Finite Group Databasebeta

← C5×#24142 #11946862

Subgroups — C5×#24142 #11946862

Order 1280.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3505C211yesmaximal, characteristic, complemented
2C5×#2626C211yesmaximal, characteristic, complemented
3C5×#2617C211yesmaximal, characteristic, complemented
4C5×#2321C211yesmaximal, characteristic, complemented
5C5×#2044C212yesmaximal, complemented
6C5×#2021C212yesmaximal, complemented
7C5×#1996C211yesmaximal, characteristic, complemented
8C5×#1964C211yesmaximal, characteristic, complemented
9C5×#1889C212yesmaximal, complemented
10C5×#1867C212yesmaximal, complemented
11C5×#1799C211yesmaximal, characteristic, complemented
12C5×#553—22no—
13C5×#553—21no—
14C5×#552—21no—
15C5×#551—22no—
16C5×#548—21no—
17C5×#546—21no—
18C5×#539—21no—
19C5×#538—21no—
20C5×#534C2212yes—
21C5×#529—21no—
22C5×#525—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C5×#120C2211yescharacteristic
26C2×C5×#120C2212yes—
27C5×#518C2212yes—
28C2×C4×C5×D4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C2×C5×#99C2212yes—
31C2×C5×#99C2212yes—
32C2×C5×#99C2212yes—
33C5×#399—21no—
34C5×#397—21no—
35C5×#396—22no—
36C5×#394—22no—
37C5×#393—21no—
38C5×#392—21no—
39C5×#390—21no—
40C5×#388—21no—
41C5×#388—21no—
42C5×#386—21no—
43C5×#386C2211yescharacteristic
44C5×#386C2212yes—
45C5×#385C2212yes—
46C5×#385C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C5×#379C2212yes—
50C5×#379C2211yescharacteristic
51C4×C5×C22⋊C4C2211yescharacteristic
52C5×#342C2212yes—
53C5×#342C2212yes—
54C5×#342C2212yes—
55#24142C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C2×C5×#41—21no—
58C22×C5×Q8D411yescharacteristic, complemented
59C22×C5×D4—21no—
60C22×C5×D4—22no—
61C22×C5×D4D411yescharacteristic, complemented
62C22×C5×D4C2311yescharacteristic
63C22×C5×D4C2312yes—
64C23×C4×C5D411yescharacteristic, complemented
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C5×#126—22no—
68C5×#126—22no—
69C5×#126—22no—
70C5×#125—21no—
71C5×#125—22no—
72C5×#124—21no—
73C5×#124—22no—
74C5×#123—22no—
75C5×#123—22no—
76C5×#123—22no—
77C5×#123—22no—
78C5×#123—22no—
79C5×C22⋊Q8—21no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—21no—
85C5×#121—21no—
86C5×#121—22no—
87C5×#121—21no—
88C5×#121—21no—
89C5×#121—21no—
90C5×#121—21no—
91C5×#121—22no—
92C5×#121—22no—
93C5×#120—22no—
94C5×#120—22no—
95C5×#120—22no—
96C5×#120—22no—
97C5×#120—24no—
98C5×#120—42no—
99C4×C5×Q8—21no—
100C4×C5×D4—22no—
101C4×C5×D4—21no—
102C4×C5×D4—21no—
103C4×C5×D4—21no—
104C4×C5×D4—21no—
105C4×C5×D4—21no—
106C4×C5×D4—22no—
107C4×C5×D4—22no—
108C4×C5×D4—22no—
109C4×C5×D4—22no—
110C5×#117—21no—
111C5×#117—22no—
112C5×#117—22no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—22no—
117C2×C5×C4⋊C4D411yescharacteristic, complemented
118C2×C5×C4⋊C4D412yescomplemented
119C2×C5×C4⋊C4D411yescharacteristic, complemented
120C2×C5×C4⋊C4D411yescharacteristic, complemented
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4—21no—
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—21no—
134C2×C5×C22⋊C4—22no—
135C2×C5×C22⋊C4—22no—
136C2×C5×C22⋊C4D411yescharacteristic, complemented
137C2×C5×C22⋊C4D412yescomplemented
