Finite Group Databasebeta

← C5×#14044 #11936764

Subgroups — C5×#14044 #11936764

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#385C211yesmaximal, characteristic
2C2×C5×#385C211yesmaximal, characteristic
3C2×C5×#385C211yesmaximal, characteristic
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
5C22×C5×#95C211yesmaximal, characteristic
6C5×#1442C212yesmaximal, complemented
7C5×#1441C212yesmaximal, complemented
8C5×#1436C212yesmaximal, complemented
9C5×C4⋊#95C212yesmaximal, complemented
10C5×C22⋊#95C211yesmaximal, characteristic
11C5×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C5C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2212yes—
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C42×C5C2212yes—
24C5×#385—24no—
25C5×#385—24no—
26C5×#385C418yescomplemented
27C4×C5×C22⋊C4—24no—
28C2×C5×#95—24no—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2212yes—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40#14044C511yesmaximal, characteristic, direct product factor, Sylow
41C25×C5C2311yescharacteristic
42C23×C4×C5—22no—
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—24no—
48C23×C4×C5—24no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5—42no—
52C23×C4×C5—42no—
53C23×C4×C5—42no—
54C23×C4×C5—42no—
55C23×C4×C5C2×C414yes—
56C23×C4×C5D414yes—
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2312yes—
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2312yes—
64C23×C4×C5C2312yes—
65C23×C4×C5C2312yes—
66C23×C4×C5C2311yescharacteristic
67C2×C5×C4⋊C4—24no—
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—24no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—42no—
73C2×C5×C4⋊C4—42no—
74C2×C5×C4⋊C4—42no—
75C2×C5×C4⋊C4—42no—
76C2×C5×C4⋊C4C2×C418yescomplemented
77C2×C5×C22⋊C4—22no—
78C2×C5×C22⋊C4—22no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4C2×C414yes—
85C2×C5×C22⋊C4C2×C414yes—
86C2×C5×C22⋊C4D414yes—
87C2×C5×C22⋊C4Q814yes—
88C2×C5×C22⋊C4Q814yes—
89C2×C42×C5—24no—
90C2×C42×C5—24no—
91C2×C42×C5—42no—
92C5×#95—24no—
93C5×#95—24no—
94C5×#95—24no—
95C5×#95—22no—
96C5×#95—22no—
97C5×#95—24no—
98C5×#95—24no—
99C5×#95—42no—
100C5×#95—42no—
101C5×#95—42no—
102C5×#95C2×C418yescomplemented
103C2×#385C2×C511yescharacteristic
104C2×#385C2×C511yescharacteristic
105C2×#385C2×C511yescharacteristic
106C2×C4×C22⋊C4C2×C511yescharacteristic
107C22×#95C2×C511yescharacteristic
108#1442C2×C512yescomplemented
109#1441C2×C512yescomplemented
110#1436C2×C512yescomplemented
111C4⋊#95C2×C512yescomplemented
112C22⋊#95C2×C511yescharacteristic
113C22⋊#95C2×C511yescharacteristic
114C24×C5—22no—
115C24×C5—22no—
116C24×C5—22no—
117C24×C5—22no—
118C24×C5C22×C412yes—
119C24×C5C2×D412yes—
120C24×C5C2×D412yes—
121C24×C5C2×Q812yes—
122C24×C5C2×Q812yes—
123C24×C5#4112yes—
124C24×C5#4112yes—
125C24×C5C2411yescharacteristic
126C22×C4×C5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—21no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—28no—
134C22×C4×C5—28no—
