Finite Group Databasebeta

← C2×#10614097 #12266954

Subgroups — C2×#10614097 #12266954

Order 1280.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic
2C22×#4035C211yesmaximal, characteristic, complemented
3C2×#65511C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic
5C2×#65499C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7C2×#65501C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#10614097C2116yesmaximal, direct product factor
10C2×#65270C211yesmaximal, characteristic, complemented
11C2×#65242C211yesmaximal, characteristic, complemented
12C2×#65237C211yesmaximal, characteristic, complemented
13C2×#65234C211yesmaximal, characteristic, complemented
14C2×#65233C211yesmaximal, characteristic, complemented
15C2×#65222C211yesmaximal, characteristic, complemented
16C2×#65222C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C2×C4×C5×D4—28no—
21C2×C4×C5×D4C2218yes—
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4035—28no—
45C2×#4035C2218yescomplemented
46#65511C2218yes—
47#65511C2218yes—
48#65501C2218yescomplemented
49#65499C2218yescomplemented
50#65499C2218yescomplemented
51C4×C22⋊Dic5C2218yescomplemented
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65270C2218yescomplemented
63#65242C2218yescomplemented
64#65237C2218yescomplemented
65#65234C2218yescomplemented
66#65233C2218yescomplemented
67#65222C2218yescomplemented
68#65222C2218yescomplemented
69C2×#2460—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C22×C5×D4—24no—
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4C2314yes—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—24no—
80C23×C4×C5—42no—
81C23×C4×C5—42no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2314yes—
84C23×C4×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C4×C5×D4—232no—
98C2×C5×C4⋊C4D418yes—
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C22⋊C4—24no—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4C2314yes—
103C2×C5×C22⋊C4C2314yes—
104C2×C42×C5—24no—
105C2×C42×C5C2314yes—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5—24no—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—42no—
113C2×C22⋊Dic5—42no—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C4⋊Dic5—24no—
123C2×C4⋊Dic5—42no—
124C2×C4⋊Dic5C2314yes—
125C2×C4⋊Dic5C2314yes—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—42no—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142#4035—232no—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#125—51no—
154C22×C4×D4D511yescharacteristic
155#2460—516no—
156C2×#397—51no—
157C2×#396—51no—
158C2×#394—51no—
159C2×#394—51no—
160C2×#388—51no—
161C2×#388—51no—
162C2×#387—51no—
163C2×#387—51no—
164C2×#387—51no—
165C2×#385—51no—
166C2×#385—51no—
167C2×#380—51no—
168C2×C4×C22⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5#4114yes—
182C24×C5#4114yes—
183C24×C5C2412yes—
184C24×C5C2412yes—
185C24×C5C2411yescharacteristic
186C2×C5×D4—232no—
187C2×C5×D4—28no—
188C2×C5×D4—28no—
189C2×C5×D4—28no—
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—28no—
202C22×C4×C5—28no—
203C22×C4×C5—28no—
204C22×C4×C5—28no—
205C22×C4×C5—44no—
206C22×C4×C5—44no—
207C22×C4×C5—416no—
208C22×C4×C5—416no—
209C22×C4×C5C2×D414yes—
210C22×C4×C5C2×D414yes—
211C22×C4×C5C2×D414yes—
212C22×C4×C5#4114yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
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×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5#4114yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C5×C4⋊C4C2×D4116yes—
251C5×C22⋊C4—28no—
252C5×C22⋊C4—28no—
253C42×C5—28no—
254C22⋊Dic5—28no—
255C22⋊Dic5—28no—
256C22⋊Dic5—28no—
257C22⋊Dic5—28no—
258C22⋊Dic5—28no—
259C22⋊Dic5—28no—
260C22⋊Dic5—44no—
261C22⋊Dic5—44no—
262C4⋊Dic5—28no—
263C4⋊Dic5—44no—
264#683—28no—
265#683—28no—
266#683—28no—
267#683—28no—
268#683—28no—
269#683—28no—
270C4×Dic5—28no—
271C4×Dic5—44no—
272C23×D4C2×D511yescharacteristic
273C24×C4C2×D511yescharacteristic
274C24×C4C2×D511yescharacteristic
275C2×#125—58no—
276C2×#125—108no—
277C2×C4×D4—28no—
278C2×C4×D4C2×D518yes—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
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⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300C22×C42C2×D511yescharacteristic
301#397—58no—
302#396—58no—
303#394—58no—
304#394—58no—
305#388—58no—
306#388—58no—
307#387—58no—
308#387—58no—
309#387—58no—
310#385—58no—
311#385—58no—
312#380—58no—
313C4×C22⋊C4—58no—
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—51no—
324C23×C5—28no—
325C23×C5—28no—
326C23×C5—28no—
327C23×C5—28no—
328C23×C5—28no—
329C23×C5—28no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—44no—
345C23×C5—44no—
346C23×C5—44no—
347C23×C5—44no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5C22×D412yes—
351C23×C5C2×#4114yes—
352C23×C5C2×#4114yes—
353C23×C5C2×#4112yes—
354C23×C5C2×#4112yes—
355C23×C5C2×#4112yes—
356C23×C5C2×#4112yes—
357C23×C5H(5,𝔽2)12yes—
358C23×C52−1+412yes—
359C23×C5C2511yescharacteristic
360C5×D4—232no—
361C2×C4×C5—28no—
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—416no—
377C2×C4×C5—416no—
378C2×C4×C5—44no—
379C2×C4×C5C22×D414yes—
380C2×C4×C5C22×D414yes—
381C2×C4×C5C22×D414yes—
382C2×C4×C5C2×#4114yes—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
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—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5—44no—
