Finite Group Databasebeta

← C2×#10607625 #12269813

Subgroups — C2×#10607625 #12269813

Order 1280.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4030C211yesmaximal, characteristic
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65248C211yesmaximal, characteristic, complemented
6C2×#65245C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic, complemented
9C2×#65234C211yesmaximal, characteristic, complemented
10C2×#65229C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607625C2116yesmaximal, direct product factor
13C2×#64954C211yesmaximal, characteristic, complemented
14C2×#64954C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64947C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
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×D5×C4⋊C4—28no—
43C2×D5×C4⋊C4C2218yescomplemented
44C2×#4030—28no—
45C2×#4030C2218yes—
46C5×#388C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65279C2218yescomplemented
58#65250C2218yescomplemented
59#65248C2218yescomplemented
60#65245C2218yescomplemented
61#65245C2218yescomplemented
62#65234C2218yescomplemented
63#65229C2218yescomplemented
64C4×#685C2218yescomplemented
65#64954C2218yescomplemented
66#64954C2218yescomplemented
67#64949C2218yescomplemented
68#64947C2218yescomplemented
69C2×#2591—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—42no—
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×D20—24no—
96C22×D20C2314yes—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—42no—
102C22×C4×D5—42no—
103C22×C4×D5—42no—
104C22×C4×D5—42no—
105C22×C4×D5D418yes—
106C22×C4×D5C2314yes—
107C22×C4×D5C2314yes—
108C22×C4×D5C2314yes—
109C2×C5×C4⋊C4—24no—
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4—42no—
114C2×C5×C22⋊C4C2314yes—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C42×C5—42no—
118C2×C42×C5C2314yes—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—42no—
129C2×#685—42no—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5C2314yes—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×C4×Dic5—42no—
146C2×C4×Dic5C2314yes—
147D5×C4⋊C4—232no—
148#4030—232no—
149C5×#95C2314yes—
150C5×#95C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#121—51no—
160C23×C4⋊C4—51no—
161#2591—516no—
162C2×#400—51no—
163C2×#400—51no—
164C2×#394—51no—
165C2×#394—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#388D511yescharacteristic, complemented
170C2×#386—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×#386—51no—
174C2×C4×C22⋊C4—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×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—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—44no—
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×Dic5C2×D414yes—
249C22×Dic5#4114yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—28no—
257C2×D20—28no—
258C2×D20—28no—
259C2×D20—416no—
260C2×C4×D5—232no—
261C2×C4×D5—28no—
262C2×C4×D5—28no—
263C2×C4×D5—28no—
264C2×C4×D5—28no—
265C2×C4×D5—416no—
266C2×C4×D5—44no—
267C2×C4×D5—44no—
268C2×C4×D5—44no—
269C2×C4×D5—44no—
270C2×C4×D5—416no—
271C2×C4×D5C2×D4116yes—
272C5×C4⋊C4—28no—
273C5×C22⋊C4—28no—
274C5×C22⋊C4—28no—
275C5×C22⋊C4—44no—
276C42×C5—44no—
277C22⋊Dic5—28no—
278C22⋊Dic5—44no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—28no—
284#685—44no—
285#685—44no—
286C4⋊Dic5—28no—
287#683—28no—
288#683—28no—
289#683—28no—
290C4×Dic5—44no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4—51no—
294C24×C4—51no—
295C24×C4—51no—
296C24×C4—51no—
297C2×#121—58no—
298C2×#121—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—58no—
304C22×C4⋊C4—108no—
305C22×C4⋊C4C2×D511yescharacteristic
306C22×C22⋊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⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42C2×D511yescharacteristic
320#400—58no—
321#400—58no—
322#394—58no—
323#394—58no—
324#388—58no—
325#388—58no—
326#388—58no—
327#388C2×D518yescomplemented
328#386—58no—
329#386—58no—
330#386—58no—
331#386—58no—
332C4×C22⋊C4—58no—
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×#95C2×D511yescharacteristic
342C2×#95C2×D511yescharacteristic
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—44no—
351C23×C5—44no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5C22×D412yes—
358C23×C5C2×#4112yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4112yes—
361C23×C5C2×#4112yes—
362C23×C5H(5,𝔽2)12yes—
363C23×C5H(5,𝔽2)12yes—
364C23×C5C2511yescharacteristic
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—22no—
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—44no—
383C22×D5—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5#124116yes—
390C22×D5C22×D414yes—
391C22×D5C2×#4114yes—
392C22×D5C2×#4114yes—
393C2×C4×C5—28no—
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—44no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5—44no—
415C2×C4×C5C22×D414yes—
416C2×C4×C5C2×#4114yes—
417C22⋊D5—416no—
418C22⋊D5—416no—
419C2×Dic5—28no—
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—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5C22×D414yes—
442C2×Dic5C2×#4114yes—
443D20—416no—
444C4×D5—232no—
445C4×D5—416no—
446C4×D5—416no—
447C25—51no—
448C25—51no—
449C25C22×D511yescharacteristic
450C22×D4—54no—
451C22×D4—54no—
452C22×D4—54no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—202no—
461C22×D4—202no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—58no—
465C23×C4—54no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—54no—
471C23×C4—54no—
472C23×C4—104no—
473C23×C4—104no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—202no—
477C23×C4—202no—
478C23×C4—202no—
479C23×C4—202no—
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486#121—1032no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—1032no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—104no—
496C2×C4⋊C4—104no—
497C2×C4⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
