Finite Group Databasebeta

← C5×#13991 #11936711

Subgroups — C5×#13991 #11936711

Order 1280.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C22⋊C4C211yesmaximal, characteristic
2C2×C5×#388C212yesmaximal, complemented
3C2×C5×#385C211yesmaximal, characteristic, complemented
4C2×C5×#379C211yesmaximal, characteristic
5C2×C5×#379C211yesmaximal, characteristic
6C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
7C5×#1440C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×#1437C212yesmaximal, 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⋊C4C2212yes—
20C22×C5×C22⋊C4C2212yes—
21C22×C5×C22⋊C4C2212yes—
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2212yes—
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2212yes—
27C22×C5×C22⋊C4C2212yes—
28C22×C42×C5C2211yescharacteristic, complemented
29C22×C42×C5C2211yescharacteristic, complemented
30C5×#388—28no—
31C5×#385—24no—
32C5×#379—24no—
33C5×#379C418yescomplemented
34C4×C5×C22⋊C4—24no—
35C2×C5×#95C2211yescharacteristic, complemented
36C2×C5×#95C2211yescharacteristic, complemented
37C2×C5×#95C2212yescomplemented
38C2×C5×#95C2212yescomplemented
39C2×C5×#95C2212yescomplemented
40C2×C5×#95C2212yescomplemented
41C2×C5×#95C2212yescomplemented
42#13991C511yesmaximal, characteristic, direct product factor, Sylow
43C25×C5—24no—
44C25×C5—22no—
45C25×C5—24no—
46C25×C5—22no—
47C25×C5—22no—
48C25×C5—22no—
49C25×C5—22no—
50C25×C5—22no—
51C25×C5—42no—
52C25×C5—42no—
53C25×C5C2×C414yes—
54C25×C5C2312yes—
55C25×C5C2311yescharacteristic
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—24no—
60C23×C4×C5—24no—
61C23×C4×C5—22no—
62C23×C4×C5—22no—
63C23×C4×C5—42no—
64C23×C4×C5—42no—
65C23×C4×C5D414yes—
66C23×C4×C5C2312yes—
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2312yes—
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2312yes—
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C2×C5×C4⋊C4—24no—
76C2×C5×C4⋊C4—24no—
77C2×C5×C4⋊C4—42no—
78C2×C5×C22⋊C4—232no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—24no—
83C2×C5×C22⋊C4—24no—
84C2×C5×C22⋊C4—22no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—24no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—24no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—24no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—24no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—24no—
99C2×C5×C22⋊C4—42no—
100C2×C5×C22⋊C4—42no—
101C2×C5×C22⋊C4—42no—
102C2×C5×C22⋊C4—42no—
103C2×C5×C22⋊C4C2×C414yes—
104C2×C5×C22⋊C4C2×C414yes—
105C2×C5×C22⋊C4C2×C418yescomplemented
106C2×C5×C22⋊C4C2×C418yescomplemented
107C2×C5×C22⋊C4D414yes—
108C2×C5×C22⋊C4D418yes—
109C2×C42×C5—22no—
110C2×C42×C5—22no—
111C2×C42×C5—24no—
112C2×C42×C5—42no—
113C5×#95—22no—
114C5×#95—22no—
115C5×#95—24no—
116C5×#95—24no—
117C5×#95—24no—
118C5×#95—42no—
119C5×#95—42no—
120C23×C22⋊C4C2×C511yescharacteristic
121C2×#388C2×C512yescomplemented
122C2×#385C2×C511yescharacteristic, complemented
123C2×#379C2×C511yescharacteristic
124C2×#379C2×C511yescharacteristic
125C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
126#1440C2×C512yescomplemented
127#1439C2×C512yescomplemented
