Finite Group Databasebeta

← C5×#14727 #11937447

Subgroups — C5×#14727 #11937447

Order 1280.

3350 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C22⋊C4C211yesmaximal, characteristic
2C2×C5×#397C212yesmaximal, complemented
3C2×C5×#385C211yesmaximal, characteristic, complemented
4C2×C5×#379C211yesmaximal, characteristic
5C2×C5×#379C211yesmaximal, characteristic
6C5×#1440C212yesmaximal, complemented
7C5×#1440C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×C22⋊#95C211yesmaximal, characteristic, complemented
10C5×C22⋊#95C211yesmaximal, characteristic, complemented
11C5×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C5C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C22×C5×C4⋊C4C2212yescomplemented
16C22×C5×C22⋊C4—24no—
17C22×C5×C22⋊C4—28no—
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2212yes—
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2212yes—
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2212yes—
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C5×#397—28no—
31C5×#385—24no—
32C5×#379—24no—
33C5×#379—24no—
34C2×C5×#95C2212yescomplemented
35C2×C5×#95C2212yescomplemented
36C2×C5×#95C2212yescomplemented
37C2×C5×#95C2212yescomplemented
38C2×C5×#95C2212yescomplemented
39C2×C5×#95C2212yescomplemented
40C2×C5×#95C2212yescomplemented
41#14727C511yesmaximal, characteristic, direct product factor, Sylow
42C25×C5—24no—
43C25×C5—24no—
44C25×C5—22no—
45C25×C5—22no—
46C25×C5—22no—
47C25×C5—22no—
48C25×C5—22no—
49C25×C5—22no—
50C25×C5—42no—
51C25×C5—42no—
52C25×C5D414yes—
53C25×C5C2311yescharacteristic
54C25×C5C2311yescharacteristic
55C25×C5C2311yescharacteristic
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—24no—
59C23×C4×C5—24no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—42no—
65C23×C4×C5—42no—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2312yes—
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2312yes—
72C23×C4×C5C2312yes—
73C23×C4×C5C2312yes—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4—24no—
76C2×C5×C4⋊C4—42no—
77C2×C5×C22⋊C4—232no—
78C2×C5×C22⋊C4—24no—
79C2×C5×C22⋊C4—24no—
80C2×C5×C22⋊C4—24no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—24no—
84C2×C5×C22⋊C4—24no—
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—24no—
94C2×C5×C22⋊C4—24no—
95C2×C5×C22⋊C4—24no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—24no—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4—42no—
106C2×C5×C22⋊C4—42no—
107C2×C5×C22⋊C4—42no—
108C2×C5×C22⋊C4D414yes—
109C2×C5×C22⋊C4D418yes—
110C5×#95—24no—
111C5×#95—24no—
112C5×#95—24no—
113C5×#95—24no—
114C5×#95—42no—
115C5×#95—42no—
116C5×#95—42no—
117C23×C22⋊C4C2×C511yescharacteristic
118C2×#397C2×C512yescomplemented
119C2×#385C2×C511yescharacteristic, complemented
120C2×#379C2×C511yescharacteristic
121C2×#379C2×C511yescharacteristic
122#1440C2×C512yescomplemented
123#1440C2×C512yescomplemented
124#1439C2×C512yescomplemented
125C22⋊#95C2×C511yescharacteristic, complemented
126C22⋊#95C2×C511yescharacteristic, complemented
127C22⋊#95C2×C511yescharacteristic, complemented
128C24×C5—22no—
129C24×C5—22no—
130C24×C5—22no—
131C24×C5—22no—
132C24×C5—216no—
133C24×C5—216no—
134C24×C5—28no—
135C24×C5—28no—
136C24×C5—28no—
137C24×C5—22no—
138C24×C5—21no—
139C24×C5—21no—
140C24×C5—21no—
141C24×C5—21no—
142C24×C5—21no—
143C24×C5—21no—
144C24×C5—22no—
145C24×C5—21no—
146C24×C5—21no—
147C24×C5—21no—
148C24×C5—21no—
149C24×C5—21no—
150C24×C5—21no—
151C24×C5—22no—
152C24×C5—22no—
153C24×C5—22no—
154C24×C5—22no—
155C24×C5—28no—
156C24×C5—28no—
157C24×C5—44no—
158C24×C5—44no—
159C24×C5—48no—
160C24×C5—48no—
161C24×C5—48no—
162C24×C5—48no—
163C24×C5—48no—
164C24×C5—48no—
165C24×C5—48no—
166C24×C5—48no—
