Finite Group Databasebeta

← C5×#16557 #11939277

Subgroups — C5×#16557 #11939277

Order 1280.

2226 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#121C211yesmaximal, characteristic
2C2×C5×#400C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×C5×#385C211yesmaximal, characteristic, complemented
5C5×#1445C211yesmaximal, characteristic, complemented
6C5×#1440C212yesmaximal, complemented
7C5×#1439C212yesmaximal, complemented
8C5×#1438C211yesmaximal, characteristic, complemented
9C5×#1438C212yesmaximal, complemented
10C5×#1438C212yesmaximal, complemented
11C5×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C5×D4C2212yes—
13C23×C5×D4C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C2×C5×#121—24no—
16C2×C5×#121—24no—
17C2×C5×#121—24no—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2212yes—
23C22×C5×C22⋊C4C2212yes—
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2212yes—
26C22×C5×C22⋊C4C2212yes—
27C22×C5×C22⋊C4C2212yes—
28C22×C5×C22⋊C4C2212yes—
29C5×#400—24no—
30C5×#394—24no—
31C5×#385—24no—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41#16557C511yesmaximal, characteristic, direct product factor, Sylow
42C25×C5C2312yes—
43C25×C5C2311yescharacteristic
44C22×C5×D4—24no—
45C22×C5×D4—24no—
46C22×C5×D4—24no—
47C22×C5×D4—24no—
48C22×C5×D4—24no—
49C22×C5×D4—22no—
50C22×C5×D4—22no—
51C22×C5×D4—42no—
52C22×C5×D4—42no—
53C22×C5×D4—42no—
54C22×C5×D4—42no—
55C22×C5×D4D414yes—
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—42no—
59C23×C4×C5—42no—
60C23×C4×C5D414yes—
61C23×C4×C5C2312yes—
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2312yes—
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2312yes—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C5×#121—232no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—42no—
78C2×C5×C4⋊C4D414yes—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—24no—
81C2×C5×C22⋊C4—24no—
82C2×C5×C22⋊C4—24no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—22no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—24no—
87C2×C5×C22⋊C4—24no—
88C2×C5×C22⋊C4—24no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—42no—
92C2×C5×C22⋊C4—42no—
93C2×C5×C22⋊C4—42no—
94C2×C5×C22⋊C4—42no—
95C2×C5×C22⋊C4—42no—
96C2×C5×C22⋊C4—42no—
97C2×C5×C22⋊C4—42no—
98C2×C5×C22⋊C4—42no—
99C2×C5×C22⋊C4—42no—
100C2×C5×C22⋊C4—42no—
101C2×C5×C22⋊C4—42no—
102C5×#95—22no—
103C5×#95—22no—
104C5×#95—22no—
105C5×#95—24no—
106C5×#95—24no—
107C5×#95—22no—
108C5×#95—42no—
109C5×#95—42no—
110C5×#95—42no—
111C22×#121C2×C511yescharacteristic
112C2×#400C2×C511yescharacteristic, complemented
113C2×#394C2×C511yescharacteristic, complemented
114C2×#385C2×C511yescharacteristic, complemented
115#1445C2×C511yescharacteristic, complemented
116#1440C2×C512yescomplemented
117#1439C2×C512yescomplemented
118#1438C2×C512yescomplemented
119#1438C2×C512yescomplemented
120#1438C2×C511yescharacteristic, complemented
121C22⋊#95C2×C511yescharacteristic, complemented
122C24×C5—21no—
123C24×C5—21no—
124C24×C5—21no—
125C24×C5—21no—
126C24×C5—21no—
127C24×C5—22no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5—21no—
131C24×C5—22no—
132C24×C5—22no—
133C24×C5—22no—
