Finite Group Databasebeta

← C2×#10606034 #12269696

Subgroups — C2×#10606034 #12269696

Order 1280.

2614 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#383C211yesmaximal, characteristic, complemented
2C2×#65229C211yesmaximal, characteristic, complemented
3C2×C4×#685C211yesmaximal, characteristic, complemented
4#10606034C2116yesmaximal, direct product factor
5C2×#64962C211yesmaximal, characteristic, complemented
6C2×#64962C211yesmaximal, characteristic, complemented
7C2×#64954C211yesmaximal, characteristic
8C2×#64954C211yesmaximal, characteristic
9C2×#64953C211yesmaximal, characteristic, complemented
10C2×#64953C211yesmaximal, characteristic, complemented
11C2×#64947C211yesmaximal, characteristic, complemented
12C2×#64961C211yesmaximal, characteristic
13C2×#64935C211yesmaximal, characteristic, complemented
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64940C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C5×#383C2218yescomplemented
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65229C2218yescomplemented
54C4×#685C2218yescomplemented
55#64962C2218yescomplemented
56#64962C2218yescomplemented
57#64961C2218yes—
58#64958C2218yescomplemented
59#64955C2218yescomplemented
60#64954C2218yes—
61#64954C2218yes—
62#64953C2218yescomplemented
63#64953C2218yescomplemented
64#64947C2218yescomplemented
65#64940C2218yescomplemented
66#64935C2218yescomplemented
67C2×#2572—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—24no—
90C22×C4×D5—24no—
91C22×C4×D5—42no—
92C22×C4×D5—42no—
93C22×C4×D5C2314yes—
94C22×C4×D5C2314yes—
95C22×Dic10—24no—
96C22×Dic10—42no—
97C22×Dic10—42no—
98C22×Dic10C2314yes—
99C2×C42×C5—24no—
100C2×C42×C5C2314yes—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685—42no—
110C2×#685—42no—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#683—42no—
122C2×#683—42no—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×C4×Dic5—24no—
126C2×C4×Dic5—42no—
127C2×C4×Dic5C2314yes—
128C2×C4×Dic5C2314yes—
129C5×#95C2314yes—
130C5×#95C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2572—516no—
146C2×#400—51no—
147C2×#394—51no—
148C2×#393—51no—
149C2×#393—51no—
150C2×#391—51no—
151C2×#388—51no—
152C2×#388—51no—
153C2×#386—51no—
154C2×#386—51no—
155C2×#383—51no—
156C2×#383D511yescharacteristic, complemented
157C2×#381—51no—
158C2×#381—51no—
159C2×C4×C22⋊C4—51no—
160C2×C4×C22⋊C4—51no—
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#4114yes—
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—22no—
197C22×C4×C5—22no—
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#4114yes—
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—28no—
237C2×C4×D5—28no—
238C2×C4×D5—44no—
239C2×C4×D5—44no—
240C2×C4×D5—416no—
241C2×C4×D5—416no—
242C2×Dic10—28no—
243C2×Dic10—44no—
244C2×Dic10—44no—
245C2×Dic10—416no—
246C42×C5—28no—
247#685—28no—
248#685—28no—
249#685—28no—
250#685—28no—
251#685—28no—
252#685—28no—
253#685—44no—
254#685—44no—
255#685—44no—
256#685—44no—
257#683—44no—
258#683—44no—
259C4×Dic5—28no—
260C4×Dic5—44no—
261C23×Q8—51no—
262C23×D4—51no—
263C24×C4—51no—
264C24×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×C42—51no—
278C22×C42—51no—
279C22×C42C2×D511yescharacteristic
280#400—58no—
281#394—58no—
282#393—58no—
283#393—58no—
284#391—58no—
285#388—58no—
286#388—58no—
287#386—58no—
288#386—58no—
289#383—58no—
290#383C2×D518yescomplemented
291#381—58no—
292#381—58no—
293C4×C22⋊C4—58no—
294C4×C22⋊C4—58no—
295C2×#95—51no—
296C2×#95—51no—
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
309C2×#95C2×D511yescharacteristic
