Finite Group Databasebeta

← C5×#16505 #11939225

Subgroups — C5×#16505 #11939225

Order 1280.

1942 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#124C211yesmaximal, characteristic
2C2×C5×#396C212yesmaximal, complemented
3C2×C5×#395C211yesmaximal, characteristic, complemented
4C2×C5×#394C211yesmaximal, characteristic
5C2×C5×#387C211yesmaximal, characteristic, complemented
6C5×#1446C211yesmaximal, characteristic, complemented
7C5×#1440C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×#1439C212yesmaximal, complemented
10C5×#1438C211yesmaximal, characteristic
11C5×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C5×Q8C2211yescharacteristic
13C23×C5×D4C2211yescharacteristic
14C2×C5×#124—28no—
15C2×C5×#124—24no—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2212yes—
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2212yes—
21C22×C5×C22⋊C4C2212yes—
22C22×C5×C22⋊C4C2212yes—
23C22×C5×C22⋊C4C2212yes—
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2212yes—
26C22×C42×C5C2211yescharacteristic
27C5×#396—28no—
28C5×#395—24no—
29C5×#394—24no—
30C5×#387—24no—
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41#16505C511yesmaximal, characteristic, direct product factor, Sylow
42C25×C5C2312yes—
43C22×C5×Q8—24no—
44C22×C5×Q8—22no—
45C22×C5×Q8—22no—
46C22×C5×Q8—22no—
47C22×C5×Q8—42no—
48C22×C5×D4—24no—
49C22×C5×D4—22no—
50C22×C5×D4—22no—
51C22×C5×D4—22no—
52C22×C5×D4—42no—
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2312yes—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2312yes—
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2312yes—
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C5×#124—232no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—22no—
66C2×C5×C4⋊C4—22no—
67C2×C5×C4⋊C4—24no—
68C2×C5×C4⋊C4—24no—
69C2×C5×C4⋊C4—24no—
70C2×C5×C4⋊C4—24no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—42no—
73C2×C5×C4⋊C4—42no—
74C2×C5×C4⋊C4D414yes—
75C2×C5×C22⋊C4—24no—
76C2×C5×C22⋊C4—24no—
77C2×C5×C22⋊C4—24no—
78C2×C5×C22⋊C4—24no—
79C2×C5×C22⋊C4—24no—
80C2×C5×C22⋊C4—24no—
81C2×C5×C22⋊C4—24no—
82C2×C5×C22⋊C4—24no—
83C2×C5×C22⋊C4—24no—
84C2×C5×C22⋊C4—24no—
85C2×C5×C22⋊C4—24no—
86C2×C5×C22⋊C4—42no—
87C2×C5×C22⋊C4—42no—
88C2×C5×C22⋊C4—42no—
89C2×C5×C22⋊C4—42no—
90C2×C5×C22⋊C4—42no—
91C2×C5×C22⋊C4—42no—
92C2×C5×C22⋊C4D418yes—
93C2×C42×C5—24no—
94C2×C42×C5D414yes—
95C5×#95—22no—
96C5×#95—22no—
97C5×#95—22no—
98C5×#95—22no—
99C5×#95—22no—
100C5×#95—24no—
101C5×#95—22no—
102C5×#95—24no—
103C5×#95—42no—
104C5×#95—42no—
105C22×#124C2×C511yescharacteristic
106C2×#396C2×C512yescomplemented
107C2×#395C2×C511yescharacteristic, complemented
108C2×#394C2×C511yescharacteristic
109C2×#387C2×C511yescharacteristic, complemented
110#1446C2×C511yescharacteristic, complemented
111#1440C2×C512yescomplemented
112#1439C2×C512yescomplemented
113#1439C2×C512yescomplemented
114#1438C2×C511yescharacteristic
115C4⋊#95C2×C511yescharacteristic, complemented
116C24×C5—22no—
117C24×C5—22no—
118C24×C5—22no—
119C24×C5—22no—
120C24×C5—22no—
121C24×C5—22no—
122C24×C5—22no—
123C24×C5—22no—
124C24×C5—22no—
125C24×C5—22no—
126C24×C5—22no—
127C24×C5—22no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5C2×D414yes—
131C24×C5C2411yescharacteristic
132C2×C5×Q8—28no—
133C2×C5×Q8—48no—
134C2×C5×Q8—48no—
135C2×C5×Q8—44no—
136C2×C5×Q8—44no—
137C2×C5×D4—28no—
138C2×C5×D4—48no—
139C2×C5×D4—48no—
140C2×C5×D4—44no—
141C2×C5×D4—44no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—21no—
168C22×C4×C5—22no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—22no—
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2×D412yes—
192C22×C4×C5C2×D412yes—
193C22×C4×C5C2×D414yes—
194C22×C4×C5C2×D414yes—
195C22×C4×C5C2×D412yes—
196C22×C4×C5C2×D412yes—
197C22×C4×C5C2×D412yes—
198C22×C4×C5#4114yes—
199C22×C4×C5#4112yes—
200C5×C4⋊C4—28no—
