Finite Group Databasebeta

← C5×#14728 #11937448

Subgroups — C5×#14728 #11937448

Order 1280.

2190 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C4⋊C4C211yesmaximal, characteristic
2C2×C5×#398C212yesmaximal, complemented
3C2×C5×#385C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic
5C2×C5×#380C211yesmaximal, characteristic
6C5×#1444C212yesmaximal, complemented
7C5×#1442C212yesmaximal, complemented
8C5×#1441C212yesmaximal, complemented
9C5×C22⋊#95C211yesmaximal, characteristic
10C5×C22⋊#95C211yesmaximal, characteristic
11C5×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C5C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C22×C5×C4⋊C4—24no—
16C22×C5×C4⋊C4—28no—
17C22×C5×C4⋊C4C2212yes—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2212yes—
20C22×C5×C4⋊C4C2212yes—
21C22×C5×C4⋊C4C2212yes—
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C5×#398—28no—
28C5×#385—24no—
29C5×#385—24no—
30C5×#380—24no—
31C2×C5×#95C2212yes—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2212yes—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41#14728C511yesmaximal, characteristic, direct product factor, Sylow
42C25×C5C2311yescharacteristic
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—24no—
46C23×C4×C5—24no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5—24no—
51C23×C4×C5—24no—
52C23×C4×C5—22no—
53C23×C4×C5—22no—
54C23×C4×C5—42no—
55C23×C4×C5—42no—
56C23×C4×C5D414yes—
57C23×C4×C5Q814yes—
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2312yes—
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2312yes—
62C23×C4×C5C2312yes—
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2312yes—
68C2×C5×C4⋊C4—232no—
69C2×C5×C4⋊C4—24no—
70C2×C5×C4⋊C4—24no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—24no—
73C2×C5×C4⋊C4—24no—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4—24no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—24no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4—24no—
81C2×C5×C4⋊C4—42no—
82C2×C5×C4⋊C4—42no—
83C2×C5×C4⋊C4—42no—
84C2×C5×C4⋊C4D418yes—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—22no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4D414yes—
96C2×C5×C22⋊C4Q814yes—
97C5×#95—24no—
98C5×#95—22no—
99C5×#95—22no—
100C5×#95—24no—
101C5×#95—24no—
102C5×#95—24no—
103C5×#95—24no—
104C5×#95—24no—
105C5×#95—24no—
106C5×#95—42no—
107C23×C4⋊C4C2×C511yescharacteristic
108C2×#398C2×C512yescomplemented
109C2×#385C2×C511yescharacteristic
110C2×#385C2×C511yescharacteristic
111C2×#380C2×C511yescharacteristic
112#1444C2×C512yescomplemented
113#1442C2×C512yescomplemented
114#1441C2×C512yescomplemented
115C22⋊#95C2×C511yescharacteristic
116C22⋊#95C2×C511yescharacteristic
117C22⋊#95C2×C511yescharacteristic
118C24×C5—22no—
119C24×C5—22no—
120C24×C5—22no—
121C24×C5—22no—
122C24×C5C2×D412yes—
123C24×C5C2×D412yes—
124C24×C5C2×Q812yes—
125C24×C5C2×Q812yes—
126C24×C5#4112yes—
127C24×C5#4112yes—
128C24×C5#4112yes—
129C24×C5C2411yescharacteristic
130C22×C4×C5—28no—
131C22×C4×C5—216no—
132C22×C4×C5—28no—
133C22×C4×C5—28no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—216no—
142C22×C4×C5—28no—
143C22×C4×C5—28no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—22no—
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—21no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
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—22no—
168C22×C4×C5—28no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—22no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
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—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—44no—
187C22×C4×C5—48no—
188C22×C4×C5—48no—
189C22×C4×C5—48no—
190C22×C4×C5—48no—
191C22×C4×C5—44no—
192C22×C4×C5—44no—
193C22×C4×C5C2×D414yes—
194C22×C4×C5C2×D412yes—
195C22×C4×C5C2×D414yes—
196C22×C4×C5C2×D414yes—
197C22×C4×C5C2×D412yes—
198C22×C4×C5C2×D414yes—
199C22×C4×C5C2×Q812yes—
200C22×C4×C5C2×Q812yes—