167C24×C5—48no—
168C24×C5—48no—
169C24×C5—44no—
170C24×C5—44no—
171C24×C5—44no—
172C24×C5—44no—
173C24×C5C2×D412yes—
174C24×C5C2×D414yes—
175C24×C5C2×D412yes—
176C24×C5C2×D412yes—
177C24×C5C2×D412yes—
178C24×C5#4114yes—
179C24×C5#4112yes—
180C24×C5#4112yes—
181C24×C5#4112yes—
182C24×C5#4112yes—
183C24×C5#4112yes—
184C24×C5C2411yescharacteristic
185C22×C4×C5—28no—
186C22×C4×C5—28no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—21no—
214C22×C4×C5—22no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—22no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—48no—
233C22×C4×C5—48no—
234C22×C4×C5—48no—
235C22×C4×C5—48no—
236C22×C4×C5—44no—
237C22×C4×C5—44no—
238C22×C4×C5—44no—
239C22×C4×C5—44no—
240C22×C4×C5C2×D414yes—
241C22×C4×C5C2×D414yes—
242C22×C4×C5C2×D414yes—
243C5×C4⋊C4—48no—
244C5×C22⋊C4—216no—
245C5×C22⋊C4—216no—
246C5×C22⋊C4—28no—
247C5×C22⋊C4—48no—
248C5×C22⋊C4—48no—
249C5×C22⋊C4—44no—
250C5×C22⋊C4—44no—
251C5×C22⋊C4—44no—
252C5×C22⋊C4—44no—
253C5×C22⋊C4—44no—
254C5×C22⋊C4—44no—
255C5×C22⋊C4—44no—
256C26C22×C511yescharacteristic
257C24×C4C22×C511yescharacteristic
258C24×C4C22×C511yescharacteristic
259C22×C4⋊C4C22×C512yescomplemented
260C22×C22⋊C4—24no—
261C22×C22⋊C4—28no—
262C22×C22⋊C4C22×C511yescharacteristic
263C22×C22⋊C4C22×C512yes—
264C22×C22⋊C4C22×C511yescharacteristic
265C22×C22⋊C4C22×C511yescharacteristic
266C22×C22⋊C4C22×C511yescharacteristic
267C22×C22⋊C4C22×C511yescharacteristic
268C22×C22⋊C4C22×C512yes—
269C22×C22⋊C4C22×C512yes—
270C22×C22⋊C4C22×C512yes—
271C22×C22⋊C4C22×C511yescharacteristic
272C22×C22⋊C4C22×C511yescharacteristic
273C22×C22⋊C4C22×C511yescharacteristic
274#397—28no—
275#385—24no—
276#379—24no—
277#379—24no—
278C2×#95C22×C512yescomplemented
279C2×#95C22×C512yescomplemented
280C2×#95C22×C512yescomplemented
281C2×#95C22×C512yescomplemented
282C2×#95C22×C512yescomplemented
283C2×#95C22×C512yescomplemented
284C2×#95C22×C512yescomplemented
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—24no—
288C23×C5—24no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—24no—
294C23×C5—24no—
295C23×C5—24no—
296C23×C5—24no—
297C23×C5—24no—
298C23×C5—24no—
299C23×C5—24no—
300C23×C5—24no—
301C23×C5—232no—
302C23×C5—22no—
303C23×C5—22no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—22no—
309C23×C5—22no—
310C23×C5—24no—
311C23×C5—24no—
312C23×C5—24no—
313C23×C5—24no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—24no—
319C23×C5—24no—
320C23×C5—24no—
321C23×C5—24no—
322C23×C5—24no—
323C23×C5—24no—
324C23×C5—24no—
325C23×C5—24no—
326C23×C5—416no—
327C23×C5—416no—
328C23×C5—416no—
329C23×C5—416no—
330C23×C5—416no—
331C23×C5—432no—
332C23×C5—432no—
333C23×C5—432no—
334C23×C5—432no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—42no—
344C23×C5—42no—
345C23×C5—42no—
346C23×C5—42no—
347C23×C5—42no—
348C23×C5—42no—
349C23×C5—42no—
350C23×C5—42no—
351C23×C5—42no—
352C23×C5—42no—
353C23×C5—42no—
354C23×C5—42no—
355C23×C5—416no—
356C23×C5#12014yes—
357C23×C5#12114yes—
358C23×C5#12314yes—
359C23×C5#12314yes—
360C23×C5#12314yes—
361C23×C5#12314yes—
362C23×C5#12414yes—
363C23×C5#12614yes—
364C23×C5#12614yes—
365C23×C5C22×D411yescharacteristic
366C23×C5C22×D412yes—
367C23×C5C22×D411yescharacteristic
368C23×C5C2×#4111yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C23×C5C2×#4111yescharacteristic
372C23×C5C2×#4112yes—
373C23×C5C2×#4111yescharacteristic
374C23×C5H(5,𝔽2)12yes—
375C23×C5H(5,𝔽2)12yes—
376C2×C4×C5—24no—
377C2×C4×C5—24no—
378C2×C4×C5—24no—
379C2×C4×C5—24no—
380C2×C4×C5—24no—
381C2×C4×C5—24no—
382C2×C4×C5—24no—
383C2×C4×C5—24no—
384C2×C4×C5—24no—
385C2×C4×C5—416no—
386C2×C4×C5—416no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5—42no—
