Finite Group Databasebeta

← C2×#10605152 #12268971

Subgroups — C2×#10605152 #12268971

Order 1280.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#376C211yesmaximal, characteristic, complemented
2C2×#65228C211yesmaximal, characteristic
3C2×#65229C211yesmaximal, characteristic, complemented
4C2×#65229C211yesmaximal, characteristic, complemented
5C2×#65229C211yesmaximal, characteristic, complemented
6C2×#65222C211yesmaximal, characteristic, complemented
7C2×C4×#685C211yesmaximal, characteristic, complemented
8#10605152C2116yesmaximal, direct product factor
9C2×#64964C211yesmaximal, characteristic, complemented
10C2×#64965C211yesmaximal, characteristic, complemented
11C2×#64954C211yesmaximal, characteristic
12C2×#64953C211yesmaximal, characteristic, complemented
13C2×#64949C211yesmaximal, characteristic, complemented
14C2×#64961C211yesmaximal, characteristic
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C5×#376C2218yescomplemented
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65229C2218yescomplemented
54#65229C2218yescomplemented
55#65229C2218yescomplemented
56#65228C2218yes—
57C4×#685C2218yescomplemented
58#65222C2218yescomplemented
59#64965C2218yescomplemented
60#64964C2218yescomplemented
61#64961C2218yes—
62#64958C2218yescomplemented
63#64954C2218yes—
64#64953C2218yescomplemented
65#64949C2218yescomplemented
66#64936C2218yescomplemented
67C2×#2526—51nomaximal, Sylow
68C24×D5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C22×D20—24no—
84C22×D20—24no—
85C22×D20—42no—
86C22×D20C2314yes—
87C22×C4×D5—24no—
88C22×C4×D5—24no—
89C22×C4×D5—42no—
90C22×C4×D5C2314yes—
91C2×C42×C5—24no—
92C2×C42×C5—24no—
93C2×C42×C5—24no—
94C2×C42×C5C2314yes—
95C2×C42×C5C2314yes—
96C2×C42×C5C2314yes—
97C2×#685—24no—
98C2×#685—24no—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—42no—
104C2×#685—42no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685C2314yes—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—42no—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—42no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×C4×Dic5—42no—
132C2×C4×Dic5C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135C5×#95C2314yes—
136C5×#95C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2526—516no—
146C2×#400—51no—
147C2×#397—51no—
148C2×#396—51no—
149C2×#394—51no—
150C2×#390—51no—
151C2×#389—51no—
152C2×#388—51no—
153C2×#388—51no—
154C2×#388—51no—
155C2×#388—51no—
156C2×#387—51no—
157C2×#386—51no—
158C2×#381—51no—
159C2×C4×C22⋊C4—51no—
160C2×#376D511yescharacteristic, complemented
161C24×C5C2411yescharacteristic
162C23×D5—22no—
163C23×D5—22no—
164C23×D5—22no—
165C23×D5—22no—
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5#4114yes—
176C23×D5C2412yes—
177C23×D5C2412yes—
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#4114yes—
197C22×C4×C5#4114yes—
198C22×C4×C5#4114yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5#4114yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C2×D20—28no—
231C2×D20—28no—
232C2×D20—44no—
233C2×D20—416no—
234C2×C4×D5—28no—
235C2×C4×D5—28no—
236C2×C4×D5—44no—
237C2×C4×D5—416no—
238C42×C5—28no—
239C42×C5—28no—
240C42×C5—28no—
241#685—28no—
242#685—28no—
243#685—28no—
244#685—28no—
245#685—28no—
246#685—28no—
247#685—44no—
248#685—44no—
249#685—44no—
250#685—44no—
251#685—44no—
252C4⋊Dic5—44no—
253#683—28no—
254#683—28no—
255#683—44no—
256#683—44no—
257#683—44no—
258C4×Dic5—44no—
259C23×D4—51no—
260C24×C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C22⋊C4—51no—
268C22×C22⋊C4—51no—
269C22×C22⋊C4—51no—
270C22×C22⋊C4—51no—
