Finite Group Databasebeta

← C2×#10606493 #12269459

Subgroups — C2×#10606493 #12269459

Order 1280.

2898 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×#4070C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic
5C2×#65510C211yesmaximal, characteristic
6C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#65241C211yesmaximal, characteristic, complemented
8C2×#65236C211yesmaximal, characteristic, complemented
9C2×#65234C211yesmaximal, characteristic, complemented
10C2×#65240C211yesmaximal, characteristic, complemented
11C2×#65240C211yesmaximal, characteristic, complemented
12#10606493C2116yesmaximal, direct product factor
13C2×#64950C211yesmaximal, characteristic, complemented
14C2×#64935C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C2×#4070—28no—
35C2×#4070C2218yescomplemented
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4025—28no—
45C2×#4025C2218yescomplemented
46C5×#386C2218yes—
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65511C2218yes—
50#65510C2218yes—
51C4×C22⋊Dic5C2218yescomplemented
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65241C2218yescomplemented
61#65240C2218yescomplemented
62#65240C2218yescomplemented
63#65236C2218yescomplemented
64#65234C2218yescomplemented
65#64950C2218yescomplemented
66#64942C2218yescomplemented
67#64938C2218yescomplemented
68#64935C2218yescomplemented
69C2×#2560—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C22×C5×D4—24no—
73C22×C5×D4—24no—
74C22×C5×D4—42no—
75C22×C5×D4C2314yes—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—42no—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2314yes—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×Dic10—24no—
94C22×Dic10—24no—
95C22×Dic10—42no—
96C22×Dic10C2314yes—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—24no—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C5×C22⋊C4C2314yes—
103C2×C22⋊Dic5—24no—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5—24no—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—42no—
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5C2314yes—
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125#4070—232no—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683D418yescomplemented
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142#4025—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×C22⋊Q8—51no—
155#2560—516no—
156C2×#398—51no—
157C2×#397—51no—
158C2×#394—51no—
159C2×#393—51no—
160C2×#391—51no—
161C2×#390—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#386D511yescharacteristic
167C2×C4×C4⋊C4—51no—
168C2×C4×C22⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5#4114yes—
183C24×C5C2412yes—
184C24×C5C2412yes—
185C24×C5C2411yescharacteristic
186C2×C5×D4—28no—
187C2×C5×D4—28no—
188C2×C5×D4—44no—
189C2×C5×D4—416no—
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—28no—
203C22×C4×C5—28no—
204C22×C4×C5—44no—
205C22×C4×C5—416no—
206C22×C4×C5C2×D414yes—
207C22×C4×C5#4114yes—
208C22×C4×C5#4114yes—
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×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5C2×D414yes—
236C22×Dic5C2×D414yes—
237C22×Dic5#4114yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C2×Dic10—28no—
247C2×Dic10—28no—
248C2×Dic10—44no—
249C2×Dic10—416no—
250C5×C22⋊C4—28no—
251C5×C22⋊C4—28no—
252C5×C22⋊C4—28no—
253C22⋊Dic5—28no—
254C22⋊Dic5—28no—
255C22⋊Dic5—28no—
256C22⋊Dic5—28no—
257C22⋊Dic5—28no—
258C22⋊Dic5—28no—
259C22⋊Dic5—28no—
260C22⋊Dic5—44no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—28no—
264#683—28no—
265#683—28no—
266#683—28no—
267#683C2×D4116yescomplemented
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—44no—
271C4×Dic5—44no—
272C23×Q8—51no—
273C23×D4C2×D511yescharacteristic
274C24×C4C2×D511yescharacteristic
275C2×#126—58no—
276C2×#126—108no—
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×C22⋊C4—51no—
287C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
295C22×C22⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C42—51no—
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301#398—58no—
302#397—58no—
303#394—58no—
304#393—58no—
305#391—58no—
306#390—58no—
307#388—58no—
308#388—58no—
309#388—58no—
310#387—58no—
311#386C2×D518yes—
312C4×C4⋊C4—58no—
313C4×C22⋊C4—58no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C23×C5—28no—
325C23×C5—28no—
326C23×C5—28no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—44no—
341C23×C5—44no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—44no—
345C23×C5—44no—
346C23×C5—44no—
347C23×C5—44no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5C22×D412yes—
352C23×C5C2×#4112yes—
353C23×C5C2×#4114yes—
354C23×C5C2×#4112yes—
355C23×C5C2×#4112yes—
356C23×C5C2×#4112yes—
357C23×C5H(5,𝔽2)12yes—
358C23×C52−1+412yes—
359C23×C5C2511yescharacteristic
360C5×D4—416no—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—28no—
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—416no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5C22×D414yes—
380C2×C4×C5C2×#4114yes—
381C2×C4×C5C2×#4114yes—
382C2×Dic5—28no—
383C2×Dic5—28no—
384C2×Dic5—28no—
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—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×Dic5—44no—
411C2×Dic5C22×D414yes—
412C2×Dic5C22×D414yes—
413C2×Dic5C2×#4114yes—
414Dic10—416no—
415C25C22×D511yescharacteristic
416C25C22×D511yescharacteristic
417C22×Q8—54no—
418C22×Q8—104no—
419C22×Q8—104no—
420C22×Q8—202no—
421C22×D4—24no—
422C22×D4—24no—
423C22×D4—42no—
