Finite Group Databasebeta

← C2×#10609419 #12265748

Subgroups — C2×#10609419 #12265748

Order 1280.

2546 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×#397C211yesmaximal, characteristic, complemented
2C2×#65278C211yesmaximal, characteristic, complemented
3C2×#65275C211yesmaximal, characteristic, complemented
4C2×#65245C211yesmaximal, characteristic
5C2×#65245C211yesmaximal, characteristic
6C2×#65245C211yesmaximal, characteristic
7C2×#65242C211yesmaximal, characteristic, complemented
8C2×#65241C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10#10609419C2116yesmaximal, direct product factor
11C2×#64957C211yesmaximal, characteristic, complemented
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×D5×#95C211yesmaximal, characteristic, complemented
14C2×C5⋊#401C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64947C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C5×#397C2218yescomplemented
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
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#65278C2218yescomplemented
54#65275C2218yescomplemented
55#65245C2218yes—
56#65245C2218yes—
57#65245C2218yes—
58#65242C2218yescomplemented
59#65241C2218yescomplemented
60#65237C2218yescomplemented
61#64957C2218yescomplemented
62#64957C2218yescomplemented
63D5×#95C2218yescomplemented
64C5⋊#401C2218yescomplemented
65#64949C2218yescomplemented
66#64947C2218yescomplemented
67C2×#2643—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—24no—
79C22×C22⋊D5C2314yes—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
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×D5—42no—
94C22×C4×D5—42no—
95C22×C4×D5—42no—
96C22×C4×D5C2314yes—
97C22×C4×D5C2314yes—
98C22×C4×D5C2314yes—
99C2×C5×C4⋊C4—42no—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C22⋊C4—42no—
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—42no—
108C2×C22⋊Dic5—42no—
109C2×C22⋊Dic5—42no—
110C2×C22⋊Dic5C2314yes—
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—42no—
120C2×C4⋊Dic5—42no—
121C2×C4⋊Dic5C2314yes—
122C2×C4⋊Dic5C2314yes—
123C2×#683—42no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C5×#95C2314yes—
130C5×#95C2314yes—
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#2643—516no—
146C2×#401—51no—
147C2×#400—51no—
148C2×#400—51no—
149C2×#400—51no—
150C2×#397—51no—
151C2×#397—51no—
152C2×#397D511yescharacteristic, complemented
153C2×#396—51no—
154C2×#386—51no—
155C2×#386—51no—
156C2×#386—51no—
157C2×#385—51no—
158C2×#385—51no—
159C2×#385—51no—
160C22×#95—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#4114yes—
175C23×D5#4114yes—
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—22no—
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—28no—
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—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×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
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—44no—
241C2×C4×D5—44no—
242C2×C4×D5—44no—
243C2×C4×D5—416no—
244C2×C4×D5—416no—
245C2×C4×D5—416no—
246C5×C4⋊C4—44no—
247C5×C22⋊C4—44no—
248C5×C22⋊C4—44no—
249C5×C22⋊C4—44no—
250C22⋊Dic5—44no—
251C22⋊Dic5—44no—
252C22⋊Dic5—44no—
253#685—28no—
254#685—28no—
255#685—28no—
256C4⋊Dic5—44no—
257C4⋊Dic5—44no—
258#683—44no—
259#683—44no—
260#683—44no—
261C23×D4—51no—
262C24×C4—51no—
263C24×C4—51no—
264C24×C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4—51no—
268C22×C4⋊C4—51no—
269C22×C4⋊C4—51no—
270C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C22⋊C4C2×D511yescharacteristic