392C2×C4×C5—42no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5—42no—
396C2×C4×C5—42no—
397C2×C4×C5—42no—
398C2×C4×C5—42no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—42no—
408C2×C4×C5—42no—
409C2×C4×C5—42no—
410C2×C4×C5—42no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—42no—
416C2×C4×C5—42no—
417C2×C4×C5—42no—
418C2×C4×C5—42no—
419C2×C4×C5—42no—
420C2×C4×C5—42no—
421C2×C4×C5—42no—
422C2×C4×C5—42no—
423C2×C4×C5—42no—
424C2×C4×C5—42no—
425C2×C4×C5—42no—
426C25—24no—
427C25—24no—
428C25—22no—
429C25—22no—
430C25—22no—
431C25—22no—
432C25—22no—
433C25—22no—
434C25—42no—
435C25—42no—
436C25C5×D414yes—
437C25C23×C511yescharacteristic
438C25C23×C511yescharacteristic
439C25C23×C511yescharacteristic
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4C23×C511yescharacteristic
451C23×C4C23×C511yescharacteristic
452C23×C4C23×C512yes—
453C23×C4C23×C511yescharacteristic
454C23×C4C23×C511yescharacteristic
455C23×C4C23×C512yes—
456C23×C4C23×C512yes—
457C23×C4C23×C512yes—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—42no—
461C2×C22⋊C4—232no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4C5×D418yes—
493C2×C22⋊C4C5×D414yes—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—42no—
499#95—42no—
500#95—42no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5—24no—
504C22×C5—24no—
505C22×C5—24no—
506C22×C5—28no—
507C22×C5—28no—
508C22×C5—28no—
509C22×C5—28no—
510C22×C5—24no—
511C22×C5—24no—
512C22×C5—24no—
513C22×C5—24no—
514C22×C5—24no—
515C22×C5—24no—
516C22×C5—24no—
517C22×C5—464no—
518C22×C5—42no—
519C22×C5—42no—
520C22×C5—42no—
521C22×C5—42no—
522C22×C5—42no—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—44no—
526C22×C5—44no—
527C22×C5—44no—
528C22×C5—44no—
529C22×C5—44no—
530C22×C5—44no—
531C22×C5—44no—
532C22×C5—44no—
533C22×C5—42no—
534C22×C5#39718yescomplemented
535C22×C5C2×#12011yescharacteristic
536C22×C5C2×#12111yescharacteristic
537C22×C5C2×#12311yescharacteristic
538C22×C5C2×#12311yescharacteristic
539C22×C5C2×#12311yescharacteristic
540C22×C5C2×#12311yescharacteristic
541C22×C5#52512yes—
542C22×C5#52512yes—
543C22×C5C2×#12411yescharacteristic
544C22×C5C2×#12611yescharacteristic
545C22×C5C2×#12611yescharacteristic
546C22×C5#53411yescharacteristic
547C22×C5#53411yescharacteristic
548C22×C5#53812yes—
549C22×C5#53812yes—
550C22×C5D4212yes—
551C22×C5#54612yes—
552C22×C5#54612yes—
553C22×C5#54612yes—
554C22×C5#54612yes—
555C22×C5#55112yes—
556C22×C5#55112yes—
557C22×C5#55112yes—
558C4×C5—44no—
559C4×C5—44no—
560C4×C5—44no—
561C4×C5—81no—
562C4×C5—81no—
563C4×C5—81no—
564C4×C5—81no—
565C4×C5—82no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—216no—
571C24—216no—
572C24—28no—
573C24—28no—
574C24—28no—
575C24—22no—
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C24—21no—
581C24—21no—
582C24—22no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—28no—
594C24—28no—
595C24—44no—
596C24—44no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—44no—
608C24—44no—
609C24—44no—
610C24—44no—
611C24C2×C5×D412yes—
612C24C2×C5×D414yes—
613C24C2×C5×D412yes—
614C24C2×C5×D412yes—
615C24C2×C5×D412yes—
616C24C5×#4114yes—
617C24C5×#4112yes—
618C24C5×#4112yes—
619C24C5×#4112yes—
620C24C5×#4112yes—
621C24C5×#4112yes—
622C24C24×C511yescharacteristic
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—48no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4C2×C5×D414yes—
679C22×C4C2×C5×D414yes—
680C22×C4C2×C5×D414yes—
681C4⋊C4—48no—
682C22⋊C4—216no—
683C22⋊C4—216no—
684C22⋊C4—28no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C2×C5—28no—
695C2×C5—44no—
696C2×C5—44no—
697C2×C5C2×#39711yescharacteristic
698C2×C5#240511yescharacteristic
699C2×C5#241011yescharacteristic
