Finite Group Databasebeta

← C5×#14758 #11937478

Subgroups — C5×#14758 #11937478

Order 1280.

2242 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C5×#395C211yesmaximal, characteristic, complemented
3C2×C5×#385C211yesmaximal, characteristic
4C2×C5×#380C212yesmaximal
5C22×C5×#95C211yesmaximal, characteristic
6C5×#1446C211yesmaximal, characteristic, complemented
7C5×#1444C212yesmaximal, complemented
8C5×#1444C211yesmaximal, characteristic, complemented
9C5×#1441C212yesmaximal, complemented
10C5×#1441C211yesmaximal, characteristic, complemented
11C5×C22⋊#95C212yesmaximal
12C23×C5×Q8C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2212yes—
15C2×C5×C22⋊Q8—24no—
16C2×C5×C22⋊Q8—28no—
17C22×C5×C4⋊C4C2211yescharacteristic
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⋊C4C2212yes—
25C22×C5×C22⋊C4C2211yescharacteristic
26C5×#395—24no—
27C5×#385—24no—
28C5×#380—28no—
29C2×C5×#95—24no—
30C2×C5×#95C2212yes—
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2211yescharacteristic
41#14758C511yesmaximal, characteristic, direct product factor, Sylow
42C25×C5C2311yescharacteristic
43C22×C5×Q8—24no—
44C22×C5×Q8—22no—
45C22×C5×Q8—22no—
46C22×C5×Q8—22no—
47C22×C5×Q8—42no—
48C23×C4×C5—24no—
49C23×C4×C5—24no—
50C23×C4×C5—24no—
51C23×C4×C5—22no—
52C23×C4×C5—24no—
53C23×C4×C5—22no—
54C23×C4×C5—24no—
55C23×C4×C5—42no—
56C23×C4×C5—42no—
57C23×C4×C5—42no—
58C23×C4×C5D414yes—
59C23×C4×C5Q818yescomplemented
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2312yes—
63C23×C4×C5C2312yes—
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2312yes—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2312yes—
70C5×C22⋊Q8—232no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—24no—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4—24no—
76C2×C5×C4⋊C4—24no—
77C2×C5×C4⋊C4—24no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—24no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—24no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—42no—
85C2×C5×C4⋊C4—42no—
86C2×C5×C4⋊C4—42no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—24no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—24no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4D418yes—
94C2×C5×C22⋊C4Q814yescomplemented
95C5×#95—22no—
96C5×#95—24no—
97C5×#95—24no—
98C5×#95—24no—
99C5×#95—22no—
100C5×#95—22no—
101C5×#95—24no—
102C5×#95—24no—
103C5×#95—42no—
104C5×#95—42no—
105C5×#95D414yes—
106C22×C22⋊Q8C2×C511yescharacteristic
107C2×#395C2×C511yescharacteristic, complemented
108C2×#385C2×C511yescharacteristic
109C2×#380C2×C512yes—
110C22×#95C2×C511yescharacteristic
111#1446C2×C511yescharacteristic, complemented
112#1444C2×C512yescomplemented
113#1444C2×C511yescharacteristic, complemented
114#1441C2×C511yescharacteristic, complemented
115#1441C2×C512yescomplemented
116C22⋊#95C2×C512yes—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—22no—
120C24×C5—22no—
121C24×C5—21no—
122C24×C5—21no—
123C24×C5C2×D412yes—
124C24×C5C2×D414yes—
125C24×C5C2×Q812yes—
126C24×C5C2×Q814yes—
127C24×C5#4112yes—
128C24×C5C2411yescharacteristic
129C2×C5×Q8—28no—
130C2×C5×Q8—48no—
131C2×C5×Q8—48no—