138C2×C5×C22⋊C4C2311yescharacteristic
139C2×C5×C22⋊C4C2312yes—
140C2×C5×C22⋊C4C2312yes—
141C2×C5×C22⋊C4C2311yescharacteristic
142C2×C5×C22⋊C4C2312yes—
143C2×C5×C22⋊C4C2311yescharacteristic
144C2×C42×C5—21no—
145C2×C42×C5D411yescharacteristic, complemented
146C5×#99—24no—
147C5×#99—42no—
148C5×#99—42no—
149C5×#95—21no—
150C5×#95—21no—
151C5×#95—21no—
152C5×#95—21no—
153C5×#95—22no—
154C5×#95—21no—
155C5×#95—22no—
156#3505C2×C511yescharacteristic, complemented
157#2626C2×C511yescharacteristic, complemented
158#2617C2×C511yescharacteristic, complemented
159#2321C2×C511yescharacteristic, complemented
160#2044C2×C512yescomplemented
161#2021C2×C512yescomplemented
162#1996C2×C511yescharacteristic, complemented
163#1964C2×C511yescharacteristic, complemented
164#1889C2×C512yescomplemented
165#1867C2×C512yescomplemented
166#1799C2×C511yescharacteristic, complemented
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—81no—
174C24×C5—81no—
175C24×C5C2×D412yes—
176C24×C5C2×D411yescharacteristic
177C24×C5#4112yescomplemented
178C24×C5C2411yescharacteristic
179C5×#41—82no—
180C2×C5×Q8—21no—
181C2×C5×Q8—21no—
182C2×C5×Q8—81no—
183C2×C5×D4—21no—
184C2×C5×D4—22no—
185C2×C5×D4—21no—
186C2×C5×D4—22no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4—22no—
190C2×C5×D4—22no—
191C2×C5×D4—22no—
192C2×C5×D4—21no—
193C2×C5×D4—21no—
194C2×C5×D4—22no—
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C2×C5×D4—24no—
198C2×C5×D4—21no—
199C2×C5×D4—21no—
200C2×C5×D4—44no—
201C2×C5×D4—81no—
202C2×C5×D4—81no—
203C2×C5×D4—81no—
204C2×C5×D4—82no—
205C2×C5×D4—82no—
206C22×C4×C5—21no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—21no—
217C22×C4×C5—81no—
218C22×C4×C5—81no—
219C22×C4×C5—81no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D412yes—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C5×C4⋊C4—22no—
233C5×C4⋊C4—22no—
234C5×C4⋊C4—22no—
235C5×C4⋊C4—22no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—22no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—22no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—81no—
245C5×C4⋊C4—81no—
246C5×C4⋊C4—81no—
247C5×C4⋊C4—82no—
248C5×C22⋊C4—22no—
249C5×C22⋊C4—22no—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—22no—
252C5×C22⋊C4—22no—
253C5×C22⋊C4—22no—
254C5×C22⋊C4—22no—
255C5×C22⋊C4—21no—
256C5×C22⋊C4—22no—
257C5×C22⋊C4—21no—
258C5×C22⋊C4—22no—
259C5×C22⋊C4—21no—
260C5×C22⋊C4—22no—
261C5×C22⋊C4—21no—
262C5×C22⋊C4—21no—
263C5×C22⋊C4—22no—
264C5×C22⋊C4—22no—
265C5×C22⋊C4—22no—
266C5×C22⋊C4—22no—
267C5×C22⋊C4—21no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—21no—
270C5×C22⋊C4—44no—
271C5×C22⋊C4—41no—
272C5×C22⋊C4—41no—
273C5×C22⋊C4—41no—
274C5×C22⋊C4—41no—
275C5×C22⋊C4—81no—
276C5×C22⋊C4—82no—
277C5×C22⋊C4—81no—
278C5×C22⋊C4—82no—
279C5×C22⋊C4—81no—
280C5×C22⋊C4—82no—
281C5×C22⋊C4#4112yescomplemented
282C42×C5—22no—
283C42×C5—22no—
284C42×C5—21no—
285C42×C5—21no—
286C42×C5—81no—
287#553—22no—
288#553—21no—
289#552—21no—
290#551—22no—
291#548—21no—
292#546—21no—
293#539—21no—
294#538—21no—
295#534C22×C512yes—
296#529—21no—
297#525—21no—
298C2×C22⋊Q8C22×C511yescharacteristic
299C2×#121C22×C511yescharacteristic