135C22×C4×C5—28no—
136C22×C4×C5—22no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—28no—
167C22×C4×C5—21no—
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—22no—
176C22×C4×C5—22no—
177C22×C4×C5—48no—
178C22×C4×C5—44no—
179C22×C4×C5—48no—
180C22×C4×C5—48no—
181C22×C4×C5—48no—
182C22×C4×C5—48no—
183C22×C4×C5—44no—
184C22×C4×C5—44no—
185C22×C4×C5—44no—
186C22×C4×C5—48no—
187C22×C4×C5—44no—
188C22×C4×C5C22×C412yes—
189C22×C4×C5C22×C412yes—
190C22×C4×C5C22×C414yes—
191C22×C4×C5C22×C414yes—
192C22×C4×C5C2×D412yes—
193C22×C4×C5C2×D414yes—
194C22×C4×C5C2×D412yes—
195C22×C4×C5C2×Q814yes—
196C22×C4×C5C2×Q814yes—
197C22×C4×C5#4114yes—
198C22×C4×C5#4114yes—
199C5×C4⋊C4—48no—
200C5×C4⋊C4—48no—
201C5×C4⋊C4—44no—
202C5×C4⋊C4—44no—
203C5×C22⋊C4—28no—
204C5×C22⋊C4—28no—
205C5×C22⋊C4—44no—
206C5×C22⋊C4C4⋊C4116yescomplemented
207C42×C5—48no—
208C24×C4C22×C511yescharacteristic
209C24×C4C22×C511yescharacteristic
210C24×C4C22×C511yescharacteristic
211C22×C4⋊C4C22×C511yescharacteristic
212C22×C4⋊C4C22×C512yes—
213C22×C4⋊C4C22×C511yescharacteristic
214C22×C4⋊C4C22×C512yes—
215C22×C22⋊C4C22×C511yescharacteristic
216C22×C22⋊C4C22×C511yescharacteristic
217C22×C22⋊C4C22×C511yescharacteristic
218C22×C22⋊C4C22×C511yescharacteristic
219C22×C42C22×C512yes—
220#385—24no—
221#385—24no—
222#385C4×C518yescomplemented
223C4×C22⋊C4—24no—
224C2×#95—24no—
225C2×#95C22×C512yes—
226C2×#95C22×C511yescharacteristic
227C2×#95C22×C512yes—
228C2×#95C22×C512yes—
229C2×#95C22×C512yes—
230C2×#95C22×C512yes—
231C2×#95C22×C511yescharacteristic
232C2×#95C22×C512yes—
233C2×#95C22×C512yes—
234C2×#95C22×C512yes—
235C2×#95C22×C512yes—
236C23×C5—24no—
237C23×C5—24no—
238C23×C5—22no—
239C23×C5—22no—
240C23×C5—24no—
241C23×C5—22no—
242C23×C5—22no—
243C23×C5—24no—
244C23×C5—24no—
245C23×C5—24no—
246C23×C5—24no—
247C23×C5—24no—
248C23×C5—24no—
249C23×C5—24no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5C2×C4⋊C414yes—
253C23×C5C4×D414yes—
254C23×C5C4×Q814yes—
255C23×C5#12114yes—
256C23×C5C22⋊Q814yes—
257C23×C5#12514yes—
258C23×C5C4⋊Q814yes—
259C23×C5C23×C411yescharacteristic
260C23×C5C22×D411yescharacteristic
261C23×C5C22×D411yescharacteristic
262C23×C5C22×Q811yescharacteristic
263C23×C5C22×Q811yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5C2×#4111yescharacteristic
266C23×C5C2×#4112yes—
267C23×C5C2×#4112yes—
268C23×C5H(5,𝔽2)12yes—
269C23×C5H(5,𝔽2)12yes—
270C2×C4×C5—24no—
271C2×C4×C5—24no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—24no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—24no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—22no—
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—24no—
291C2×C4×C5—22no—
292C2×C4×C5—24no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—416no—
297C2×C4×C5—416no—
298C2×C4×C5—416no—
299C2×C4×C5—42no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—41no—
305C2×C4×C5—42no—
306C2×C4×C5—41no—
307C2×C4×C5—42no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5C2×C4⋊C418yes—