201C5×C4⋊C4—48no—
202C5×C4⋊C4—48no—
203C5×C4⋊C4—44no—
204C5×C22⋊C4—216no—
205C5×C22⋊C4—216no—
206C5×C22⋊C4—48no—
207C5×C22⋊C4—48no—
208C5×C22⋊C4—48no—
209C5×C22⋊C4—48no—
210C42×C5—28no—
211C23×Q8C22×C511yescharacteristic
212C23×D4C22×C511yescharacteristic
213C2×#124—28no—
214C2×#124—24no—
215C22×C4⋊C4C22×C511yescharacteristic
216C22×C4⋊C4C22×C512yes—
217C22×C4⋊C4C22×C512yes—
218C22×C4⋊C4C22×C511yescharacteristic
219C22×C22⋊C4C22×C512yes—
220C22×C22⋊C4C22×C512yes—
221C22×C22⋊C4C22×C512yes—
222C22×C22⋊C4C22×C512yes—
223C22×C22⋊C4C22×C512yes—
224C22×C22⋊C4C22×C512yes—
225C22×C42C22×C511yescharacteristic
226#396—28no—
227#395—24no—
228#394—24no—
229#387—24no—
230C2×#95C22×C511yescharacteristic
231C2×#95C22×C511yescharacteristic
232C2×#95C22×C512yes—
233C2×#95C22×C512yes—
234C2×#95C22×C511yescharacteristic
235C2×#95C22×C511yescharacteristic
236C2×#95C22×C511yescharacteristic
237C2×#95C22×C511yescharacteristic
238C2×#95C22×C512yes—
239C2×#95C22×C512yes—
240C23×C5—24no—
241C23×C5—24no—
242C23×C5—24no—
243C23×C5—24no—
244C23×C5—24no—
245C23×C5—24no—
246C23×C5—24no—
247C23×C5—42no—
248C23×C5—42no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5—42no—
255C23×C5—42no—
256C23×C5—42no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5—42no—
261C23×C5—42no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5—42no—
265C23×C5—42no—
266C23×C5—42no—
267C23×C5—42no—
268C23×C5—42no—
269C23×C5—42no—
270C23×C5—42no—
271C23×C5—42no—
272C23×C5—42no—
273C23×C5—42no—
274C23×C5—42no—
275C23×C5C22×D411yescharacteristic
276C23×C5C22×D412yes—
277C23×C5C22×D411yescharacteristic
278C23×C5C2×#4111yescharacteristic
279C23×C5C2×#4112yes—
280C23×C5H(5,𝔽2)11yescharacteristic
281C23×C5H(5,𝔽2)11yescharacteristic
282C23×C5H(5,𝔽2)12yes—
283C23×C52−1+411yescharacteristic
284C23×C52−1+412yes—
285C23×C52−1+411yescharacteristic
286C5×Q8—416no—
287C5×D4—416no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—24no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—22no—
297C2×C4×C5—24no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—24no—
305C2×C4×C5—24no—
306C2×C4×C5—24no—
307C2×C4×C5—24no—
308C2×C4×C5—24no—
309C2×C4×C5—24no—
310C2×C4×C5—41no—
311C2×C4×C5—42no—
312C2×C4×C5—41no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—42no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—42no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—42no—
334C2×C4×C5—41no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5#12014yes—
345C2×C4×C5#12114yes—
346C25C23×C512yes—
347C22×Q8—24no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—42no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—42no—
357C23×C4C23×C511yescharacteristic
358C23×C4C23×C512yes—
359C23×C4C23×C511yescharacteristic
360C23×C4C23×C511yescharacteristic
361C23×C4C23×C512yes—
362C23×C4C23×C511yescharacteristic
363C23×C4C23×C511yescharacteristic
364C23×C4C23×C512yes—
365C23×C4C23×C511yescharacteristic
366C23×C4C23×C511yescharacteristic
367#124—232no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4C5×D414yes—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4C5×D418yes—
397C2×C42—24no—
398C2×C42C5×D414yes—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95—42no—
409C22×C5—44no—
410C22×C5—44no—
411C22×C5—44no—
412C22×C5—44no—
413C22×C5—44no—
414C22×C5—44no—
415C22×C5—44no—
416C22×C5—82no—
417C22×C5—82no—
418C22×C5—82no—
419C22×C5—82no—
420C22×C5—82no—
421C22×C5—82no—
422C22×C5—82no—
423C22×C5—82no—
424C22×C5C2×#12011yescharacteristic
425C22×C5C2×#12111yescharacteristic
426C22×C5#53211yescharacteristic
427C22×C5#53511yescharacteristic
428C22×C5#53511yescharacteristic
429C22×C5#53611yescharacteristic
430C22×C5#53612yes—
431C22×C5#53611yescharacteristic
432C22×C5#53711yescharacteristic
433C22×C5#53711yescharacteristic
434C22×C5#53712yes—
435C22×C5#53812yes—