300C2×#120C22×C511yescharacteristic
301C2×#120C22×C512yes—
302#518C22×C512yes—
303C2×C4×D4C22×C511yescharacteristic
304C22×C22⋊C4C22×C511yescharacteristic
305C2×#99C22×C512yes—
306C2×#99C22×C512yes—
307C2×#99C22×C512yes—
308#399—21no—
309#397—21no—
310#396—22no—
311#394—22no—
312#393—21no—
313#392—21no—
314#390—21no—
315#388—21no—
316#388—21no—
317#386—21no—
318#386C22×C511yescharacteristic
319#386C22×C512yes—
320#385C22×C511yescharacteristic
321#385C22×C512yes—
322#380C22×C511yescharacteristic
323#380C22×C511yescharacteristic
324#379C22×C511yescharacteristic
325#379C22×C512yes—
326C4×C22⋊C4C22×C511yescharacteristic
327#342C22×C512yes—
328#342C22×C512yes—
329#342C22×C512yes—
330C23×C5—21no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—21no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—21no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—42no—
344C23×C5—41no—
345C23×C5—42no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—42no—
349C23×C5—41no—
350C23×C5—42no—
351C23×C5—42no—
352C23×C5—42no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5—82no—
358C23×C5—82no—
359C23×C5—82no—
360C23×C5—82no—
361C23×C5C22×D411yescharacteristic
362C23×C5C22×D411yescharacteristic
363C23×C5C22×D411yescharacteristic
364C23×C5C2×#4111yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5H(5,𝔽2)11yescharacteristic
367C23×C52−1+411yescharacteristic
368C5×Q8—42no—
369C5×Q8—81no—
370C5×D4—42no—
371C5×D4—42no—
372C5×D4—42no—
373C5×D4—41no—
374C5×D4—41no—
375C5×D4—41no—
376C5×D4—42no—
377C5×D4—41no—
378C5×D4—42no—
379C5×D4—81no—
380C5×D4—82no—
381C5×D4—84no—
382C5×D4—82no—
383C5×D4—88no—
384C2×C4×C5—21no—
385C2×C4×C5—22no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—21no—
391C2×C4×C5—22no—
392C2×C4×C5—21no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—42no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—42no—
406C2×C4×C5—41no—
407C2×C4×C5—42no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—42no—
411C2×C4×C5—42no—
412C2×C4×C5—41no—
413C2×C4×C5—42no—
414C2×C4×C5—42no—
415C2×C4×C5—42no—
416C2×C4×C5—41no—
417C2×C4×C5—42no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—42no—
421C2×C4×C5—42no—
422C2×C4×C5—81no—
423C2×C4×C5—82no—
424C2×C4×C5—82no—
425C2×C4×C5#12011yescharacteristic
426C2×C4×C5#12011yescharacteristic
427C2×C4×C5#12011yescharacteristic
428C2×C4×C5#12011yescharacteristic
429C25C23×C511yescharacteristic
430C2×#41—21no—
431C22×Q8C5×D411yescharacteristic, complemented
432C22×D4—21no—
433C22×D4—22no—
434C22×D4C5×D411yescharacteristic, complemented
435C22×D4C23×C511yescharacteristic
436C22×D4C23×C512yes—
437C23×C4C5×D411yescharacteristic, complemented
438C23×C4C23×C511yescharacteristic
439C23×C4C23×C511yescharacteristic
440#126—22no—
441#126—22no—
442#126—22no—
443#125—21no—
444#125—22no—
445#124—21no—
446#124—22no—
447#123—22no—
448#123—22no—
449#123—22no—
450#123—22no—
451#123—22no—
452C22⋊Q8—21no—
453C22⋊Q8—22no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458#121—21no—
459#121—22no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—22no—
465#121—22no—
466#120—22no—
467#120—22no—
468#120—22no—
469#120—22no—