128#1437C2×C512yescomplemented
129C22⋊#95C2×C511yescharacteristic, complemented
130C22⋊#95C2×C511yescharacteristic, complemented
131C24×C5—22no—
132C24×C5—22no—
133C24×C5—22no—
134C24×C5—22no—
135C24×C5—28no—
136C24×C5—28no—
137C24×C5—216no—
138C24×C5—216no—
139C24×C5—28no—
140C24×C5—22no—
141C24×C5—22no—
142C24×C5—22no—
143C24×C5—22no—
144C24×C5—22no—
145C24×C5—22no—
146C24×C5—22no—
147C24×C5—22no—
148C24×C5—22no—
149C24×C5—22no—
150C24×C5—22no—
151C24×C5—22no—
152C24×C5—28no—
153C24×C5—28no—
154C24×C5—48no—
155C24×C5—48no—
156C24×C5—48no—
157C24×C5—48no—
158C24×C5—48no—
159C24×C5—48no—
160C24×C5—48no—
161C24×C5—48no—
162C24×C5—48no—
163C24×C5—44no—
164C24×C5—44no—
165C24×C5—48no—
166C24×C5—44no—
167C24×C5—44no—
168C24×C5—44no—
169C24×C5—44no—
170C24×C5C22×C414yes—
171C24×C5C22×C412yes—
172C24×C5C2×D414yes—
173C24×C5C2×D412yes—
174C24×C5C2×D412yes—
175C24×C5#4114yes—
176C24×C5#4112yes—
177C24×C5#4112yes—
178C24×C5#4112yes—
179C24×C5#4112yes—
180C24×C5C2411yescharacteristic
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—22no—
184C22×C4×C5—28no—
185C22×C4×C5—28no—
186C22×C4×C5—22no—
187C22×C4×C5—21no—
188C22×C4×C5—22no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
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—21no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—22no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—44no—
227C22×C4×C5—48no—
228C22×C4×C5—48no—
229C22×C4×C5—48no—
230C22×C4×C5—48no—
231C22×C4×C5—44no—
232C22×C4×C5—44no—
233C22×C4×C5C22×C412yes—
234C22×C4×C5C22×C414yes—
235C22×C4×C5C22×C412yes—
236C22×C4×C5C2×D412yes—
237C22×C4×C5C2×D412yes—
238C22×C4×C5C2×D412yes—
239C22×C4×C5C2×D414yes—
240C22×C4×C5C2×D412yes—
241C22×C4×C5C2×D414yes—
242C5×C4⋊C4—48no—
243C5×C22⋊C4—216no—
244C5×C22⋊C4—28no—
245C5×C22⋊C4—28no—
246C5×C22⋊C4—216no—
247C5×C22⋊C4—28no—
248C5×C22⋊C4—216no—
249C5×C22⋊C4—48no—
250C5×C22⋊C4—48no—
251C5×C22⋊C4—48no—
252C5×C22⋊C4—44no—
253C42×C5—44no—
254C42×C5—44no—
255C26C22×C511yescharacteristic
256C24×C4C22×C511yescharacteristic
257C24×C4C22×C511yescharacteristic
258C22×C4⋊C4C22×C512yescomplemented
259C22×C22⋊C4—24no—
260C22×C22⋊C4—28no—
261C22×C22⋊C4C22×C512yes—
262C22×C22⋊C4C22×C511yescharacteristic
263C22×C22⋊C4C22×C512yes—
264C22×C22⋊C4C22×C512yes—
265C22×C22⋊C4C22×C511yescharacteristic
266C22×C22⋊C4C22×C511yescharacteristic
267C22×C22⋊C4C22×C512yes—
268C22×C22⋊C4C22×C512yes—
269C22×C22⋊C4C22×C511yescharacteristic
270C22×C22⋊C4C22×C512yes—
271C22×C42C22×C511yescharacteristic, complemented
272C22×C42C22×C511yescharacteristic, complemented
273#388—28no—
274#385—24no—
275#379—24no—
276#379C4×C518yescomplemented
277C4×C22⋊C4—24no—
278C2×#95C22×C512yescomplemented
279C2×#95C22×C512yescomplemented
280C2×#95C22×C512yescomplemented
281C2×#95C22×C511yescharacteristic, complemented
282C2×#95C22×C511yescharacteristic, complemented
283C2×#95C22×C512yescomplemented
284C2×#95C22×C512yescomplemented
285C23×C5—24no—
286C23×C5—24no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—24no—
290C23×C5—22no—
291C23×C5—22no—
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—24no—
303C23×C5—24no—
304C23×C5—24no—
305C23×C5—24no—
306C23×C5—24no—
