Finite Group Databasebeta

← C2×#10609921 #12269768

Subgroups — C2×#10609921 #12269768

Order 1280.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#400C211yesmaximal, characteristic, complemented
2C2×#65280C211yesmaximal, characteristic
3C2×#65278C211yesmaximal, characteristic, complemented
4C2×#65276C211yesmaximal, characteristic, complemented
5C2×#65267C211yesmaximal, characteristic, complemented
6#10609921C2116yesmaximal, direct product factor
7C2×#64964C211yesmaximal, characteristic, complemented
8C2×#64954C211yesmaximal, characteristic
9C2×#64954C211yesmaximal, characteristic
10C2×#64963C211yesmaximal, characteristic, complemented
11C2×#64958C211yesmaximal, characteristic, complemented
12C2×#64958C211yesmaximal, characteristic, complemented
13C2×#64942C211yesmaximal, characteristic, complemented
14C2×#64940C211yesmaximal, characteristic, complemented
15C2×#64955C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C5×#400C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65280C2218yes—
54#65278C2218yescomplemented
55#65276C2218yescomplemented
56#65267C2218yescomplemented
57#64964C2218yescomplemented
58#64963C2218yescomplemented
59#64958C2218yescomplemented
60#64958C2218yescomplemented
61#64955C2218yescomplemented
62#64955C2218yescomplemented
63#64954C2218yes—
64#64954C2218yes—
65#64942C2218yescomplemented
66#64940C2218yescomplemented
67C2×#2578—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—42no—
91C22×C4×D5—42no—
92C22×C4×D5—42no—
93C22×C4×D5C2314yes—
94C22×C4×D5C2314yes—
95C2×C5×C4⋊C4—42no—
96C2×C5×C4⋊C4—42no—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—42no—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×C4×Dic5—24no—
126C2×C4×Dic5—42no—
127C2×C4×Dic5—42no—
128C2×C4×Dic5C2314yes—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135C5×#95C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2578—516no—
146C2×#400D511yescharacteristic, complemented
147C2×#397—51no—
148C2×#397—51no—
149C2×#394—51no—
150C2×#388—51no—
151C2×#388—51no—
152C2×#387—51no—
153C2×#387—51no—
154C2×#386—51no—
155C2×#386—51no—
156C2×#385—51no—
157C2×#383—51no—
158C2×#380—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—44no—
238C2×C4×D5—44no—
239C2×C4×D5—44no—
240C2×C4×D5—416no—
241C2×C4×D5—416no—
242C5×C4⋊C4—44no—
243C5×C4⋊C4—44no—
244#685—28no—
245#685—28no—
246#685—28no—
247#685—28no—
248#685—28no—
249#685—28no—
250#685—28no—
251#685—44no—
252#685—44no—
253#685—44no—
254C4⋊Dic5—28no—
255#683—28no—
256#683—44no—
257C4×Dic5—28no—
258C4×Dic5—44no—
259C4×Dic5—44no—
260C23×D4—51no—
261C24×C4—51no—
262C24×C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4C2×D511yescharacteristic
267C22×C4⋊C4C2×D511yescharacteristic
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×C42—51no—
280C22×C42—51no—
281#400C2×D518yescomplemented
282#397—58no—
283#397—58no—
284#394—58no—
285#388—58no—
286#388—58no—
287#387—58no—
288#387—58no—
289#386—58no—
290#386—58no—
291#385—58no—
292#383—58no—
293#380—58no—
294C4×C22⋊C4—58no—
295C4×C22⋊C4—58no—
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
310C23×C5C2×#4112yes—
311C23×C5C2×#4112yes—
312C23×C5C2×#4112yes—
313C23×C5C2×#4112yes—
314C23×C5C2×#4112yes—
315C23×C5H(5,𝔽2)12yes—
316C23×C5H(5,𝔽2)12yes—
317C23×C5C2511yescharacteristic
318C22×D5—28no—
319C22×D5—28no—
320C22×D5—28no—
321C22×D5—28no—
322C22×D5—28no—
323C22×D5—28no—
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—22no—
334C22×D5—22no—
335C22×D5—22no—
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—
345C22×D5C2×#4114yes—
346C2×C4×C5—28no—
347C2×C4×C5—22no—
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—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C2×C4×C5—44no—
373C2×C4×C5C2×#4114yes—
374C2×Dic5—28no—
375C2×Dic5—28no—
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—22no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5C2×#4114yes—
397C2×Dic5C2×#4114yes—
398D20—416no—
399C4×D5—416no—
400C4×D5—416no—
401C25—51no—
402C25—51no—
403C22×D4—54no—
404C22×D4—104no—
405C22×D4—104no—
406C22×D4—202no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—54no—
414C23×C4—54no—
415C23×C4—104no—
416C23×C4—104no—
417C23×C4—104no—
418C23×C4—202no—
419C23×C4—202no—
420C23×C4—202no—
421C23×C4C22×D511yescharacteristic
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—104no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4C22×D514yes—
437C2×C4⋊C4C22×D514yes—
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—104no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C42—54no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—104no—
462C2×C42—202no—
463C2×C42—202no—
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#95C22×D514yes—
474#95C22×D514yes—
475#95C22×D514yes—
476#95C22×D514yes—
477#95C22×D514yes—
478C22×C5#52914yes—
479C22×C5#52914yes—
480C22×C5#53814yes—
481C22×C5#55114yes—
482C22×C5#55114yes—
483C22×C5#55314yes—
484C22×C5#55314yes—
485C22×C5C22×#4111yescharacteristic
486C22×C5C22×#4111yescharacteristic
