Finite Group Databasebeta

← C2×#10609762 #12268727

Subgroups — C2×#10609762 #12268727

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×#399C211yesmaximal, characteristic, complemented
2C2×#65282C211yesmaximal, characteristic, complemented
3C2×#65279C211yesmaximal, characteristic, complemented
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65267C211yesmaximal, characteristic, complemented
6C2×#65267C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic
9C2×#65246C211yesmaximal, characteristic
10C2×#65233C211yesmaximal, characteristic, complemented
11C2×#65247C211yesmaximal, characteristic
12C2×#65232C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10609762C2116yesmaximal, direct product factor
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C5×#399C2218yescomplemented
41C2×C5×#95C2211yescharacteristic
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#65279C2218yescomplemented
56#65267C2218yescomplemented
57#65267C2218yescomplemented
58C4⋊C4×Dic5C2218yescomplemented
59#65250C2218yes—
60#65247C2218yes—
61#65246C2218yes—
62#65233C2218yescomplemented
63#65232C2218yescomplemented
64C22⋊C4×Dic5C2218yescomplemented
65#64958C2218yescomplemented
66#64949C2218yescomplemented
67C2×#2516—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×Dic5C2314yes—
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C2×C5×C4⋊C4—24no—
92C2×C5×C4⋊C4—42no—
93C2×C5×C4⋊C4—42no—
94C2×C5×C4⋊C4C2314yes—
95C2×C5×C4⋊C4C2314yes—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—42no—
99C2×C5×C22⋊C4—42no—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C5×C22⋊C4C2314yes—
103C2×C22⋊Dic5—24no—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5C2314yes—
106C2×C22⋊Dic5C2314yes—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—42no—
111C2×#685—42no—
112C2×#685—42no—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×C4×Dic5—24no—
126C2×C4×Dic5—42no—
127C2×C4×Dic5—42no—
128C2×C4×Dic5—42no—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C2×C4×Dic5C2314yes—
132C2×C4×Dic5C2314yes—
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#2516—516no—
146C2×#400—51no—
147C2×#399D511yescharacteristic, complemented
148C2×#397—51no—
149C2×#394—51no—
150C2×#390—51no—
151C2×#388—51no—
152C2×#388—51no—
153C2×#388—51no—
154C2×#388—51no—
155C2×#387—51no—
156C2×#387—51no—
157C2×#386—51no—
158C2×#381—51no—
159C2×C4×C4⋊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—22no—
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—22no—
214C22×Dic5—22no—
215C22×Dic5—28no—
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—28no—
226C22×Dic5—44no—
227C22×Dic5—416no—
228C22×Dic5#4114yes—
229C22×Dic5#4114yes—
230C22×Dic5#4114yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C5×C4⋊C4—28no—
239C5×C4⋊C4—44no—
240C5×C4⋊C4—44no—
241C5×C22⋊C4—28no—
242C5×C22⋊C4—44no—
243C5×C22⋊C4—44no—
244C22⋊Dic5—28no—
245C22⋊Dic5—28no—
246#685—28no—
247#685—28no—
248#685—28no—
249#685—44no—
250#685—44no—
251#685—44no—
252C4⋊Dic5—28no—
253#683—28no—
254#683—28no—
255C4×Dic5—28no—
256C4×Dic5—44no—
257C4×Dic5—44no—
258C4×Dic5—44no—
259C23×D4—51no—
260C24×C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4C2×D511yescharacteristic
265C22×C4⋊C4C2×D511yescharacteristic
266C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
276C22×C22⋊C4C2×D511yescharacteristic
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C42—51no—
279C22×C42—51no—
280C22×C42—51no—
281C22×C42—51no—
282#400—58no—
283#399C2×D518yescomplemented
284#397—58no—
285#394—58no—
286#390—58no—
287#388—58no—
288#388—58no—
289#388—58no—
290#388—58no—
291#387—58no—
292#387—58no—
293#386—58no—
294#381—58no—
295C4×C4⋊C4—58no—
296C4×C22⋊C4—58no—
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×#95C2×D511yescharacteristic
309C23×C5—28no—
310C23×C5—28no—
311C23×C5—28no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5C2×#4112yes—
323C23×C5C2×#4114yes—
324C23×C5C2×#4112yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C5C2511yescharacteristic
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
345C2×C4×C5—28no—
346C2×C4×C5—22no—
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—44no—
364C2×C4×C5—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5C2×#4114yes—
369C22⋊D5—416no—
370C2×Dic5—28no—
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—416no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5C2×#4114yes—
397C2×Dic5C2×#4114yes—
398C2×Dic5C2×#4114yes—
399C25—51no—
400C25C22×D511yescharacteristic
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—51no—
412C23×C4—54no—
413C23×C4—104no—
414C23×C4—104no—
415C23×C4—202no—
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C2×C4⋊C4—24no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4C22×D514yes—
432C2×C4⋊C4C22×D514yes—
433C2×C4⋊C4C22×D514yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
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—202no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4C22×D514yes—
