Finite Group Databasebeta

← C5×#14312 #11937032

Subgroups — C5×#14312 #11937032

Order 1280.

1766 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic
3C2×C5×#388C212yesmaximal, complemented
4C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#1444C211yesmaximal, characteristic, complemented
6C5×#1441C211yesmaximal, characteristic, complemented
7C5×#1439C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×#1438C211yesmaximal, characteristic
10C5×#1437C212yesmaximal, complemented
11C5×#1434C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C22⋊C4C2212yes—
18C22×C5×C22⋊C4C2212yes—
19C22×C5×C22⋊C4C2212yes—
20C22×C5×C22⋊C4C2212yes—
21C22×C5×C22⋊C4C2212yes—
22C22×C5×C22⋊C4C2212yes—
23C22×C42×C5C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C5×#394C418yescomplemented
27C5×#390—24no—
28C5×#388—28no—
29C4×C5×C4⋊C4—24no—
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2211yescharacteristic
39#14312C511yesmaximal, characteristic, direct product factor, Sylow
40C25×C5C2312yes—
41C22×C5×D4—22no—
42C22×C5×D4—22no—
43C22×C5×D4—42no—
44C22×C5×D4—42no—
45C22×C5×D4C2×C414yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2312yes—
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—24no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—42no—
64C2×C5×C4⋊C4—42no—
65C2×C5×C4⋊C4—42no—
66C2×C5×C4⋊C4C2×C414yes—
67C2×C5×C22⋊C4—24no—
68C2×C5×C22⋊C4—24no—
69C2×C5×C22⋊C4—24no—
70C2×C5×C22⋊C4—24no—
71C2×C5×C22⋊C4—24no—
72C2×C5×C22⋊C4—24no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—24no—
75C2×C5×C22⋊C4—42no—
76C2×C5×C22⋊C4—42no—
77C2×C5×C22⋊C4—42no—
78C2×C5×C22⋊C4—42no—
79C2×C5×C22⋊C4—42no—
80C2×C5×C22⋊C4—42no—
81C2×C5×C22⋊C4—42no—
82C2×C5×C22⋊C4—42no—
83C2×C5×C22⋊C4C2×C418yes—
84C2×C5×C22⋊C4C2×C418yes—
85C2×C42×C5—22no—
86C2×C42×C5—22no—
87C2×C42×C5—22no—
88C2×C42×C5—42no—
89C2×C42×C5—42no—
90C2×C42×C5D414yes—
91C2×C42×C5D414yescomplemented
92C5×#95—22no—
93C5×#95—22no—
94C5×#95—24no—
95C5×#95—24no—
96C5×#95—22no—
97C5×#95—42no—
98C5×#95—42no—
99C5×#95—42no—
100C5×#95C2×C414yes—
101C2×#394C2×C511yescharacteristic
102C2×#390C2×C511yescharacteristic
103C2×#388C2×C512yescomplemented
104C2×C4×C4⋊C4C2×C511yescharacteristic, complemented
105#1444C2×C511yescharacteristic, complemented
106#1441C2×C511yescharacteristic, complemented
107#1439C2×C512yescomplemented
108#1439C2×C512yescomplemented
109#1438C2×C511yescharacteristic
110#1437C2×C512yescomplemented
111#1434C2×C511yescharacteristic, complemented
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—22no—
115C24×C5—22no—
116C24×C5—22no—
117C24×C5—22no—
118C24×C5—22no—
119C24×C5—22no—
120C24×C5—22no—
121C24×C5—22no—
122C24×C5—22no—
123C24×C5—22no—
124C24×C5—22no—
125C24×C5—22no—
126C24×C5C22×C414yes—
127C24×C5C2411yescharacteristic
128C2×C5×D4—28no—
129C2×C5×D4—48no—
130C2×C5×D4—44no—
131C2×C5×D4—44no—
132C2×C5×D4—48no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—22no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
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—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5C22×C412yes—
178C22×C4×C5C22×C414yes—
179C22×C4×C5C22×C412yes—
180C22×C4×C5C22×C412yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×D412yes—
186C22×C4×C5C2×D412yes—
187C22×C4×C5#4112yes—
188C22×C4×C5#4112yes—
189C22×C4×C5#4112yes—
190C22×C4×C5#4112yes—
191C5×C4⋊C4—28no—
192C5×C4⋊C4—28no—
193C5×C4⋊C4—44no—
194C5×C4⋊C4—48no—
195C5×C22⋊C4—216no—
196C5×C22⋊C4—48no—
197C5×C22⋊C4—48no—
198C5×C22⋊C4—48no—
199C5×C22⋊C4—48no—
200C5×C22⋊C4—48no—
201C42×C5—28no—
202C42×C5—44no—
203C42×C5—44no—
204C23×D4C22×C511yescharacteristic
205C22×C4⋊C4C22×C511yescharacteristic
206C22×C4⋊C4C22×C511yescharacteristic
207C22×C4⋊C4C22×C512yes—