201C22×C4×C5C2×Q814yes—
202C22×C4×C5#4114yes—
203C5×C4⋊C4—216no—
204C5×C4⋊C4—216no—
205C5×C4⋊C4—48no—
206C5×C4⋊C4—48no—
207C5×C4⋊C4—44no—
208C5×C4⋊C4—44no—
209C5×C22⋊C4—28no—
210C5×C22⋊C4—28no—
211C5×C22⋊C4—44no—
212C5×C22⋊C4—44no—
213C24×C4C22×C511yescharacteristic
214C24×C4C22×C511yescharacteristic
215C24×C4C22×C511yescharacteristic
216C22×C4⋊C4—24no—
217C22×C4⋊C4—28no—
218C22×C4⋊C4C22×C511yescharacteristic
219C22×C4⋊C4C22×C512yes—
220C22×C4⋊C4C22×C512yes—
221C22×C4⋊C4C22×C512yes—
222C22×C4⋊C4C22×C512yes—
223C22×C4⋊C4C22×C511yescharacteristic
224C22×C22⋊C4C22×C511yescharacteristic
225C22×C22⋊C4C22×C511yescharacteristic
226C22×C22⋊C4C22×C511yescharacteristic
227C22×C22⋊C4C22×C511yescharacteristic
228#398—28no—
229#385—24no—
230#385—24no—
231#380—24no—
232C2×#95C22×C512yes—
233C2×#95C22×C512yes—
234C2×#95C22×C512yes—
235C2×#95C22×C512yes—
236C2×#95C22×C512yes—
237C2×#95C22×C511yescharacteristic
238C2×#95C22×C512yes—
239C2×#95C22×C511yescharacteristic
240C2×#95C22×C512yes—
241C2×#95C22×C512yes—
242C23×C5—22no—
243C23×C5—24no—
244C23×C5—22no—
245C23×C5—24no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—24no—
249C23×C5—24no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5—24no—
253C23×C5—24no—
254C23×C5—24no—
255C23×C5—24no—
256C23×C5—24no—
257C23×C5—24no—
258C23×C5#12114yes—
259C23×C5C22⋊Q814yes—
260C23×C5C22⋊Q814yes—
261C23×C5#12314yes—
262C23×C5#12514yes—
263C23×C5#12514yes—
264C23×C5C4⋊Q814yes—
265C23×C5C22×D411yescharacteristic
266C23×C5C22×D412yes—
267C23×C5C22×D411yescharacteristic
268C23×C5C22×Q811yescharacteristic
269C23×C5C22×Q811yescharacteristic
270C23×C5C2×#4111yescharacteristic
271C23×C5C2×#4111yescharacteristic
272C23×C5C2×#4111yescharacteristic
273C23×C5C2×#4112yes—
274C23×C5H(5,𝔽2)12yes—
275C23×C52−1+412yes—
276C2×C4×C5—232no—
277C2×C4×C5—24no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—22no—
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—24no—
293C2×C4×C5—22no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—24no—
298C2×C4×C5—24no—
299C2×C4×C5—24no—
300C2×C4×C5—416no—
301C2×C4×C5—416no—
302C2×C4×C5—41no—
303C2×C4×C5—42no—
304C2×C4×C5—41no—
305C2×C4×C5—42no—
306C2×C4×C5—41no—
307C2×C4×C5—42no—
308C2×C4×C5—41no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—42no—
322C2×C4×C5—41no—
323C2×C4×C5—42no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5#12014yes—
336C2×C4×C5C22⋊Q818yes—
337C25C23×C511yescharacteristic
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—42no—
350C23×C4—42no—
351C23×C4C5×D414yes—
352C23×C4C5×Q814yes—
353C23×C4C23×C511yescharacteristic
354C23×C4C23×C512yes—
355C23×C4C23×C511yescharacteristic
356C23×C4C23×C512yes—
357C23×C4C23×C511yescharacteristic
358C23×C4C23×C512yes—
359C23×C4C23×C511yescharacteristic
360C23×C4C23×C511yescharacteristic
361C23×C4C23×C511yescharacteristic
362C23×C4C23×C512yes—
363C2×C4⋊C4—232no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4C5×D418yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4C5×D414yes—
391C2×C22⋊C4C5×Q814yes—
392#95—24no—
393#95—22no—
394#95—22no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—42no—
402C22×C5—24no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5—24no—
406C22×C5—24no—
407C22×C5—24no—
408C22×C5—28no—
409C22×C5—28no—
410C22×C5—28no—
411C22×C5—28no—
412C22×C5#39818yescomplemented
413C22×C5C2×#12011yescharacteristic
414C22×C5C2×#12111yescharacteristic
415C22×C5C2×C22⋊Q811yescharacteristic
416C22×C5C2×C22⋊Q811yescharacteristic
417C22×C5C2×C22⋊Q812yes—
418C22×C5C2×#12311yescharacteristic
419C22×C5#52511yescharacteristic
420C22×C5#52512yes—
421C22×C5C2×#12511yescharacteristic
422C22×C5C2×#12511yescharacteristic
423C22×C5C2×C4⋊Q811yescharacteristic
424C22×C5#53411yescharacteristic
425C22×C5#53611yescharacteristic
426C22×C5#53912yes—
427C22×C5#54412yes—
428C22×C5D4212yes—
429C22×C5#54612yes—
430C22×C5#54712yes—
431C22×C5#54812yes—
432C22×C5D4×Q812yes—
433C22×C5#55212yes—