134C24×C5—22no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5—22no—
138C24×C5—22no—
139C24×C5—22no—
140C24×C5—22no—
141C24×C5—22no—
142C24×C5—22no—
143C24×C5—22no—
144C24×C5—22no—
145C24×C5C2×D414yes—
146C24×C5C2×D412yes—
147C24×C5#4114yes—
148C24×C5C2411yescharacteristic
149C2×C5×D4—216no—
150C2×C5×D4—28no—
151C2×C5×D4—48no—
152C2×C5×D4—48no—
153C2×C5×D4—48no—
154C2×C5×D4—44no—
155C2×C5×D4—44no—
156C2×C5×D4—48no—
157C2×C5×D4—48no—
158C2×C5×D4—48no—
159C2×C5×D4—48no—
160C2×C5×D4—48no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—21no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—21no—
183C22×C4×C5—28no—
184C22×C4×C5—21no—
185C22×C4×C5—22no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
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—21no—
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—22no—
206C22×C4×C5—22no—
207C22×C4×C5—21no—
208C22×C4×C5—44no—
209C22×C4×C5—44no—
210C22×C4×C5—48no—
211C22×C4×C5—48no—
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2×D414yes—
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5#4112yes—
218C22×C4×C5#4112yes—
219C5×C4⋊C4—28no—
220C5×C4⋊C4—44no—
221C5×C4⋊C4—44no—
222C5×C22⋊C4—28no—
223C5×C22⋊C4—216no—
224C5×C22⋊C4—48no—
225C5×C22⋊C4—48no—
226C5×C22⋊C4—44no—
227C5×C22⋊C4—48no—
228C5×C22⋊C4—48no—
229C5×C22⋊C4—48no—
230C23×D4C22×C512yes—
231C23×D4C22×C511yescharacteristic
232C24×C4C22×C511yescharacteristic
233C2×#121—24no—
234C2×#121—24no—
235C2×#121—24no—
236C22×C4⋊C4C22×C511yescharacteristic
237C22×C4⋊C4C22×C511yescharacteristic
238C22×C4⋊C4C22×C511yescharacteristic
239C22×C22⋊C4C22×C512yes—
240C22×C22⋊C4C22×C511yescharacteristic
241C22×C22⋊C4C22×C512yes—
242C22×C22⋊C4C22×C512yes—
243C22×C22⋊C4C22×C512yes—
244C22×C22⋊C4C22×C512yes—
245C22×C22⋊C4C22×C511yescharacteristic
246C22×C22⋊C4C22×C512yes—
247#400—24no—
248#394—24no—
249#385—24no—
250C2×#95C22×C511yescharacteristic
251C2×#95C22×C511yescharacteristic
252C2×#95C22×C512yes—
253C2×#95C22×C512yes—
254C2×#95C22×C511yescharacteristic
255C2×#95C22×C511yescharacteristic
256C2×#95C22×C512yes—
257C2×#95C22×C512yes—
258C2×#95C22×C512yes—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—22no—
263C23×C5—22no—
264C23×C5—22no—
265C23×C5—24no—
266C23×C5—24no—
267C23×C5—24no—
268C23×C5—24no—
269C23×C5—24no—
270C23×C5—24no—
271C23×C5—24no—
272C23×C5—24no—
273C23×C5—24no—
274C23×C5—24no—
275C23×C5—24no—
276C23×C5—24no—
277C23×C5—24no—
278C23×C5—42no—
279C23×C5—42no—
280C23×C5—42no—
281C23×C5—42no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—41no—
285C23×C5—41no—
286C23×C5—42no—
287C23×C5—42no—
288C23×C5—42no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—42no—
292C23×C5—42no—
293C23×C5—42no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5—42no—
298C23×C5—42no—
299C23×C5—42no—
300C23×C5—42no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5—42no—
304C23×C5—42no—
305C23×C5—42no—
306C23×C5—42no—
307C23×C5—42no—
308C23×C5—42no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5—42no—
312C23×C5—42no—
313C23×C5—42no—
314C23×C5—42no—
315C23×C5—42no—
316C23×C5#12414yes—
317C23×C5C22×D411yescharacteristic
318C23×C5C22×D411yescharacteristic
