
256#385—21no—
257#384C22×C511yescharacteristic
258#382C22×C511yescharacteristic
259#380C22×C511yescharacteristic
260#380C22×C511yescharacteristic
261#380C22×C511yescharacteristic
262#380C22×C511yescharacteristic
263C4×C4⋊C4C22×C511yescharacteristic
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
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×C5AGL(1,ℤ/8)12yes—
287C23×C5#13712yes—
288C23×C5C22×D411yescharacteristic
289C5×Q8—22no—
290C5×Q8—22no—
291C5×Q8—41no—
292C5×Q8—41no—
293C5×D4—28no—
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—22no—
301C2×C4×C5—22no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
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—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—84no—
337C2×C4×C5—84no—
338C2×C4×C5#12312yes—
339C2×C4×C5#12312yes—
340C2×C4×C5C2×#4111yescharacteristic
341C2×C4×C5C2×#4111yescharacteristic
342C2×C4×C5C2×#4111yescharacteristic
343C2×C4×C5C2×#4111yescharacteristic
344C2×C4×C5H(5,𝔽2)11yescharacteristic
345C2×C4×C5H(5,𝔽2)11yescharacteristic
346C5×C8—41no—
347C5×C8—41no—
348C5×C8—41no—
349C5×C8—41no—
350C22×Q8C23×C511yescharacteristic
351C22×D4C5×D411yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4C23×C511yescharacteristic
355C23×C4C23×C511yescharacteristic
356C22×C8C23×C511yescharacteristic
357C22×C8C23×C511yescharacteristic
358C22×C8C23×C511yescharacteristic
359C22×C8C23×C511yescharacteristic
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—41no—
363C22⋊Q8—41no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—44no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4C5×D411yescharacteristic
381C2×C4⋊C4C23×C511yescharacteristic
382C2×C4⋊C4C23×C511yescharacteristic
383C2×C4⋊C4C23×C511yescharacteristic
384C2×C4⋊C4C23×C511yescharacteristic
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4C5×D411yescharacteristic
395C2×C22⋊C4C5×D411yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C511yescharacteristic
399#107—41no—
400#106—41no—
401C4⋊C8—22no—
402#103—22no—
403#103—22no—
404#103—41no—
405#103—41no—
406C22⋊C8—41no—
407C22⋊C8—41no—
408C22⋊C8—41no—
409C22⋊C8—41no—
410#97—22no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—22no—
421C22×C5—22no—
422C22×C5—22no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5C2×#12311yescharacteristic
433C22×C5#54611yescharacteristic
434C22×C5#54611yescharacteristic
435C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
436C22×C5C2×#13711yescharacteristic
437C22×C5#57711yescharacteristic
438C22×C5#57811yescharacteristic
439C4×C5—22no—
440C4×C5—22no—
441C4×C5—41no—
442C4×C5—41no—
443C4×C5—42no—
444C4×C5—42no—
445C4×C5—81no—
446C4×C5—81no—
447C4×C5—81no—
448C4×C5—81no—
449C4×C5—81no—
450C4×C5—81no—
451C4×C5#52911yescharacteristic
452C4×C5#54011yescharacteristic
453C4×C5#55311yescharacteristic
454C4×C5#55511yescharacteristic
455C24C2×C5×D411yescharacteristic
456C24C2×C5×D411yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C5×#4112yes—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
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—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4C2×C5×D411yescharacteristic
493C22×C4C2×C5×D411yescharacteristic
494C22×C4C2×C5×D411yescharacteristic
495C22×C4C2×C5×D411yescharacteristic
496C22×C4C24×C511yescharacteristic
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—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C4⋊C4—22no—
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—42no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—81no—
530C4⋊C4C5×#4112yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C42—42no—
540C42—42no—
541C42C5×#4112yes—
542C42C5×#4112yes—
543C2×C5—42no—
544C2×C5—42no—
545C2×C5#242011yescharacteristic
546C2×C5#309211yescharacteristic
547C2×C5#309711yescharacteristic
548C2×C5#330811yescharacteristic
549C2×C5#331011yescharacteristic
550C2×C5#331211yescharacteristic
551C2×C5#331611yescharacteristic
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23C5×AGL(1,ℤ/8)12yes—
565C23C5×#13712yes—
566C23C22×C5×D411yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571D4—28no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
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—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—84no—
615C2×C4—84no—
616C2×C4C5×#12312yes—
617C2×C4C5×#12312yes—
618C2×C4C2×C5×#4111yescharacteristic
619C2×C4C2×C5×#4111yescharacteristic
620C2×C4C2×C5×#4111yescharacteristic
621C2×C4C2×C5×#4111yescharacteristic
622C2×C4C5×H(5,𝔽2)11yescharacteristic
623C2×C4C5×H(5,𝔽2)11yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C5#2497911yescharacteristic, direct product factor, Sylow
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C2×C5×#12311yescharacteristic
644C22C5×#54611yescharacteristic
645C22C5×#54611yescharacteristic
646C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
647C22C2×C5×#13711yescharacteristic
648C22C5×#57711yescharacteristic
649C22C5×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C5×#52911yescharacteristic
663C4C5×#54011yescharacteristic
664C4C5×#55311yescharacteristic
665C4C5×#55511yescharacteristic
666C2—42no—
667C2—42no—
668C2C5×#242011yescharacteristic
669C2C5×#309211yescharacteristic
670C2C5×#309711yescharacteristic
671C2C5×#330811yescharacteristic
672C2C5×#331011yescharacteristic
673C2C5×#331211yescharacteristic
674C2C5×#331611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×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
3. C5×#2077C2semidirect
4. C5×#2075C2semidirect
5. C5×#2036C2semidirect
6. C5×#2035C2semidirect
8. C5×#1949C2semidirect
9. C5×#1872C2semidirect
10. C5×#1872C2semidirect
11. C5×#1836C2semidirect
12. C5×#1824C2semidirect
13. C5×#1823C2semidirect
14. C5×#1803C2semidirect
15. C5×#1763C2semidirect
59. #24979C5direct (N × H)
130. #2077C2×C5semidirect
131. #2075C2×C5semidirect
132. #2036C2×C5semidirect
133. #2035C2×C5semidirect
135. #1949C2×C5semidirect
136. #1872C2×C5semidirect
137. #1872C2×C5semidirect
138. #1836C2×C5semidirect
139. #1824C2×C5semidirect
140. #1823C2×C5semidirect
141. #1803C2×C5semidirect
142. #1763C2×C5semidirect
628. C5#24979direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25362
C5×D4×C4⋊C42
C5×#20772
C5×#20752
C5×#20362
C5×#20352
C5×#19552
C5×#19492
C5×#18722
C5×#18362
C5×#18242
C5×#18232
C5×#18032
C5×#17632
#249795