Finite Group Databasebeta

← C2×#10607599 #12268237

Subgroups — C2×#10607599 #12268237

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×#4043C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65275C211yesmaximal, characteristic, complemented
5C2×#65245C211yesmaximal, characteristic
6C2×#65245C211yesmaximal, characteristic
7C2×#65242C211yesmaximal, characteristic, complemented
8C2×#65236C211yesmaximal, characteristic, complemented
9C2×#65240C211yesmaximal, characteristic, complemented
10C2×#65225C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607599C2116yesmaximal, direct product factor
13C2×#64953C211yesmaximal, characteristic, complemented
14C2×D5×#95C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64935C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4043—28no—
39C2×#4043C2218yescomplemented
40C2×#4029—28no—
41C2×#4029C2218yes—
42C5×#388C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65275C2218yescomplemented
58#65245C2218yes—
59#65245C2218yes—
60#65242C2218yescomplemented
61#65240C2218yescomplemented
62#65236C2218yescomplemented
63C4×#685C2218yescomplemented
64#65225C2218yescomplemented
65#64953C2218yescomplemented
66D5×#95C2218yescomplemented
67#64949C2218yescomplemented
68#64935C2218yescomplemented
69C2×#2488—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5—24no—
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5C2314yes—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C22×Dic10—24no—
102C22×Dic10—24no—
103C22×Dic10—42no—
104C22×Dic10C2314yes—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C42×C5—24no—
114C2×C42×C5C2314yes—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—42no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685D418yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×C4⋊Dic5—24no—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5—24no—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2314yes—
133C2×#683—24no—
134C2×#683C2314yes—
135C2×C4×Dic5—42no—
136C2×C4×Dic5C2314yes—
137#4043—232no—
138#4029—232no—
139C5×#95C2314yes—
140C5×#95C2314yes—
141#3963C2314yes—
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×#393—51no—
160C2×#391—51no—
161C2×#388—51no—
162C2×#388D511yescharacteristic, complemented
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—
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×C5C2×D414yes—
202C22×C4×C5#4114yes—
203C22×C4×C5#4114yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C2×C22⋊D5—28no—
211C2×C22⋊D5—28no—
212C2×C22⋊D5—28no—
213C2×C22⋊D5—416no—
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×Dic5C2×D414yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—28no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—44no—
250C2×C4×D5—44no—
251C2×C4×D5—416no—
252C2×C4×D5—416no—
253C2×C4×D5—416no—
254C2×Dic10—28no—
255C2×Dic10—28no—
256C2×Dic10—44no—
257C2×Dic10—416no—
258C5×C4⋊C4—28no—
259C5×C22⋊C4—28no—
260C5×C22⋊C4—28no—
261C5×C22⋊C4—28no—
262C42×C5—28no—
263C22⋊Dic5—28no—
264C22⋊Dic5—44no—
265C22⋊Dic5—44no—
266#685—28no—
267#685—28no—
268#685C2×D4116yes—
269C4⋊Dic5—28no—
270C4⋊Dic5—28no—
271C4⋊Dic5—28no—
272#683—28no—
273C4×Dic5—44no—
274C23×Q8—51no—
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⋊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⋊C4C2×D511yescharacteristic
295C22×C22⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C42—51no—
298C22×C42C2×D511yescharacteristic
299#400—58no—
300#400—58no—
301#397—58no—
302#393—58no—
303#391—58no—
304#388—58no—
305#388C2×D518yescomplemented
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—51no—
323C2×#95—58no—
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—
362C2×C4×C5—28no—
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—44no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5C22×D414yes—
384C2×C4×C5C2×#4114yes—
385C2×C4×C5C2×#4114yes—
386C22⋊D5—416no—
387C2×Dic5—28no—
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—22no—
407C2×Dic5—22no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5—44no—
414C2×Dic5C22×D414yes—
415C4×D5—416no—
416C4×D5—416no—
417C4×D5—416no—
418Dic10—416no—
419C25—51no—
420C25C22×D511yescharacteristic
421C22×Q8—54no—
422C22×Q8—104no—
423C22×Q8—104no—
424C22×Q8—202no—
