Finite Group Databasebeta

← C2×#10608598 #12268227

Subgroups — C2×#10608598 #12268227

Order 1280.

3114 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4092C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C2×C5×#393C211yesmaximal, characteristic, complemented
4C2×#65519C211yesmaximal, characteristic, complemented
5C2×#65245C211yesmaximal, characteristic
6C2×#65245C211yesmaximal, characteristic
7C2×#65241C211yesmaximal, characteristic, complemented
8C2×#65234C211yesmaximal, characteristic, complemented
9C2×#65240C211yesmaximal, characteristic, complemented
10#10608598C2116yesmaximal, direct product factor
11C2×#64953C211yesmaximal, characteristic, complemented
12C2×D5×#95C211yesmaximal, characteristic, complemented
13C2×#64948C211yesmaximal, characteristic, complemented
14C2×#64949C211yesmaximal, characteristic, complemented
15C2×#64939C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C2×#4092—28no—
29C2×#4092C2218yescomplemented
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4029—28no—
41C2×#4029C2218yes—
42C5×#393C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46#65519C2218yescomplemented
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65245C2218yes—
59#65245C2218yes—
60#65241C2218yescomplemented
61#65240C2218yescomplemented
62#65234C2218yescomplemented
63#64955C2218yescomplemented
64#64953C2218yescomplemented
65D5×#95C2218yescomplemented
66#64949C2218yescomplemented
67#64948C2218yescomplemented
68#64939C2218yescomplemented
69C2×#2488—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C22×C5×Q8—24no—
73C22×C5×Q8—24no—
74C22×C5×Q8—42no—
75C22×C5×Q8C2314yes—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5C2314yes—
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—24no—
100C22×C4×D5—42no—
101C22×C4×D5—42no—
102C22×C4×D5C2314yes—
103C22×C4×D5C2314yes—
104C22×C4×D5C2314yes—
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4—42no—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—42no—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117#4092—232no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685D418yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—42no—
136C2×C4×Dic5C2314yes—
137C2×C4×Dic5C2314yes—
138#4029—232no—
139C5×#95C2314yes—
140C5×#95C2314yes—
141C5×#95C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#123—51no—
154C22×C22⋊Q8—51no—
155#2488—516no—
156C2×#400—51no—
157C2×#400—51no—
158C2×#397—51no—
159C2×#393D511yescharacteristic, complemented
160C2×#391—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#386—51no—
164C2×#386—51no—
165C2×#382—51no—
166C2×#381—51no—
167C2×C4×C22⋊C4—51no—
168C22×#95—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5C2×D414yes—
183C23×D5#4114yes—
184C23×D5#4114yes—
185C23×D5C2412yes—
186C2×C5×Q8—28no—
187C2×C5×Q8—28no—
188C2×C5×Q8—44no—
189C2×C5×Q8—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—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5C2×D414yes—
207C22×C4×C5#4114yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C2×C22⋊D5—28no—
215C2×C22⋊D5—28no—
216C2×C22⋊D5—28no—
217C2×C22⋊D5—416no—
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×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5C2×D414yes—
238C22×Dic5#4114yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—28no—
251C2×C4×D5—28no—
252C2×C4×D5—28no—
253C2×C4×D5—44no—
254C2×C4×D5—44no—
255C2×C4×D5—416no—
256C2×C4×D5—416no—
257C2×C4×D5—416no—
258C5×C22⋊C4—28no—
259C5×C22⋊C4—28no—
260C5×C22⋊C4—44no—
261C22⋊Dic5—28no—
262C22⋊Dic5—28no—
263C22⋊Dic5—44no—
264#685—28no—
265#685—28no—
266#685C2×D4116yes—
267C4⋊Dic5—28no—
268C4⋊Dic5—28no—
269#683—28no—
270#683—28no—
271#683—28no—
272C4×Dic5—28no—
273C4×Dic5—44no—
274C23×Q8C2×D511yescharacteristic
275C23×D4—51no—
276C24×C4—51no—
277C24×C4—51no—
278C24×C4—51no—
279C2×#123—58no—
280C2×#123—108no—
281C2×C22⋊Q8—58no—
282C2×C22⋊Q8—108no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4—51no—
287C22×C4⋊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—
