Finite Group Databasebeta

← C2×#10606723 #12266964

Subgroups — C2×#10606723 #12266964

Order 1280.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4036C211yesmaximal, characteristic, complemented
2C22×C4×D20C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65280C211yesmaximal, characteristic
6C2×#65279C211yesmaximal, characteristic, complemented
7C2×#65222C211yesmaximal, characteristic, complemented
8#10606723C2116yesmaximal, direct product factor
9C2×#64964C211yesmaximal, characteristic, complemented
10C2×#64957C211yesmaximal, characteristic, complemented
11C2×#64957C211yesmaximal, characteristic, complemented
12C2×#64956C211yesmaximal, characteristic, complemented
13C2×#64961C211yesmaximal, characteristic
14C2×#64959C211yesmaximal, characteristic, complemented
15C2×#64943C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4036—28no—
43C2×#4036C2218yescomplemented
44C2×C4×D20—28no—
45C2×C4×D20C2218yes—
46C5×#387C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65280C2218yes—
59#65279C2218yescomplemented
60#65222C2218yescomplemented
61#64964C2218yescomplemented
62#64961C2218yes—
63#64959C2218yescomplemented
64#64957C2218yescomplemented
65#64957C2218yescomplemented
66#64956C2218yescomplemented
67#64955C2218yescomplemented
68#64943C2218yescomplemented
69C2×#2460—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×D20—24no—
86C22×D20—24no—
87C22×D20—24no—
88C22×D20C2314yes—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—42no—
94C22×C4×D5—42no—
95C22×C4×D5C2314yes—
96C22×C4×D5C2314yes—
97C2×C5×C4⋊C4—24no—
98C2×C5×C4⋊C4—24no—
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C4⋊C4C2314yes—
101C2×C42×C5—24no—
102C2×C42×C5C2314yes—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—42no—
112C2×#685—42no—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5D418yes—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683—42no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—42no—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141#4036—232no—
142C4×D20—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146C5×#95C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#125—51no—
154C22×C4×D4—51no—
155#2460—516no—
156C2×#397—51no—
157C2×#396—51no—
158C2×#394—51no—
159C2×#394—51no—
160C2×#388—51no—
161C2×#388—51no—
162C2×#387—51no—
163C2×#387—51no—
164C2×#387D511yescharacteristic, complemented
165C2×#385—51no—
166C2×#385—51no—
167C2×#380—51no—
168C2×C4×C22⋊C4—51no—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5#4114yes—
183C23×D5#4114yes—
184C23×D5C2412yes—
185C23×D5C2412yes—
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—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5C2×D414yes—
205C22×C4×C5#4114yes—
206C22×C4×C5#4114yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
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×Dic5C2×D414yes—
231C22×Dic5C2×D414yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×D20—232no—
239C2×D20—28no—
240C2×D20—28no—
241C2×D20—28no—
242C2×C4×D5—28no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—44no—
247C2×C4×D5—44no—
248C2×C4×D5—416no—
249C2×C4×D5—416no—
250C5×C4⋊C4—28no—
251C5×C4⋊C4—28no—
252C42×C5—28no—
253#685—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—28no—
261#685—44no—
262#685—44no—
263C4⋊Dic5—28no—
264C4⋊Dic5—28no—
265C4⋊Dic5C2×D4116yes—
266#683—28no—
267#683—28no—
268#683—28no—
269#683—44no—
270C4×Dic5—28no—
271C4×Dic5—44no—
272C23×D4—51no—
273C24×C4—51no—
274C24×C4—51no—
275C2×#125—58no—
276C2×#125—108no—
277C2×C4×D4—58no—
278C2×C4×D4—108no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C22⋊C4—51no—
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C42—51no—
299C22×C42—51no—
300C22×C42C2×D511yescharacteristic
301#397—58no—
302#396—58no—
303#394—58no—
304#394—58no—
305#388—58no—
306#388—58no—
307#387—58no—
308#387—58no—
309#387C2×D518yescomplemented
310#385—58no—
311#385—58no—
312#380—58no—
313C4×C22⋊C4—58no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95C2×D511yescharacteristic
321C2×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C23×C5C22×D412yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C52−1+412yes—
331C23×C5C2511yescharacteristic
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—28no—
336C22×D5—28no—
337C22×D5—28no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—44no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5C2×#4114yes—
359C22×D5C2×#4114yes—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5C22×D414yes—
386C2×C4×C5C2×#4114yes—
387C2×C4×C5C2×#4114yes—
388C2×Dic5—28no—
389C2×Dic5—28no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5C22×D414yes—
411C2×Dic5C22×D414yes—
412D20—232no—
413C4×D5—416no—
414C4×D5—416no—
415C25—51no—
416C25—51no—
417C22×D4—54no—
418C22×D4—104no—
419C22×D4—104no—
420C22×D4—104no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—54no—
428C23×C4—54no—
429C23×C4—104no—
430C23×C4—104no—
431C23×C4—104no—
432C23×C4—104no—
433C23×C4—202no—
434C23×C4—202no—
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#125—1032no—