470#120—24no—
471#120—42no—
472C4×Q8—21no—
473C4×D4—22no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483#117—21no—
484#117—22no—
485#117—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4C5×D411yescharacteristic, complemented
491C2×C4⋊C4C5×D411yescharacteristic, complemented
492C2×C4⋊C4C5×D412yescomplemented
493C2×C4⋊C4C5×D411yescharacteristic, complemented
494C2×C22⋊C4—22no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4C5×D411yescharacteristic, complemented
510C2×C22⋊C4C5×D412yescomplemented
511C2×C22⋊C4C23×C512yes—
512C2×C22⋊C4C23×C511yescharacteristic
513C2×C22⋊C4C23×C512yes—
514C2×C22⋊C4C23×C511yescharacteristic
515C2×C22⋊C4C23×C512yes—
516C2×C22⋊C4C23×C511yescharacteristic
517C2×C42—21no—
518C2×C42C5×D411yescharacteristic, complemented
519#99—24no—
520#99—42no—
521#99—42no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—21no—
528#95—22no—
529C22×C5—21no—
530C22×C5—21no—
531C22×C5—21no—
532C22×C5—21no—
533C22×C5—21no—
534C22×C5—21no—
535C22×C5—41no—
536C22×C5—41no—
537C22×C5—41no—
538C22×C5—41no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—44no—
542C22×C5—42no—
543C22×C5—44no—
544C22×C5—41no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—41no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—41no—
551C22×C5—82no—
552C22×C5—81no—
553C22×C5—82no—
554C22×C5—82no—
555C22×C5—81no—
556C22×C5—81no—
557C22×C5—82no—
558C22×C5—81no—
559C22×C5—81no—
560C22×C5C2×#12011yescharacteristic
561C22×C5#52511yescharacteristic
562C22×C5#53711yescharacteristic
563C22×C5#54611yescharacteristic
564C22×C5#54711yescharacteristic
565C22×C5#54811yescharacteristic
566C22×C5#55011yescharacteristic
567C4×C5—21no—
568C4×C5—21no—
569C4×C5—21no—
570C4×C5—21no—
571C4×C5—42no—
572C4×C5—41no—
573C4×C5—42no—
574C4×C5—41no—
575C4×C5—42no—
576C4×C5—41no—
577C4×C5—42no—
578C4×C5—82no—
579C4×C5—81no—
580C4×C5—82no—
581C4×C5—81no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—81no—
589C24—81no—
590C24C2×C5×D412yes—
591C24C2×C5×D411yescharacteristic
592C24C5×#4112yescomplemented
593C24C24×C511yescharacteristic
594#41—82no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—81no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—44no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—82no—
620C2×D4—82no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4C2×C5×D411yescharacteristic
636C22×C4C2×C5×D412yes—
637C22×C4C2×C5×D411yescharacteristic
638C22×C4C2×C5×D412yes—
639C22×C4C2×C5×D411yescharacteristic
640C22×C4C2×C5×D412yes—
641C22×C4C2×C5×D411yescharacteristic
642C22×C4C2×C5×D411yescharacteristic
643C22×C4C2×C5×D411yescharacteristic
644C22×C4C2×C5×D411yescharacteristic
645C22×C4C2×C5×D411yescharacteristic
646C22×C4C2×C5×D411yescharacteristic
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—81no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—82no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—21no—
675C22⋊C4—22no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—21no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—44no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—81no—
691C22⋊C4—82no—
692C22⋊C4—81no—
693C22⋊C4—82no—