299#400—58no—
300#400—58no—
301#397—58no—
302#393C2×D518yescomplemented
303#391—58no—
304#388—58no—
305#388—58no—
306#386—58no—
307#386—58no—
308#382—58no—
309#381—58no—
310C4×C22⋊C4—58no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
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×#95—58no—
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C2×#95C2×D511yescharacteristic
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5—44no—
339C23×C5—44no—
340C23×C5C22×D412yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4112yes—
344C23×C5C2×#4112yes—
345C23×C5H(5,𝔽2)12yes—
346C23×C52−1+412yes—
347C23×C5C2511yescharacteristic
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—28no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5#124116yes—
359C22×D5C22×D414yes—
360C22×D5C2×#4114yes—
361C22×D5C2×#4114yes—
362C5×Q8—416no—
363C2×C4×C5—28no—
364C2×C4×C5—28no—
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—
387C22⋊D5—416no—
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—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5—44no—
414C2×Dic5C22×D414yes—
415C2×Dic5C2×#4114yes—
416C4×D5—416no—
417C4×D5—416no—
418C4×D5—416no—
419C25—51no—
420C25C22×D511yescharacteristic
421C22×Q8—24no—
422C22×Q8—24no—
423C22×Q8—42no—
424C22×Q8C22×D514yes—
425C22×D4—54no—
426C22×D4—104no—
427C22×D4—104no—
428C22×D4—104no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4—54no—
437C23×C4—54no—
438C23×C4—54no—
439C23×C4—104no—
440C23×C4—104no—
441C23×C4—104no—
442C23×C4—104no—
443C23×C4—104no—
444C23×C4—104no—
445C23×C4—104no—
446C23×C4—202no—
447C23×C4—202no—
448C23×C4C22×D511yescharacteristic
449C23×C4C22×D511yescharacteristic
450C23×C4C22×D511yescharacteristic
451C23×C4C22×D511yescharacteristic
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454#123—1032no—
455C22⋊Q8—1032no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—54no—
459C2×C4⋊C4—54no—
460C2×C4⋊C4—54no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4—104no—
464C2×C4⋊C4—104no—
465C2×C4⋊C4—104no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—58no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
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×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4C22×D514yes—
482C2×C22⋊C4C22×D514yes—
483C2×C22⋊C4C22×D514yes—
484C2×C42—54no—
485C2×C42—54no—
486C2×C42—104no—
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#95—54no—
497#95—54no—
498#95—54no—
499#95C22×D514yes—
500#95C22×D514yes—
501#95C22×D514yes—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—42no—
508C22×C5—42no—
509C22×C5—88no—
510C22×C5C2×#12414yes—
511C22×C5#52914yes—
512C22×C5#53914yes—
513C22×C5#54614yes—
514C22×C5#54714yes—
515C22×C5#55114yes—
516C22×C5#55214yes—
517C22×C5C23×D411yescharacteristic
518C22×C5C22×#4111yescharacteristic
519C22×C5C22×#4111yescharacteristic
520C22×C5C22×#4111yescharacteristic
521C22×C5C22×#4111yescharacteristic
522C22×C5C2×H(5,𝔽2)11yescharacteristic
523C22×C5C2×2−1+411yescharacteristic
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—24no—
529C2×D5—24no—
530C2×D5—232no—
531C2×D5C2×#12418yes—
532C4×C5—24no—
533C4×C5—24no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—42no—
538Dic5—24no—
539Dic5—24no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—54no—
553C24—54no—
554C24—54no—
555C24—52no—
556C24—102no—
557C24—102no—
558C24—102no—
559C24—102no—
560C24C23×D512yes—
561C24C23×D511yescharacteristic
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—44no—
565C2×Q8—416no—
566C2×D4—108no—
567C2×D4—108no—
568C2×D4—108no—
569C2×D4—2016no—
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—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—54no—
587C22×C4—54no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—52no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—108no—
598C22×C4—108no—
599C22×C4—108no—
600C22×C4—108no—
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—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4—108no—