310C2×#95C2×D511yescharacteristic
311C23×C5C2×#4112yes—
312C23×C5C2×#4112yes—
313C23×C5C2×#4112yes—
314C23×C5C2×#4112yes—
315C23×C5C2×#4112yes—
316C23×C5H(5,𝔽2)12yes—
317C23×C5H(5,𝔽2)12yes—
318C23×C5C2511yescharacteristic
319C22×D5—28no—
320C22×D5—28no—
321C22×D5—28no—
322C22×D5—28no—
323C22×D5—28no—
324C22×D5—28no—
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—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—44no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
345C22×D5C2×#4114yes—
346C22×D5C2×#4114yes—
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—22no—
367C2×C4×C5—22no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C2×C4×C5—44no—
373C2×C4×C5—44no—
374C2×C4×C5C2×#4114yes—
375C2×Dic5—28no—
376C2×Dic5—28no—
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—22no—
392C2×Dic5—22no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5C2×#4114yes—
398C2×Dic5C2×#4114yes—
399D20—416no—
400C4×D5—416no—
401C4×D5—416no—
402Dic10—416no—
403C25—51no—
404C25—51no—
405C22×Q8—54no—
406C22×Q8—104no—
407C22×Q8—202no—
408C22×Q8—202no—
409C22×D4—54no—
410C22×D4—104no—
411C22×D4—104no—
412C22×D4—202no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—54no—
420C23×C4—54no—
421C23×C4—104no—
422C23×C4—104no—
423C23×C4—104no—
424C23×C4—104no—
425C23×C4—202no—
426C23×C4—202no—
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—202no—
437C2×C4⋊C4—202no—
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—54no—
446C2×C22⋊C4—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—104no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C42—24no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—104no—
462C2×C42—202no—
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#95—54no—
473#95—54no—
474#95C22×D514yes—
475#95C22×D514yes—
476#95C22×D514yes—
477#95C22×D514yes—
478#95C22×D514yes—
479#95C22×D514yes—
480C22×C5#52914yes—
481C22×C5#52914yes—
482C22×C5#53814yes—
483C22×C5#55114yes—
484C22×C5#55114yes—
485C22×C5#55114yes—
486C22×C5#55514yes—
487C22×C5C22×#4111yescharacteristic
488C22×C5C22×#4111yescharacteristic
489C22×C5C22×#4111yescharacteristic
490C22×C5C22×#4111yescharacteristic
491C22×C5C22×#4111yescharacteristic
492C22×C5C2×H(5,𝔽2)11yescharacteristic
493C22×C5C2×H(5,𝔽2)11yescharacteristic
494C2×D5—24no—
495C2×D5—24no—
496C2×D5—24no—
497C2×D5—24no—
498C2×D5—24no—
499C2×D5—24no—
500C2×D5—416no—
501C2×D5—416no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C2×D5—42no—
509C2×D5—42no—
510C4×C5—24no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514C4×C5—42no—
515C4×C5—42no—
516C4×C5—42no—
517Dic5—24no—
518Dic5—24no—
519Dic5—42no—
520Dic5—42no—
521Dic5—42no—
522Dic5—42no—
523C24—54no—
524C24—54no—
525C24—52no—
526C24—52no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24—102no—
537C24—102no—
538C24—102no—
539C24C23×D511yescharacteristic
540C2×Q8—108no—
541C2×Q8—204no—
542C2×Q8—204no—
543C2×Q8—2016no—
544C2×D4—108no—
545C2×D4—108no—
546C2×D4—204no—
547C2×D4—2016no—
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—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—54no—
569C22×C4—54no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—108no—
577C22×C4—108no—
578C22×C4—108no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—108no—
596C22×C4—204no—
597C22×C4—204no—
598C22×C4—2016no—
599C22×C4—2016no—
600C22×C4#70914yes—
601C22×C4C23×D512yes—
602C22×C4C23×D512yes—
603C22×C4C23×D512yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C4⋊C4—204no—
609C4⋊C4—204no—
610C22⋊C4—108no—
611C22⋊C4—108no—
612C22⋊C4—108no—
613C22⋊C4—108no—