694C22⋊C4—81no—
695C22⋊C4—82no—
696C22⋊C4C5×#4112yescomplemented
697C42—22no—
698C42—22no—
699C42—21no—
700C42—21no—
701C42—81no—
702C2×C5—21no—
703C2×C5—21no—
704C2×C5—21no—
705C2×C5—21no—
706C2×C5—21no—
707C2×C5—21no—
708C2×C5—82no—
709C2×C5—81no—
710C2×C5—82no—
711C2×C5#240711yescharacteristic
712C2×C5#302611yescharacteristic
713C2×C5#302711yescharacteristic
714C23—21no—
715C23—22no—
716C23—22no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—82no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23C22×C5×D411yescharacteristic
746C23C22×C5×D411yescharacteristic
747C23C22×C5×D411yescharacteristic
748C23C2×C5×#4111yescharacteristic
749C23C2×C5×#4111yescharacteristic
750C23C5×H(5,𝔽2)11yescharacteristic
751C23C5×2−1+411yescharacteristic
752Q8—42no—
753Q8—81no—
754D4—42no—
755D4—42no—
756D4—42no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—42no—
761D4—42no—
762D4—41no—
763D4—81no—
764D4—84no—
765D4—82no—
766D4—82no—
767D4—88no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—81no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4C5×#12011yescharacteristic
810C2×C4C5×#12011yescharacteristic
811C2×C4C5×#12011yescharacteristic
812C2×C4C5×#12011yescharacteristic
813C5#2414211yescharacteristic, direct product factor, Sylow
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×C5×#12011yescharacteristic
846C22C5×#52511yescharacteristic
847C22C5×#53711yescharacteristic
848C22C5×#54611yescharacteristic
849C22C5×#54711yescharacteristic
850C22C5×#54811yescharacteristic
851C22C5×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C5×#240711yescharacteristic
877C2C5×#302611yescharacteristic
878C2C5×#302711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3505C2semidirect
2. C5×#2626C2semidirect
3. C5×#2617C2semidirect
4. C5×#2321C2semidirect
5. C5×#2044C2semidirect
6. C5×#2021C2semidirect
7. C5×#1996C2semidirect
8. C5×#1964C2semidirect
9. C5×#1889C2semidirect
10. C5×#1867C2semidirect
11. C5×#1799C2semidirect
55. #24142C5direct (N × H)
58. C22×C5×Q8D4semidirect
61. C22×C5×D4D4semidirect
64. C23×C4×C5D4semidirect
117. C2×C5×C4⋊C4D4semidirect
118. C2×C5×C4⋊C4D4semidirect
119. C2×C5×C4⋊C4D4semidirect
120. C2×C5×C4⋊C4D4semidirect
136. C2×C5×C22⋊C4D4semidirect
137. C2×C5×C22⋊C4D4semidirect
145. C2×C42×C5D4semidirect
156. #3505C2×C5semidirect
157. #2626C2×C5semidirect
158. #2617C2×C5semidirect
159. #2321C2×C5semidirect
160. #2044C2×C5semidirect
161. #2021C2×C5semidirect
162. #1996C2×C5semidirect
163. #1964C2×C5semidirect
164. #1889C2×C5semidirect
165. #1867C2×C5semidirect
166. #1799C2×C5semidirect
177. C24×C5#41semidirect
281. C5×C22⋊C4#41semidirect
431. C22×Q8C5×D4semidirect
434. C22×D4C5×D4semidirect
437. C23×C4C5×D4semidirect
490. C2×C4⋊C4C5×D4semidirect
491. C2×C4⋊C4C5×D4semidirect
492. C2×C4⋊C4C5×D4semidirect
493. C2×C4⋊C4C5×D4semidirect
509. C2×C22⋊C4C5×D4semidirect
510. C2×C22⋊C4C5×D4semidirect
518. C2×C42C5×D4semidirect
592. C24C5×#41semidirect
696. C22⋊C4C5×#41semidirect
813. C5#24142direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35052
C5×#26262
C5×#26172
C5×#23212
C5×#20442
C5×#20212
C5×#19962
C5×#19642
C5×#18892
C5×#18672
C5×#17992
#241425