Finite Group Databasebeta

← C2×#10607580 #12267040

Subgroups — C2×#10607580 #12267040

Order 1280.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4030C211yesmaximal, characteristic
2C22×C4×D20C211yesmaximal, characteristic, complemented
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65282C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65248C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic, complemented
10C2×#65242C211yesmaximal, characteristic, complemented
11C2×#65222C211yesmaximal, characteristic, complemented
12#10607580C2116yesmaximal, direct product factor
13C2×#64954C211yesmaximal, characteristic, complemented
14C2×#64953C211yesmaximal, characteristic, complemented
15C2×D5×#95C211yesmaximal, characteristic, complemented
16C2×#64948C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C2×#4030—28no—
41C2×#4030C2218yes—
42C2×C4×D20—28no—
43C2×C4×D20C2218yescomplemented
44C5×#388C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65282C2218yescomplemented
58#65278C2218yescomplemented
59#65248C2218yescomplemented
60#65245C2218yescomplemented
61#65245C2218yescomplemented
62#65245C2218yescomplemented
63#65242C2218yescomplemented
64#65222C2218yescomplemented
65#64954C2218yescomplemented
66#64953C2218yescomplemented
67D5×#95C2218yescomplemented
68#64948C2218yescomplemented
69C2×#2444—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—42no—
85C22×C22⋊D5C2314yes—
86C22×C22⋊D5C2314yes—
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×D20—24no—
94C22×D20—24no—
95C22×D20D418yes—
96C22×D20C2314yes—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—42no—
105C22×C4×D5—42no—
106C22×C4×D5—42no—
107C22×C4×D5—42no—
108C22×C4×D5—42no—
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C22×C4×D5C2314yes—
112C22×C4×D5C2314yes—
113C2×C5×C4⋊C4—42no—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4—24no—
117C2×C5×C22⋊C4—42no—
118C2×C5×C22⋊C4C2314yes—
119C2×C5×C22⋊C4C2314yes—
120C2×C5×C22⋊C4C2314yes—
121C2×C42×C5—24no—
122C2×C42×C5C2314yes—
123C2×C22⋊Dic5—42no—
124C2×C22⋊Dic5—42no—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—42no—
132C2×#685—42no—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5C2314yes—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683C2314yes—
144C2×#683C2314yes—
145#4030—232no—
146C4×D20—232no—
147C5×#95C2314yes—
148C5×#95C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#121—51no—
160C22×C4×D4—51no—
161#2444—516no—
162C2×#400—51no—
163C2×#397—51no—
164C2×#397—51no—
165C2×#394—51no—
166C2×#388D511yescharacteristic, complemented
167C2×#387—51no—
168C2×#386—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#385—51no—
173C2×#381—51no—
174C22×#95—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5C2×D414yes—
195C23×D5C2×D414yes—
196C23×D5#4114yes—
197C23×D5#4114yes—
198C23×D5C2412yes—
199C23×D5C2412yes—
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×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5C2×D414yes—
217C22×C4×C5#4114yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—28no—
226C2×C22⋊D5—28no—
227C2×C22⋊D5—28no—
228C2×C22⋊D5—28no—
229C2×C22⋊D5—44no—
230C2×C22⋊D5—416no—
231C2×C22⋊D5—416no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5#4114yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—232no—
257C2×D20—28no—
258C2×D20—28no—
259C2×D20C2×D4116yes—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—28no—
263C2×C4×D5—28no—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—28no—
267C2×C4×D5—44no—
268C2×C4×D5—44no—
269C2×C4×D5—44no—
270C2×C4×D5—44no—
271C2×C4×D5—44no—
272C2×C4×D5—416no—
273C2×C4×D5—416no—
274C2×C4×D5—416no—
275C2×C4×D5—416no—
276C5×C4⋊C4—44no—
277C5×C22⋊C4—28no—
278C5×C22⋊C4—28no—
279C5×C22⋊C4—44no—
280C42×C5—28no—
281C22⋊Dic5—44no—
282C22⋊Dic5—44no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685—28no—
287#685—44no—
288#685—44no—
289C4⋊Dic5—28no—
290#683—28no—
291#683—28no—
292C23×D4—51no—
293C23×D4—51no—
294C23×D4—51no—
295C24×C4—51no—
296C24×C4—51no—
297C24×C4—51no—
298C24×C4—51no—
299C2×#121—58no—
300C2×#121—108no—
301C2×C4×D4—58no—
302C2×C4×D4—108no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4C2×D511yescharacteristic
