Finite Group Databasebeta

← C2×#10608548 #12265794

Subgroups — C2×#10608548 #12265794

Order 1280.

2394 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×#393C211yesmaximal, characteristic, complemented
2C2×#65520C211yesmaximal, characteristic, complemented
3C2×#65519C211yesmaximal, characteristic, complemented
4C2×#65248C211yesmaximal, characteristic
5C2×#65245C211yesmaximal, characteristic
6C2×#65241C211yesmaximal, characteristic, complemented
7C2×#65250C211yesmaximal, characteristic
8C2×#65234C211yesmaximal, characteristic, complemented
9C2×#65240C211yesmaximal, characteristic, complemented
10#10608548C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×C5⋊#401C211yesmaximal, characteristic, complemented
14C2×#64946C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C5×#393C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42#65520C2218yescomplemented
43#65519C2218yescomplemented
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55#65250C2218yes—
56#65248C2218yes—
57#65245C2218yes—
58#65241C2218yescomplemented
59#65240C2218yescomplemented
60#65234C2218yescomplemented
61#64964C2218yescomplemented
62#64957C2218yescomplemented
63#64955C2218yescomplemented
64C5⋊#401C2218yescomplemented
65#64946C2218yescomplemented
66#64942C2218yescomplemented
67C2×#2653—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C22×C5×Q8—24no—
71C22×C5×Q8—42no—
72C22×C5×Q8—42no—
73C22×C5×Q8C2314yes—
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—24no—
81C22×C22⋊D5—42no—
82C22×C22⋊D5—42no—
83C22×C22⋊D5C2314yes—
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C22×C4×D5—24no—
92C22×C4×D5—42no—
93C22×C4×D5—42no—
94C22×C4×D5C2314yes—
95C2×C5×C22⋊C4—24no—
96C2×C5×C22⋊C4—42no—
97C2×C5×C22⋊C4—42no—
98C2×C5×C22⋊C4C2314yes—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C22⋊Dic5—24no—
102C2×C22⋊Dic5—42no—
103C2×C22⋊Dic5—42no—
104C2×C22⋊Dic5C2314yes—
105C2×C22⋊Dic5C2314yes—
106C2×C22⋊Dic5C2314yes—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—42no—
111C2×#685—42no—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×C4⋊Dic5—24no—
118C2×C4⋊Dic5—42no—
119C2×C4⋊Dic5C2314yes—
120C2×C4⋊Dic5C2314yes—
121C2×#683—42no—
122C2×#683—42no—
123C2×#683—42no—
124C2×#683C2314yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×C4×Dic5—42no—
128C2×C4×Dic5—42no—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
133C5×#95C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2653—516no—
146C2×#401—51no—
147C2×#398—51no—
148C2×#397—51no—
149C2×#397—51no—
150C2×#394—51no—
151C2×#394—51no—
152C2×#393—51no—
153C2×#393D511yescharacteristic, complemented
154C2×#391—51no—
155C2×#388—51no—
156C2×#388—51no—
157C2×#387—51no—
158C2×#386—51no—
159C2×#385—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—22no—
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—
178C2×C5×Q8—28no—
179C2×C5×Q8—44no—
180C2×C5×Q8—44no—
181C2×C5×Q8—416no—
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—22no—
199C22×C4×C5#4114yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C2×C22⋊D5—28no—
207C2×C22⋊D5—44no—
208C2×C22⋊D5—44no—
209C2×C22⋊D5—416no—
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—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
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×C22⋊C4—28no—
243C5×C22⋊C4—44no—
244C5×C22⋊C4—44no—
245C22⋊Dic5—28no—
246C22⋊Dic5—44no—
247C22⋊Dic5—44no—
248#685—28no—
249#685—28no—
250#685—28no—
251#685—44no—
252#685—44no—
253C4⋊Dic5—28no—
254C4⋊Dic5—44no—
255#683—44no—
256#683—44no—
257#683—44no—
258C4×Dic5—44no—
259C4×Dic5—44no—
260C23×Q8C2×D511yescharacteristic
261C23×D4—51no—
262C24×C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊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⋊C4C2×D511yescharacteristic
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C42—51no—
280C22×C42—51no—
281#401—58no—
282#398—58no—
283#397—58no—
284#397—58no—
285#394—58no—
286#394—58no—
287#393—58no—
288#393C2×D518yescomplemented
289#391—58no—
290#388—58no—
291#388—58no—
292#387—58no—
293#386—58no—
294#385—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×#95C2×D511yescharacteristic
308C2×#95C2×D511yescharacteristic
309C2×#95C2×D511yescharacteristic
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5—44no—
324C23×C5C2×#4112yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5H(5,𝔽2)12yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C52−1+412yes—
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—
346C5×Q8—416no—
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—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5C2×#4114yes—
371C22⋊D5—416no—
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—22no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399C2×Dic5C2×#4114yes—
400C4×D5—416no—
401C25—51no—
402C25C22×D511yescharacteristic
403C22×Q8—24no—
404C22×Q8—42no—
405C22×Q8—42no—
406C22×Q8C22×D514yes—
407C22×D4—54no—
408C22×D4—104no—
409C22×D4—202no—
410C22×D4—202no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—54no—
