Finite Group Databasebeta

← C5×#14016 #11936736

Subgroups — C5×#14016 #11936736

Order 1280.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic
2C2×C5×#386C211yesmaximal, characteristic
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#385C211yesmaximal, characteristic, complemented
5C22×C5×#95C211yesmaximal, characteristic, complemented
6C5×#1442C212yesmaximal, complemented
7C5×#1439C212yesmaximal, complemented
8C5×#1436C212yesmaximal, complemented
9C5×C22⋊#95C212yesmaximal, complemented
10C5×C22⋊#95C211yesmaximal, characteristic, complemented
11C5×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C24×C4×C5C2211yescharacteristic
16C24×C4×C5C2211yescharacteristic
17C2×C4×C5×D4—24no—
18C2×C4×C5×D4—24no—
19C2×C4×C5×D4—24no—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2212yes—
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2212yes—
28C22×C42×C5C2211yescharacteristic
29C5×#386—24no—
30C5×#386C418yescomplemented
31C5×#385—24no—
32C2×C5×#95—24no—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41C2×C5×#95C2212yes—
42#14016C511yesmaximal, characteristic, direct product factor, Sylow
43C25×C5C2311yescharacteristic
44C25×C5C2311yescharacteristic
45C22×C5×D4—22no—
46C22×C5×D4—22no—
47C22×C5×D4—22no—
48C22×C5×D4—22no—
49C22×C5×D4C2×C414yes—
50C22×C5×D4D414yes—
51C22×C5×D4Q814yes—
52C23×C4×C5—22no—
53C23×C4×C5—22no—
54C23×C4×C5—22no—
55C23×C4×C5—22no—
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—24no—
61C23×C4×C5—24no—
62C23×C4×C5—22no—
63C23×C4×C5—22no—
64C23×C4×C5—24no—
65C23×C4×C5—42no—
66C23×C4×C5—42no—
67C23×C4×C5—42no—
68C23×C4×C5—42no—
69C23×C4×C5—42no—
70C23×C4×C5C2×C414yescomplemented
71C23×C4×C5D414yes—
72C23×C4×C5C2312yes—
73C23×C4×C5C2312yes—
74C23×C4×C5C2312yes—
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2312yes—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C4×C5×D4—232no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—24no—
86C2×C5×C4⋊C4—24no—
87C2×C5×C4⋊C4—42no—
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⋊C4—24no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4—42no—
101C2×C5×C22⋊C4—42no—
102C2×C5×C22⋊C4—42no—
103C2×C5×C22⋊C4C2×C414yescomplemented
104C2×C5×C22⋊C4C2×C418yescomplemented
105C2×C5×C22⋊C4D414yes—
106C2×C42×C5—22no—
107C2×C42×C5—22no—
108C2×C42×C5—22no—
109C5×#95—24no—
110C5×#95—24no—
111C5×#95—24no—
112C5×#95—24no—
113C5×#95—24no—
114C5×#95—42no—
115C5×#95—42no—
116C5×#95—42no—
117C5×#95C2×C418yescomplemented
118C22×C4×D4C2×C511yescharacteristic
119C2×#386C2×C511yescharacteristic
120C2×#386C2×C511yescharacteristic
121C2×#385C2×C511yescharacteristic, complemented
122C22×#95C2×C511yescharacteristic, complemented
123#1442C2×C512yescomplemented
124#1439C2×C512yescomplemented
125#1436C2×C512yescomplemented
126C22⋊#95C2×C511yescharacteristic, complemented
127C22⋊#95C2×C511yescharacteristic, complemented
128C22⋊#95C2×C512yescomplemented
129C24×C5—22no—
130C24×C5—22no—
131C24×C5—22no—
132C24×C5—22no—
133C24×C5—21no—
134C24×C5—21no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5—21no—
138C24×C5—21no—
139C24×C5—22no—
140C24×C5—22no—
141C24×C5C22×C412yes—
142C24×C5C22×C412yes—
143C24×C5C2×D412yes—
144C24×C5C2×D412yes—
145C24×C5C2×D412yes—
146C24×C5C2×D412yes—
147C24×C5C2×Q812yes—
148C24×C5C2×Q812yes—
149C24×C5#4112yes—
150C24×C5#4112yes—
151C24×C5C2411yescharacteristic
152C2×C5×D4—28no—
153C2×C5×D4—28no—
154C2×C5×D4—28no—
155C2×C5×D4—28no—
