Finite Group Databasebeta

← C2×#10605859 #12267032

Subgroups — C2×#10605859 #12267032

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×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#4030C211yesmaximal, characteristic
3C2×C5×#381C211yesmaximal, characteristic, complemented
4C2×#65502C211yesmaximal, characteristic, complemented
5C2×#65245C211yesmaximal, characteristic, complemented
6C2×#65241C211yesmaximal, characteristic, complemented
7C2×#65250C211yesmaximal, characteristic, complemented
8#10605859C2116yesmaximal, direct product factor
9C2×#64964C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic, complemented
11C2×#64954C211yesmaximal, characteristic, complemented
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×D5×#95C211yesmaximal, characteristic, complemented
14C2×#64947C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64943C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C2×C4×C22⋊D5—28no—
29C2×C4×C22⋊D5C2218yescomplemented
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4030—28no—
43C2×#4030C2218yes—
44C5×#381C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65502C2218yescomplemented
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65250C2218yescomplemented
59#65245C2218yescomplemented
60#65241C2218yescomplemented
61#64964C2218yescomplemented
62#64958C2218yescomplemented
63#64957C2218yescomplemented
64#64954C2218yescomplemented
65#64954C2218yescomplemented
66D5×#95C2218yescomplemented
67#64947C2218yescomplemented
68#64943C2218yescomplemented
69C2×#2444—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5—24no—
74C23×C4×C5—24no—
75C23×C4×C5—42no—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2314yes—
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—42no—
88C22×C22⋊D5D418yes—
89C22×C22⋊D5C2314yes—
90C22×C22⋊D5C2314yes—
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C22×D20—24no—
98C22×D20—24no—
99C22×D20—24no—
100C22×D20C2314yes—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—42no—
107C22×C4×D5—42no—
108C22×C4×D5—42no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C22×C4×D5C2314yes—
112C22×C4×D5C2314yes—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—42no—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C4×C22⋊D5—232no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—42no—
127C2×#685—42no—
128C2×#685—42no—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×C4⋊Dic5—24no—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—42no—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5C2314yes—
146#4030—232no—
147C5×#95C2314yes—
148C5×#95C2314yes—
149C5×#95C2314yes—
150C5×#95C2314yes—
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×#388—51no—
167C2×#387—51no—
168C2×#386—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#385—51no—
173C2×#381D511yescharacteristic, complemented
174C22×#95—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5C2×D414yes—
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×D5—22no—
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—28no—
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×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—44no—
220C22×C4×C5—416no—
221C22×C4×C5#4114yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—232no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—416no—
235C2×C22⋊D5C2×D4116yes—
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—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5C2×D414yes—
253C22×Dic5#4114yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×D20—28no—
261C2×D20—28no—
262C2×D20—28no—
263C2×D20—416no—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—28no—
267C2×C4×D5—28no—
268C2×C4×D5—28no—
269C2×C4×D5—44no—
270C2×C4×D5—44no—
271C2×C4×D5—44no—
272C2×C4×D5—44no—
273C2×C4×D5—416no—
274C2×C4×D5—416no—
275C2×C4×D5—416no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—44no—
278C22⋊Dic5—28no—
279C22⋊Dic5—44no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—28no—
284#685—44no—
285#685—44no—
286#685—44no—
287C4⋊Dic5—28no—
288#683—28no—
289#683—28no—
290#683—44no—
291C4×Dic5—28no—
292C23×D4—51no—
293C23×D4—51no—
294C23×D4—51no—
295C24×C4—51no—
296C24×C4—51no—
297C24×C4—51no—
298C24×C4C2×D511yescharacteristic
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⋊C4—51no—
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⋊C4—51no—
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319#400—58no—
320#397—58no—
321#397—58no—
322#394—58no—
323#388—58no—
324#387—58no—
325#386—58no—
326#386—58no—
327#386—58no—
328#386—58no—
329#385—58no—
330#381C2×D518yescomplemented
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—58no—
340C2×#95C2×D511yescharacteristic
341C2×#95C2×D511yescharacteristic
342C2×#95C2×D511yescharacteristic
343C2×#95C2×D511yescharacteristic
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5C22×D414yes—
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—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5#123116yes—
391C22×D5C22×D414yes—
392C22×D5C2×#4114yes—
393C22×D5C2×#4114yes—
394C2×C4×C5—28no—
395C2×C4×C5—22no—
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—416no—
413C2×C4×C5—44no—
414C2×C4×C5—44no—
415C2×C4×C5—44no—
416C2×C4×C5—44no—
417C2×C4×C5—44no—
418C2×C4×C5C2×#4114yes—
419C22⋊D5—232no—
420C22⋊D5—416no—
421C2×Dic5—28no—
422C2×Dic5—28no—
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—22no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C22×D414yes—
444C2×Dic5C2×#4114yes—
445D20—416no—
446C4×D5—416no—
447C4×D5—416no—
448C4×D5—416no—
449C25—51no—
450C25—51no—
451C25C22×D511yescharacteristic
452C22×D4—58no—
453C22×D4—54no—
454C22×D4—54no—
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—24no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—54no—
474C23×C4—54no—
475C23×C4—54no—
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×C4C22×D511yescharacteristic