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—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4C22×D514yes—
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—42no—
523C2×C42—54no—
524C2×C42—202no—
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#95C22×D514yes—
535#95C22×D514yes—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—88no—
544C22×C5#52514yes—
545C22×C5C2×#12414yes—
546C22×C5#53414yes—
547C22×C5#55314yes—
548C22×C5#55314yes—
549C22×C5#55314yes—
550C22×C5#55314yes—
551C22×C5C23×D411yescharacteristic
552C22×C5C22×#4111yescharacteristic
553C22×C5C22×#4111yescharacteristic
554C22×C5C22×#4111yescharacteristic
555C22×C5C22×#4111yescharacteristic
556C22×C5C2×H(5,𝔽2)11yescharacteristic
557C22×C5C2×H(5,𝔽2)11yescharacteristic
558C2×D5—232no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—24no—
562C2×D5—24no—
563C2×D5—24no—
564C2×D5—24no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—88no—
573C2×D5C2×#12418yes—
574C4×C5—24no—
575C4×C5—24no—
576C4×C5—42no—
577C4×C5—42no—
578C4×C5—42no—
579C4×C5—42no—
580Dic5—24no—
581Dic5—24no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—54no—
594C24—54no—
595C24—54no—
596C24—52no—
597C24—52no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24—102no—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—108no—
612C2×D4—108no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—108no—
618C2×D4—2016no—
619C2×D4—204no—
620C2×D4—204no—
621C2×D4—2016no—
622C2×D4—2016no—
623C22×C4—22no—
624C22×C4—22no—
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—54no—
640C22×C4—54no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—516no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—108no—
649C22×C4—108no—
650C22×C4—1032no—
651C22×C4—108no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—108no—
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—2016no—
670C22×C4—204no—
671C22×C4—204no—
672C22×C4—204no—
673C22×C4—204no—
674C22×C4—2016no—
675C22×C4#70914yes—
676C22×C4D4×D514yes—
677C22×C4C23×D512yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—28no—
684C4⋊C4—108no—
685C4⋊C4—108no—
686C4⋊C4—108no—
687C4⋊C4—108no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—44no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—108no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4—204no—
700C42—44no—
701C42—204no—
702C2×C5—82no—
703C2×C5#259118yescomplemented
704C2×C5C2×#52511yescharacteristic
705C2×C5C22×#12411yescharacteristic
706C2×C5C2×#53411yescharacteristic
707C2×C5C2×#55311yescharacteristic
708C2×C5C2×#55311yescharacteristic
709C2×C5C2×#55311yescharacteristic
710C2×C5C2×#55311yescharacteristic
711D5—28no—
712D5—82no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—516no—
728C23—54no—
729C23—54no—
730C23—54no—
731C23—108no—
732C23—108no—
733C23—108no—
734C23—108no—
735C23—108no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—108no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—204no—
749C23—204no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23—204no—
754C23—204no—
755C23C2×#70912yes—
756C23C2×D4×D512yes—
757C23#414412yes—
758C23D5×#4112yes—
759C23D5×#4112yes—
760C23D5×#4112yes—
761C23#414912yes—
762C23C24×D511yescharacteristic
763D4—2016no—
764D4—2016no—
765D4—2016no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
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—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—54no—
789C2×C4—54no—
790C2×C4—1032no—
791C2×C4—108no—
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—2016no—
810C2×C4—2016no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4C2×#70914yes—
816C2×C4C2×D4×D514yes—
817C5C2×#259111yescharacteristic, complemented, Sylow
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—58no—
826C22—88no—
827C22—1032no—
828C22—104no—
829C22—104no—
830C22—104no—
831C22—104no—
832C22—104no—
833C22—104no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—202no—
838C22—202no—
839C22—202no—
840C22—202no—
841C22—408no—
842C22#6586414yes—
843C22#6588114yes—
844C22#6589214yes—
845C22#6593914yes—
846C22#6599514yes—
847C22D5×#12414yes—
848C22#6604314yes—
849C22C22×#70911yescharacteristic
850C22C22×D4×D511yescharacteristic
851C22C2×#414411yescharacteristic
852C22C2×D5×#4111yescharacteristic
853C22C2×D5×#4111yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×#414911yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—104no—
863C4—104no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—82no—
869C2—108no—
870C2—402no—
871C2#1060762518yesdirect product factor
872C2C2×#6586411yescharacteristic
873C2C2×#6588111yescharacteristic
874C2C2×#6589211yescharacteristic
875C2C2×#6593911yescharacteristic
876C2C2×#6599511yescharacteristic
877C2C2×D5×#12411yescharacteristic
878C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#388D5
hypocenterC5C2×#2591
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65279C2semidirect
5. C2×#65248C2semidirect
6. C2×#65245C2semidirect
7. C2×#65245C2semidirect
8. C2×#65250C2semidirect
9. C2×#65234C2semidirect
10. C2×#65229C2semidirect
11. C2×C4×#685C2semidirect
12. #10607625C2direct (N × H)
13. C2×#64954C2semidirect
14. C2×#64954C2semidirect
15. C2×#64949C2semidirect
16. C2×#64947C2semidirect
43. C2×D5×C4⋊C4C22semidirect
46. C5×#388C22semidirect
57. #65279C22semidirect
58. #65250C22semidirect
59. #65248C22semidirect
60. #65245C22semidirect
61. #65245C22semidirect
62. #65234C22semidirect
63. #65229C22semidirect
64. C4×#685C22semidirect
65. #64954C22semidirect
66. #64954C22semidirect
67. #64949C22semidirect
68. #64947C22semidirect
169. C2×#388D5semidirect
327. #388C2×D5semidirect
703. C2×C5#2591semidirect
817. C5C2×#2591semidirect
871. C2#10607625direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C22×#40302
C2×C5×#3882
C2×#652792
C2×#652482
C2×#652452
C2×#652502
C2×#652342
C2×#652292
C2×C4×#6852
#106076252
C2×#649542
C2×#649492
C2×#649472
C2×#25915