487C22×C5C22×#4111yescharacteristic
488C22×C5C22×#4111yescharacteristic
489C22×C5C22×#4111yescharacteristic
490C22×C5C2×H(5,𝔽2)11yescharacteristic
491C22×C5C2×H(5,𝔽2)11yescharacteristic
492C2×D5—24no—
493C2×D5—24no—
494C2×D5—24no—
495C2×D5—24no—
496C2×D5—24no—
497C2×D5—24no—
498C2×D5—416no—
499C2×D5—416no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C4×C5—24no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514C4×C5—42no—
515Dic5—24no—
516Dic5—24no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521C24—54no—
522C24—54no—
523C24—52no—
524C24—52no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24—102no—
537C24C23×D511yescharacteristic
538C2×D4—108no—
539C2×D4—108no—
540C2×D4—204no—
541C2×D4—2016no—
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—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—54no—
563C22×C4—54no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—108no—
571C22×C4—108no—
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—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—108no—
589C22×C4—204no—
590C22×C4—204no—
591C22×C4—204no—
592C22×C4—2016no—
593C22×C4—2016no—
594C22×C4#71314yes—
595C22×C4C23×D512yes—
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D512yes—
599C22×C4C23×D512yes—
600C22×C4C23×D512yes—
601C22×C4C23×D512yes—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—108no—
605C4⋊C4—108no—
606C4⋊C4—204no—
607C22⋊C4—108no—
608C22⋊C4—108no—
609C22⋊C4—108no—
610C22⋊C4—108no—
611C22⋊C4—108no—
612C22⋊C4—108no—
613C22⋊C4—108no—
614C22⋊C4—204no—
615C22⋊C4—204no—
616C22⋊C4—204no—
617C42—108no—
618C42—204no—
619C42—204no—
620C2×C5#257818yescomplemented
621C2×C5C2×#52911yescharacteristic
622C2×C5C2×#52911yescharacteristic
623C2×C5C2×#53811yescharacteristic
624C2×C5C2×#55111yescharacteristic
625C2×C5C2×#55111yescharacteristic
626C2×C5C2×#55311yescharacteristic
627C2×C5C2×#55311yescharacteristic
628D5—44no—
629D5—44no—
630C23—54no—
631C23—54no—
632C23—108no—
633C23—108no—
634C23—102no—
635C23—102no—
636C23—102no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—108no—
645C23—102no—
646C23—102no—
647C23—108no—
648C23—108no—
649C23—108no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23—204no—
658C23#414412yes—
659C23C2×#71312yes—
660C23D5×#4112yes—
661C23D5×#4112yes—
662C23D5×#4112yes—
663C23D5×#4112yes—
664C23#414912yes—
665C23C24×D511yescharacteristic
666D4—2016no—
667C2×C4—28no—
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—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—54no—
695C2×C4—54no—
696C2×C4—108no—
697C2×C4—108no—
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—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—2016no—
715C2×C4—2016no—
716C2×C4—204no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4C2×#71314yes—
721C5C2×#257811yescharacteristic, complemented, Sylow
722C22—104no—
723C22—104no—
724C22—104no—
725C22—104no—
726C22—104no—
727C22—104no—
728C22—2016no—
729C22—2016no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—202no—
734C22—202no—
735C22—202no—
736C22—202no—
737C22—202no—
738C22#6597114yes—
739C22#6599114yes—
740C22#6601314yes—
741C22#6602514yes—
742C22#6602914yes—
743C22#6604014yes—
744C22#6604314yes—
745C22C2×#414411yescharacteristic
746C22C22×#71311yescharacteristic
747C22C2×D5×#4111yescharacteristic
748C22C2×D5×#4111yescharacteristic
749C22C2×D5×#4111yescharacteristic
750C22C2×D5×#4111yescharacteristic
751C22C2×#414911yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—104no—
760C4—104no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C2—204no—
766C2—204no—
767C2#1060992118yesdirect product factor
768C2C2×#6597111yescharacteristic
769C2C2×#6599111yescharacteristic
770C2C2×#6601311yescharacteristic
771C2C2×#6602511yescharacteristic
772C2C2×#6602911yescharacteristic
773C2C2×#6604011yescharacteristic
774C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#400C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#400D5
hypocenterC5C2×#2578
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C2×C5×#400C2semidirect
3. C2×#65278C2semidirect
4. C2×#65276C2semidirect
5. C2×#65267C2semidirect
6. #10609921C2direct (N × H)
7. C2×#64964C2semidirect
10. C2×#64963C2semidirect
11. C2×#64958C2semidirect
12. C2×#64958C2semidirect
13. C2×#64942C2semidirect
14. C2×#64940C2semidirect
15. C2×#64955C2semidirect
16. C2×#64955C2semidirect
38. C5×#400C22semidirect
54. #65278C22semidirect
55. #65276C22semidirect
56. #65267C22semidirect
57. #64964C22semidirect
58. #64963C22semidirect
59. #64958C22semidirect
60. #64958C22semidirect
61. #64955C22semidirect
62. #64955C22semidirect
65. #64942C22semidirect
66. #64940C22semidirect
146. C2×#400D5semidirect
281. #400C2×D5semidirect
620. C2×C5#2578semidirect
721. C5C2×#2578semidirect
767. C2#10609921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4002
C2×#652802
C2×#652782
C2×#652762
C2×#652672
#106099212
C2×#649642
C2×#649542
C2×#649632
C2×#649582
C2×#649422
C2×#649402
C2×#649552
C2×#25785