280#401—58no—
281#400—58no—
282#400—58no—
283#400—58no—
284#397—58no—
285#397—58no—
286#397C2×D518yescomplemented
287#396—58no—
288#386—58no—
289#386—58no—
290#386—58no—
291#385—58no—
292#385—58no—
293#385—58no—
294C2×#95—51no—
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×#95—51no—
306C2×#95—51no—
307C2×#95—58no—
308C2×#95C2×D511yescharacteristic
309C2×#95C2×D511yescharacteristic
310C2×#95C2×D511yescharacteristic
311C23×C5—22no—
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×C5—44no—
323C23×C5—44no—
324C23×C5—44no—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C5H(5,𝔽2)12yes—
331C23×C52−1+412yes—
332C23×C5C2511yescharacteristic
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—28no—
336C22×D5—28no—
337C22×D5—28no—
338C22×D5—28no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5#126116yes—
344C22×D5C2×#4114yes—
345C22×D5C2×#4114yes—
346C22×D5C2×#4114yes—
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—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C22⋊D5—416no—
372C2×Dic5—22no—
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×Dic5—44no—
400C4×D5—416no—
401C4×D5—416no—
402C4×D5—416no—
403C25—51no—
404C25C22×D511yescharacteristic
405C22×D4—54no—
406C22×D4—104no—
407C22×D4—104no—
408C22×D4—104no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—54no—
417C23×C4—54no—
418C23×C4—54no—
419C23×C4—104no—
420C23×C4—104no—
421C23×C4—104no—
422C23×C4—202no—
423C23×C4—202no—
424C23×C4—202no—
425C23×C4—202no—
426C23×C4—202no—
427C23×C4—202no—
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C2×C4⋊C4—42no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—202no—
441C2×C4⋊C4—202no—
442C2×C4⋊C4—202no—
443C2×C4⋊C4—202no—
444C2×C4⋊C4—202no—
445C2×C4⋊C4C22×D514yes—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—54no—
452C2×C22⋊C4—54no—
453C2×C22⋊C4—54no—
454C2×C22⋊C4—54no—
455C2×C22⋊C4—104no—
456C2×C22⋊C4—104no—
457C2×C22⋊C4—104no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4—202no—
460C2×C22⋊C4—202no—
461C2×C22⋊C4C22×D514yes—
462C2×C22⋊C4C22×D514yes—
463C2×C22⋊C4C22×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#95—54no—
475#95—54no—
476#95—54no—
477#95C22×D514yes—
478#95C22×D514yes—
479#95C22×D514yes—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5—42no—
487C22×C5—88no—
488C22×C5C2×#12614yes—
489C22×C5#53814yes—
490C22×C5#53814yes—
491C22×C5#53814yes—
492C22×C5#53914yes—
493C22×C5#53914yes—
494C22×C5#53914yes—
495C22×C5C22×#4111yescharacteristic
496C22×C5C22×#4111yescharacteristic
497C22×C5C22×#4111yescharacteristic
498C22×C5C2×H(5,𝔽2)11yescharacteristic
499C22×C5C2×H(5,𝔽2)11yescharacteristic
500C22×C5C2×H(5,𝔽2)11yescharacteristic
501C22×C5C2×2−1+411yescharacteristic
502C2×D5—232no—
503C2×D5—24no—
504C2×D5—24no—
505C2×D5—24no—
506C2×D5—24no—
507C2×D5—24no—
508C2×D5—24no—
509C2×D5C2×#12618yes—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514C4×C5—42no—
515C4×C5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521Dic5—42no—
522Dic5—42no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—54no—
531C24—54no—
532C24—54no—
533C24—52no—
534C24—102no—
535C24—102no—
536C24—102no—
537C24—102no—
538C24C23×D512yes—
539C24C23×D511yescharacteristic
540C2×D4—108no—
541C2×D4—108no—
542C2×D4—108no—
543C2×D4—2016no—
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—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—108no—
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—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—204no—
594C22×C4—204no—
595C22×C4—204no—
596C22×C4—204no—