132C2×C5×Q8—44no—
133C2×C5×Q8—44no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—28no—
141C22×C4×C5—216no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
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—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—21no—
172C22×C4×C5—22no—
173C22×C4×C5—21no—
174C22×C4×C5—28no—
175C22×C4×C5—216no—
176C22×C4×C5—21no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—44no—
187C22×C4×C5—48no—
188C22×C4×C5—48no—
189C22×C4×C5—48no—
190C22×C4×C5—48no—
191C22×C4×C5—48no—
192C22×C4×C5—48no—
193C22×C4×C5—48no—
194C22×C4×C5C2×D414yes—
195C22×C4×C5C2×D414yes—
196C22×C4×C5C2×D412yes—
197C22×C4×C5C2×D412yes—
198C22×C4×C5C2×D412yes—
199C22×C4×C5C2×D414yes—
200C22×C4×C5C2×Q812yes—
201C22×C4×C5C2×Q812yes—
202C22×C4×C5C2×Q814yes—
203C22×C4×C5C2×Q814yes—
204C22×C4×C5#4112yes—
205C22×C4×C5#4114yes—
206C5×C4⋊C4—28no—
207C5×C4⋊C4—216no—
208C5×C4⋊C4—48no—
209C5×C4⋊C4—48no—
210C5×C4⋊C4—44no—
211C5×C4⋊C4—44no—
212C5×C22⋊C4—216no—
213C5×C22⋊C4—28no—
214C5×C22⋊C4—44no—
215C23×Q8C22×C511yescharacteristic
216C24×C4C22×C511yescharacteristic
217C24×C4C22×C512yes—
218C2×C22⋊Q8—24no—
219C2×C22⋊Q8—28no—
220C22×C4⋊C4C22×C511yescharacteristic
221C22×C4⋊C4C22×C511yescharacteristic
222C22×C4⋊C4C22×C512yes—
223C22×C4⋊C4C22×C512yes—
224C22×C4⋊C4C22×C512yes—
225C22×C4⋊C4C22×C511yescharacteristic
226C22×C22⋊C4C22×C511yescharacteristic
227C22×C22⋊C4C22×C512yes—
228C22×C22⋊C4C22×C511yescharacteristic
229#395—24no—
230#385—24no—
231#380—28no—
232C2×#95—24no—
233C2×#95C22×C512yes—
234C2×#95C22×C512yes—
235C2×#95C22×C511yescharacteristic
236C2×#95C22×C512yes—
237C2×#95C22×C512yes—
238C2×#95C22×C511yescharacteristic
239C2×#95C22×C512yes—
240C2×#95C22×C511yescharacteristic
241C2×#95C22×C512yes—
242C2×#95C22×C512yes—
243C2×#95C22×C511yescharacteristic
244C23×C5—22no—
245C23×C5—24no—
246C23×C5—22no—
247C23×C5—24no—
248C23×C5—22no—
249C23×C5—22no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5—24no—
253C23×C5—22no—
254C23×C5—24no—
255C23×C5—24no—
256C23×C5—24no—
257C23×C5—22no—
258C23×C5—24no—
259C23×C5—22no—
260C23×C5—24no—
261C23×C5—22no—
262C23×C5#12014yes—
263C23×C5C22⋊Q814yes—
264C23×C5C22⋊Q818yes—
265C23×C5C4⋊Q814yes—
266C23×C5C4⋊Q818yes—
267C23×C5C22×D411yescharacteristic
268C23×C5C22×D412yes—
269C23×C5C22×D411yescharacteristic
270C23×C5C22×Q812yes—
271C23×C5C22×Q811yescharacteristic
272C23×C5C2×#4111yescharacteristic
273C23×C5C2×#4111yescharacteristic
274C23×C5C2×#4112yes—
275C23×C5H(5,𝔽2)12yes—
276C23×C5H(5,𝔽2)11yescharacteristic
277C23×C52−1+411yescharacteristic
278C5×Q8—416no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—24no—
290C2×C4×C5—24no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—22no—
298C2×C4×C5—24no—
299C2×C4×C5—24no—
300C2×C4×C5—24no—
301C2×C4×C5—24no—
302C2×C4×C5—24no—
303C2×C4×C5—22no—
304C2×C4×C5—24no—
305C2×C4×C5—22no—
306C2×C4×C5—416no—
307C2×C4×C5—432no—
308C2×C4×C5—41no—
309C2×C4×C5—42no—
310C2×C4×C5—41no—
311C2×C4×C5—42no—
312C2×C4×C5—41no—
313C2×C4×C5—42no—
314C2×C4×C5—41no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—41no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