486C23×C4C22×D511yescharacteristic
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D514yes—
491C23×C4C22×D511yescharacteristic
492#121—1032no—
493C4×D4—1032no—
494C2×C4⋊C4—54no—
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⋊C4—202no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—54no—
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—104no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4—202no—
520C2×C22⋊C4—202no—
521C2×C22⋊C4—202no—
522C2×C22⋊C4C22×D514yes—
523C2×C22⋊C4C22×D514yes—
524C2×C42—54no—
525C2×C42—104no—
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#95C22×D514yes—
535#95C22×D514yes—
536#95C22×D514yes—
537#95C22×D514yes—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—416no—
544C22×C5—42no—
545C22×C5—42no—
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—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—42no—
574C2×D5—88no—
575C2×D5C2×#12318yes—
576C4×C5—24no—
577C4×C5—42no—
578C4×C5—42no—
579C4×C5—42no—
580C4×C5—42no—
581C4×C5—42no—
582Dic5—24no—
583Dic5—24no—
584Dic5—42no—
585Dic5—42no—
586Dic5—42no—
587Dic5—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—54no—
595C24—54no—
596C24—54no—
597C24—52no—
598C24—52no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24—102no—
609C24—102no—
610C24D4×D514yes—
611C24C23×D512yes—
612C24C23×D511yescharacteristic
613C2×D4—516no—
614C2×D4—108no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—108no—
618C2×D4—1032no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—108no—
622C2×D4—2016no—
623C2×D4—204no—
624C2×D4—2016no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
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—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—44no—
645C22×C4—416no—
646C22×C4—54no—
647C22×C4—54no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—52no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—108no—
655C22×C4—108no—
656C22×C4—108no—
657C22×C4—108no—
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—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—108no—
675C22×C4—204no—
676C22×C4—204no—
677C22×C4—204no—
678C22×C4—204no—
679C22×C4—2016no—
680C22×C4—2016no—
681C22×C4—2016no—
682C22×C4#70914yes—
683C22×C4C23×D512yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—108no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—204no—
693C22⋊C4—28no—
694C22⋊C4—44no—
695C22⋊C4—108no—
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—108no—
705C2×C5—44no—
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—82no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—516no—
730C23—54no—
731C23—54no—
732C23—54no—
733C23—108no—
734C23—108no—
735C23—108no—
736C23—108no—
737C23—108no—
738C23—108no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23—204no—
754C23—204no—
755C23—204no—
756C23—204no—
757C23C2×#70912yes—
758C23C2×D4×D514yes—
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—22no—
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—416no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—54no—
794C2×C4—54no—
795C2×C4—108no—
796C2×C4—108no—
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—102no—
811C2×C4—102no—
812C2×C4—102no—
813C2×C4—2016no—
814C2×C4—2016no—
815C2×C4—2016no—
816C2×C4—204no—
817C2×C4—204no—
818C2×C4—204no—
819C2×C4—204no—
820C2×C4C2×#70914yes—
821C5C2×#244411yescharacteristic, complemented, Sylow
822C22—24no—
823C22—24no—
824C22—24no—
825C22—42no—
826C22—416no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—58no—
831C22—104no—
832C22—1032no—
833C22—104no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22—104no—
838C22—202no—
839C22—202no—
840C22—202no—
841C22—202no—
842C22—202no—
843C22—202no—
844C22—202no—
845C22—408no—
846C22#6582414yes—
847C22#6586214yes—
848C22#6586414yes—
849C22D5×#12314yes—
850C22#6598814yes—
851C22#6599114yes—
852C22#6599514yes—
853C22C22×#70911yescharacteristic
854C22C22×D4×D511yescharacteristic
855C22C2×#414411yescharacteristic
856C22C2×D5×#4111yescharacteristic
857C22C2×D5×#4111yescharacteristic
858C22C2×D5×#4111yescharacteristic
859C22C2×#414911yescharacteristic
860C4—24no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—104no—
867C4—104no—
868C4—202no—
869C4—202no—
870C4—202no—
871C4—202no—
872C2—44no—
873C2—108no—
874C2—402no—
875C2#1060585918yesdirect product factor
876C2C2×#6582411yescharacteristic
877C2C2×#6586211yescharacteristic
878C2C2×#6586411yescharacteristic
879C2C2×#6599511yescharacteristic
880C2C2×D5×#12311yescharacteristic
881C2C2×#6599111yescharacteristic
882C2C2×#6598811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#381C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#381D5
hypocenterC5C2×#2444
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D5C2semidirect
3. C2×C5×#381C2semidirect
4. C2×#65502C2semidirect
5. C2×#65245C2semidirect
6. C2×#65241C2semidirect
7. C2×#65250C2semidirect
8. #10605859C2direct (N × H)
9. C2×#64964C2semidirect
10. C2×#64954C2semidirect
11. C2×#64954C2semidirect
12. C2×#64957C2semidirect
13. C2×D5×#95C2semidirect
14. C2×#64947C2semidirect
15. C2×#64958C2semidirect
16. C2×#64943C2semidirect
29. C2×C4×C22⋊D5C22semidirect
44. C5×#381C22semidirect
49. #65502C22semidirect
58. #65250C22semidirect
59. #65245C22semidirect
60. #65241C22semidirect
61. #64964C22semidirect
62. #64958C22semidirect
63. #64957C22semidirect
64. #64954C22semidirect
65. #64954C22semidirect
66. D5×#95C22semidirect
67. #64947C22semidirect
68. #64943C22semidirect
173. C2×#381D5semidirect
330. #381C2×D5semidirect
706. C2×C5#2444semidirect
821. C5C2×#2444semidirect
875. C2#10605859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×#40302
C2×C5×#3812
C2×#655022
C2×#652452
C2×#652412
C2×#652502
#106058592
C2×#649642
C2×#649542
C2×#649572
C2×D5×#952
C2×#649472
C2×#649582
C2×#649432
C2×#24445