208C22×C4⋊C4C22×C511yescharacteristic
209C22×C22⋊C4C22×C512yes—
210C22×C22⋊C4C22×C512yes—
211C22×C22⋊C4C22×C512yes—
212C22×C22⋊C4C22×C512yes—
213C22×C22⋊C4C22×C512yes—
214C22×C22⋊C4C22×C512yes—
215C22×C42C22×C511yescharacteristic
216C22×C42C22×C511yescharacteristic
217C22×C42C22×C511yescharacteristic
218#394C4×C518yescomplemented
219#390—24no—
220#388—28no—
221C4×C4⋊C4—24no—
222C2×#95C22×C512yes—
223C2×#95C22×C511yescharacteristic
224C2×#95C22×C511yescharacteristic
225C2×#95C22×C511yescharacteristic
226C2×#95C22×C512yes—
227C2×#95C22×C512yes—
228C2×#95C22×C512yes—
229C2×#95C22×C512yes—
230C2×#95C22×C511yescharacteristic
231C23×C5—24no—
232C23×C5—24no—
233C23×C5—24no—
234C23×C5—24no—
235C23×C5—24no—
236C23×C5—24no—
237C23×C5—24no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5—42no—
244C23×C5—42no—
245C23×C5—42no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—42no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5—42no—
255C23×C5—42no—
256C23×C5—42no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5—42no—
261C23×C5—42no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5—42no—
265C23×C5—42no—
266C23×C5C23×C411yescharacteristic
267C23×C5C22×D411yescharacteristic
268C23×C5C22×D411yescharacteristic
269C23×C5C2×#4111yescharacteristic
270C23×C5C2×#4111yescharacteristic
271C23×C5C2×#4111yescharacteristic
272C23×C5C2×#4111yescharacteristic
273C23×C5H(5,𝔽2)12yes—
274C23×C5H(5,𝔽2)12yes—
275C23×C5H(5,𝔽2)12yes—
276C23×C52−1+412yes—
277C5×D4—416no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—24no—
290C2×C4×C5—24no—
291C2×C4×C5—24no—
292C2×C4×C5—24no—
293C2×C4×C5—22no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—24no—
303C2×C4×C5—24no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—42no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
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—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5C4×D414yes—
334C2×C4×C5C4×D414yes—
335C2×C4×C5#12114yes—
336C25C23×C512yes—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4C2×C4×C514yes—
342C23×C4C23×C512yes—
343C23×C4C23×C512yes—
344C23×C4C23×C512yes—
345C23×C4C23×C511yescharacteristic
346C23×C4C23×C511yescharacteristic
347C23×C4C23×C511yescharacteristic
348C23×C4C23×C511yescharacteristic
349C23×C4C23×C511yescharacteristic
350C23×C4C23×C511yescharacteristic
351C23×C4C23×C511yescharacteristic
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4C2×C4×C514yes—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4C2×C4×C518yes—
380C2×C22⋊C4C2×C4×C518yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42C5×D414yes—
387C2×C42C5×D414yescomplemented
388#95—22no—
389#95—22no—
390#95—24no—
391#95—24no—
392#95—22no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95C2×C4×C514yes—
397C22×C5—44no—
398C22×C5—44no—
399C22×C5—44no—
400C22×C5—44no—
401C22×C5—44no—
402C22×C5—44no—
403C22×C5—44no—
404C22×C5—82no—
405C22×C5—82no—
406C22×C5—82no—
407C22×C5—82no—
408C22×C5—82no—
409C22×C5—82no—
410C22×C5—82no—
411C22×C5—82no—
412C22×C5C2×C4×D411yescharacteristic
413C22×C5C2×C4×D411yescharacteristic
414C22×C5C4×#4111yescharacteristic
415C22×C5#51812yes—
416C22×C5#52012yes—
417C22×C5C2×#12111yescharacteristic
418C22×C5#52511yescharacteristic
419C22×C5#52911yescharacteristic
420C22×C5#53211yescharacteristic
421C22×C5#53411yescharacteristic
422C22×C5#53511yescharacteristic
423C22×C5#53512yes—
424C22×C5#53511yescharacteristic
425C22×C5#53611yescharacteristic
426C22×C5#53712yes—
427C22×C5#53812yes—
428C22×C5#53812yes—
429C22×C5#53912yes—
430C22×C5#54012yes—
431C22×C5#54012yes—
432C22×C5#54212yes—
433C22×C5#54212yes—
434C22×C5#54212yes—
435C4×C5—24no—
436C4×C5—24no—
437C4×C5—24no—
438C4×C5—42no—
439C4×C5—44no—