330C2×C4×C5#12314yes—
331C25C23×C511yescharacteristic
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—42no—
345C23×C4C2×C4×C514yes—
346C23×C4C5×D414yes—
347C23×C4C23×C511yescharacteristic
348C23×C4C23×C511yescharacteristic
349C23×C4C23×C511yescharacteristic
350C23×C4C23×C511yescharacteristic
351C23×C4C23×C512yes—
352C23×C4C23×C511yescharacteristic
353C23×C4C23×C512yes—
354C23×C4C23×C512yes—
355C23×C4C23×C512yes—
356C23×C4C23×C511yescharacteristic
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4C2×C4×C518yescomplemented
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4C2×C4×C514yes—
375C2×C22⋊C4C2×C4×C514yes—
376C2×C22⋊C4C5×D414yes—
377C2×C22⋊C4C5×Q814yes—
378C2×C22⋊C4C5×Q814yes—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—42no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—22no—
386#95—22no—
387#95—24no—
388#95—24no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95C2×C4×C518yescomplemented
393C22×C5—24no—
394C22×C5—24no—
395C22×C5—28no—
396C22×C5—28no—
397C22×C5—24no—
398C22×C5—24no—
399C22×C5—28no—
400C22×C5—24no—
401C22×C5—28no—
402C22×C5—24no—
403C22×C5#38918yes—
404C22×C5C22×C4⋊C411yescharacteristic
405C22×C5C2×C4×D411yescharacteristic
406C22×C5C2×C4×Q811yescharacteristic
407C22×C5C4×#4112yes—
408C22×C5#51812yes—
409C22×C5C2×#12111yescharacteristic
410C22×C5C2×C22⋊Q811yescharacteristic
411C22×C5C2×#12311yescharacteristic
412C22×C5#52511yescharacteristic
413C22×C5C2×#12511yescharacteristic
414C22×C5#52912yes—
415C22×C5C2×C4⋊Q811yescharacteristic
416C22×C5#53411yescharacteristic
417C22×C5#53511yescharacteristic
418C22×C5#53812yes—
419C22×C5#54612yes—
420C22×C5#54612yes—
421C22×C5#55112yes—
422C22×C5#55112yes—
423C22×C5#55412yes—
424C22×C5#55412yes—
425C22×C5#55412yes—
426C22×C5#55412yes—
427C4×C5—28no—
428C4×C5—24no—
429C4×C5—42no—
430C4×C5—44no—
431C4×C5—44no—
432C4×C5—42no—
433C4×C5—44no—
434C4×C5—42no—
435C4×C5—81no—
436C4×C5—81no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24C22×C4×C512yes—
442C24C2×C5×D412yes—
443C24C2×C5×D412yes—
444C24C2×C5×Q812yes—
445C24C2×C5×Q812yes—
446C24C5×#4112yes—
447C24C5×#4112yes—
448C24C24×C511yescharacteristic
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—28no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—48no—
501C22×C4—44no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—48no—
510C22×C4—44no—
511C22×C4C22×C4×C512yes—
512C22×C4C22×C4×C514yes—
513C22×C4C22×C4×C512yes—
514C22×C4C22×C4×C514yes—
515C22×C4C2×C5×D412yes—
516C22×C4C2×C5×D414yes—
517C22×C4C2×C5×D412yes—
518C22×C4C2×C5×Q814yes—
519C22×C4C2×C5×Q814yes—
520C22×C4C5×#4114yes—
521C22×C4C5×#4114yes—
522C4⋊C4—48no—
523C4⋊C4—48no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C22⋊C4—28no—
527C22⋊C4—28no—
528C22⋊C4—44no—
529C22⋊C4C5×C4⋊C4116yescomplemented
530C42—48no—
531C2×C5—28no—
532C2×C5C2×#38911yescharacteristic
533C2×C5C4×#12311yescharacteristic
534C2×C5#232111yescharacteristic
535C2×C5#234912yes—