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C22⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C22⋊C4—51no—
278C22×C42—51no—
279C22×C42C2×D511yescharacteristic
280C22×C42C2×D511yescharacteristic
281C22×C42C2×D511yescharacteristic
282#400—58no—
283#397—58no—
284#396—58no—
285#394—58no—
286#390—58no—
287#389—58no—
288#388—58no—
289#388—58no—
290#388—58no—
291#388—58no—
292#387—58no—
293#386—58no—
294#381—58no—
295C4×C22⋊C4—58no—
296#376C2×D518yescomplemented
297C2×#95—51no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95C2×D511yescharacteristic
306C2×#95C2×D511yescharacteristic
307C2×#95C2×D511yescharacteristic
308C2×#95C2×D511yescharacteristic
309C23×C5C2×#4112yes—
310C23×C5C2×#4112yes—
311C23×C5C2×#4112yes—
312C23×C5C2×#4112yes—
313C23×C5C2×#4112yes—
314C23×C5H(5,𝔽2)12yes—
315C23×C5H(5,𝔽2)12yes—
316C23×C5C2511yescharacteristic
317C22×D5—28no—
318C22×D5—28no—
319C22×D5—28no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—22no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—44no—
334C22×D5—44no—
335C22×D5—44no—
336C22×D5—44no—
337C22×D5—44no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5C2×#4114yes—
345C2×C4×C5—28no—
346C2×C4×C5—28no—
347C2×C4×C5—28no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5C2×#4114yes—
371C2×C4×C5C2×#4114yes—
372C2×C4×C5C2×#4114yes—
373C2×Dic5—28no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5C2×#4114yes—
397D20—416no—
398C4×D5—416no—
399C25—51no—
400C25—51no—
401C22×D4—54no—
402C22×D4—104no—
403C22×D4—104no—
404C22×D4—202no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—54no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4—202no—
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C2×C4⋊C4—54no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—202no—
431C2×C4⋊C4—202no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4—202no—
434C2×C22⋊C4—54no—
435C2×C22⋊C4—54no—
436C2×C22⋊C4—54no—
437C2×C22⋊C4—54no—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—54no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—54no—
443C2×C22⋊C4—54no—
444C2×C22⋊C4—54no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C22⋊C4—104no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C42—24no—
457C2×C42—24no—
458C2×C42—24no—
459C2×C42—54no—
460C2×C42—202no—
461C2×C42C22×D514yes—
462C2×C42C22×D514yes—
463C2×C42C22×D514yes—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95C22×D514yes—
473#95C22×D514yes—
474#95C22×D514yes—
475#95C22×D514yes—
476C22×C5#52914yes—
477C22×C5#52914yes—
478C22×C5#54014yes—
479C22×C5#55114yes—
480C22×C5#55114yes—
481C22×C5#55314yes—
482C22×C5#55514yes—
483C22×C5C22×#4111yescharacteristic
484C22×C5C22×#4111yescharacteristic
485C22×C5C22×#4111yescharacteristic
486C22×C5C22×#4111yescharacteristic
487C22×C5C22×#4111yescharacteristic
488C22×C5C2×H(5,𝔽2)11yescharacteristic
489C22×C5C2×H(5,𝔽2)11yescharacteristic
490C2×D5—24no—
491C2×D5—24no—
492C2×D5—24no—
493C2×D5—42no—
494C2×D5—42no—
495C2×D5—42no—
496C2×D5—42no—
497C2×D5—416no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—88no—
506C4×C5—24no—
507C4×C5—24no—
508C4×C5—24no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513Dic5—24no—
514Dic5—42no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519C24—54no—
520C24—52no—
521C24—52no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24C23×D511yescharacteristic
536C2×D4—108no—
537C2×D4—108no—
538C2×D4—204no—
539C2×D4—2016no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—54no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—108no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—108no—
584C22×C4—204no—
585C22×C4—2016no—
586C22×C4#70914yes—
587C22×C4#70914yes—
588C22×C4#70914yes—