307C23×C5—24no—
308C23×C5—24no—
309C23×C5—24no—
310C23×C5—24no—
311C23×C5—24no—
312C23×C5—24no—
313C23×C5—24no—
314C23×C5—24no—
315C23×C5—24no—
316C23×C5—24no—
317C23×C5—24no—
318C23×C5—24no—
319C23×C5—24no—
320C23×C5—432no—
321C23×C5—432no—
322C23×C5—416no—
323C23×C5—416no—
324C23×C5—416no—
325C23×C5—432no—
326C23×C5—432no—
327C23×C5—416no—
328C23×C5—416no—
329C23×C5—42no—
330C23×C5—42no—
331C23×C5—42no—
332C23×C5—42no—
333C23×C5—42no—
334C23×C5—42no—
335C23×C5—42no—
336C23×C5—42no—
337C23×C5—42no—
338C23×C5—42no—
339C23×C5—42no—
340C23×C5—42no—
341C23×C5—42no—
342C23×C5—42no—
343C23×C5—42no—
344C23×C5—42no—
345C23×C5—416no—
346C23×C5#11714yes—
347C23×C5C4×D418yes—
348C23×C5C4×D414yes—
349C23×C5C4×D414yes—
350C23×C5#12114yes—
351C23×C5#12314yes—
352C23×C5#12414yes—
353C23×C5#12614yes—
354C23×C5C23×C411yescharacteristic
355C23×C5C22×D411yescharacteristic
356C23×C5C22×D412yes—
357C23×C5C22×D411yescharacteristic
358C23×C5C2×#4111yescharacteristic
359C23×C5C2×#4111yescharacteristic
360C23×C5C2×#4111yescharacteristic
361C23×C5C2×#4111yescharacteristic
362C23×C5C2×#4112yes—
363C23×C5H(5,𝔽2)12yes—
364C23×C5H(5,𝔽2)12yes—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—24no—
368C2×C4×C5—24no—
369C2×C4×C5—22no—
370C2×C4×C5—24no—
371C2×C4×C5—24no—
372C2×C4×C5—22no—
373C2×C4×C5—24no—
374C2×C4×C5—24no—
375C2×C4×C5—24no—
376C2×C4×C5—22no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—24no—
383C2×C4×C5—24no—
384C2×C4×C5—24no—
385C2×C4×C5—24no—
386C2×C4×C5—416no—
387C2×C4×C5—416no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—42no—
391C2×C4×C5—41no—
392C2×C4×C5—42no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—42no—
399C2×C4×C5—42no—
400C2×C4×C5—42no—
401C2×C4×C5—42no—
402C2×C4×C5—42no—
403C2×C4×C5—42no—
404C2×C4×C5—42no—
405C2×C4×C5—42no—
406C2×C4×C5—42no—
407C2×C4×C5—42no—
408C2×C4×C5—42no—
409C2×C4×C5—42no—
410C2×C4×C5—42no—
411C2×C4×C5—42no—
412C2×C4×C5—42no—
413C2×C4×C5—42no—
414C2×C4×C5—42no—
415C2×C4×C5—42no—
416C2×C4×C5—42no—
417C2×C4×C5#12014yes—
418C25—24no—
419C25—22no—
420C25—24no—
421C25—22no—
422C25—22no—
423C25—22no—
424C25—22no—
425C25—22no—
426C25—42no—
427C25—42no—
428C25C2×C4×C514yes—
429C25C23×C512yes—
430C25C23×C511yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4C5×D414yes—
441C23×C4C23×C512yes—
442C23×C4C23×C512yes—
443C23×C4C23×C511yescharacteristic
444C23×C4C23×C511yescharacteristic
445C23×C4C23×C511yescharacteristic
446C23×C4C23×C511yescharacteristic
447C23×C4C23×C512yes—
448C23×C4C23×C511yescharacteristic
449C23×C4C23×C511yescharacteristic
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—42no—
453C2×C22⋊C4—232no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4C2×C4×C514yes—
479C2×C22⋊C4C2×C4×C514yes—
480C2×C22⋊C4C2×C4×C518yescomplemented
481C2×C22⋊C4C2×C4×C518yescomplemented
482C2×C22⋊C4C5×D418yes—
483C2×C22⋊C4C5×D414yes—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—24no—
487C2×C42—42no—
488#95—22no—
489#95—22no—
490#95—24no—
491#95—24no—
492#95—24no—
493#95—42no—
494#95—42no—
495C22×C5—24no—
496C22×C5—28no—
497C22×C5—28no—
498C22×C5—24no—
499C22×C5—24no—
500C22×C5—28no—
501C22×C5—28no—
502C22×C5—24no—