536C2×C5#236812yes—
537C2×C5#241111yescharacteristic
538C2×C5#241211yescharacteristic
539C2×C5#245012yes—
540C2×C5#250211yescharacteristic
541C2×C5#250512yes—
542C2×C5#258311yescharacteristic
543C23—24no—
544C23—24no—
545C23—22no—
546C23—22no—
547C23—24no—
548C23—22no—
549C23—22no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23C2×C5×C4⋊C414yes—
560C23C4×C5×D414yes—
561C23C4×C5×Q814yes—
562C23C5×#12114yes—
563C23C5×C22⋊Q814yes—
564C23C5×#12514yes—
565C23C5×C4⋊Q814yes—
566C23C23×C4×C511yescharacteristic
567C23C22×C5×D411yescharacteristic
568C23C22×C5×D411yescharacteristic
569C23C22×C5×Q811yescharacteristic
570C23C22×C5×Q811yescharacteristic
571C23C2×C5×#4111yescharacteristic
572C23C2×C5×#4111yescharacteristic
573C23C2×C5×#4112yes—
574C23C2×C5×#4112yes—
575C23C5×H(5,𝔽2)12yes—
576C23C5×H(5,𝔽2)12yes—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—416no—
604C2×C4—416no—
605C2×C4—416no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4C2×C5×C4⋊C418yes—
637C2×C4C5×#12314yes—
638C5#1404411yescharacteristic, direct product factor, Sylow
639C22—24no—
640C22—28no—
641C22—24no—
642C22—24no—
643C22—24no—
644C22—28no—
645C22—28no—
646C22—24no—
647C22—24no—
648C22—28no—
649C22C5×#38918yes—
650C22C22×C5×C4⋊C411yescharacteristic
651C22C2×C4×C5×D411yescharacteristic
652C22C2×C4×C5×Q811yescharacteristic
653C22C4×C5×#4112yes—
654C22C5×#51812yes—
655C22C2×C5×#12111yescharacteristic
656C22C2×C5×C22⋊Q811yescharacteristic
657C22C2×C5×#12311yescharacteristic
658C22C5×#52511yescharacteristic
659C22C2×C5×#12511yescharacteristic
660C22C5×#52912yes—
661C22C2×C5×C4⋊Q811yescharacteristic
662C22C5×#53411yescharacteristic
663C22C5×#53511yescharacteristic
664C22C5×#53812yes—
665C22C5×#54612yes—
666C22C5×#54612yes—
667C22C5×#55112yes—
668C22C5×#55112yes—
669C22C5×#55412yes—
670C22C5×#55412yes—
671C22C5×#55412yes—
672C22C5×#55412yes—
673C4—28no—
674C4—24no—
675C4—42no—
676C4—44no—
677C4—42no—
678C4—44no—
679C4—42no—
680C4—44no—
681C4—81no—
682C4—81no—
683C2—28no—
684C2C2×C5×#38911yescharacteristic
685C2C4×C5×#12311yescharacteristic
686C2C5×#232111yescharacteristic
687C2C5×#234912yes—
688C2C5×#236812yes—
689C2C5×#241111yescharacteristic
690C2C5×#241211yescharacteristic
691C2C5×#245012yes—
692C2C5×#250211yescharacteristic
693C2C5×#250512yes—
694C2C5×#258311yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C5×#1442C2semidirect
7. C5×#1441C2semidirect
8. C5×#1436C2semidirect
9. C5×C4⋊#95C2semidirect
26. C5×#385C4semidirect
40. #14044C5direct (N × H)
76. C2×C5×C4⋊C4C2×C4semidirect
102. C5×#95C2×C4semidirect
108. #1442C2×C5semidirect
109. #1441C2×C5semidirect
110. #1436C2×C5semidirect
111. C4⋊#95C2×C5semidirect
206. C5×C22⋊C4C4⋊C4semidirect
222. #385C4×C5semidirect
366. C2×C4⋊C4C2×C4×C5semidirect
392. #95C2×C4×C5semidirect
529. C22⋊C4C5×C4⋊C4semidirect
638. C5#14044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3852
C2×C4×C5×C22⋊C42
C22×C5×#952
C5×#14422
C5×#14412
C5×#14362
C5×C4⋊#952
C5×C22⋊#952
#140445