440C4×C5—42no—
441C4×C5—42no—
442C4×C5—42no—
443C4×C5—82no—
444C4×C5—82no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C22×C4×C514yes—
460C24C24×C511yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4C22×C4×C514yes—
511C22×C4C22×C4×C512yes—
512C22×C4C22×C4×C512yes—
513C22×C4C22×C4×C512yes—
514C22×C4C2×C5×D412yes—
515C22×C4C2×C5×D412yes—
516C22×C4C2×C5×D412yes—
517C22×C4C2×C5×D412yes—
518C22×C4C2×C5×D412yes—
519C22×C4C2×C5×D412yes—
520C22×C4C5×#4112yes—
521C22×C4C5×#4112yes—
522C22×C4C5×#4112yes—
523C22×C4C5×#4112yes—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—44no—
527C4⋊C4—48no—
528C22⋊C4—216no—
529C22⋊C4—48no—
530C22⋊C4—48no—
531C22⋊C4—48no—
532C22⋊C4—48no—
533C22⋊C4—48no—
534C42—28no—
535C42—44no—
536C42—44no—
537C2×C5—84no—
538C2×C5C4×#12111yescharacteristic
539C2×C5#232111yescharacteristic
540C2×C5#232412yes—
541C2×C5#232611yescharacteristic
542C2×C5#233512yes—
543C2×C5#261811yescharacteristic
544C2×C5#261911yescharacteristic
545C2×C5#263211yescharacteristic
546C2×C5#263511yescharacteristic
547C2×C5#265112yes—
548C2×C5#266212yes—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23C23×C4×C511yescharacteristic
585C23C22×C5×D411yescharacteristic
586C23C22×C5×D411yescharacteristic
587C23C2×C5×#4111yescharacteristic
588C23C2×C5×#4111yescharacteristic
589C23C2×C5×#4111yescharacteristic
590C23C2×C5×#4111yescharacteristic
591C23C5×H(5,𝔽2)12yes—
592C23C5×H(5,𝔽2)12yes—
593C23C5×H(5,𝔽2)12yes—
594C23C5×2−1+412yes—
595D4—416no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4C4×C5×D414yes—
652C2×C4C4×C5×D414yes—
653C2×C4C5×#12114yes—
654C5#1431211yescharacteristic, direct product factor, Sylow
655C22—44no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22—44no—
661C22—44no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—82no—
666C22—82no—
667C22—82no—
668C22—82no—
669C22—82no—
670C22C2×C4×C5×D411yescharacteristic
671C22C2×C4×C5×D411yescharacteristic
672C22C4×C5×#4111yescharacteristic
673C22C5×#51812yes—
674C22C5×#52012yes—
675C22C2×C5×#12111yescharacteristic
676C22C5×#52511yescharacteristic
677C22C5×#52911yescharacteristic
678C22C5×#53211yescharacteristic
679C22C5×#53411yescharacteristic
680C22C5×#53511yescharacteristic
681C22C5×#53512yes—
682C22C5×#53511yescharacteristic
683C22C5×#53611yescharacteristic
684C22C5×#53712yes—
685C22C5×#53812yes—
686C22C5×#53812yes—
687C22C5×#53912yes—
688C22C5×#54012yes—
689C22C5×#54012yes—
690C22C5×#54212yes—
691C22C5×#54212yes—
692C22C5×#54212yes—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—44no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—82no—
702C4—82no—
703C2—84no—
704C2C4×C5×#12111yescharacteristic
705C2C5×#232111yescharacteristic
706C2C5×#232412yes—
707C2C5×#232611yescharacteristic
708C2C5×#233512yes—
709C2C5×#261811yescharacteristic
710C2C5×#261911yescharacteristic
711C2C5×#263211yescharacteristic
712C2C5×#263511yescharacteristic
713C2C5×#265112yes—
714C2C5×#266212yes—
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
3. C2×C5×#388C2semidirect
4. C2×C4×C5×C4⋊C4C2semidirect
5. C5×#1444C2semidirect
6. C5×#1441C2semidirect
7. C5×#1439C2semidirect
8. C5×#1439C2semidirect
10. C5×#1437C2semidirect
11. C5×#1434C2semidirect
26. C5×#394C4semidirect
39. #14312C5direct (N × H)
91. C2×C42×C5D4semidirect
103. C2×#388C2×C5semidirect
104. C2×C4×C4⋊C4C2×C5semidirect
105. #1444C2×C5semidirect
106. #1441C2×C5semidirect
107. #1439C2×C5semidirect
108. #1439C2×C5semidirect
110. #1437C2×C5semidirect
111. #1434C2×C5semidirect
218. #394C4×C5semidirect
387. C2×C42C5×D4semidirect
654. C5#14312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×C5×#3902
C2×C5×#3882
C2×C4×C5×C4⋊C42
C5×#14442
C5×#14412
C5×#14392
C5×#14382
C5×#14372
C5×#14342
#143125