589C22×C4C23×D512yes—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C4⋊C4—108no—
597C4⋊C4—108no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C4⋊C4—204no—
601C4⋊C4—204no—
602C22⋊C4—108no—
603C22⋊C4—108no—
604C22⋊C4—108no—
605C22⋊C4—108no—
606C22⋊C4—108no—
607C22⋊C4—108no—
608C22⋊C4—204no—
609C22⋊C4—204no—
610C22⋊C4—204no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C42—28no—
614C42—28no—
615C42—28no—
616C42—204no—
617C2×C5#252618yescomplemented
618C2×C5C2×#52911yescharacteristic
619C2×C5C2×#52911yescharacteristic
620C2×C5C2×#54011yescharacteristic
621C2×C5C2×#55111yescharacteristic
622C2×C5C2×#55111yescharacteristic
623C2×C5C2×#55311yescharacteristic
624C2×C5C2×#55511yescharacteristic
625D5—44no—
626D5—82no—
627C23—54no—
628C23—108no—
629C23—108no—
630C23—108no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—102no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—204no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23C2×#70912yes—
656C23C2×#70912yes—
657C23C2×#70912yes—
658C23D5×#4112yes—
659C23D5×#4112yes—
660C23#414912yes—
661C23#414912yes—
662C23C24×D511yescharacteristic
663D4—2016no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—28no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—54no—
690C2×C4—108no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—2016no—
709C2×C4—204no—
710C2×C4—204no—
711C2×C4—204no—
712C2×C4—204no—
713C2×C4—204no—
714C2×C4C2×#70914yes—
715C2×C4C2×#70914yes—
716C2×C4C2×#70914yes—
717C5C2×#252611yescharacteristic, complemented, Sylow
718C22—104no—
719C22—104no—
720C22—104no—
721C22—202no—
722C22—202no—
723C22—202no—
724C22—2016no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—408no—
734C22#6581314yes—
735C22#6586114yes—
736C22#6586114yes—
737C22#6586214yes—
738C22#6586414yes—
739C22#6586614yes—
740C22#6586914yes—
741C22C22×#70911yescharacteristic
742C22C22×#70911yescharacteristic
743C22C22×#70911yescharacteristic
744C22C2×D5×#4111yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×#414911yescharacteristic
747C22C2×#414911yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—104no—
756C4—202no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C2—204no—
762C2—402no—
763C2#1060515218yesdirect product factor
764C2C2×#6581311yescharacteristic
765C2C2×#6586211yescharacteristic
766C2C2×#6586911yescharacteristic
767C2C2×#6586111yescharacteristic
768C2C2×#6586111yescharacteristic
769C2C2×#6586411yescharacteristic
770C2C2×#6586611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#376C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#376D5
hypocenterC5C2×#2526
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. C2×C5×#376C2semidirect
3. C2×#65229C2semidirect
4. C2×#65229C2semidirect
5. C2×#65229C2semidirect
6. C2×#65222C2semidirect
7. C2×C4×#685C2semidirect
8. #10605152C2direct (N × H)
9. C2×#64964C2semidirect
10. C2×#64965C2semidirect
12. C2×#64953C2semidirect
13. C2×#64949C2semidirect
15. C2×#64936C2semidirect
16. C2×#64958C2semidirect
40. C5×#376C22semidirect
53. #65229C22semidirect
54. #65229C22semidirect
55. #65229C22semidirect
57. C4×#685C22semidirect
58. #65222C22semidirect
59. #64965C22semidirect
60. #64964C22semidirect
62. #64958C22semidirect
64. #64953C22semidirect
65. #64949C22semidirect
66. #64936C22semidirect
160. C2×#376D5semidirect
296. #376C2×D5semidirect
617. C2×C5#2526semidirect
717. C5C2×#2526semidirect
763. C2#10605152direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3762
C2×#652282
C2×#652292
C2×#652222
C2×C4×#6852
#106051522
C2×#649642
C2×#649652
C2×#649542
C2×#649532
C2×#649492
C2×#649612
C2×#649362
C2×#649582
C2×#25265