Finite Group Databasebeta

← C2×#10607978 #12269527

Subgroups — C2×#10607978 #12269527

Order 1280.

3094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic
2C22×D5×C4⋊C4C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×#65278C211yesmaximal, characteristic
5C2×#65278C211yesmaximal, characteristic
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×#65268C211yesmaximal, characteristic, complemented
8C2×#65261C211yesmaximal, characteristic, complemented
9C2×#65261C211yesmaximal, characteristic, complemented
10C2×#65217C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic
12#10607978C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic
14C2×#64957C211yesmaximal, characteristic
15C2×#64946C211yesmaximal, characteristic, complemented
16C2×#64945C211yesmaximal, characteristic, complemented
17C23×C4×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4042—28no—
43C2×#4042C2218yes—
44C2×D5×C4⋊C4—28no—
45C2×D5×C4⋊C4C2218yes—
46C5×#389C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65278C2218yes—
58#65278C2218yes—
59#65273C2218yescomplemented
60#65268C2218yescomplemented
61#65261C2218yescomplemented
62#65261C2218yescomplemented
63C4×#685C2218yes—
64#65217C2218yescomplemented
65#64957C2218yes—
66#64957C2218yes—
67#64946C2218yescomplemented
68#64945C2218yescomplemented
69C2×#2583—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×C4×D5—24no—
86C22×C4×D5—24no—
87C22×C4×D5—24no—
88C22×C4×D5—24no—
89C22×C4×D5—42no—
90C22×C4×D5—42no—
91C22×C4×D5—42no—
92C22×C4×D5—42no—
93C22×C4×D5D418yes—
94C22×C4×D5C2314yes—
95C22×C4×D5C2314yes—
96C22×C4×D5C2314yes—
97C22×Dic10—24no—
98C22×Dic10—42no—
99C22×Dic10—42no—
100C22×Dic10C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4—42no—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C42×C5—42no—
110C2×C42×C5C2314yes—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685Q818yescomplemented
114C2×#685Q818yescomplemented
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5—42no—
122C2×C4⋊Dic5C2314yes—
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×#683—24no—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—42no—
132C2×#683—42no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×#683C2314yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×C4×Dic5—42no—
142C2×C4×Dic5C2314yes—
143#4042—232no—
144D5×C4⋊C4—232no—
145C5×#95C2314yes—
146C5×#95C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155C22×C22⋊Q8—51no—
156C23×C4⋊C4—51no—
157#2583—516no—
158C2×#398—51no—
159C2×#398—51no—
160C2×#395—51no—
161C2×#395—51no—
162C2×#389—51no—
163C2×#389—51no—
164C2×#389—51no—
165C2×#389D511yescharacteristic, complemented
166C2×#385—51no—
167C2×#385—51no—
168C2×#385—51no—
169C2×#385—51no—
170C2×C4×C22⋊C4—51no—
171C24×C5C2411yescharacteristic
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5C2×D414yes—
177C23×D5C2×Q814yes—
178C23×D5C2×Q814yes—
179C23×D5C2412yes—
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×C5—22no—
197C22×C4×C5C2×D414yes—
198C22×C4×C5C2×Q814yes—
199C22×C4×C5C2×Q814yes—
200C22×C4×C5#4114yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
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×Dic5C2×D414yes—
226C22×Dic5C2×Q814yes—
227C22×Dic5C2×Q814yes—
228C22×Dic5#4114yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C2×C4×D5—232no—
237C2×C4×D5—28no—
238C2×C4×D5—28no—
239C2×C4×D5—28no—
240C2×C4×D5—28no—
241C2×C4×D5—416no—
242C2×C4×D5—44no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×C4×D5—44no—
246C2×C4×D5—416no—
247C2×C4×D5C2×D4116yes—
248C2×Dic10—28no—
249C2×Dic10—44no—
250C2×Dic10—44no—
251C2×Dic10—416no—
252C5×C4⋊C4—28no—
253C5×C4⋊C4—28no—
254C5×C4⋊C4—28no—
255C5×C4⋊C4—44no—
256C42×C5—44no—
257#685—28no—
258#685—28no—
259#685C2×Q8116yescomplemented
260#685C2×Q8116yescomplemented
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—44no—
264#683—28no—
265#683—28no—
266#683—28no—
267#683—28no—
268#683—28no—
269#683—28no—
270#683—44no—
271#683—44no—
272C4×Dic5—44no—