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42C2×D511yescharacteristic
319#400—58no—
320#397—58no—
321#397—58no—
322#394—58no—
323#388C2×D518yescomplemented
324#387—58no—
325#386—58no—
326#386—58no—
327#386—58no—
328#386—58no—
329#385—58no—
330#381—58no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—58no—
342C2×#95C2×D511yescharacteristic
343C2×#95C2×D511yescharacteristic
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—44no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5C22×D412yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4112yes—
361C23×C5C2×#4112yes—
362C23×C5C2×#4112yes—
363C23×C5H(5,𝔽2)12yes—
364C23×C5H(5,𝔽2)12yes—
365C23×C5C2511yescharacteristic
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—28no—
377C22×D5—28no—
378C22×D5—28no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5#123116yes—
390C22×D5C22×D414yes—
391C22×D5C22×D414yes—
392C22×D5C2×#4114yes—
393C22×D5C2×#4114yes—
394C2×C4×C5—28no—
395C2×C4×C5—28no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5—44no—
415C2×C4×C5—44no—
416C2×C4×C5C22×D414yes—
417C2×C4×C5C2×#4114yes—
418C22⋊D5—416no—
419C22⋊D5—416no—
420C2×Dic5—28no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C2×#4114yes—
444D20—232no—
445C4×D5—416no—
446C4×D5—416no—
447C4×D5—416no—
448C4×D5—416no—
449C25—51no—
450C25—51no—
451C25C22×D511yescharacteristic
452C22×D4—54no—
453C22×D4—54no—
454C22×D4—58no—
455C22×D4—54no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—104no—
461C22×D4—104no—
462C22×D4—104no—
463C22×D4—202no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—54no—
471C23×C4—54no—
472C23×C4—54no—
473C23×C4—54no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—104no—
478C23×C4—104no—
479C23×C4—104no—
480C23×C4—104no—
481C23×C4—202no—
482C23×C4—202no—
483C23×C4—202no—
484C23×C4—202no—
485C23×C4—202no—
486C23×C4C22×D511yescharacteristic
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D511yescharacteristic
491C23×C4C22×D511yescharacteristic
492#121—1032no—
493C4×D4—1032no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—54no—
498C2×C4⋊C4—104no—
499C2×C4⋊C4—104no—
500C2×C4⋊C4—104no—
501C2×C4⋊C4C22×D514yes—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—54no—
509C2×C22⋊C4—54no—
510C2×C22⋊C4—54no—
511C2×C22⋊C4—54no—
512C2×C22⋊C4—54no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4—202no—
520C2×C22⋊C4—202no—
521C2×C22⋊C4C22×D514yes—
522C2×C22⋊C4C22×D514yes—
523C2×C22⋊C4C22×D514yes—
524C2×C42—24no—
525C2×C42C22×D514yes—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95—54no—
536#95C22×D514yes—
537#95C22×D514yes—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—88no—
546C22×C5C2×#12314yes—
547C22×C5#52914yes—
548C22×C5#53814yes—
549C22×C5#54614yes—
550C22×C5#54614yes—
551C22×C5#55314yes—
552C22×C5#55314yes—
553C22×C5C23×D411yescharacteristic
554C22×C5C22×#4111yescharacteristic
555C22×C5C22×#4111yescharacteristic
556C22×C5C22×#4111yescharacteristic
557C22×C5C22×#4111yescharacteristic
558C22×C5C2×H(5,𝔽2)11yescharacteristic
559C22×C5C2×H(5,𝔽2)11yescharacteristic
560C2×D5—24no—
561C2×D5—24no—
562C2×D5—24no—
563C2×D5—24no—
564C2×D5—232no—
565C2×D5—24no—
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—24no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—416no—
573C2×D5—42no—
574C2×D5—42no—
575C2×D5C2×#12318yes—
576C4×C5—24no—
577C4×C5—24no—
578C4×C5—42no—
579C4×C5—42no—
580C4×C5—42no—
581C4×C5—42no—
582Dic5—24no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
586Dic5—42no—
587Dic5—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—54no—
596C24—54no—
597C24—54no—
598C24—52no—
599C24—54no—
600C24—52no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24—102no—
609C24—102no—
610C24—102no—
611C24C23×D512yes—
612C24C23×D511yescharacteristic
613C2×D4—516no—
614C2×D4—1032no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—108no—
618C2×D4—108no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—108no—
622C2×D4—204no—
623C2×D4—2016no—
624C2×D4—2016no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—54no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—108no—
649C22×C4—108no—
650C22×C4—108no—
651C22×C4—108no—