319C23×C5C22×D411yescharacteristic
320C23×C5C2×#4111yescharacteristic
321C23×C5C2×#4111yescharacteristic
322C23×C5C2×#4112yes—
323C23×C5H(5,𝔽2)12yes—
324C23×C5H(5,𝔽2)12yes—
325C23×C5H(5,𝔽2)12yes—
326C23×C5H(5,𝔽2)11yescharacteristic
327C23×C52−1+411yescharacteristic
328C5×D4—416no—
329C5×D4—432no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—24no—
333C2×C4×C5—24no—
334C2×C4×C5—22no—
335C2×C4×C5—24no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—24no—
341C2×C4×C5—22no—
342C2×C4×C5—24no—
343C2×C4×C5—24no—
344C2×C4×C5—22no—
345C2×C4×C5—416no—
346C2×C4×C5—41no—
347C2×C4×C5—42no—
348C2×C4×C5—41no—
349C2×C4×C5—42no—
350C2×C4×C5—41no—
351C2×C4×C5—42no—
352C2×C4×C5—42no—
353C2×C4×C5—41no—
354C2×C4×C5—42no—
355C2×C4×C5—42no—
356C2×C4×C5—42no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—42no—
362C2×C4×C5—42no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—42no—
370C2×C4×C5—42no—
371C2×C4×C5—42no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5#12014yes—
384C25C23×C512yes—
385C25C23×C511yescharacteristic
386C22×D4—24no—
387C22×D4—24no—
388C22×D4—24no—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—42no—
396C22×D4—42no—
397C22×D4C5×D414yes—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C5×D414yes—
403C23×C4C23×C511yescharacteristic
404C23×C4C23×C512yes—
405C23×C4C23×C511yescharacteristic
406C23×C4C23×C512yes—
407C23×C4C23×C511yescharacteristic
408C23×C4C23×C512yes—
409C23×C4C23×C511yescharacteristic
410C23×C4C23×C511yescharacteristic
411C23×C4C23×C511yescharacteristic
412#121—232no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4C5×D414yes—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—24no—
448#95—22no—
449#95—24no—
450#95—42no—
451#95—42no—
452#95—42no—
453C22×C5—24no—
454C22×C5—24no—
455C22×C5—24no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—42no—
459C22×C5—44no—
460C22×C5—44no—
461C22×C5—44no—
462C22×C5—44no—
463C22×C5—42no—
464C22×C5—44no—
465C22×C5—44no—
466C22×C5—44no—
467C22×C5—44no—
468C22×C5—44no—
469C22×C5—44no—
470C22×C5—44no—
471C22×C5—82no—
472C22×C5—82no—
473C22×C5—82no—
474C22×C5—82no—
475C22×C5—82no—
476C22×C5—82no—
477C22×C5—82no—
478C22×C5—82no—
479C22×C5C2×#12011yescharacteristic
480C22×C5#52511yescharacteristic
481C22×C5C2×#12411yescharacteristic
482C22×C5#53411yescharacteristic
483C22×C5#53411yescharacteristic
484C22×C5#53412yes—
485C22×C5#53512yes—
486C22×C5#53511yescharacteristic
487C22×C5#53711yescharacteristic
488C22×C5#53812yes—
489C22×C5#53812yes—
490C22×C5#53912yes—
491C22×C5#54012yes—
492C22×C5#54611yescharacteristic
493C22×C5#54612yes—
494C22×C5#54612yes—
495C22×C5#54711yescharacteristic
496C22×C5#54811yescharacteristic
497C22×C5#55011yescharacteristic
498C22×C5#55312yes—
499C22×C5#55312yes—
500C22×C5#56012yes—
501C22×C5#56212yes—
502C4×C5—24no—
503C4×C5—42no—
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—44no—
507C4×C5—81no—
508C4×C5—82no—
509C4×C5—82no—
510C4×C5—81no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24C2×C5×D414yes—
535C24C2×C5×D412yes—
536C24C5×#4114yes—
537C24C24×C511yescharacteristic
538C2×D4—216no—
539C2×D4—28no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4C2×C5×D414yes—
