Finite Group Databasebeta

← C2×#10609054 #12269752

Subgroups — C2×#10609054 #12269752

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×#396C211yesmaximal, characteristic, complemented
2C2×#65282C211yesmaximal, characteristic, complemented
3C2×#65278C211yesmaximal, characteristic, complemented
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65267C211yesmaximal, characteristic, complemented
6C2×#65270C211yesmaximal, characteristic, complemented
7C2×#65266C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic
9C2×#65250C211yesmaximal, characteristic
10C2×#65233C211yesmaximal, characteristic, complemented
11C2×#65247C211yesmaximal, characteristic
12C2×#65232C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10609054C2116yesmaximal, direct product factor
15C2×C5⋊#401C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C5×#396C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65282C2218yescomplemented
54#65279C2218yescomplemented
55#65278C2218yescomplemented
56#65270C2218yescomplemented
57#65267C2218yescomplemented
58#65266C2218yescomplemented
59#65250C2218yes—
60#65247C2218yes—
61#65245C2218yes—
62#65233C2218yescomplemented
63#65232C2218yescomplemented
64C22⋊C4×Dic5C2218yescomplemented
65#64955C2218yescomplemented
66C5⋊#401C2218yescomplemented
67C2×#2576—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C22×C22⋊D5—24no—
77C22×C22⋊D5—24no—
78C22×C22⋊D5—42no—
79C22×C22⋊D5C2314yes—
80C23×Dic5—24no—
81C23×Dic5—24no—
82C23×Dic5—42no—
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2314yes—
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C22×C4×D5—24no—
92C22×C4×D5—42no—
93C22×C4×D5—42no—
94C22×C4×D5C2314yes—
95C2×C5×C4⋊C4—24no—
96C2×C5×C4⋊C4—42no—
97C2×C5×C4⋊C4—42no—
98C2×C5×C4⋊C4C2314yes—
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4—42no—
103C2×C5×C22⋊C4—42no—
104C2×C5×C22⋊C4C2314yes—
105C2×C5×C22⋊C4C2314yes—
106C2×C5×C22⋊C4C2314yes—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5—24no—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—42no—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—42no—
122C2×C4⋊Dic5C2314yes—
123C2×#683—24no—
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—
132#3963C2314yes—
133#3963C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2576—516no—
146C2×#401—51no—
147C2×#397—51no—
148C2×#396D511yescharacteristic, complemented
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×#382—51no—
158C2×#381—51no—
159C2×C4×C22⋊C4—51no—
160C2×C4×C22⋊C4—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5#4114yes—
168C24×C5C2412yes—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5#4114yes—
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#4114yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C2×C22⋊D5—28no—
203C2×C22⋊D5—28no—
204C2×C22⋊D5—44no—
205C2×C22⋊D5—416no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—28no—
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—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—28no—
227C22×Dic5—44no—
228C22×Dic5—416no—
229C22×Dic5#4114yes—
230C22×Dic5#4114yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×C4×D5—28no—
239C2×C4×D5—44no—
240C2×C4×D5—44no—
241C2×C4×D5—416no—
242C5×C4⋊C4—28no—
243C5×C4⋊C4—44no—
244C5×C4⋊C4—44no—
245C5×C22⋊C4—28no—
246C5×C22⋊C4—44no—
247C5×C22⋊C4—44no—
248C22⋊Dic5—28no—
249C22⋊Dic5—28no—
250#685—28no—
251#685—28no—
252#685—28no—
253#685—28no—
254#685—44no—
255C4⋊Dic5—44no—
256#683—28no—
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⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
276C22×C22⋊C4C2×D511yescharacteristic
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C42—51no—
279C22×C42—51no—
280C22×C42—51no—
281#401—58no—
282#397—58no—
283#396C2×D518yescomplemented
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#382—58no—
293#381—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×#95—51no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95C2×D511yescharacteristic
310C23×C5—28no—
311C23×C5—28no—
312C23×C5—28no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5C2×#4112yes—
324C23×C5C2×#4114yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C5H(5,𝔽2)12yes—
331C23×C5C2511yescharacteristic
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
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—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5C2×#4114yes—
370C22⋊D5—416no—
371C2×Dic5—28no—
372C2×Dic5—28no—
373C2×Dic5—22no—
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—22no—
392C2×Dic5—416no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5C2×#4114yes—
399C2×Dic5C2×#4114yes—
400C4×D5—416no—
401C25—51no—
402C25C22×D511yescharacteristic
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—51no—
414C23×C4—54no—
415C23×C4—54no—
416C23×C4—104no—
417C23×C4—104no—
418C23×C4—104no—
419C23×C4—202no—
420C23×C4—202no—
421C23×C4—202no—
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×C4⋊C4—24no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4C22×D514yes—
436C2×C4⋊C4C22×D514yes—
437C2×C4⋊C4C22×D514yes—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
