Finite Group Databasebeta

← C2×#10609409 #12268239

Subgroups — C2×#10609409 #12268239

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×#4042C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C2×C5×#397C211yesmaximal, characteristic, complemented
4C2×#65266C211yesmaximal, characteristic, complemented
5C2×#65245C211yesmaximal, characteristic
6C2×#65245C211yesmaximal, characteristic
7C2×#65236C211yesmaximal, characteristic, complemented
8C2×#65234C211yesmaximal, characteristic, complemented
9C2×#65233C211yesmaximal, characteristic, complemented
10#10609409C2116yesmaximal, direct product factor
11C2×#64953C211yesmaximal, characteristic, complemented
12C2×D5×#95C211yesmaximal, characteristic, complemented
13C2×#64948C211yesmaximal, characteristic, complemented
14C2×#64947C211yesmaximal, characteristic, complemented
15C2×#64935C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, 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×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4042—28no—
39C2×#4042C2218yescomplemented
40C2×#4029—28no—
41C2×#4029C2218yes—
42C5×#397C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65266C2218yescomplemented
58#65245C2218yes—
59#65245C2218yes—
60#65236C2218yescomplemented
61#65234C2218yescomplemented
62#65233C2218yescomplemented
63#64955C2218yescomplemented
64#64953C2218yescomplemented
65D5×#95C2218yescomplemented
66#64948C2218yescomplemented
67#64947C2218yescomplemented
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—42no—
109C2×C5×C22⋊C4—42no—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5C2314yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685D418yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5C2314yes—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×C4×Dic5—24no—
134C2×C4×Dic5—42no—
135C2×C4×Dic5C2314yes—
136C2×C4×Dic5C2314yes—
137#4042—232no—
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×#397D511yescharacteristic, complemented
159C2×#393—51no—
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—
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×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5C2×D414yes—
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×Dic5C2×D414yes—
233C22×Dic5#4114yes—
234C22×Dic5#4114yes—
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—44no—
261C5×C22⋊C4—44no—
262C22⋊Dic5—28no—
263C22⋊Dic5—28no—
264C22⋊Dic5—28no—
265#685—28no—
266#685—28no—
267#685C2×D4116yes—
268C4⋊Dic5—28no—
269#683—28no—
270#683—28no—
271#683—28no—
272C4×Dic5—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×C42—51no—
299#400—58no—
300#400—58no—
301#397C2×D518yescomplemented
302#393—58no—
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—
362C2×C4×C5—28no—
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—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×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5C22×D414yes—
386C22⋊D5—416no—
387C2×Dic5—28no—
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—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5C22×D414yes—
413C2×Dic5C2×#4114yes—
414C2×Dic5C2×#4114yes—
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—42no—
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—104no—
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—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—42no—
538Dic5—24no—
539Dic5—24no—
540Dic5—24no—
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—22no—
586C22×C4—22no—
587C22×C4—54no—
588C22×C4—54no—
589C22×C4—54no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—52no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—108no—
598C22×C4—108no—
599C22×C4—108no—
600C22×C4—108no—
601C22×C4—108no—
602C22×C4—108no—
603C22×C4—108no—
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—102no—
621C22×C4—102no—
622C22×C4—204no—
623C22×C4—204no—
624C22×C4—2016no—
625C22×C4—2016no—
626C22×C4—2016no—
627C22×C4D4×D514yes—
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—44no—
641C22⋊C4—44no—
642C22⋊C4—516no—
643C22⋊C4—108no—
644C22⋊C4—108no—
645C22⋊C4—108no—
646C22⋊C4—108no—
647C22⋊C4—108no—
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—102no—
683C23—102no—
684C23—102no—
685C23—102no—
686C23—108no—
687C23—108no—
688C23C2×D4×D512yes—
689C23#414412yes—
690C23D5×#4112yes—
691C23D5×#4112yes—
692C23D5×#4112yes—
693C23D5×#4112yes—
694C23#415012yes—
695C23C24×D511yescharacteristic
696Q8—2016no—
697D4—2016no—
698C2×C4—28no—
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—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—44no—
721C2×C4—54no—
722C2×C4—54no—
723C2×C4—54no—
724C2×C4—108no—
725C2×C4—108no—
726C2×C4—108no—
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—102no—
744C2×C4—102no—
745C2×C4—2016no—
746C2×C4—2016no—
747C2×C4—2016no—
748C2×C4—204no—
749C2×C4—204no—
750C2×C4—204no—
751C2×C4—204no—
752C2×C4C2×D4×D514yes—
753C5C2×#248811yescharacteristic, complemented, Sylow
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—58no—
762C22—88no—
763C22—1032no—
764C22—104no—
765C22—104no—
766C22—104no—
767C22—104no—
768C22—104no—
769C22—104no—
770C22#6594614yes—
771C22#6598914yes—
772C22#6599314yes—
773C22#6599414yes—
774C22D5×#12414yes—
775C22#6604014yes—
776C22#6604214yes—
777C22C22×D4×D511yescharacteristic
778C22C2×#414411yescharacteristic
779C22C2×D5×#4111yescharacteristic
780C22C2×D5×#4111yescharacteristic
781C22C2×D5×#4111yescharacteristic
782C22C2×D5×#4111yescharacteristic
783C22C2×#415011yescharacteristic
784C4—24no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—104no—
791C4—104no—
792C4—104no—
793C4—202no—
794C4—202no—
795C4—202no—
796C4—202no—
797C2—82no—
798C2—108no—
799C2#1060940918yesdirect product factor
800C2C2×#6594611yescharacteristic
801C2C2×#6599411yescharacteristic
802C2C2×#6598911yescharacteristic
803C2C2×#6599311yescharacteristic
804C2C2×D5×#12411yescharacteristic
805C2C2×#6604011yescharacteristic
806C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2488
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
3. C2×C5×#397C2semidirect
4. C2×#65266C2semidirect
7. C2×#65236C2semidirect
8. C2×#65234C2semidirect
9. C2×#65233C2semidirect
10. #10609409C2direct (N × H)
11. C2×#64953C2semidirect
12. C2×D5×#95C2semidirect
13. C2×#64948C2semidirect
14. C2×#64947C2semidirect
15. C2×#64935C2semidirect
16. C2×#64955C2semidirect
39. C2×#4042C22semidirect
42. C5×#397C22semidirect
57. #65266C22semidirect
60. #65236C22semidirect
61. #65234C22semidirect
62. #65233C22semidirect
63. #64955C22semidirect
64. #64953C22semidirect
65. D5×#95C22semidirect
66. #64948C22semidirect
67. #64947C22semidirect
68. #64935C22semidirect
158. C2×#397D5semidirect
301. #397C2×D5semidirect
651. C2×C5#2488semidirect
753. C5C2×#2488semidirect
799. C2#10609409direct (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×#40292
C2×C5×#3972
C2×#652662
C2×#652452
C2×#652362
C2×#652342
C2×#652332
#106094092
C2×#649532
C2×D5×#952
C2×#649482
C2×#649472
C2×#649352
C2×#649552
C2×#24885