Finite Group Databasebeta

← C2×#10606696 #12258820

Subgroups — C2×#10606696 #12258820

Order 1280.

3614 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
1C22×#4042C211yesmaximal, characteristic
2C22×D5×C4⋊C4C211yesmaximal, characteristic
3C22×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×C5×#387C211yesmaximal, characteristic, complemented
5C2×#65261C211yesmaximal, characteristic, complemented
6C2×#65274C211yesmaximal, characteristic, complemented
7C2×C4×#685C211yesmaximal, characteristic
8#10606696C2116yesmaximal, direct product factor
9C2×#64957C211yesmaximal, characteristic
10C2×#64957C211yesmaximal, characteristic
11C2×#64935C211yesmaximal, characteristic, complemented
12C2×#64936C211yesmaximal, characteristic, complemented
13C2×#64944C211yesmaximal, characteristic, complemented
14C2×#64938C211yesmaximal, characteristic, complemented
15C2×#64955C211yesmaximal, characteristic
16C2×#64955C211yesmaximal, characteristic
17C23×C4×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4042C4116yescomplemented
43C2×#4042C2218yes—
44C2×D5×C4⋊C4—28no—
45C2×D5×C4⋊C4C2218yes—
46C2×C4×Dic10—28no—
47C2×C4×Dic10C2218yescomplemented
48C5×#387C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65274C2218yescomplemented
60#65261C2218yescomplemented
61C4×#685C2218yes—
62#64957C2218yes—
63#64957C2218yes—
64#64955C2218yes—
65#64955C2218yes—
66#64944C2218yescomplemented
67#64938C2218yescomplemented
68#64936C2218yescomplemented
69#64935C2218yescomplemented
70C2×#2360—51nomaximal, Sylow
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
85C23×Dic5C2311yescharacteristic
86C22×C4×D5—24no—
87C22×C4×D5—24no—
88C22×C4×D5—24no—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—42no—
93C22×C4×D5—42no—
94C22×C4×D5C2×C418yes—
95C22×C4×D5C2314yes—
96C22×C4×D5C2314yes—
97C22×C4×D5C2314yes—
98C22×Dic10—24no—
99C22×Dic10—24no—
100C22×Dic10C2×C418yescomplemented
101C22×Dic10C2314yes—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4C2×C418yescomplemented
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C4⋊C4C2314yes—
106C2×C42×C5—24no—
107C2×C42×C5C2314yes—
108C2×#685—24no—
109C2×#685C2×C418yes—
110C2×#685C2×C418yes—
111C2×#685Q818yescomplemented
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×C4⋊Dic5—24no—
117C2×C4⋊Dic5—24no—
118C2×C4⋊Dic5—42no—
119C2×C4⋊Dic5C2314yes—
120C2×C4⋊Dic5C2314yes—
121C2×C4⋊Dic5C2314yes—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—42no—
125C2×#683C2×C418yescomplemented
126C2×#683C2×C418yescomplemented
127C2×#683D418yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5—42no—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143C2×C4×Dic5C2314yes—
144#4042C2×C4164yescomplemented
145D5×C4⋊C4—232no—
146C4×Dic10—232no—
147C5×#95C2314yes—
148C5×#95C2314yes—
149C5×#95C2314yes—
150C5×#95C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157C22×C22⋊Q8—51no—
158C22×C4×Q8—51no—
159C23×C4⋊C4—51no—
160#2360—516no—
161C2×#391—51no—
162C2×#389—51no—
163C2×#389—51no—
164C2×#389—51no—
165C2×#387—51no—
166C2×#387D511yescharacteristic, complemented
167C2×#385—51no—
168C2×#385—51no—
169C2×C4×C4⋊C4—51no—
170C2×C4×C22⋊C4—51no—
171C2×C4×C22⋊C4—51no—
172C2×C4×C22⋊C4—51no—
173C24×C5C2411yescharacteristic
174C23×D5—22no—
175C23×D5—22no—
176C23×D5—22no—
177C23×D5—22no—
178C23×D5C22×C414yes—
179C23×D5C2×Q814yes—
180C23×D5#4114yes—
181C23×D5C2412yes—