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—42no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5#12114yes—
340C2×C4×C5C22⋊Q818yescomplemented
341C25C23×C511yescharacteristic
342C22×Q8—24no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—42no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—24no—
350C23×C4—22no—
351C23×C4—24no—
352C23×C4—22no—
353C23×C4—24no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4C5×D414yes—
358C23×C4C5×Q818yescomplemented
359C23×C4C23×C511yescharacteristic
360C23×C4C23×C511yescharacteristic
361C23×C4C23×C512yes—
362C23×C4C23×C512yes—
363C23×C4C23×C511yescharacteristic
364C23×C4C23×C511yescharacteristic
365C23×C4C23×C511yescharacteristic
366C23×C4C23×C512yes—
367C23×C4C23×C511yescharacteristic
368C23×C4C23×C512yes—
369C22⋊Q8—232no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4C5×D418yes—
393C2×C22⋊C4C5×Q814yescomplemented
394#95—22no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—22no—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—42no—
403#95—42no—
404#95C5×D414yes—
405C22×C5—24no—
406C22×C5—24no—
407C22×C5—24no—
408C22×C5—24no—
409C22×C5—24no—
410C22×C5—24no—
411C22×C5—28no—
412C22×C5—28no—
413C22×C5—28no—
414C22×C5—28no—
415C22×C5#39518yescomplemented
416C22×C5C2×#12011yescharacteristic
417C22×C5C2×#12111yescharacteristic
418C22×C5C2×C22⋊Q811yescharacteristic
419C22×C5C2×C22⋊Q812yes—
420C22×C5C2×C22⋊Q812yes—
421C22×C5C2×C4⋊Q811yescharacteristic
422C22×C5C2×C4⋊Q812yes—
423C22×C5#53211yescharacteristic
424C22×C5#53312yes—
425C22×C5#53411yescharacteristic
426C22×C5#53711yescharacteristic
427C22×C5#54312yes—
428C22×C5#54412yes—
429C22×C5D4212yes—
430C22×C5#54612yes—
431C22×C5#54611yescharacteristic
432C22×C5#54612yes—
433C22×C5#54712yes—
434C22×C5D4×Q811yescharacteristic
435C22×C5#55112yes—
436C22×C5#55211yescharacteristic
437C22×C5#55412yes—
438C22×C5#55411yescharacteristic
439C4×C5—24no—
440C4×C5—28no—
441C4×C5—42no—
442C4×C5—42no—
443C4×C5—44no—
444C4×C5—42no—
445C4×C5—44no—
446C4×C5—44no—
447C4×C5—81no—
448C4×C5—81no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24C2×C5×D412yes—
456C24C2×C5×D414yes—
457C24C2×C5×Q812yes—
458C24C2×C5×Q814yes—
459C24C5×#4112yes—
460C24C24×C511yescharacteristic
461C2×Q8—28no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—44no—
465C2×Q8—44no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—216no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—28no—
507C22×C4—216no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—44no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4C2×C5×D414yes—
527C22×C4C2×C5×D414yes—
528C22×C4C2×C5×D412yes—
529C22×C4C2×C5×D412yes—
530C22×C4C2×C5×D412yes—
531C22×C4C2×C5×D414yes—
532C22×C4C2×C5×Q812yes—
533C22×C4C2×C5×Q812yes—
534C22×C4C2×C5×Q814yes—
535C22×C4C2×C5×Q814yes—
536C22×C4C5×#4112yes—
537C22×C4C5×#4114yes—
538C4⋊C4—28no—
539C4⋊C4—216no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C22⋊C4—216no—
545C22⋊C4—28no—
546C22⋊C4—44no—
547C2×C5—28no—
548C2×C5C2×#39511yescharacteristic
549C2×C5#241011yescharacteristic
550C2×C5#241711yescharacteristic
551C2×C5#243011yescharacteristic