424C22×D4C22×D514yes—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—42no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D514yes—
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#126—1032no—
443C22⋊Q8—1032no—
444C2×C4⋊C4—58no—
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—104no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—104no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—54no—
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—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—104no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—202no—
477C2×C22⋊C4C22×D514yes—
478C2×C22⋊C4C22×D514yes—
479C2×C22⋊C4C22×D514yes—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—202no—
487C2×C42—202no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95—54no—
496#95C22×D514yes—
497#95C22×D514yes—
498C22×C5—24no—
499C22×C5—24no—
500C22×C5—24no—
501C22×C5—416no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—42no—
508C22×C5—42no—
509C22×C5—42no—
510C22×C5—42no—
511C22×C5—42no—
512C22×C5—42no—
513C22×C5—88no—
514C22×C5#52914yes—
515C22×C5#53214yes—
516C22×C5#53914yes—
517C22×C5#54614yes—
518C22×C5#54814yes—
519C22×C5#55114yes—
520C22×C5#55614yes—
521C22×C5C23×D411yescharacteristic
522C22×C5C22×#4111yescharacteristic
523C22×C5C22×#4111yescharacteristic
524C22×C5C22×#4111yescharacteristic
525C22×C5C22×#4111yescharacteristic
526C22×C5C2×H(5,𝔽2)11yescharacteristic
527C22×C5C2×2−1+411yescharacteristic
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533Dic5—24no—
534Dic5—24no—
535Dic5—24no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24#71114yes—
555C24C23×D512yes—
556C24C23×D512yes—
557C24C23×D511yescharacteristic
558C2×Q8—108no—
559C2×Q8—108no—
560C2×Q8—204no—
561C2×Q8—2016no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—44no—
565C2×D4—416no—
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—28no—
579C22×C4—28no—
580C22×C4—44no—
581C22×C4—416no—
582C22×C4—54no—
583C22×C4—54no—
584C22×C4—54no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
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—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4#70914yes—
615C22×C4D4×D514yes—
616C22×C4#71114yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—516no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—204no—
640C42—108no—
641C42—108no—
642C42—204no—
643C42—204no—
644C2×C5—44no—
645C2×C5—82no—
646C2×C5#256018yescomplemented
647C2×C5C2×#52911yescharacteristic
648C2×C5C2×#53211yescharacteristic
649C2×C5C2×#53911yescharacteristic
650C2×C5C2×#54611yescharacteristic
651C2×C5C2×#54811yescharacteristic
652C2×C5C2×#55111yescharacteristic
653C2×C5C2×#55611yescharacteristic
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23C2×#70912yes—
682C23C2×D4×D512yes—
683C23C2×#71114yes—
684C23C2×#71112yes—
685C23C2×#71112yes—
686C23#414412yes—
687C23D5×#4112yes—
688C23#415012yes—
689C23C24×D511yescharacteristic
690Q8—2016no—
691D4—416no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
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—416no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—54no—
711C2×C4—54no—
712C2×C4—54no—
713C2×C4—108no—
714C2×C4—108no—
715C2×C4—108no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
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—102no—
737C2×C4—204no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4C2×#70914yes—
743C2×C4C2×D4×D514yes—
744C2×C4C2×#71114yes—
745C5C2×#256011yescharacteristic, complemented, Sylow
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—88no—
762C22#6582914yes—
763C22#6587614yes—
764C22#6588214yes—
765C22#6592514yes—
766C22#6593214yes—
767C22#6593414yes—
768C22#6599414yes—
769C22C22×#70911yescharacteristic
770C22C22×D4×D511yescharacteristic
771C22C22×#71111yescharacteristic
772C22C22×#71111yescharacteristic
773C22C2×#414411yescharacteristic
774C22C2×D5×#4111yescharacteristic
775C22C2×#415011yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—104no—
782C4—104no—
783C4—104no—
784C4—202no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—44no—
790C2—82no—
791C2#1060649318yesdirect product factor
792C2C2×#6582911yescharacteristic
793C2C2×#6587611yescharacteristic
794C2C2×#6588211yescharacteristic
795C2C2×#6592511yescharacteristic
796C2C2×#6593411yescharacteristic
797C2C2×#6593211yescharacteristic
798C2C2×#6599411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#386D5
hypocenterC5C2×#2560
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#4070C2semidirect
2. C22×#4025C2semidirect
6. C2×C4×C22⋊Dic5C2semidirect
7. C2×#65241C2semidirect
8. C2×#65236C2semidirect
9. C2×#65234C2semidirect
10. C2×#65240C2semidirect
11. C2×#65240C2semidirect
12. #10606493C2direct (N × H)
13. C2×#64950C2semidirect
14. C2×#64935C2semidirect
15. C2×#64942C2semidirect
16. C2×#64938C2semidirect
35. C2×#4070C22semidirect
45. C2×#4025C22semidirect
51. C4×C22⋊Dic5C22semidirect
60. #65241C22semidirect
61. #65240C22semidirect
62. #65240C22semidirect
63. #65236C22semidirect
64. #65234C22semidirect
65. #64950C22semidirect
66. #64942C22semidirect
67. #64938C22semidirect
68. #64935C22semidirect
129. C2×#683D4semidirect
267. #683C2×D4semidirect
646. C2×C5#2560semidirect
745. C5C2×#2560semidirect
791. C2#10606493direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40702
C22×#40252
C2×C5×#3862
C2×#655112
C2×#655102
C2×C4×C22⋊Dic52
C2×#652412
C2×#652362
C2×#652342
C2×#652402
#106064932
C2×#649502
C2×#649352
C2×#649422
C2×#649382
C2×#25605