156C2×C5×D4—28no—
157C2×C5×D4—28no—
158C2×C5×D4C4⋊C4116yescomplemented
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—22no—
166C22×C4×C5—28no—
167C22×C4×C5—28no—
168C22×C4×C5—28no—
169C22×C4×C5—28no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
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—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
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—28no—
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—22no—
208C22×C4×C5—48no—
209C22×C4×C5—44no—
210C22×C4×C5—48no—
211C22×C4×C5—48no—
212C22×C4×C5—48no—
213C22×C4×C5—48no—
214C22×C4×C5—48no—
215C22×C4×C5—48no—
216C22×C4×C5—44no—
217C22×C4×C5—44no—
218C22×C4×C5—44no—
219C22×C4×C5—44no—
220C22×C4×C5—48no—
221C22×C4×C5—44no—
222C22×C4×C5—44no—
223C22×C4×C5C22×C414yes—
224C22×C4×C5C22×C414yes—
225C22×C4×C5C22×C412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2×D412yes—
230C22×C4×C5C2×D412yes—
231C22×C4×C5C2×Q812yes—
232C22×C4×C5#4114yes—
233C22×C4×C5#4114yes—
234C5×C4⋊C4—28no—
235C5×C4⋊C4—48no—
236C5×C22⋊C4—28no—
237C5×C22⋊C4—28no—
238C5×C22⋊C4—28no—
239C5×C22⋊C4—48no—
240C5×C22⋊C4—48no—
241C5×C22⋊C4—44no—
242C42×C5—28no—
243C23×D4C22×C511yescharacteristic
244C24×C4C22×C511yescharacteristic
245C24×C4C22×C511yescharacteristic
246C24×C4C22×C511yescharacteristic
247C24×C4C22×C511yescharacteristic
248C2×C4×D4—24no—
249C2×C4×D4—24no—
250C2×C4×D4—24no—
251C22×C4⋊C4C22×C511yescharacteristic
252C22×C4⋊C4C22×C512yes—
253C22×C22⋊C4C22×C511yescharacteristic
254C22×C22⋊C4C22×C511yescharacteristic
255C22×C22⋊C4C22×C512yes—
256C22×C22⋊C4C22×C511yescharacteristic
257C22×C22⋊C4C22×C511yescharacteristic
258C22×C22⋊C4C22×C512yes—
259C22×C42C22×C511yescharacteristic
260#386—24no—
261#386C4×C518yescomplemented
262#385—24no—
263C2×#95—24no—
264C2×#95C22×C512yes—
265C2×#95C22×C512yes—
266C2×#95C22×C512yes—
267C2×#95C22×C512yes—
268C2×#95C22×C512yes—
269C2×#95C22×C512yes—
270C2×#95C22×C512yes—
271C2×#95C22×C512yes—
272C2×#95C22×C512yes—
273C23×C5—24no—
274C23×C5—24no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—24no—
278C23×C5—22no—
279C23×C5—22no—
280C23×C5—24no—
281C23×C5—24no—
282C23×C5—24no—
283C23×C5—24no—
284C23×C5—24no—
285C23×C5—24no—
286C23×C5—24no—
287C23×C5—24no—
288C23×C5—24no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—22no—
297C23×C5—24no—
298C23×C5—24no—
299C23×C5—24no—
300C23×C5—24no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—42no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—42no—
307C23×C5—42no—
308C23×C5—42no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5C2×C4⋊C414yes—
312C23×C5C2×C4⋊C414yes—
313C23×C5C4×D414yes—
314C23×C5C4×D414yes—
315C23×C5#12014yes—
316C23×C5C22⋊Q814yes—
317C23×C5C22⋊Q814yes—
318C23×C5#12314yes—
319C23×C5C23×C411yescharacteristic
320C23×C5C22×D411yescharacteristic
321C23×C5C22×D411yescharacteristic
322C23×C5C22×D411yescharacteristic
323C23×C5C22×Q811yescharacteristic
324C23×C5C2×#4111yescharacteristic
325C23×C5C2×#4111yescharacteristic
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C5×D4—232no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—24no—
340C2×C4×C5—24no—
341C2×C4×C5—24no—
342C2×C4×C5—24no—
343C2×C4×C5—24no—
344C2×C4×C5—24no—
345C2×C4×C5—24no—
346C2×C4×C5—24no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—24no—
352C2×C4×C5—22no—
353C2×C4×C5—24no—
354C2×C4×C5—24no—
355C2×C4×C5—24no—
356C2×C4×C5—24no—
357C2×C4×C5—416no—