503C22×C5—24no—
504C22×C5—24no—
505C22×C5—28no—
506C22×C5—28no—
507C22×C5—28no—
508C22×C5—464no—
509C22×C5—44no—
510C22×C5—44no—
511C22×C5—44no—
512C22×C5—44no—
513C22×C5—44no—
514C22×C5—44no—
515C22×C5—44no—
516C22×C5—44no—
517C22×C5—44no—
518C22×C5—44no—
519C22×C5—44no—
520C22×C5—44no—
521C22×C5#38818yescomplemented
522C22×C5C2×#11711yescharacteristic
523C22×C5C2×C4×D411yescharacteristic
524C22×C5C2×C4×D412yes—
525C22×C5C2×C4×D411yescharacteristic
526C22×C5#51812yes—
527C22×C5C2×#12011yescharacteristic
528C22×C5C2×#12111yescharacteristic
529C22×C5C2×#12311yescharacteristic
530C22×C5#52512yes—
531C22×C5#52511yescharacteristic
532C22×C5C2×#12411yescharacteristic
533C22×C5C2×#12611yescharacteristic
534C22×C5#53411yescharacteristic
535C22×C5#53511yescharacteristic
536C22×C5#53812yes—
537C22×C5D4212yes—
538C22×C5#54612yes—
539C22×C5#54612yes—
540C22×C5#54612yes—
541C22×C5#54612yes—
542C22×C5#55112yes—
543C22×C5#55112yes—
544C22×C5#55112yes—
545C4×C5—24no—
546C4×C5—42no—
547C4×C5—44no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—44no—
551C4×C5—42no—
552C4×C5—42no—
553C4×C5—82no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—28no—
559C24—28no—
560C24—216no—
561C24—216no—
562C24—28no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—28no—
576C24—28no—
577C24—48no—
578C24—48no—
579C24—48no—
580C24—48no—
581C24—48no—
582C24—48no—
583C24—48no—
584C24—48no—
585C24—48no—
586C24—44no—
587C24—44no—
588C24—48no—
589C24—44no—
590C24—44no—
591C24—44no—
592C24—44no—
593C24C22×C4×C514yes—
594C24C22×C4×C512yes—
595C24C2×C5×D414yes—
596C24C2×C5×D412yes—
597C24C2×C5×D412yes—
598C24C5×#4114yes—
599C24C5×#4112yes—
600C24C5×#4112yes—
601C24C5×#4112yes—
602C24C5×#4112yes—
603C24C24×C511yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
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—28no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—44no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4C22×C4×C512yes—
657C22×C4C22×C4×C514yes—
658C22×C4C22×C4×C512yes—
659C22×C4C2×C5×D412yes—
660C22×C4C2×C5×D412yes—
661C22×C4C2×C5×D414yes—
662C22×C4C2×C5×D412yes—
663C22×C4C2×C5×D414yes—
664C22×C4C2×C5×D412yes—
665C4⋊C4—48no—
666C22⋊C4—216no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—216no—
670C22⋊C4—28no—
671C22⋊C4—216no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—44no—
676C42—44no—
677C42—44no—
678C2×C5—28no—
679C2×C5—48no—
680C2×C5C2×#38811yescharacteristic
681C2×C5C4×#12011yescharacteristic
682C2×C5#232111yescharacteristic
683C2×C5#234212yes—
684C2×C5#235812yes—
685C2×C5#240511yescharacteristic
686C2×C5#240811yescharacteristic
687C2×C5#247212yes—
688C2×C5#248012yes—
689C2×C5#248211yescharacteristic
690C2×C5#253411yescharacteristic
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—232no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—432no—
727C23—432no—
728C23—432no—
729C23—432no—
730C23—416no—
731C23—416no—
732C23—416no—
733C23—416no—
734C23—416no—
735C23—416no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23C5×#11714yes—
753C23C4×C5×D418yes—
754C23C4×C5×D414yes—
755C23C4×C5×D414yes—
756C23C5×#12114yes—
757C23C5×#12314yes—