443C4×D4—1032no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—58no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—104no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—202no—
460C2×C4⋊C4C22×D514yes—
461C2×C4⋊C4C22×D514yes—
462C2×C22⋊C4—54no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4—202no—
482C2×C42—24no—
483C2×C42—54no—
484C2×C42—54no—
485C2×C42—104no—
486C2×C42—202no—
487C2×C42C22×D514yes—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95C22×D514yes—
495#95C22×D514yes—
496#95C22×D514yes—
497#95C22×D514yes—
498C22×C5#52514yes—
499C22×C5#52914yes—
500C22×C5#53914yes—
501C22×C5#54614yes—
502C22×C5#54814yes—
503C22×C5#55214yes—
504C22×C5#55314yes—
505C22×C5C23×D411yescharacteristic
506C22×C5C22×#4111yescharacteristic
507C22×C5C22×#4111yescharacteristic
508C22×C5C22×#4111yescharacteristic
509C22×C5C22×#4111yescharacteristic
510C22×C5C2×H(5,𝔽2)11yescharacteristic
511C22×C5C2×2−1+411yescharacteristic
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—24no—
516C2×D5—24no—
517C2×D5—24no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—416no—
527C2×D5—416no—
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535Dic5—24no—
536Dic5—24no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—54no—
542C24—54no—
543C24—52no—
544C24—52no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24C23×D511yescharacteristic
558C2×D4—108no—
559C2×D4—108no—
560C2×D4—1032no—
561C2×D4—108no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—54no—
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—108no—
589C22×C4—108no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—108no—
607C22×C4—108no—
608C22×C4—204no—
609C22×C4—204no—
610C22×C4—2016no—
611C22×C4—2016no—
612C22×C4#70914yes—
613C22×C4D4×D514yes—
614C22×C4#71314yes—
615C22×C4C23×D512yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—516no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C4⋊C4—108no—
630C4⋊C4—204no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—204no—
640C22⋊C4—204no—
641C42—28no—
642C42—108no—
643C42—204no—
644C2×C5#246018yescomplemented
645C2×C5C2×#52511yescharacteristic
646C2×C5C2×#52911yescharacteristic
647C2×C5C2×#53911yescharacteristic
648C2×C5C2×#54611yescharacteristic
649C2×C5C2×#54811yescharacteristic
650C2×C5C2×#55211yescharacteristic
651C2×C5C2×#55311yescharacteristic
652D5—44no—
653D5—44no—
654C23—54no—
655C23—54no—
656C23—108no—
657C23—108no—
658C23—108no—
659C23—108no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—108no—
673C23—108no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23C2×#70912yes—
683C23C2×D4×D512yes—
684C23C2×#71312yes—
685C23D5×#4112yes—
686C23D5×#4112yes—
687C23#414912yes—
688C23#415012yes—
689C23C24×D511yescharacteristic
690D4—1032no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—54no—
717C2×C4—54no—
718C2×C4—108no—
719C2×C4—108no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—2016no—
737C2×C4—2016no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4C2×#70914yes—
743C2×C4C2×D4×D514yes—
744C2×C4C2×#71314yes—
745C5C2×#246011yescharacteristic, complemented, Sylow
746C22—104no—
747C22—104no—
748C22—104no—
749C22—104no—
750C22—104no—
751C22—104no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22—2016no—
759C22—2016no—
760C22—202no—
761C22—202no—
762C22#6586414yes—
763C22#6588614yes—
764C22#6591414yes—
765C22#6596414yes—
766C22#6599014yes—
767C22#6602814yes—
768C22#6604114yes—
769C22C22×#70911yescharacteristic
770C22C22×D4×D511yescharacteristic
771C22C22×#71311yescharacteristic
772C22C2×D5×#4111yescharacteristic
773C22C2×D5×#4111yescharacteristic
774C22C2×#414911yescharacteristic
775C22C2×#415011yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—104no—
784C4—104no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—204no—
790C2—204no—
791C2#1060672318yesdirect product factor
792C2C2×#6586411yescharacteristic
793C2C2×#6588611yescharacteristic
794C2C2×#6591411yescharacteristic
795C2C2×#6596411yescharacteristic
796C2C2×#6599011yescharacteristic
797C2C2×#6602811yescharacteristic
798C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2460
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#4036C2semidirect
3. C2×C5×#387C2semidirect
4. C2×#65283C2semidirect
6. C2×#65279C2semidirect
7. C2×#65222C2semidirect
8. #10606723C2direct (N × H)
9. C2×#64964C2semidirect
10. C2×#64957C2semidirect
11. C2×#64957C2semidirect
12. C2×#64956C2semidirect
14. C2×#64959C2semidirect
15. C2×#64943C2semidirect
16. C2×#64955C2semidirect
43. C2×#4036C22semidirect
46. C5×#387C22semidirect
57. #65283C22semidirect
59. #65279C22semidirect
60. #65222C22semidirect
61. #64964C22semidirect
63. #64959C22semidirect
64. #64957C22semidirect
65. #64957C22semidirect
66. #64956C22semidirect
67. #64955C22semidirect
68. #64943C22semidirect
164. C2×#387D5semidirect
309. #387C2×D5semidirect
644. C2×C5#2460semidirect
745. C5C2×#2460semidirect
791. C2#10606723direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40362
C22×C4×D202
C2×C5×#3872
C2×#652832
C2×#652802
C2×#652792
C2×#652222
#106067232
C2×#649642
C2×#649572
C2×#649562
C2×#649612
C2×#649592
C2×#649432
C2×#649552
C2×#24605