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×C5C22×C414yes—
199C22×C4×C5C22×C414yes—
200C22×C4×C5C22×C414yes—
201C22×C4×C5C2×D414yes—
202C22×C4×C5C2×Q814yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
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×Dic5C22×C414yes—
225C22×Dic5C22×C414yes—
226C22×Dic5C22×C414yes—
227C22×Dic5C2×D414yes—
228C22×Dic5C2×D414yes—
229C22×Dic5C2×Q814yes—
230C22×Dic5#4114yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×C4×D5—232no—
239C2×C4×D5—28no—
240C2×C4×D5—28no—
241C2×C4×D5—28no—
242C2×C4×D5—28no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—44no—
246C2×C4×D5—44no—
247C2×C4×D5—416no—
248C2×C4×D5—416no—
249C2×C4×D5C22×C4116yes—
250C2×Dic10—232no—
251C2×Dic10—28no—
252C2×Dic10—28no—
253C2×Dic10C22×C4116yescomplemented
254C5×C4⋊C4—28no—
255C5×C4⋊C4C22×C4116yescomplemented
256C42×C5—28no—
257#685—28no—
258#685C22×C4116yes—
259#685C22×C4116yes—
260#685C2×Q8116yescomplemented
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—44no—
264#683—28no—
265#683—28no—
266#683—44no—
267#683C22×C4116yescomplemented
268#683C22×C4116yescomplemented
269#683C2×D4116yes—
270C4×Dic5—28no—
271C4×Dic5—28no—
272C4×Dic5—28no—
273C4×Dic5—44no—
274C4×Dic5—44no—
275C23×Q8—51no—
276C24×C4—51no—
277C24×C4—51no—
278C24×C4—51no—
279C2×C22⋊Q8—516no—
280C2×C22⋊Q8—58no—
281C2×C4×Q8—58no—
282C2×C4×Q8—108no—
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—51no—
291C22×C4⋊C4—51no—
292C22×C4⋊C4—58no—
293C22×C4⋊C4—108no—
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×C42—51no—
302C22×C42—51no—
303C22×C42—51no—
304C22×C42—51no—
305C22×C42C2×D511yescharacteristic
306#391—58no—
307#389—58no—
308#389—58no—
309#389—58no—
310#387—58no—
311#387C2×D518yescomplemented
312#385—58no—
313#385—58no—
314C4×C4⋊C4—58no—
315C4×C22⋊C4—58no—
316C4×C22⋊C4—58no—
317C4×C22⋊C4—58no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95C2×D511yescharacteristic
325C2×#95C2×D511yescharacteristic
326C2×#95C2×D511yescharacteristic
327C2×#95C2×D511yescharacteristic
328C23×C5C23×C412yes—
329C23×C5C22×D412yes—
330C23×C5C22×Q812yes—
331C23×C5C2×#4112yes—
332C23×C5C2×#4112yes—
333C23×C5H(5,𝔽2)12yes—
334C23×C52−1+412yes—
335C23×C5C2511yescharacteristic
336C22×D5—28no—
337C22×D5—28no—
338C22×D5—28no—
339C22×D5—28no—
340C22×D5—28no—
341C22×D5—28no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5C4×Q8116yescomplemented
347C22×D5C23×C414yes—
348C22×D5C22×Q814yes—
349C22×D5C2×#4114yes—
350C2×C4×C5—28no—
351C2×C4×C5—28no—
352C2×C4×C5—28no—
353C2×C4×C5—28no—
354C2×C4×C5—28no—
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—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—44no—
372C2×C4×C5—44no—
373C2×C4×C5C23×C414yes—
374C2×C4×C5C23×C414yes—
375C2×C4×C5C23×C414yes—
376C2×C4×C5C22×D414yes—
377C2×C4×C5C22×Q814yes—
378C2×Dic5—28no—
379C2×Dic5—28no—
380C2×Dic5—28no—
381C2×Dic5—28no—
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×Dic5C4×D4116yes—
399C2×Dic5C23×C414yes—
400C2×Dic5C23×C414yes—
401C2×Dic5C23×C414yes—
402C2×Dic5C22×D414yes—
403C2×Dic5C22×D414yes—
404C2×Dic5C22×Q814yes—
405C2×Dic5C2×#4114yes—
406C4×D5—232no—
407C4×D5—416no—
408C4×D5—416no—
409Dic10—232no—
410C25—51no—
411C22×Q8—58no—
412C22×Q8—54no—
413C22×Q8—104no—
414C22×Q8—104no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—58no—
421C23×C4—54no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—54no—