414C2×Dic5C2×#4114yes—
415C25C22×D511yescharacteristic
416C25C22×D511yescharacteristic
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—24no—
420C22×D4C22×D514yes—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D514yes—
437C23×C4C22×D514yes—
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#125—1032no—
443C4×D4—232no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—104no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—202no—
460C2×C4⋊C4C22⋊D518yes—
461C2×C4⋊C4C22×D514yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—202no—
479C2×C22⋊C4—202no—
480C2×C22⋊C4C22×D514yes—
481C2×C22⋊C4C22×D514yes—
482C2×C42—24no—
483C2×C42—54no—
484C2×C42—54no—
485C2×C42—104no—
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—
498C22×C5—24no—
499C22×C5—24no—
500C22×C5—24no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5—24no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—42no—
508C22×C5—42no—
509C22×C5—42no—
510C22×C5—42no—
511C22×C5—42no—
512C22×C5—416no—
513C22×C5—416no—
514C22×C5#52514yes—
515C22×C5#52914yes—
516C22×C5#53914yes—
517C22×C5#54614yes—
518C22×C5#54814yes—
519C22×C5#55214yes—
520C22×C5#55314yes—
521C22×C5C23×D411yescharacteristic
522C22×C5C22×#4111yescharacteristic
523C22×C5C22×#4111yescharacteristic
524C22×C5C22×#4111yescharacteristic
525C22×C5C22×#4111yescharacteristic
526C22×C5C2×H(5,𝔽2)11yescharacteristic
527C22×C5C2×2−1+411yescharacteristic
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—42no—
533Dic5—24no—
534Dic5—42no—
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24#70914yes—
554C24#70914yes—
555C24C23×D512yes—
556C24C23×D512yes—
557C24C23×D511yescharacteristic
558C2×D4—232no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—416no—
580C22×C4—416no—
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
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#71114yes—
614C22×C4C2×C22⋊D514yes—
615C22×C4C2×C22⋊D514yes—
616C22×C4C2×C22⋊D514yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—108no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C4⋊C4—204no—
630C4⋊C4C2×C22⋊D5116yes—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—204no—
640C22⋊C4—204no—
641C42—28no—
642C42—108no—
643C42—204no—
644C2×C5—44no—
645C2×C5—44no—
646C2×C5#246018yescomplemented
647C2×C5C2×#52511yescharacteristic
648C2×C5C2×#52911yescharacteristic
649C2×C5C2×#53911yescharacteristic
650C2×C5C2×#54611yescharacteristic
651C2×C5C2×#54811yescharacteristic
652C2×C5C2×#55211yescharacteristic
653C2×C5C2×#55311yescharacteristic
654C23—28no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23C2×#70914yes—
681C23C2×#70914yes—
682C23C2×#70912yes—
683C23C2×#70912yes—
684C23C2×#71112yes—
685C23#414412yes—
686C23D5×#4112yes—
687C23#415012yes—
688C23C22×C22⋊D512yes—
689C23C24×D511yescharacteristic
690D4—232no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—416no—
707C2×C4—416no—
708C2×C4—44no—
709C2×C4—54no—
710C2×C4—108no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
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—204no—
735C2×C4—204no—
736C2×C4—204no—
737C2×C4—204no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4C2×#71114yes—
742C2×C4C22×C22⋊D514yes—
743C2×C4C22×C22⋊D514yes—
744C2×C4C22×C22⋊D514yes—
745C5C2×#246011yescharacteristic, complemented, Sylow
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—416no—
759C22—416no—
760C22—42no—
761C22—42no—
762C22#6587214yes—
763C22#6587414yes—
764C22#6587514yes—
765C22#6589814yes—
766C22#6612514yes—
767C22#6614014yes—
768C22#6616514yes—
769C22C22×#70911yescharacteristic
770C22C22×#70911yescharacteristic
771C22C22×#71111yescharacteristic
772C22C2×#414411yescharacteristic
773C22C2×D5×#4111yescharacteristic
774C22C2×#415011yescharacteristic
775C22C23×C22⋊D511yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—104no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—44no—
790C2—44no—
791C2#1061409718yesdirect product factor
792C2C2×#6587211yescharacteristic
793C2C2×#6589811yescharacteristic
794C2C2×#6587511yescharacteristic
795C2C2×#6587411yescharacteristic
796C2C2×#6612511yescharacteristic
797C2C2×#6614011yescharacteristic
798C2C2×#6616511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C4×C5×D4C2
socleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC22×C4×D4D5
hypocenterC5C2×#2460
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#4035C2semidirect
5. C2×#65499C2semidirect
6. C2×#65499C2semidirect
7. C2×#65501C2semidirect
8. C2×C4×C22⋊Dic5C2semidirect
9. #10614097C2direct (N × H)
10. C2×#65270C2semidirect
11. C2×#65242C2semidirect
12. C2×#65237C2semidirect
13. C2×#65234C2semidirect
14. C2×#65233C2semidirect
15. C2×#65222C2semidirect
16. C2×#65222C2semidirect
45. C2×#4035C22semidirect
48. #65501C22semidirect
49. #65499C22semidirect
50. #65499C22semidirect
51. C4×C22⋊Dic5C22semidirect
62. #65270C22semidirect
63. #65242C22semidirect
64. #65237C22semidirect
65. #65234C22semidirect
66. #65233C22semidirect
67. #65222C22semidirect
68. #65222C22semidirect
646. C2×C5#2460semidirect
745. C5C2×#2460semidirect
791. C2#10614097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C22×#40352
C2×#655112
C2×#654992
C2×#655012
C2×C4×C22⋊Dic52
#106140972
C2×#652702
C2×#652422
C2×#652372
C2×#652342
C2×#652332
C2×#652222
C2×#24605