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—24no—
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⋊C4C22×D514yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
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—202no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4C22×D514yes—
482C2×C22⋊C4C22×D514yes—
483C2×C22⋊C4C22×D514yes—
484C2×C42—24no—
485C2×C42—54no—
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#95—54no—
495#95—54no—
496#95—54no—
497#95—54no—
498#95—54no—
499#95—54no—
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—24no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—42no—
538Dic5—24no—
539Dic5—42no—
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—108no—
563C2×Q8—108no—
564C2×Q8—204no—
565C2×Q8—2016no—
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—54no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—108no—
594C22×C4—108no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—108no—
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—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—108no—
619C22×C4—108no—
620C22×C4—204no—
621C22×C4—204no—
622C22×C4—2016no—
623C22×C4—2016no—
624C22×C4—2016no—
625C22×C4#70914yes—
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—28no—
635C4⋊C4—108no—
636C4⋊C4—108no—
637C4⋊C4—108no—
638C4⋊C4—108no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—516no—
643C22⋊C4—108no—
644C22⋊C4—108no—
645C22⋊C4—108no—
646C22⋊C4—204no—
647C22⋊C4—204no—
648C42—28no—
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—102no—
684C23—102no—
685C23—102no—
686C23—102no—
687C23—108no—
688C23C2×#70912yes—
689C23C2×D4×D512yes—
690C23C2×#71112yes—
691C23D5×#4112yes—
692C23D5×#4112yes—
693C23#414912yes—
694C23#415012yes—
695C23C24×D511yescharacteristic
696Q8—2016no—
697D4—2016no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
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—54no—
720C2×C4—108no—
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—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—2016no—
742C2×C4—2016no—
743C2×C4—2016no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4—204no—
748C2×C4—204no—
749C2×C4—204no—
750C2×C4C2×#70914yes—
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—104no—
769C22—1032no—
770C22#6586314yes—
771C22#6588414yes—
772C22#6589114yes—
773C22#6594514yes—
774C22#6599214yes—
775C22D5×#12414yes—
776C22#6604114yes—
777C22C22×#70911yescharacteristic
778C22C22×D4×D511yescharacteristic
779C22C22×#71111yescharacteristic
780C22C2×D5×#4111yescharacteristic
781C22C2×D5×#4111yescharacteristic
782C22C2×#414911yescharacteristic
783C22C2×#415011yescharacteristic
784C4—24no—
785C4—24no—
786C4—24no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—104no—
791C4—202no—
792C4—202no—
793C4—202no—
794C4—202no—
795C4—202no—
796C4—202no—
797C2—82no—
798C2—108no—
799C2#1060759918yesdirect product factor
800C2C2×#6586311yescharacteristic
801C2C2×#6589111yescharacteristic
802C2C2×#6588411yescharacteristic
803C2C2×#6594511yescharacteristic
804C2C2×#6599211yescharacteristic
805C2C2×D5×#12411yescharacteristic
806C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2488
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4043C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65275C2semidirect
7. C2×#65242C2semidirect
8. C2×#65236C2semidirect
9. C2×#65240C2semidirect
10. C2×#65225C2semidirect
11. C2×C4×#685C2semidirect
12. #10607599C2direct (N × H)
13. C2×#64953C2semidirect
14. C2×D5×#95C2semidirect
15. C2×#64949C2semidirect
16. C2×#64935C2semidirect
39. C2×#4043C22semidirect
42. C5×#388C22semidirect
57. #65275C22semidirect
60. #65242C22semidirect
61. #65240C22semidirect
62. #65236C22semidirect
63. C4×#685C22semidirect
64. #65225C22semidirect
65. #64953C22semidirect
66. D5×#95C22semidirect
67. #64949C22semidirect
68. #64935C22semidirect
162. C2×#388D5semidirect
305. #388C2×D5semidirect
651. C2×C5#2488semidirect
753. C5C2×#2488semidirect
799. C2#10607599direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40432
C22×#40292
C2×C5×#3882
C2×#652752
C2×#652452
C2×#652422
C2×#652362
C2×#652402
C2×#652252
C2×C4×#6852
#106075992
C2×#649532
C2×D5×#952
C2×#649492
C2×#649352
C2×#24885