425C23×C4—54no—
426C23×C4—104no—
427C23×C4—104no—
428C23×C4—104no—
429C23×C4—104no—
430C23×C4—104no—
431C23×C4—104no—
432C23×C4—202no—
433C23×C4—202no—
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C22⋊Q8—564no—
442C4×Q8—1032no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—58no—
445C2×C4⋊C4—58no—
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—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—1032no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—202no—
462C2×C4⋊C4—202no—
463C2×C4⋊C4C4×D518yescomplemented
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—58no—
467C2×C22⋊C4—58no—
468C2×C22⋊C4—58no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—104no—
474C2×C42—24no—
475C2×C42—54no—
476C2×C42—54no—
477C2×C42—54no—
478C2×C42—54no—
479C2×C42—54no—
480C2×C42—104no—
481C2×C42—104no—
482C2×C42—104no—
483C2×C42—202no—
484C2×C42—202no—
485C2×C42C22×D514yes—
486#95—54no—
487#95—54no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95C22×D514yes—
493#95C22×D514yes—
494#95C22×D514yes—
495#95C22×D514yes—
496C22×C5C2×C4×D414yes—
497C22×C5C2×C4×Q814yes—
498C22×C5#52014yes—
499C22×C5#54614yes—
500C22×C5D4×Q814yes—
501C22×C5#55214yes—
502C22×C5#55414yes—
503C22×C5C24×C411yescharacteristic
504C22×C5C23×D411yescharacteristic
505C22×C5C23×Q811yescharacteristic
506C22×C5C22×#4111yescharacteristic
507C22×C5C22×#4111yescharacteristic
508C22×C5C2×H(5,𝔽2)11yescharacteristic
509C22×C5C2×2−1+411yescharacteristic
510C2×D5—232no—
511C2×D5—24no—
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—24no—
516C2×D5—24no—
517C2×D5C2×C4×Q818yescomplemented
518C4×C5—24no—
519C4×C5—24no—
520C4×C5—24no—
521C4×C5—24no—
522C4×C5—24no—
523C4×C5—42no—
524C4×C5—42no—
525Dic5—24no—
526Dic5—24no—
527Dic5—24no—
528Dic5—24no—
529Dic5—42no—
530Dic5—42no—
531Dic5C2×C4×D418yes—
532C24—54no—
533C24—54no—
534C24—54no—
535C24—52no—
536C24—102no—
537C24—102no—
538C24—102no—
539C24—102no—
540C24C23×D511yescharacteristic
541C2×Q8—516no—
542C2×Q8—108no—
543C2×Q8—1032no—
544C2×Q8—108no—
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—54no—
562C22×C4—54no—
563C22×C4—54no—
564C22×C4—52no—
565C22×C4—54no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—54no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—516no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—108no—
577C22×C4—1032no—
578C22×C4—108no—
579C22×C4—108no—
580C22×C4—108no—
581C22×C4—108no—
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—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—108no—
597C22×C4—204no—
598C22×C4—204no—
599C22×C4—2016no—
600C22×C4—2016no—
601C22×C4C2×C4×D514yes—
602C22×C4C2×C4×D514yes—
603C22×C4C2×C4×D514yes—
604C22×C4D4×D514yes—
605C22×C4Q8×D514yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C4⋊C4—28no—
614C4⋊C4—516no—
615C4⋊C4—516no—
616C4⋊C4—516no—
617C4⋊C4—108no—
618C4⋊C4—108no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—204no—
622C4⋊C4—204no—
623C4⋊C4C2×C4×D5116yescomplemented
624C22⋊C4—516no—
625C22⋊C4—516no—
626C22⋊C4—516no—
627C22⋊C4—108no—
628C42—28no—
629C42—108no—
630C42—108no—
631C42—108no—
632C42—204no—
633C42—204no—
634C2×C5#236018yescomplemented
635C2×C5C22×C4×D411yescharacteristic
636C2×C5C22×C4×Q811yescharacteristic
637C2×C5C2×#52011yescharacteristic
638C2×C5C2×#54611yescharacteristic
639C2×C5C2×D4×Q811yescharacteristic
640C2×C5C2×#55211yescharacteristic