552C2×C5#243712yes—
553C2×C5#243812yes—
554C2×C5#244012yes—
555C2×C5#254912yes—
556C2×C5#256411yescharacteristic
557C2×C5#265911yescharacteristic
558C2×C5#285711yescharacteristic
559C23—22no—
560C23—24no—
561C23—22no—
562C23—24no—
563C23—22no—
564C23—22no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—22no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—22no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—24no—
577C23C5×#12014yes—
578C23C5×C22⋊Q814yes—
579C23C5×C22⋊Q818yes—
580C23C5×C4⋊Q818yes—
581C23C5×C4⋊Q814yes—
582C23C22×C5×D411yescharacteristic
583C23C22×C5×D412yes—
584C23C22×C5×D411yescharacteristic
585C23C22×C5×Q812yes—
586C23C22×C5×Q811yescharacteristic
587C23C2×C5×#4111yescharacteristic
588C23C2×C5×#4111yescharacteristic
589C23C2×C5×#4112yes—
590C23C5×H(5,𝔽2)12yes—
591C23C5×H(5,𝔽2)11yescharacteristic
592C23C5×2−1+411yescharacteristic
593Q8—416no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—416no—
622C2×C4—432no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4C5×#12114yes—
655C2×C4C5×C22⋊Q818yescomplemented
656C5#1475811yescharacteristic, direct product factor, Sylow
657C22—28no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—28no—
665C22—28no—
666C22—28no—
667C22C5×#39518yescomplemented
668C22C2×C5×#12011yescharacteristic
669C22C2×C5×#12111yescharacteristic
670C22C2×C5×C22⋊Q811yescharacteristic
671C22C2×C5×C22⋊Q812yes—
672C22C2×C5×C22⋊Q812yes—
673C22C2×C5×C4⋊Q812yes—
674C22C2×C5×C4⋊Q811yescharacteristic
675C22C5×#53211yescharacteristic
676C22C5×#53312yes—
677C22C5×#53411yescharacteristic
678C22C5×#53711yescharacteristic
679C22C5×#54312yes—
680C22C5×#54412yes—
681C22C5×D4212yes—
682C22C5×#54612yes—
683C22C5×#54612yes—
684C22C5×#54611yescharacteristic
685C22C5×#54712yes—
686C22C5×D4×Q811yescharacteristic
687C22C5×#55112yes—
688C22C5×#55211yescharacteristic
689C22C5×#55411yescharacteristic
690C22C5×#55412yes—
691C4—24no—
692C4—28no—
693C4—42no—
694C4—42no—
695C4—44no—
696C4—42no—
697C4—44no—
698C4—44no—
699C4—81no—
700C4—81no—
701C2—28no—
702C2C2×C5×#39511yescharacteristic
703C2C5×#241011yescharacteristic
704C2C5×#241711yescharacteristic
705C2C5×#243011yescharacteristic
706C2C5×#243712yes—
707C2C5×#243812yes—
708C2C5×#244012yes—
709C2C5×#254912yes—
710C2C5×#256411yescharacteristic
711C2C5×#265911yescharacteristic
712C2C5×#285711yescharacteristic
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×#395C2semidirect
6. C5×#1446C2semidirect
7. C5×#1444C2semidirect
8. C5×#1444C2semidirect
9. C5×#1441C2semidirect
10. C5×#1441C2semidirect
41. #14758C5direct (N × H)
59. C23×C4×C5Q8semidirect
94. C2×C5×C22⋊C4Q8semidirect
107. C2×#395C2×C5semidirect
111. #1446C2×C5semidirect
112. #1444C2×C5semidirect
113. #1444C2×C5semidirect
114. #1441C2×C5semidirect
115. #1441C2×C5semidirect
340. C2×C4×C5C22⋊Q8semidirect
358. C23×C4C5×Q8semidirect
393. C2×C22⋊C4C5×Q8semidirect
415. C22×C5#395semidirect
655. C2×C4C5×C22⋊Q8semidirect
656. C5#14758direct (N × H)
667. C22C5×#395semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×C5×#3952
C2×C5×#3852
C2×C5×#3802
C22×C5×#952
C5×#14462
C5×#14442
C5×#14412
C5×C22⋊#952
#147585