358C2×C4×C5—416no—
359C2×C4×C5—416no—
360C2×C4×C5—416no—
361C2×C4×C5—42no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—42no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—42no—
368C2×C4×C5—42no—
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—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5C2×C4⋊C414yes—
389C2×C4×C5#12314yes—
390C25C23×C511yescharacteristic
391C25C23×C511yescharacteristic
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4C2×C4×C514yes—
397C22×D4C5×D414yes—
398C22×D4C5×Q814yes—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4C2×C4×C514yescomplemented
418C23×C4C5×D414yes—
419C23×C4C23×C512yes—
420C23×C4C23×C512yes—
421C23×C4C23×C512yes—
422C23×C4C23×C511yescharacteristic
423C23×C4C23×C511yescharacteristic
424C23×C4C23×C511yescharacteristic
425C23×C4C23×C512yes—
426C23×C4C23×C511yescharacteristic
427C23×C4C23×C511yescharacteristic
428C4×D4—232no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—42no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4C2×C4×C514yescomplemented
451C2×C22⋊C4C2×C4×C518yescomplemented
452C2×C22⋊C4C5×D414yes—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95C2×C4×C518yescomplemented
465C22×C5—24no—
466C22×C5—24no—
467C22×C5—28no—
468C22×C5—28no—
469C22×C5—24no—
470C22×C5—24no—
471C22×C5—28no—
472C22×C5—28no—
473C22×C5—24no—
474C22×C5—24no—
475C22×C5—28no—
476C22×C5—24no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5—44no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—44no—
483C22×C5—44no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5#38518yes—
487C22×C5C22×C4⋊C411yescharacteristic
488C22×C5C2×C4×D411yescharacteristic
489C22×C5C2×C4×D411yescharacteristic
490C22×C5C4×#4112yes—
491C22×C5#51812yes—
492C22×C5C2×#12011yescharacteristic
493C22×C5C2×C22⋊Q811yescharacteristic
494C22×C5C2×C22⋊Q811yescharacteristic
495C22×C5C2×#12311yescharacteristic
496C22×C5C2×#12311yescharacteristic
497C22×C5#52511yescharacteristic
498C22×C5#52912yes—
499C22×C5#53411yescharacteristic
500C22×C5#53511yescharacteristic
501C22×C5#53812yes—
502C22×C5#54612yes—
503C22×C5#54612yes—
504C22×C5#54612yes—
505C22×C5#54612yes—
506C22×C5#55312yes—
507C22×C5#55312yes—
508C22×C5#55412yes—
509C22×C5#55412yes—
510C4×C5—24no—
511C4×C5—24no—
512C4×C5—44no—
513C4×C5—44no—
514C4×C5—42no—
515C4×C5—44no—
516C4×C5—42no—
517C4×C5—42no—
518C4×C5—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—21no—
528C24—21no—
529C24—22no—
530C24—22no—
531C24C22×C4×C512yes—
532C24C22×C4×C512yes—
533C24C2×C5×D412yes—
534C24C2×C5×D412yes—
535C24C2×C5×D412yes—
536C24C2×C5×D412yes—
537C24C2×C5×Q812yes—
538C24C2×C5×Q812yes—
539C24C5×#4112yes—
540C24C5×#4112yes—
541C24C24×C511yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4C5×C4⋊C4116yescomplemented
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
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—28no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4C22×C4×C514yes—
614C22×C4C22×C4×C514yes—
615C22×C4C22×C4×C512yes—
616C22×C4C2×C5×D412yes—
617C22×C4C2×C5×D412yes—
618C22×C4C2×C5×D412yes—
619C22×C4C2×C5×D412yes—
620C22×C4C2×C5×D412yes—
621C22×C4C2×C5×Q812yes—
622C22×C4C5×#4114yes—
623C22×C4C5×#4114yes—
624C4⋊C4—28no—
625C4⋊C4—48no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C42—28no—
633C2×C5—28no—
634C2×C5—44no—
635C2×C5C2×#38511yescharacteristic
636C2×C5C4×#12311yescharacteristic
637C2×C5#232111yescharacteristic