641C2×C5C2×#55411yescharacteristic
642D5—28no—
643C23—516no—
644C23—54no—
645C23—54no—
646C23—54no—
647C23—108no—
648C23—108no—
649C23—108no—
650C23—108no—
651C23—102no—
652C23—108no—
653C23—102no—
654C23—102no—
655C23—102no—
656C23—108no—
657C23C22×C4×D512yes—
658C23C2×D4×D512yes—
659C23C2×Q8×D512yes—
660C23D5×#4112yes—
661C23D5×#4112yes—
662C23#414912yes—
663C23#415012yes—
664C23C24×D511yescharacteristic
665Q8—1032no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
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—44no—
688C2×C4—44no—
689C2×C4—516no—
690C2×C4—54no—
691C2×C4—54no—
692C2×C4—54no—
693C2×C4—54no—
694C2×C4—54no—
695C2×C4—54no—
696C2×C4—54no—
697C2×C4—1032no—
698C2×C4—108no—
699C2×C4—108no—
700C2×C4—108no—
701C2×C4—102no—
702C2×C4—108no—
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—102no—
716C2×C4—2016no—
717C2×C4—2016no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4C22×C4×D514yes—
721C2×C4C22×C4×D514yes—
722C2×C4C22×C4×D514yes—
723C2×C4C2×D4×D514yes—
724C2×C4C2×Q8×D514yes—
725C5C2×#236011yescharacteristic, complemented, Sylow
726C22—58no—
727C22—104no—
728C22—104no—
729C22—104no—
730C22—104no—
731C22—1032no—
732C22—104no—
733C22—104no—
734C22#6585714yes—
735C22C4×D4×D514yes—
736C22C4×Q8×D514yes—
737C22#6596614yes—
738C22#6598814yes—
739C22#6602414yes—
740C22#6604214yes—
741C22C23×C4×D511yescharacteristic
742C22C22×D4×D511yescharacteristic
743C22C22×Q8×D511yescharacteristic
744C22C2×D5×#4111yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×#414911yescharacteristic
747C22C2×#415011yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—58no—
756C4—104no—
757C4—104no—
758C4—104no—
759C4—104no—
760C4—202no—
761C4—202no—
762C2—108no—
763C2#1060669618yesdirect product factor
764C2C2×#6585711yescharacteristic
765C2C2×C4×D4×D511yescharacteristic
766C2C2×C4×Q8×D511yescharacteristic
767C2C2×#6596611yescharacteristic
768C2C2×#6598811yescharacteristic
769C2C2×#6602411yescharacteristic
770C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC24×D5C23
cosocleC23×C5C25
hypercenterC2×#387D5
hypocenterC5C2×#2360
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic10C2semidirect
4. C2×C5×#387C2semidirect
5. C2×#65261C2semidirect
6. C2×#65274C2semidirect
8. #10606696C2direct (N × H)
11. C2×#64935C2semidirect
12. C2×#64936C2semidirect
13. C2×#64944C2semidirect
14. C2×#64938C2semidirect
42. C2×#4042C4semidirect
47. C2×C4×Dic10C22semidirect
48. C5×#387C22semidirect
59. #65274C22semidirect
60. #65261C22semidirect
66. #64944C22semidirect
67. #64938C22semidirect
68. #64936C22semidirect
69. #64935C22semidirect
100. C22×Dic10C2×C4semidirect
103. C2×C5×C4⋊C4C2×C4semidirect
111. C2×#685Q8semidirect
125. C2×#683C2×C4semidirect
126. C2×#683C2×C4semidirect
144. #4042C2×C4semidirect
166. C2×#387D5semidirect
253. C2×Dic10C22×C4semidirect
255. C5×C4⋊C4C22×C4semidirect
260. #685C2×Q8semidirect
267. #683C22×C4semidirect
268. #683C22×C4semidirect
311. #387C2×D5semidirect
346. C22×D5C4×Q8semidirect
463. C2×C4⋊C4C4×D5semidirect
517. C2×D5C2×C4×Q8semidirect
623. C4⋊C4C2×C4×D5semidirect
634. C2×C5#2360semidirect
725. C5C2×#2360semidirect
763. C2#10606696direct (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
C22×C4×Dic102
C2×C5×#3872
C2×#652612
C2×#652742
C2×C4×#6852
#106066962
C2×#649572
C2×#649352
C2×#649362
C2×#649442
C2×#649382
C2×#649552
C2×#23605