700C2×C5#241211yescharacteristic
701C2×C5#241812yes—
702C2×C5#247212yes—
703C2×C5#248012yes—
704C2×C5#248012yes—
705C2×C5#248311yescharacteristic
706C2×C5#262211yescharacteristic
707C2×C5#284911yescharacteristic
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—232no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—416no—
750C23—416no—
751C23—416no—
752C23—416no—
753C23—432no—
754C23—432no—
755C23—432no—
756C23—416no—
757C23—432no—
758C23—416no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23C5×#12014yes—
780C23C5×#12114yes—
781C23C5×#12314yes—
782C23C5×#12314yes—
783C23C5×#12314yes—
784C23C5×#12314yes—
785C23C5×#12414yes—
786C23C5×#12614yes—
787C23C5×#12614yes—
788C23C22×C5×D411yescharacteristic
789C23C22×C5×D412yes—
790C23C22×C5×D411yescharacteristic
791C23C2×C5×#4111yescharacteristic
792C23C2×C5×#4111yescharacteristic
793C23C2×C5×#4111yescharacteristic
794C23C2×C5×#4111yescharacteristic
795C23C2×C5×#4112yes—
796C23C2×C5×#4111yescharacteristic
797C23C5×H(5,𝔽2)12yes—
798C23C5×H(5,𝔽2)12yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C5#1472711yescharacteristic, direct product factor, Sylow
850C22—28no—
851C22—28no—
852C22—28no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—28no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—464no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—44no—
882C22—44no—
883C22C5×#39718yescomplemented
884C22C2×C5×#12011yescharacteristic
885C22C2×C5×#12111yescharacteristic
886C22C2×C5×#12311yescharacteristic
887C22C2×C5×#12311yescharacteristic
888C22C2×C5×#12311yescharacteristic
889C22C2×C5×#12311yescharacteristic
890C22C5×#52512yes—
891C22C5×#52512yes—
892C22C2×C5×#12411yescharacteristic
893C22C2×C5×#12611yescharacteristic
894C22C2×C5×#12611yescharacteristic
895C22C5×#53411yescharacteristic
896C22C5×#53411yescharacteristic
897C22C5×#53812yes—
898C22C5×#53812yes—
899C22C5×D4212yes—
900C22C5×#54612yes—
901C22C5×#54612yes—
902C22C5×#54612yes—
903C22C5×#54612yes—
904C22C5×#55112yes—
905C22C5×#55112yes—
906C22C5×#55112yes—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—82no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4—81no—
915C2—28no—
916C2—44no—
917C2—44no—
918C2C2×C5×#39711yescharacteristic
919C2C5×#240511yescharacteristic
920C2C5×#241011yescharacteristic
921C2C5×#241211yescharacteristic
922C2C5×#241812yes—
923C2C5×#247212yes—
924C2C5×#248012yes—
925C2C5×#248012yes—
926C2C5×#248311yescharacteristic
927C2C5×#262211yescharacteristic
928C2C5×#284911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC26×C5C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#397C2semidirect
3. C2×C5×#385C2semidirect
6. C5×#1440C2semidirect
7. C5×#1440C2semidirect
8. C5×#1439C2semidirect
9. C5×C22⋊#95C2semidirect
10. C5×C22⋊#95C2semidirect
11. C5×C22⋊#95C2semidirect
15. C22×C5×C4⋊C4C22semidirect
34. C2×C5×#95C22semidirect
35. C2×C5×#95C22semidirect
36. C2×C5×#95C22semidirect
37. C2×C5×#95C22semidirect
38. C2×C5×#95C22semidirect
39. C2×C5×#95C22semidirect
40. C2×C5×#95C22semidirect
41. #14727C5direct (N × H)
118. C2×#397C2×C5semidirect
119. C2×#385C2×C5semidirect
122. #1440C2×C5semidirect
123. #1440C2×C5semidirect
124. #1439C2×C5semidirect
125. C22⋊#95C2×C5semidirect
126. C22⋊#95C2×C5semidirect
127. C22⋊#95C2×C5semidirect
259. C22×C4⋊C4C22×C5semidirect
278. C2×#95C22×C5semidirect
279. C2×#95C22×C5semidirect
280. C2×#95C22×C5semidirect
281. C2×#95C22×C5semidirect
282. C2×#95C22×C5semidirect
283. C2×#95C22×C5semidirect
284. C2×#95C22×C5semidirect
534. C22×C5#397semidirect
849. C5#14727direct (N × H)
883. C22C5×#397semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C22⋊C42
C2×C5×#3972
C2×C5×#3852
C2×C5×#3792
C5×#14402
C5×#14392
C5×C22⋊#952
#147275