436C22×C5#54211yescharacteristic
437C22×C5#54211yescharacteristic
438C22×C5#54212yes—
439C22×C5D4212yes—
440C22×C5#54612yes—
441C22×C5#54612yes—
442C22×C5#54712yes—
443C22×C5#54812yes—
444C22×C5#55612yes—
445C22×C5#56212yes—
446C22×C5#56312yes—
447C4×C5—24no—
448C4×C5—24no—
449C4×C5—42no—
450C4×C5—42no—
451C4×C5—42no—
452C4×C5—44no—
453C4×C5—44no—
454C4×C5—81no—
455C4×C5—82no—
456C4×C5—81no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×C5×D414yes—
472C24C24×C511yescharacteristic
473C2×Q8—28no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×D4—28no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—44no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4C2×C5×D412yes—
532C22×C4C2×C5×D412yes—
533C22×C4C2×C5×D414yes—
534C22×C4C2×C5×D412yes—
535C22×C4C2×C5×D412yes—
536C22×C4C2×C5×D414yes—
537C22×C4C2×C5×D412yes—
538C22×C4C2×C5×D412yes—
539C22×C4C5×#4114yes—
540C22×C4C5×#4112yes—
541C4⋊C4—28no—
542C4⋊C4—48no—
543C4⋊C4—48no—
544C4⋊C4—44no—
545C22⋊C4—216no—
546C22⋊C4—216no—
547C22⋊C4—48no—
548C22⋊C4—48no—
549C22⋊C4—48no—
550C22⋊C4—48no—
551C42—28no—
552C2×C5—84no—
553C2×C5#240811yescharacteristic
554C2×C5#243011yescharacteristic
555C2×C5#254511yescharacteristic
556C2×C5#261611yescharacteristic
557C2×C5#262011yescharacteristic
558C2×C5#266211yescharacteristic
559C2×C5#267412yes—
560C2×C5#267612yes—
561C2×C5#270012yes—
562C2×C5#271512yes—
563C2×C5#282011yescharacteristic
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23C22×C5×D411yescharacteristic
600C23C22×C5×D412yes—
601C23C22×C5×D411yescharacteristic
602C23C2×C5×#4111yescharacteristic
603C23C2×C5×#4112yes—
604C23C5×H(5,𝔽2)11yescharacteristic
605C23C5×H(5,𝔽2)11yescharacteristic
606C23C5×H(5,𝔽2)12yes—
607C23C5×2−1+411yescharacteristic
608C23C5×2−1+412yes—
609C23C5×2−1+411yescharacteristic
610Q8—416no—
611D4—416no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4C5×#12014yes—
669C2×C4C5×#12114yes—
670C5#1650511yescharacteristic, direct product factor, Sylow
671C22—44no—
672C22—44no—
673C22—44no—
674C22—44no—
675C22—44no—
676C22—44no—
677C22—44no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22C2×C5×#12011yescharacteristic
687C22C2×C5×#12111yescharacteristic
688C22C5×#53211yescharacteristic
689C22C5×#53511yescharacteristic
690C22C5×#53511yescharacteristic
691C22C5×#53611yescharacteristic
692C22C5×#53612yes—
693C22C5×#53611yescharacteristic
694C22C5×#53711yescharacteristic
695C22C5×#53711yescharacteristic
696C22C5×#53712yes—
697C22C5×#53812yes—
698C22C5×#54211yescharacteristic
699C22C5×#54211yescharacteristic
700C22C5×#54212yes—
701C22C5×D4212yes—
702C22C5×#54612yes—
703C22C5×#54612yes—
704C22C5×#54712yes—
705C22C5×#54812yes—
706C22C5×#55612yes—
707C22C5×#56212yes—
708C22C5×#56312yes—
709C4—24no—
710C4—24no—
711C4—42no—
712C4—42no—
713C4—44no—
714C4—42no—
715C4—44no—
716C4—81no—
717C4—82no—
718C4—81no—
719C2—84no—
720C2C5×#240811yescharacteristic
721C2C5×#243011yescharacteristic
722C2C5×#254511yescharacteristic
723C2C5×#261611yescharacteristic
724C2C5×#262011yescharacteristic
725C2C5×#266211yescharacteristic
726C2C5×#267412yes—
727C2C5×#267612yes—
728C2C5×#270012yes—
729C2C5×#271512yes—
730C2C5×#282011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#396C2semidirect
3. C2×C5×#395C2semidirect
5. C2×C5×#387C2semidirect
6. C5×#1446C2semidirect
7. C5×#1440C2semidirect
8. C5×#1439C2semidirect
9. C5×#1439C2semidirect
11. C5×C4⋊#95C2semidirect
41. #16505C5direct (N × H)
106. C2×#396C2×C5semidirect
107. C2×#395C2×C5semidirect
109. C2×#387C2×C5semidirect
110. #1446C2×C5semidirect
111. #1440C2×C5semidirect
112. #1439C2×C5semidirect
113. #1439C2×C5semidirect
115. C4⋊#95C2×C5semidirect
670. C5#16505direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1242
C2×C5×#3962
C2×C5×#3952
C2×C5×#3942
C2×C5×#3872
C5×#14462
C5×#14402
C5×#14392
C5×#14382
C5×C4⋊#952
#165055