652C22×C4—108no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—108no—
671C22×C4—108no—
672C22×C4—204no—
673C22×C4—204no—
674C22×C4—204no—
675C22×C4—204no—
676C22×C4—204no—
677C22×C4—2016no—
678C22×C4—2016no—
679C22×C4—2016no—
680C22×C4—2016no—
681C22×C4#70914yes—
682C22×C4D4×D514yes—
683C22×C4C23×D512yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—44no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—108no—
693C22⋊C4—28no—
694C22⋊C4—28no—
695C22⋊C4—44no—
696C22⋊C4—108no—
697C22⋊C4—108no—
698C22⋊C4—108no—
699C22⋊C4—108no—
700C22⋊C4—204no—
701C22⋊C4—204no—
702C22⋊C4—204no—
703C22⋊C4—204no—
704C42—28no—
705C2×C5—82no—
706C2×C5#244418yescomplemented
707C2×C5C22×#12311yescharacteristic
708C2×C5C2×#52911yescharacteristic
709C2×C5C2×#53811yescharacteristic
710C2×C5C2×#54611yescharacteristic
711C2×C5C2×#54611yescharacteristic
712C2×C5C2×#55311yescharacteristic
713C2×C5C2×#55311yescharacteristic
714D5—28no—
715D5—44no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—516no—
731C23—54no—
732C23—54no—
733C23—54no—
734C23—54no—
735C23—108no—
736C23—108no—
737C23—108no—
738C23—108no—
739C23—108no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—108no—
745C23—108no—
746C23—108no—
747C23—108no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23—102no—
754C23—204no—
755C23—204no—
756C23—204no—
757C23—204no—
758C23C2×#70912yes—
759C23C2×D4×D512yes—
760C23#414412yes—
761C23D5×#4112yes—
762C23D5×#4112yes—
763C23D5×#4112yes—
764C23#414912yes—
765C23C24×D511yescharacteristic
766D4—1032no—
767D4—2016no—
768D4—2016no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—54no—
792C2×C4—108no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—2016no—
811C2×C4—2016no—
812C2×C4—2016no—
813C2×C4—2016no—
814C2×C4—204no—
815C2×C4—204no—
816C2×C4—204no—
817C2×C4—204no—
818C2×C4—204no—
819C2×C4C2×#70914yes—
820C2×C4C2×D4×D514yes—
821C5C2×#244411yescharacteristic, complemented, Sylow
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—58no—
830C22—88no—
831C22—104no—
832C22—104no—
833C22—104no—
834C22—104no—
835C22—104no—
836C22—1032no—
837C22—104no—
838C22—104no—
839C22—104no—
840C22—104no—
841C22—202no—
842C22—202no—
843C22—202no—
844C22—202no—
845C22—2016no—
846C22#6586214yes—
847C22#6588414yes—
848C22#6589214yes—
849C22#6594614yes—
850C22D5×#12314yes—
851C22#6601214yes—
852C22#6604314yes—
853C22C22×#70911yescharacteristic
854C22C22×D4×D511yescharacteristic
855C22C2×#414411yescharacteristic
856C22C2×D5×#4111yescharacteristic
857C22C2×D5×#4111yescharacteristic
858C22C2×D5×#4111yescharacteristic
859C22C2×#414911yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—104no—
867C4—202no—
868C4—202no—
869C4—202no—
870C4—202no—
871C4—202no—
872C2—82no—
873C2—108no—
874C2—204no—
875C2#1060758018yesdirect product factor
876C2C2×#6586211yescharacteristic
877C2C2×#6588411yescharacteristic
878C2C2×#6589211yescharacteristic
879C2C2×#6594611yescharacteristic
880C2C2×D5×#12311yescharacteristic
881C2C2×#6601211yescharacteristic
882C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#388D5
hypocenterC5C2×#2444
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D20C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65282C2semidirect
5. C2×#65278C2semidirect
6. C2×#65248C2semidirect
7. C2×#65245C2semidirect
8. C2×#65245C2semidirect
9. C2×#65245C2semidirect
10. C2×#65242C2semidirect
11. C2×#65222C2semidirect
12. #10607580C2direct (N × H)
13. C2×#64954C2semidirect
14. C2×#64953C2semidirect
15. C2×D5×#95C2semidirect
16. C2×#64948C2semidirect
43. C2×C4×D20C22semidirect
44. C5×#388C22semidirect
57. #65282C22semidirect
58. #65278C22semidirect
59. #65248C22semidirect
60. #65245C22semidirect
61. #65245C22semidirect
62. #65245C22semidirect
63. #65242C22semidirect
64. #65222C22semidirect
65. #64954C22semidirect
66. #64953C22semidirect
67. D5×#95C22semidirect
68. #64948C22semidirect
166. C2×#388D5semidirect
323. #388C2×D5semidirect
706. C2×C5#2444semidirect
821. C5C2×#2444semidirect
875. C2#10607580direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40302
C22×C4×D202
C2×C5×#3882
C2×#652822
C2×#652782
C2×#652482
C2×#652452
C2×#652422
C2×#652222
#106075802
C2×#649542
C2×#649532
C2×D5×#952
C2×#649482
C2×#24445