434C22×C5#55312yes—
435C22×C5#55412yes—
436C4×C5—28no—
437C4×C5—24no—
438C4×C5—42no—
439C4×C5—42no—
440C4×C5—42no—
441C4×C5—44no—
442C4×C5—44no—
443C4×C5—81no—
444C4×C5—81no—
445C4×C5—82no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24C2×C5×D412yes—
451C24C2×C5×D412yes—
452C24C2×C5×Q812yes—
453C24C2×C5×Q812yes—
454C24C5×#4112yes—
455C24C5×#4112yes—
456C24C5×#4112yes—
457C24C24×C511yescharacteristic
458C22×C4—28no—
459C22×C4—216no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—216no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—44no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4C2×C5×D414yes—
522C22×C4C2×C5×D412yes—
523C22×C4C2×C5×D414yes—
524C22×C4C2×C5×D412yes—
525C22×C4C2×C5×D414yes—
526C22×C4C2×C5×D414yes—
527C22×C4C2×C5×Q812yes—
528C22×C4C2×C5×Q812yes—
529C22×C4C2×C5×Q814yes—
530C22×C4C5×#4114yes—
531C4⋊C4—216no—
532C4⋊C4—216no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—44no—
536C4⋊C4—44no—
537C22⋊C4—28no—
538C22⋊C4—28no—
539C22⋊C4—44no—
540C22⋊C4—44no—
541C2×C5—28no—
542C2×C5C2×#39811yescharacteristic
543C2×C5#240911yescharacteristic
544C2×C5#241011yescharacteristic
545C2×C5#241311yescharacteristic
546C2×C5#244012yes—
547C2×C5#244212yes—
548C2×C5#244312yes—
549C2×C5#247312yes—
550C2×C5#257911yescharacteristic
551C2×C5#262711yescharacteristic
552C2×C5#284811yescharacteristic
553C23—22no—
554C23—24no—
555C23—22no—
556C23—24no—
557C23—22no—
558C23—22no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23C5×#12114yes—
570C23C5×C22⋊Q814yes—
571C23C5×C22⋊Q814yes—
572C23C5×#12314yes—
573C23C5×#12514yes—
574C23C5×#12514yes—
575C23C5×C4⋊Q814yes—
576C23C22×C5×D411yescharacteristic
577C23C22×C5×D412yes—
578C23C22×C5×D411yescharacteristic
579C23C22×C5×Q811yescharacteristic
580C23C22×C5×Q811yescharacteristic
581C23C2×C5×#4111yescharacteristic
582C23C2×C5×#4111yescharacteristic
583C23C2×C5×#4111yescharacteristic
584C23C2×C5×#4112yes—
585C23C5×H(5,𝔽2)12yes—
586C23C5×2−1+412yes—
587C2×C4—232no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—416no—
612C2×C4—416no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4C5×#12014yes—
647C2×C4C5×C22⋊Q818yes—
648C5#1472811yescharacteristic, direct product factor, Sylow
649C22—28no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—24no—
654C22—24no—
655C22—24no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C5×#39818yescomplemented
660C22C2×C5×#12011yescharacteristic
661C22C2×C5×#12111yescharacteristic
662C22C2×C5×C22⋊Q811yescharacteristic
663C22C2×C5×C22⋊Q811yescharacteristic
664C22C2×C5×C22⋊Q812yes—
665C22C2×C5×#12311yescharacteristic
666C22C5×#52512yes—
667C22C5×#52511yescharacteristic
668C22C2×C5×#12511yescharacteristic
669C22C2×C5×#12511yescharacteristic
670C22C2×C5×C4⋊Q811yescharacteristic
671C22C5×#53411yescharacteristic
672C22C5×#53611yescharacteristic
673C22C5×#53912yes—
674C22C5×#54412yes—
675C22C5×D4212yes—
676C22C5×#54612yes—
677C22C5×#54712yes—
678C22C5×#54812yes—
679C22C5×D4×Q812yes—
680C22C5×#55212yes—
681C22C5×#55312yes—
682C22C5×#55412yes—
683C4—28no—
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—44no—
689C4—44no—
690C4—81no—
691C4—81no—
692C4—82no—
693C2—28no—
694C2C2×C5×#39811yescharacteristic
695C2C5×#240911yescharacteristic
696C2C5×#241011yescharacteristic
697C2C5×#241311yescharacteristic
698C2C5×#244012yes—
699C2C5×#244212yes—
700C2C5×#244312yes—
701C2C5×#247312yes—
702C2C5×#257911yescharacteristic
703C2C5×#262711yescharacteristic
704C2C5×#284811yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#398C2semidirect
6. C5×#1444C2semidirect
7. C5×#1442C2semidirect
8. C5×#1441C2semidirect
41. #14728C5direct (N × H)
108. C2×#398C2×C5semidirect
112. #1444C2×C5semidirect
113. #1442C2×C5semidirect
114. #1441C2×C5semidirect
412. C22×C5#398semidirect
648. C5#14728direct (N × H)
659. C22C5×#398semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C4⋊C42
C2×C5×#3982
C2×C5×#3852
C2×C5×#3802
C5×#14442
C5×#14422
C5×#14412
C5×C22⋊#952
#147285