621C22×C4—204no—
622C22×C4—204no—
623C22×C4—2016no—
624C22×C4—2016no—
625C22×C4—2016no—
626C22×C4D4×D514yes—
627C22×C4#71114yes—
628C22×C4C23×D512yes—
629C22×C4C23×D512yes—
630C22×C4C23×D512yes—
631C22×C4C23×D512yes—
632C22×C4C23×D512yes—
633C22×C4C23×D512yes—
634C4⋊C4—108no—
635C4⋊C4—108no—
636C4⋊C4—108no—
637C4⋊C4—108no—
638C4⋊C4—108no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—44no—
642C22⋊C4—516no—
643C22⋊C4—108no—
644C22⋊C4—108no—
645C22⋊C4—108no—
646C22⋊C4—108no—
647C22⋊C4—204no—
648C42—108no—
649C42—204no—
650C2×C5—82no—
651C2×C5#248818yescomplemented
652C2×C5C22×#12411yescharacteristic
653C2×C5C2×#52911yescharacteristic
654C2×C5C2×#53911yescharacteristic
655C2×C5C2×#54611yescharacteristic
656C2×C5C2×#54711yescharacteristic
657C2×C5C2×#55111yescharacteristic
658C2×C5C2×#55211yescharacteristic
659D5—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—516no—
675C23—54no—
676C23—54no—
677C23—54no—
678C23—108no—
679C23—108no—
680C23—108no—
681C23—108no—
682C23—108no—
683C23—108no—
684C23—102no—
685C23—102no—
686C23—102no—
687C23—102no—
688C23C2×D4×D512yes—
689C23C2×#71112yes—
690C23#414412yes—
691C23#414712yes—
692C23D5×#4112yes—
693C23D5×#4112yes—
694C23D5×#4112yes—
695C23C24×D511yescharacteristic
696Q8—416no—
697D4—2016no—
698C2×C4—28no—
699C2×C4—28no—
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—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—54no—
721C2×C4—54no—
722C2×C4—108no—
723C2×C4—108no—
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—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—2016no—
744C2×C4—2016no—
745C2×C4—2016no—
746C2×C4—204no—
747C2×C4—204no—
748C2×C4—204no—
749C2×C4—204no—
750C2×C4—204no—
751C2×C4C2×D4×D514yes—
752C2×C4C2×#71114yes—
753C5C2×#248811yescharacteristic, complemented, Sylow
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—58no—
762C22—88no—
763C22—104no—
764C22—104no—
765C22—104no—
766C22—104no—
767C22—104no—
768C22—1032no—
769C22—104no—
770C22#6592514yes—
771C22#6596514yes—
772C22#6597214yes—
773C22#6597314yes—
774C22D5×#12414yes—
775C22#6601314yes—
776C22#6601414yes—
777C22C22×D4×D511yescharacteristic
778C22C22×#71111yescharacteristic
779C22C2×#414411yescharacteristic
780C22C2×#414711yescharacteristic
781C22C2×D5×#4111yescharacteristic
782C22C2×D5×#4111yescharacteristic
783C22C2×D5×#4111yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—104no—
791C4—104no—
792C4—202no—
793C4—202no—
794C4—202no—
795C4—202no—
796C4—202no—
797C2—82no—
798C2—108no—
799C2#1060859818yesdirect product factor
800C2C2×#6592511yescharacteristic
801C2C2×#6597211yescharacteristic
802C2C2×#6596511yescharacteristic
803C2C2×#6597311yescharacteristic
804C2C2×#6601411yescharacteristic
805C2C2×D5×#12411yescharacteristic
806C2C2×#6601311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#393C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#393D5
hypocenterC5C2×#2488
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#4092C2semidirect
3. C2×C5×#393C2semidirect
4. C2×#65519C2semidirect
7. C2×#65241C2semidirect
8. C2×#65234C2semidirect
9. C2×#65240C2semidirect
10. #10608598C2direct (N × H)
11. C2×#64953C2semidirect
12. C2×D5×#95C2semidirect
13. C2×#64948C2semidirect
14. C2×#64949C2semidirect
15. C2×#64939C2semidirect
16. C2×#64955C2semidirect
29. C2×#4092C22semidirect
42. C5×#393C22semidirect
46. #65519C22semidirect
60. #65241C22semidirect
61. #65240C22semidirect
62. #65234C22semidirect
63. #64955C22semidirect
64. #64953C22semidirect
65. D5×#95C22semidirect
66. #64949C22semidirect
67. #64948C22semidirect
68. #64939C22semidirect
159. C2×#393D5semidirect
302. #393C2×D5semidirect
651. C2×C5#2488semidirect
753. C5C2×#2488semidirect
799. C2#10608598direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40922
C22×#40292
C2×C5×#3932
C2×#655192
C2×#652452
C2×#652412
C2×#652342
C2×#652402
#106085982
C2×#649532
C2×D5×#952
C2×#649482
C2×#649492
C2×#649392
C2×#649552
C2×#24885