614C22⋊C4—108no—
615C22⋊C4—108no—
616C22⋊C4—204no—
617C22⋊C4—204no—
618C22⋊C4—204no—
619C22⋊C4—204no—
620C42—28no—
621C42—108no—
622C42—204no—
623C2×C5#257218yescomplemented
624C2×C5C2×#52911yescharacteristic
625C2×C5C2×#52911yescharacteristic
626C2×C5C2×#53811yescharacteristic
627C2×C5C2×#55111yescharacteristic
628C2×C5C2×#55111yescharacteristic
629C2×C5C2×#55111yescharacteristic
630C2×C5C2×#55511yescharacteristic
631D5—44no—
632D5—44no—
633C23—54no—
634C23—54no—
635C23—108no—
636C23—108no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—102no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—108no—
650C23—108no—
651C23—108no—
652C23—108no—
653C23—204no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23—204no—
658C23—204no—
659C23—204no—
660C23—204no—
661C23C2×#70912yes—
662C23D5×#4112yes—
663C23D5×#4112yes—
664C23D5×#4112yes—
665C23D5×#4112yes—
666C23#414912yes—
667C23#414912yes—
668C23C24×D511yescharacteristic
669Q8—2016no—
670D4—2016no—
671C2×C4—28no—
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—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—54no—
699C2×C4—54no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—108no—
705C2×C4—108no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—2016no—
719C2×C4—2016no—
720C2×C4—204no—
721C2×C4—204no—
722C2×C4—204no—
723C2×C4—204no—
724C2×C4C2×#70914yes—
725C5C2×#257211yescharacteristic, complemented, Sylow
726C22—104no—
727C22—104no—
728C22—104no—
729C22—104no—
730C22—104no—
731C22—104no—
732C22—202no—
733C22—202no—
734C22—202no—
735C22—202no—
736C22—202no—
737C22—202no—
738C22—202no—
739C22—202no—
740C22—2016no—
741C22—2016no—
742C22#6586114yes—
743C22#6586214yes—
744C22#6586614yes—
745C22#6603814yes—
746C22#6603914yes—
747C22#6603914yes—
748C22#6604014yes—
749C22C22×#70911yescharacteristic
750C22C2×D5×#4111yescharacteristic
751C22C2×D5×#4111yescharacteristic
752C22C2×D5×#4111yescharacteristic
753C22C2×D5×#4111yescharacteristic
754C22C2×#414911yescharacteristic
755C22C2×#414911yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—104no—
764C4—104no—
765C4—202no—
766C4—202no—
767C4—202no—
768C4—202no—
769C2—204no—
770C2—204no—
771C2#1060603418yesdirect product factor
772C2C2×#6586211yescharacteristic
773C2C2×#6586111yescharacteristic
774C2C2×#6586611yescharacteristic
775C2C2×#6604011yescharacteristic
776C2C2×#6603811yescharacteristic
777C2C2×#6603911yescharacteristic
778C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#383C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#383D5
hypocenterC5C2×#2572
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C2×C5×#383C2semidirect
2. C2×#65229C2semidirect
3. C2×C4×#685C2semidirect
4. #10606034C2direct (N × H)
5. C2×#64962C2semidirect
6. C2×#64962C2semidirect
9. C2×#64953C2semidirect
10. C2×#64953C2semidirect
11. C2×#64947C2semidirect
13. C2×#64935C2semidirect
14. C2×#64958C2semidirect
15. C2×#64940C2semidirect
16. C2×#64955C2semidirect
36. C5×#383C22semidirect
53. #65229C22semidirect
54. C4×#685C22semidirect
55. #64962C22semidirect
56. #64962C22semidirect
58. #64958C22semidirect
59. #64955C22semidirect
62. #64953C22semidirect
63. #64953C22semidirect
64. #64947C22semidirect
65. #64940C22semidirect
66. #64935C22semidirect
156. C2×#383D5semidirect
290. #383C2×D5semidirect
623. C2×C5#2572semidirect
725. C5C2×#2572semidirect
771. C2#10606034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3832
C2×#652292
C2×C4×#6852
#106060342
C2×#649622
C2×#649542
C2×#649532
C2×#649472
C2×#649612
C2×#649352
C2×#649582
C2×#649402
C2×#649552
C2×#25725