273C23×Q8—51no—
274C24×C4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C2×C22⋊Q8—58no—
278C2×C22⋊Q8—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⋊C4—51no—
287C22×C4⋊C4—51no—
288C22×C4⋊C4—51no—
289C22×C4⋊C4—51no—
290C22×C4⋊C4—58no—
291C22×C4⋊C4—108no—
292C22×C4⋊C4C2×D511yescharacteristic
293C22×C4⋊C4C2×D511yescharacteristic
294C22×C4⋊C4C2×D511yescharacteristic
295C22×C4⋊C4C2×D511yescharacteristic
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C22⋊C4—51no—
299C22×C22⋊C4—51no—
300C22×C42—51no—
301C22×C42C2×D511yescharacteristic
302#398—58no—
303#398—58no—
304#395—58no—
305#395—58no—
306#389—58no—
307#389—58no—
308#389—58no—
309#389C2×D518yescomplemented
310#385—58no—
311#385—58no—
312#385—58no—
313#385—58no—
314C4×C22⋊C4—58no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C23×C5C22×D412yes—
326C23×C5C22×Q812yes—
327C23×C5C22×Q812yes—
328C23×C5C2×#4112yes—
329C23×C5C2×#4112yes—
330C23×C5H(5,𝔽2)12yes—
331C23×C5H(5,𝔽2)12yes—
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×D5C4⋊Q8116yes—
344C22×D5C22×D414yes—
345C22×D5C22×Q814yes—
346C22×D5C22×Q814yes—
347C2×C4×C5—28no—
348C2×C4×C5—28no—
349C2×C4×C5—28no—
350C2×C4×C5—28no—
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—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5C22×D414yes—
372C2×C4×C5C22×Q814yes—
373C2×C4×C5C22×Q814yes—
374C2×C4×C5C2×#4114yes—
375C2×Dic5—28no—
376C2×Dic5—28no—
377C2×Dic5—28no—
378C2×Dic5—28no—
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—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399C2×Dic5C22×D414yes—
400C2×Dic5C22×Q814yes—
401C2×Dic5C22×Q814yes—
402C2×Dic5C2×#4114yes—
403C4×D5—232no—
404C4×D5—416no—
405C4×D5—416no—
406Dic10—416no—
407C25—51no—
408C22×Q8—54no—
409C22×Q8—104no—
410C22×Q8—202no—
411C22×Q8—202no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—58no—
417C23×C4—54no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—54no—
422C23×C4—54no—
423C23×C4—104no—
424C23×C4—104no—
425C23×C4—104no—
426C23×C4—104no—
427C23×C4—202no—
428C23×C4—202no—
429C23×C4—202no—
430C23×C4—202no—
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C22⋊Q8—1032no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
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—1032no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4—202no—
464C2×C4⋊C4—202no—
465C2×C4⋊C4—202no—
466C2×C4⋊C4C22×D514yes—
467C2×C4⋊C4C22×D514yes—
468C2×C4⋊C4C22×D514yes—
469C2×C4⋊C4C22×D514yes—
470C2×C22⋊C4—58no—
471C2×C22⋊C4—58no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—54no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C42—42no—
479C2×C42—54no—
480C2×C42—202no—
481C2×C42C22×D514yes—
482#95—54no—
483#95—54no—
484#95—54no—
485#95—54no—
486#95—54no—
487#95—54no—
488#95—54no—
489#95—54no—
490#95C22×D514yes—
491#95C22×D514yes—
492C22×C5#52514yes—
493C22×C5C2×C4⋊Q814yes—
494C22×C5#53414yes—
495C22×C5#55414yes—
496C22×C5#55414yes—
497C22×C5#55414yes—
498C22×C5#55414yes—
499C22×C5C23×D411yescharacteristic
500C22×C5C23×Q811yescharacteristic
501C22×C5C23×Q811yescharacteristic
502C22×C5C22×#4111yescharacteristic
503C22×C5C22×#4111yescharacteristic
504C22×C5C2×H(5,𝔽2)11yescharacteristic
505C22×C5C2×H(5,𝔽2)11yescharacteristic
506C2×D5—232no—
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—24no—
511C2×D5—24no—
512C2×D5—24no—
513C2×D5C2×C4⋊Q818yes—
514C4×C5—24no—
515C4×C5—24no—
516C4×C5—24no—
517C4×C5—24no—
518C4×C5—42no—
519C4×C5—42no—
520C4×C5—42no—
521Dic5—24no—
522Dic5—24no—
523Dic5—24no—
524Dic5—24no—
525Dic5—42no—
526Dic5—42no—
527Dic5—42no—
528C24—54no—
529C24—54no—
530C24—54no—
531C24—52no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24C23×D511yescharacteristic
537C2×Q8—108no—
538C2×Q8—204no—
539C2×Q8—204no—
540C2×Q8—2016no—
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—22no—
558C22×C4—54no—
559C22×C4—54no—
560C22×C4—54no—
561C22×C4—54no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—516no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—108no—