602C22×C4C2×C5×D412yes—
603C22×C4C2×C5×D412yes—
604C22×C4C2×C5×D412yes—
605C22×C4C2×C5×D412yes—
606C22×C4C5×#4112yes—
607C22×C4C5×#4112yes—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C22⋊C4—216no—
612C22⋊C4—28no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C2×C5—44no—
620C2×C5—84no—
621C2×C5#240711yescharacteristic
622C2×C5#243511yescharacteristic
623C2×C5#259111yescharacteristic
624C2×C5#261311yescharacteristic
625C2×C5#263511yescharacteristic
626C2×C5#263911yescharacteristic
627C2×C5#268812yes—
628C2×C5#270812yes—
629C2×C5#271112yes—
630C2×C5#271412yes—
631C2×C5#281311yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23C5×#12414yes—
690C23C22×C5×D411yescharacteristic
691C23C22×C5×D411yescharacteristic
692C23C22×C5×D411yescharacteristic
693C23C2×C5×#4111yescharacteristic
694C23C2×C5×#4111yescharacteristic
695C23C2×C5×#4112yes—
696C23C5×H(5,𝔽2)12yes—
697C23C5×H(5,𝔽2)12yes—
698C23C5×H(5,𝔽2)12yes—
699C23C5×H(5,𝔽2)11yescharacteristic
700C23C5×2−1+411yescharacteristic
701D4—416no—
702D4—432no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—416no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C5×#12014yes—
757C5#1655711yescharacteristic, direct product factor, Sylow
758C22—24no—
759C22—24no—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C2×C5×#12011yescharacteristic
785C22C5×#52511yescharacteristic
786C22C2×C5×#12411yescharacteristic
787C22C5×#53411yescharacteristic
788C22C5×#53411yescharacteristic
789C22C5×#53412yes—
790C22C5×#53511yescharacteristic
791C22C5×#53512yes—
792C22C5×#53711yescharacteristic
793C22C5×#53812yes—
794C22C5×#53812yes—
795C22C5×#53912yes—
796C22C5×#54012yes—
797C22C5×#54611yescharacteristic
798C22C5×#54612yes—
799C22C5×#54612yes—
800C22C5×#54711yescharacteristic
801C22C5×#54811yescharacteristic
802C22C5×#55011yescharacteristic
803C22C5×#55312yes—
804C22C5×#55312yes—
805C22C5×#56012yes—
806C22C5×#56212yes—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—44no—
812C4—81no—
813C4—81no—
814C4—82no—
815C4—82no—
816C2—44no—
817C2—84no—
818C2C5×#240711yescharacteristic
819C2C5×#243511yescharacteristic
820C2C5×#259111yescharacteristic
821C2C5×#261311yescharacteristic
822C2C5×#263511yescharacteristic
823C2C5×#263911yescharacteristic
824C2C5×#268812yes—
825C2C5×#270812yes—
826C2C5×#271112yes—
827C2C5×#271412yes—
828C2C5×#281311yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC22×C5×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#400C2semidirect
3. C2×C5×#394C2semidirect
4. C2×C5×#385C2semidirect
5. C5×#1445C2semidirect
6. C5×#1440C2semidirect
7. C5×#1439C2semidirect
8. C5×#1438C2semidirect
9. C5×#1438C2semidirect
10. C5×#1438C2semidirect
11. C5×C22⋊#95C2semidirect
41. #16557C5direct (N × H)
112. C2×#400C2×C5semidirect
113. C2×#394C2×C5semidirect
114. C2×#385C2×C5semidirect
115. #1445C2×C5semidirect
116. #1440C2×C5semidirect
117. #1439C2×C5semidirect
118. #1438C2×C5semidirect
119. #1438C2×C5semidirect
120. #1438C2×C5semidirect
121. C22⋊#95C2×C5semidirect
757. C5#16557direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1212
C2×C5×#4002
C2×C5×#3942
C2×C5×#3852
C5×#14452
C5×#14402
C5×#14392
C5×#14382
C5×C22⋊#952
#165575