454C2×C22⋊C4C22×D514yes—
455C2×C22⋊C4C22×D514yes—
456C2×C42—54no—
457C2×C42—54no—
458C2×C42—54no—
459C2×C42—54no—
460C2×C42—104no—
461C2×C42—202no—
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—
476C22×C5—24no—
477C22×C5—24no—
478C22×C5—24no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—416no—
484C22×C5#52914yes—
485C22×C5#52914yes—
486C22×C5#54014yes—
487C22×C5#55114yes—
488C22×C5#55114yes—
489C22×C5#55314yes—
490C22×C5#55914yes—
491C22×C5C22×#4111yescharacteristic
492C22×C5C22×#4111yescharacteristic
493C22×C5C22×#4111yescharacteristic
494C22×C5C22×#4111yescharacteristic
495C22×C5C22×#4111yescharacteristic
496C22×C5C2×H(5,𝔽2)11yescharacteristic
497C22×C5C2×H(5,𝔽2)11yescharacteristic
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—42no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512Dic5—24no—
513Dic5—24no—
514Dic5—24no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—52no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24#71314yes—
534C24C23×D512yes—
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—54no—
558C22×C4—54no—
559C22×C4—54no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—108no—
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—108no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—204no—
588C22×C4—2016no—
589C22×C4#71114yes—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C4⋊C4—28no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—108no—
600C4⋊C4—108no—
601C4⋊C4—108no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—108no—
606C22⋊C4—108no—
607C22⋊C4—108no—
608C22⋊C4—108no—
609C22⋊C4—108no—
610C22⋊C4—204no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C42—108no—
614C42—204no—
615C42—204no—
616C42—204no—
617C2×C5—44no—
618C2×C5#251618yescomplemented
619C2×C5C2×#52911yescharacteristic
620C2×C5C2×#52911yescharacteristic
621C2×C5C2×#54011yescharacteristic
622C2×C5C2×#55111yescharacteristic
623C2×C5C2×#55111yescharacteristic
624C2×C5C2×#55311yescharacteristic
625C2×C5C2×#55911yescharacteristic
626D5—82no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—102no—
645C23—102no—
646C23—102no—
647C23—204no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23C2×#71112yes—
655C23#414412yes—
656C23#414412yes—
657C23C2×#71314yes—
658C23C2×#71312yes—
659C23D5×#4112yes—
660C23D5×#4112yes—
661C23D5×#4112yes—
662C23C24×D511yescharacteristic
663D4—2016no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
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—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—54no—
688C2×C4—54no—
689C2×C4—54no—
690C2×C4—108no—
691C2×C4—108no—
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—2016no—
712C2×C4—204no—
713C2×C4—204no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4C2×#71114yes—
717C5C2×#251611yescharacteristic, complemented, Sylow
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—416no—
725C22—42no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—408no—
734C22#6595814yes—
735C22#6597114yes—
736C22#6597114yes—
737C22#6598314yes—
738C22#6599514yes—
739C22#6599814yes—
740C22#6605314yes—
741C22C22×#71111yescharacteristic
742C22C2×#414411yescharacteristic
743C22C2×#414411yescharacteristic
744C22C22×#71311yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×D5×#4111yescharacteristic
747C22C2×D5×#4111yescharacteristic
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—104no—
755C4—104no—
756C4—104no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C2—44no—
762C2—402no—
763C2#1060976218yesdirect product factor
764C2C2×#6595811yescharacteristic
765C2C2×#6597111yescharacteristic
766C2C2×#6597111yescharacteristic
767C2C2×#6598311yescharacteristic
768C2C2×#6599511yescharacteristic
769C2C2×#6599811yescharacteristic
770C2C2×#6605311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#399C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#399D5
hypocenterC5C2×#2516
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×C5×#399C2semidirect
2. C2×#65282C2semidirect
3. C2×#65279C2semidirect
4. C2×#65279C2semidirect
5. C2×#65267C2semidirect
6. C2×#65267C2semidirect
7. C2×C4⋊C4×Dic5C2semidirect
10. C2×#65233C2semidirect
12. C2×#65232C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10609762C2direct (N × H)
15. C2×#64949C2semidirect
16. C2×#64958C2semidirect
40. C5×#399C22semidirect
53. #65282C22semidirect
54. #65279C22semidirect
55. #65279C22semidirect
56. #65267C22semidirect
57. #65267C22semidirect
58. C4⋊C4×Dic5C22semidirect
62. #65233C22semidirect
63. #65232C22semidirect
64. C22⋊C4×Dic5C22semidirect
65. #64958C22semidirect
66. #64949C22semidirect
147. C2×#399D5semidirect
283. #399C2×D5semidirect
618. C2×C5#2516semidirect
717. C5C2×#2516semidirect
763. C2#10609762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3992
C2×#652822
C2×#652792
C2×#652672
C2×C4⋊C4×Dic52
C2×#652502
C2×#652462
C2×#652332
C2×#652472
C2×#652322
C2×C22⋊C4×Dic52
#106097622
C2×#649492
C2×#649582
C2×#25165