758C23C5×#12414yes—
759C23C5×#12614yes—
760C23C23×C4×C511yescharacteristic
761C23C22×C5×D411yescharacteristic
762C23C22×C5×D412yes—
763C23C22×C5×D411yescharacteristic
764C23C2×C5×#4111yescharacteristic
765C23C2×C5×#4111yescharacteristic
766C23C2×C5×#4111yescharacteristic
767C23C2×C5×#4111yescharacteristic
768C23C2×C5×#4112yes—
769C23C5×H(5,𝔽2)12yes—
770C23C5×H(5,𝔽2)12yes—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—416no—
793C2×C4—416no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
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—42no—
823C2×C4C5×#12014yes—
824C5#1399111yescharacteristic, direct product factor, Sylow
825C22—28no—
826C22—28no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—28no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22C5×#38818yescomplemented
852C22C2×C5×#11711yescharacteristic
853C22C2×C4×C5×D411yescharacteristic
854C22C2×C4×C5×D411yescharacteristic
855C22C2×C4×C5×D412yes—
856C22C5×#51812yes—
857C22C2×C5×#12011yescharacteristic
858C22C2×C5×#12111yescharacteristic
859C22C2×C5×#12311yescharacteristic
860C22C5×#52512yes—
861C22C5×#52511yescharacteristic
862C22C2×C5×#12411yescharacteristic
863C22C2×C5×#12611yescharacteristic
864C22C5×#53411yescharacteristic
865C22C5×#53511yescharacteristic
866C22C5×#53812yes—
867C22C5×D4212yes—
868C22C5×#54612yes—
869C22C5×#54612yes—
870C22C5×#54612yes—
871C22C5×#54612yes—
872C22C5×#55112yes—
873C22C5×#55112yes—
874C22C5×#55112yes—
875C4—24no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—44no—
882C4—42no—
883C4—82no—
884C2—28no—
885C2—48no—
886C2C2×C5×#38811yescharacteristic
887C2C4×C5×#12011yescharacteristic
888C2C5×#232111yescharacteristic
889C2C5×#234212yes—
890C2C5×#235812yes—
891C2C5×#240511yescharacteristic
892C2C5×#240811yescharacteristic
893C2C5×#247212yes—
894C2C5×#248012yes—
895C2C5×#248211yescharacteristic
896C2C5×#253411yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC26×C5C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#388C2semidirect
3. C2×C5×#385C2semidirect
6. C2×C4×C5×C22⋊C4C2semidirect
7. C5×#1440C2semidirect
8. C5×#1439C2semidirect
9. C5×#1437C2semidirect
10. C5×C22⋊#95C2semidirect
11. C5×C22⋊#95C2semidirect
15. C22×C5×C4⋊C4C22semidirect
28. C22×C42×C5C22semidirect
29. C22×C42×C5C22semidirect
33. C5×#379C4semidirect
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. C2×C5×#95C22semidirect
42. #13991C5direct (N × H)
105. C2×C5×C22⋊C4C2×C4semidirect
106. C2×C5×C22⋊C4C2×C4semidirect
121. C2×#388C2×C5semidirect
122. C2×#385C2×C5semidirect
125. C2×C4×C22⋊C4C2×C5semidirect
126. #1440C2×C5semidirect
127. #1439C2×C5semidirect
128. #1437C2×C5semidirect
129. C22⋊#95C2×C5semidirect
130. C22⋊#95C2×C5semidirect
258. C22×C4⋊C4C22×C5semidirect
271. C22×C42C22×C5semidirect
272. C22×C42C22×C5semidirect
276. #379C4×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
480. C2×C22⋊C4C2×C4×C5semidirect
481. C2×C22⋊C4C2×C4×C5semidirect
521. C22×C5#388semidirect
824. C5#13991direct (N × H)
851. C22C5×#388semidirect

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×#3882
C2×C5×#3852
C2×C5×#3792
C2×C4×C5×C22⋊C42
C5×#14402
C5×#14392
C5×#14372
C5×C22⋊#952
#139915