571C22×C4—108no—
572C22×C4—1032no—
573C22×C4—108no—
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—108no—
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—2016no—
593C22×C4—204no—
594C22×C4—204no—
595C22×C4—204no—
596C22×C4—204no—
597C22×C4—2016no—
598C22×C4#70914yes—
599C22×C4D4×D514yes—
600C22×C4Q8×D514yes—
601C22×C4Q8×D514yes—
602C22×C4C23×D512yes—
603C22×C4C23×D512yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—44no—
613C4⋊C4—108no—
614C4⋊C4—108no—
615C4⋊C4—108no—
616C4⋊C4—108no—
617C4⋊C4—108no—
618C4⋊C4—108no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—204no—
622C4⋊C4—204no—
623C4⋊C4—204no—
624C22⋊C4—516no—
625C22⋊C4—516no—
626C22⋊C4—108no—
627C22⋊C4—108no—
628C42—44no—
629C42—204no—
630C2×C5#258318yescomplemented
631C2×C5C2×#52511yescharacteristic
632C2×C5C22×C4⋊Q811yescharacteristic
633C2×C5C2×#53411yescharacteristic
634C2×C5C2×#55411yescharacteristic
635C2×C5C2×#55411yescharacteristic
636C2×C5C2×#55411yescharacteristic
637C2×C5C2×#55411yescharacteristic
638D5—28no—
639C23—516no—
640C23—54no—
641C23—54no—
642C23—54no—
643C23—108no—
644C23—108no—
645C23—108no—
646C23—108no—
647C23—108no—
648C23—102no—
649C23—102no—
650C23—108no—
651C23—102no—
652C23—102no—
653C23C2×#70912yes—
654C23C2×D4×D512yes—
655C23#414412yes—
656C23C2×Q8×D512yes—
657C23C2×Q8×D512yes—
658C23D5×#4112yes—
659C23#414912yes—
660C23C24×D511yescharacteristic
661Q8—2016no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—28no—
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—22no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—54no—
687C2×C4—54no—
688C2×C4—54no—
689C2×C4—54no—
690C2×C4—1032no—
691C2×C4—108no—
692C2×C4—108no—
693C2×C4—108no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—108no—
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—2016no—
713C2×C4—2016no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C2×C4C2×#70914yes—
718C2×C4C2×D4×D514yes—
719C2×C4C2×Q8×D514yes—
720C2×C4C2×Q8×D514yes—
721C5C2×#258311yescharacteristic, complemented, Sylow
722C22—58no—
723C22—104no—
724C22—104no—
725C22—104no—
726C22—1032no—
727C22—104no—
728C22—104no—
729C22—104no—
730C22#6584514yes—
731C22#6588114yes—
732C22#6591314yes—
733C22#6593914yes—
734C22#6597014yes—
735C22#6602414yes—
736C22D5×C4⋊Q814yes—
737C22C22×#70911yescharacteristic
738C22C22×D4×D511yescharacteristic
739C22C2×#414411yescharacteristic
740C22C22×Q8×D511yescharacteristic
741C22C22×Q8×D511yescharacteristic
742C22C2×D5×#4111yescharacteristic
743C22C2×#414911yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—104no—
752C4—104no—
753C4—104no—
754C4—104no—
755C4—202no—
756C4—202no—
757C4—202no—
758C2—108no—
759C2#1060797818yesdirect product factor
760C2C2×#6584511yescharacteristic
761C2C2×#6588111yescharacteristic
762C2C2×#6591311yescharacteristic
763C2C2×#6593911yescharacteristic
764C2C2×#6597011yescharacteristic
765C2C2×#6602411yescharacteristic
766C2C2×D5×C4⋊Q811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#389C2
socleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#389D5
hypocenterC5C2×#2583
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C2×C5×#389C2semidirect
6. C2×#65273C2semidirect
7. C2×#65268C2semidirect
8. C2×#65261C2semidirect
9. C2×#65261C2semidirect
10. C2×#65217C2semidirect
12. #10607978C2direct (N × H)
15. C2×#64946C2semidirect
16. C2×#64945C2semidirect
46. C5×#389C22semidirect
59. #65273C22semidirect
60. #65268C22semidirect
61. #65261C22semidirect
62. #65261C22semidirect
64. #65217C22semidirect
67. #64946C22semidirect
68. #64945C22semidirect
113. C2×#685Q8semidirect
114. C2×#685Q8semidirect
165. C2×#389D5semidirect
259. #685C2×Q8semidirect
260. #685C2×Q8semidirect
309. #389C2×D5semidirect
630. C2×C5#2583semidirect
721. C5C2×#2583semidirect
759. C2#10607978direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×D5×C4⋊C42
C2×C5×#3892
C2×#652782
C2×#652732
C2×#652682
C2×#652612
C2×#652172
C2×C4×#6852
#106079782
C2×#649572
C2×#649462
C2×#649452
C2×#25835