638C2×C5#234912yes—
639C2×C5#236412yes—
640C2×C5#240411yescharacteristic
641C2×C5#240511yescharacteristic
642C2×C5#244412yes—
643C2×C5#245012yes—
644C2×C5#248711yescharacteristic
645C2×C5#257911yescharacteristic
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23C2×C5×C4⋊C414yes—
685C23C2×C5×C4⋊C414yes—
686C23C4×C5×D414yes—
687C23C4×C5×D414yes—
688C23C5×#12014yes—
689C23C5×C22⋊Q814yes—
690C23C5×C22⋊Q814yes—
691C23C5×#12314yes—
692C23C23×C4×C511yescharacteristic
693C23C22×C5×D411yescharacteristic
694C23C22×C5×D411yescharacteristic
695C23C22×C5×D411yescharacteristic
696C23C22×C5×Q811yescharacteristic
697C23C2×C5×#4111yescharacteristic
698C23C2×C5×#4111yescharacteristic
699C23C2×C5×#4112yes—
700C23C2×C5×#4112yes—
701C23C5×H(5,𝔽2)12yes—
702C23C5×H(5,𝔽2)12yes—
703D4—232no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—416no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
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×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4C2×C5×C4⋊C414yes—
762C2×C4C5×#12314yes—
763C5#1401611yescharacteristic, direct product factor, Sylow
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—28no—
769C22—28no—
770C22—24no—
771C22—24no—
772C22—28no—
773C22—28no—
774C22—24no—
775C22—28no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22C5×#38518yes—
786C22C22×C5×C4⋊C411yescharacteristic
787C22C2×C4×C5×D411yescharacteristic
788C22C2×C4×C5×D411yescharacteristic
789C22C4×C5×#4112yes—
790C22C5×#51812yes—
791C22C2×C5×#12011yescharacteristic
792C22C2×C5×C22⋊Q811yescharacteristic
793C22C2×C5×C22⋊Q811yescharacteristic
794C22C2×C5×#12311yescharacteristic
795C22C2×C5×#12311yescharacteristic
796C22C5×#52511yescharacteristic
797C22C5×#52912yes—
798C22C5×#53411yescharacteristic
799C22C5×#53511yescharacteristic
800C22C5×#53812yes—
801C22C5×#54612yes—
802C22C5×#54612yes—
803C22C5×#54612yes—
804C22C5×#54612yes—
805C22C5×#55312yes—
806C22C5×#55312yes—
807C22C5×#55412yes—
808C22C5×#55412yes—
809C4—24no—
810C4—24no—
811C4—44no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—82no—
818C2—28no—
819C2—44no—
820C2C2×C5×#38511yescharacteristic
821C2C4×C5×#12311yescharacteristic
822C2C5×#232111yescharacteristic
823C2C5×#234912yes—
824C2C5×#236412yes—
825C2C5×#240411yescharacteristic
826C2C5×#240511yescharacteristic
827C2C5×#244412yes—
828C2C5×#245012yes—
829C2C5×#248711yescharacteristic
830C2C5×#257911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C5×#385C2semidirect
5. C22×C5×#95C2semidirect
6. C5×#1442C2semidirect
7. C5×#1439C2semidirect
8. C5×#1436C2semidirect
9. C5×C22⋊#95C2semidirect
10. C5×C22⋊#95C2semidirect
11. C5×C22⋊#95C2semidirect
30. C5×#386C4semidirect
42. #14016C5direct (N × H)
70. C23×C4×C5C2×C4semidirect
103. C2×C5×C22⋊C4C2×C4semidirect
104. C2×C5×C22⋊C4C2×C4semidirect
117. C5×#95C2×C4semidirect
121. C2×#385C2×C5semidirect
122. C22×#95C2×C5semidirect
123. #1442C2×C5semidirect
124. #1439C2×C5semidirect
125. #1436C2×C5semidirect
126. C22⋊#95C2×C5semidirect
127. C22⋊#95C2×C5semidirect
128. C22⋊#95C2×C5semidirect
158. C2×C5×D4C4⋊C4semidirect
261. #386C4×C5semidirect
417. C23×C4C2×C4×C5semidirect
450. C2×C22⋊C4C2×C4×C5semidirect
451. C2×C22⋊C4C2×C4×C5semidirect
464. #95C2×C4×C5semidirect
548. C2×D4C5×C4⋊C4semidirect
763. C5#14016direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C2×C5×#3862
C2×C5×#3852
C22×C5×#952
C5×#14422
C5×#14392
C5×#14362
C5×C22⋊#952
#140165