597C22×C4—204no—
598C22×C4—204no—
599C22×C4—2016no—
600C22×C4—2016no—
601C22×C4—2016no—
602C22×C4C23×D512yes—
603C22×C4C23×D512yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C4⋊C4—44no—
609C4⋊C4—204no—
610C4⋊C4—204no—
611C4⋊C4—204no—
612C4⋊C4—204no—
613C4⋊C4—204no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—108no—
618C22⋊C4—108no—
619C22⋊C4—108no—
620C22⋊C4—204no—
621C22⋊C4—204no—
622C22⋊C4—204no—
623C2×C5—82no—
624C2×C5#264318yescomplemented
625C2×C5C22×#12611yescharacteristic
626C2×C5C2×#53811yescharacteristic
627C2×C5C2×#53811yescharacteristic
628C2×C5C2×#53811yescharacteristic
629C2×C5C2×#53911yescharacteristic
630C2×C5C2×#53911yescharacteristic
631C2×C5C2×#53911yescharacteristic
632D5—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—54no—
648C23—54no—
649C23—54no—
650C23—516no—
651C23—108no—
652C23—108no—
653C23—108no—
654C23—108no—
655C23—108no—
656C23—102no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—108no—
661C23#414412yes—
662C23#414412yes—
663C23D5×#4112yes—
664C23D5×#4112yes—
665C23D5×#4112yes—
666C23#414912yes—
667C23#415012yes—
668C23C24×D511yescharacteristic
669D4—2016no—
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—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—102no—
714C2×C4—102no—
715C2×C4—2016no—
716C2×C4—2016no—
717C2×C4—2016no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4—204no—
721C2×C4—204no—
722C2×C4—204no—
723C2×C4—204no—
724C2×C4—204no—
725C5C2×#264311yescharacteristic, complemented, Sylow
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—58no—
734C22—88no—
735C22—1032no—
736C22—104no—
737C22—104no—
738C22—104no—
739C22—104no—
740C22—104no—
741C22—104no—
742C22#6594714yes—
743C22#6599114yes—
744C22#6599414yes—
745C22#6599414yes—
746C22#6601214yes—
747C22D5×#12614yes—
748C22#6604114yes—
749C22C2×#414411yescharacteristic
750C22C2×#414411yescharacteristic
751C22C2×D5×#4111yescharacteristic
752C22C2×D5×#4111yescharacteristic
753C22C2×D5×#4111yescharacteristic
754C22C2×#414911yescharacteristic
755C22C2×#415011yescharacteristic
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—202no—
763C4—202no—
764C4—202no—
765C4—202no—
766C4—202no—
767C4—202no—
768C4—202no—
769C2—82no—
770C2—108no—
771C2#1060941918yesdirect product factor
772C2C2×#6594711yescharacteristic
773C2C2×#6599111yescharacteristic
774C2C2×#6599411yescharacteristic
775C2C2×#6599411yescharacteristic
776C2C2×#6601211yescharacteristic
777C2C2×D5×#12611yescharacteristic
778C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2643
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C5×#397C2semidirect
2. C2×#65278C2semidirect
3. C2×#65275C2semidirect
7. C2×#65242C2semidirect
8. C2×#65241C2semidirect
9. C2×#65237C2semidirect
10. #10609419C2direct (N × H)
11. C2×#64957C2semidirect
12. C2×#64957C2semidirect
13. C2×D5×#95C2semidirect
14. C2×C5⋊#401C2semidirect
15. C2×#64949C2semidirect
16. C2×#64947C2semidirect
36. C5×#397C22semidirect
53. #65278C22semidirect
54. #65275C22semidirect
58. #65242C22semidirect
59. #65241C22semidirect
60. #65237C22semidirect
61. #64957C22semidirect
62. #64957C22semidirect
63. D5×#95C22semidirect
64. C5⋊#401C22semidirect
65. #64949C22semidirect
66. #64947C22semidirect
152. C2×#397D5semidirect
286. #397C2×D5semidirect
624. C2×C5#2643semidirect
725. C5C2×#2643semidirect
771. C2#10609419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×#652782
C2×#652752
C2×#652452
C2×#652422
C2×#652412
C2×#652372
#106094192
C2×#649572
C2×D5×#952
C2×C5⋊#4012
C2×#649492
C2×#649472
C2×#26435