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⋊C4C22×D514yes—
456C2×C22⋊C4C22×D514yes—
457C2×C22⋊C4C22×D514yes—
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#95—54no—
474#95—54no—
475#95—54no—
476#95—54no—
477#95C22×D514yes—
478C22×C5—24no—
479C22×C5—24no—
480C22×C5—24no—
481C22×C5—416no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5#52914yes—
487C22×C5#52914yes—
488C22×C5#53814yes—
489C22×C5#55114yes—
490C22×C5#55114yes—
491C22×C5#55314yes—
492C22×C5#55314yes—
493C22×C5C22×#4111yescharacteristic
494C22×C5C22×#4111yescharacteristic
495C22×C5C22×#4111yescharacteristic
496C22×C5C22×#4111yescharacteristic
497C22×C5C22×#4111yescharacteristic
498C22×C5C2×H(5,𝔽2)11yescharacteristic
499C22×C5C2×H(5,𝔽2)11yescharacteristic
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—24no—
503C2×D5—416no—
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—
514Dic5—24no—
515Dic5—24no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—54no—
528C24—52no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24#71314yes—
536C24C23×D512yes—
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—54no—
560C22×C4—54no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—108no—
569C22×C4—108no—
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—108no—
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—204no—
591C22×C4—204no—
592C22×C4—2016no—
593C22×C4—204no—
594C22×C4—2016no—
595C22×C4#71114yes—
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D512yes—
599C22×C4C23×D512yes—
600C22×C4C23×D512yes—
601C22×C4C23×D512yes—
602C4⋊C4—28no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—108no—
606C4⋊C4—204no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—108no—
611C22⋊C4—108no—
612C22⋊C4—108no—
613C22⋊C4—108no—
614C22⋊C4—108no—
615C22⋊C4—108no—
616C22⋊C4—204no—
617C42—108no—
618C42—204no—
619C42—204no—
620C2×C5—44no—
621C2×C5#257618yescomplemented
622C2×C5C2×#52911yescharacteristic
623C2×C5C2×#52911yescharacteristic
624C2×C5C2×#53811yescharacteristic
625C2×C5C2×#55111yescharacteristic
626C2×C5C2×#55111yescharacteristic
627C2×C5C2×#55311yescharacteristic
628C2×C5C2×#55311yescharacteristic
629D5—44no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—54no—
644C23—108no—
645C23—108no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—102no—
651C23—102no—
652C23—108no—
653C23—204no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23C2×#71112yes—
658C23#414412yes—
659C23#414412yes—
660C23C2×#71314yes—
661C23C2×#71312yes—
662C23D5×#4112yes—
663C23D5×#4112yes—
664C23D5×#4112yes—
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—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—54no—
691C2×C4—54no—
692C2×C4—108no—
693C2×C4—108no—
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—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—2016no—
714C2×C4—2016no—
715C2×C4—204no—
716C2×C4—204no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4C2×#71114yes—
721C5C2×#257611yescharacteristic, complemented, Sylow
722C22—24no—
723C22—24no—
724C22—24no—
725C22—42no—
726C22—416no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—104no—
731C22—104no—
732C22—104no—
733C22—202no—
734C22—202no—
735C22—2016no—
736C22—202no—
737C22—202no—
738C22#6593514yes—
739C22#6594714yes—
740C22#6594814yes—
741C22#6595814yes—
742C22#6597114yes—
743C22#6597114yes—
744C22#6604014yes—
745C22C22×#71111yescharacteristic
746C22C2×#414411yescharacteristic
747C22C2×#414411yescharacteristic
748C22C22×#71311yescharacteristic
749C22C2×D5×#4111yescharacteristic
750C22C2×D5×#4111yescharacteristic
751C22C2×D5×#4111yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—104no—
759C4—104no—
760C4—202no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C2—44no—
766C2—204no—
767C2#1060905418yesdirect product factor
768C2C2×#6593511yescharacteristic
769C2C2×#6594711yescharacteristic
770C2C2×#6594811yescharacteristic
771C2C2×#6595811yescharacteristic
772C2C2×#6597111yescharacteristic
773C2C2×#6597111yescharacteristic
774C2C2×#6604011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2576
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C2×C5×#396C2semidirect
2. C2×#65282C2semidirect
3. C2×#65278C2semidirect
4. C2×#65279C2semidirect
5. C2×#65267C2semidirect
6. C2×#65270C2semidirect
7. C2×#65266C2semidirect
10. C2×#65233C2semidirect
12. C2×#65232C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10609054C2direct (N × H)
15. C2×C5⋊#401C2semidirect
16. C2×#64955C2semidirect
38. C5×#396C22semidirect
53. #65282C22semidirect
54. #65279C22semidirect
55. #65278C22semidirect
56. #65270C22semidirect
57. #65267C22semidirect
58. #65266C22semidirect
62. #65233C22semidirect
63. #65232C22semidirect
64. C22⋊C4×Dic5C22semidirect
65. #64955C22semidirect
66. C5⋊#401C22semidirect
148. C2×#396D5semidirect
283. #396C2×D5semidirect
621. C2×C5#2576semidirect
721. C5C2×#2576semidirect
767. C2#10609054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3962
C2×#652822
C2×#652782
C2×#652792
C2×#652672
C2×#652702
C2×#652662
C2×#652452
C2×#652502
C2×#652332
C2×#652472
C2×#652322
C2×C22⋊C4×Dic52
#106090542
C2×C5⋊#4012
C2×#649552
C2×#25765