419C23×C4—104no—
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—54no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4—202no—
437C2×C4⋊C4—202no—
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—54no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4C22×D514yes—
458C2×C22⋊C4C22×D514yes—
459C2×C22⋊C4C22×D514yes—
460C2×C42—54no—
461C2×C42—54no—
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#95C22×D514yes—
476#95C22×D514yes—
477#95C22×D514yes—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—88no—
486C22×C5#52914yes—
487C22×C5#53814yes—
488C22×C5#53814yes—
489C22×C5#53814yes—
490C22×C5#53914yes—
491C22×C5#54214yes—
492C22×C5#54214yes—
493C22×C5C22×#4111yescharacteristic
494C22×C5C22×#4111yescharacteristic
495C22×C5C22×#4111yescharacteristic
496C22×C5C2×H(5,𝔽2)11yescharacteristic
497C22×C5C2×H(5,𝔽2)11yescharacteristic
498C22×C5C2×H(5,𝔽2)11yescharacteristic
499C22×C5C2×2−1+411yescharacteristic
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—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—54no—
529C24—52no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24C23×D512yes—
537C24C23×D511yescharacteristic
538C2×Q8—28no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—416no—
542C2×D4—108no—
543C2×D4—204no—
544C2×D4—204no—
545C2×D4—2016no—
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—22no—
563C22×C4—54no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—52no—
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—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—204no—
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—108no—
603C4⋊C4—204no—
604C4⋊C4—204no—
605C4⋊C4—204no—
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—204no—
615C22⋊C4—204no—
616C22⋊C4—204no—
617C22⋊C4—204no—
618C42—204no—
619C42—204no—
620C2×C5—82no—
621C2×C5#265318yescomplemented
622C2×C5C2×#52911yescharacteristic
623C2×C5C2×#53811yescharacteristic
624C2×C5C2×#53811yescharacteristic
625C2×C5C2×#53811yescharacteristic
626C2×C5C2×#53911yescharacteristic
627C2×C5C2×#54211yescharacteristic
628C2×C5C2×#54211yescharacteristic
629D5—44no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—54no—
645C23—108no—
646C23—108no—
647C23—108no—
648C23—102no—
649C23—102no—
650C23—102no—
651C23—102no—
652C23—102no—
653C23—102no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23—204no—
658C23C2×#71112yes—
659C23#414412yes—
660C23#414412yes—
661C23#414712yes—
662C23D5×#4112yes—
663C23D5×#4112yes—
664C23#414912yes—
665C23C24×D511yescharacteristic
666Q8—416no—
667D4—2016no—
668C2×C4—28no—
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—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—54no—
692C2×C4—108no—
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—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—2016no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4C2×#71114yes—
721C5C2×#265311yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—88no—
730C22—104no—
731C22—104no—
732C22—104no—
733C22—202no—
734C22—202no—
735C22—202no—
736C22—2016no—
737C22—202no—
738C22#6592714yes—
739C22#6597214yes—
740C22#6597414yes—
741C22#6597714yes—
742C22#6601214yes—
743C22#6601214yes—
744C22#6601414yes—
745C22C22×#71111yescharacteristic
746C22C2×#414411yescharacteristic
747C22C2×#414411yescharacteristic
748C22C2×#414711yescharacteristic
749C22C2×D5×#4111yescharacteristic
750C22C2×D5×#4111yescharacteristic
751C22C2×#414911yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—104no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C2—82no—
766C2—204no—
767C2#1060854818yesdirect product factor
768C2C2×#6592711yescharacteristic
769C2C2×#6597711yescharacteristic
770C2C2×#6597411yescharacteristic
771C2C2×#6597211yescharacteristic
772C2C2×#6601411yescharacteristic
773C2C2×#6601211yescharacteristic
774C2C2×#6601211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#393C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#393D5
hypocenterC5C2×#2653
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×C5×#393C2semidirect
2. C2×#65520C2semidirect
3. C2×#65519C2semidirect
6. C2×#65241C2semidirect
8. C2×#65234C2semidirect
9. C2×#65240C2semidirect
10. #10608548C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64957C2semidirect
13. C2×C5⋊#401C2semidirect
14. C2×#64946C2semidirect
15. C2×#64942C2semidirect
16. C2×#64955C2semidirect
38. C5×#393C22semidirect
42. #65520C22semidirect
43. #65519C22semidirect
58. #65241C22semidirect
59. #65240C22semidirect
60. #65234C22semidirect
61. #64964C22semidirect
62. #64957C22semidirect
63. #64955C22semidirect
64. C5⋊#401C22semidirect
65. #64946C22semidirect
66. #64942C22semidirect
153. C2×#393D5semidirect
288. #393C2×D5semidirect
621. C2×C5#2653semidirect
721. C5C2×#2653semidirect
767. C2#10608548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3932
C2×#655202
C2×#655192
C2×#652482
C2×#652452
C2×#652412
C2×#652502
C2×#652342
C2×#652402
#106085482
C2×#649642
C2×#649572
C2×C5⋊#4012
C2×#649462
C2×#649422
C2×#649552
C2×#26535