Finite Group Databasebeta

← C2×#10609059 #12269961

Subgroups — C2×#10609059 #12269961

Order 1280.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×#65274C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic
10C2×#65250C211yesmaximal, characteristic
11C2×#65246C211yesmaximal, characteristic
12C2×#65240C211yesmaximal, characteristic, complemented
13C2×#65240C211yesmaximal, characteristic, complemented
14#10609059C2116yesmaximal, direct product factor
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64941C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4038—28no—
45C2×#4038C2218yescomplemented
46C2×#4025—28no—
47C2×#4025C2218yescomplemented
48C5×#396C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65278C2218yescomplemented
59#65274C2218yescomplemented
60#65273C2218yescomplemented
61C4⋊C4×Dic5C2218yescomplemented
62#65250C2218yes—
63#65246C2218yes—
64#65245C2218yes—
65#65240C2218yescomplemented
66#65240C2218yescomplemented
67#64959C2218yescomplemented
68#64941C2218yescomplemented
69C2×#2601—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—42no—
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×D5C2314yes—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4—24no—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4—24no—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4C2314yes—
103C2×C5×C22⋊C4C2314yes—
104C2×C5×C22⋊C4C2314yes—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—42no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—42no—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5—24no—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—42no—
125C2×C4⋊Dic5C2314yes—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5D418yescomplemented
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143#4038—232no—
144#4025—232no—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#117—51no—
155#2601—516no—
156C2×#398—51no—
157C2×#396—51no—
158C2×#396D511yescharacteristic, complemented
159C2×#394—51no—
160C2×#390—51no—
161C2×#389—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#386—51no—
167C2×#385—51no—
168C2×C4×C4⋊C4—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×D5—22no—
183C23×D5—22no—
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×C5C2×D414yes—
202C22×C4×C5#4114yes—
203C22×C4×C5#4114yes—
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—44no—
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×Dic5C2×D414yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—232no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C5×C4⋊C4—28no—
247C5×C4⋊C4—28no—
248C5×C4⋊C4—28no—
249C5×C22⋊C4—28no—
250C5×C22⋊C4—28no—
251C5×C22⋊C4—28no—
252C22⋊Dic5—28no—
253C22⋊Dic5—28no—
254C22⋊Dic5—44no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—44no—
260C4⋊Dic5—28no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—44no—
264#683—28no—
265#683—28no—
266#683—28no—
267C4×Dic5—28no—
268C4×Dic5—44no—
269C4×Dic5—44no—
270C4×Dic5C2×D4116yescomplemented
271C23×D4—51no—
272C24×C4—51no—
273C2×#126—58no—
274C2×#126—108no—
275C2×#117—58no—
276C2×#117—108no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301C22×C42—51no—
302#398—58no—
303#396—58no—
304#396C2×D518yescomplemented
305#394—58no—
306#390—58no—
307#389—58no—
308#388—58no—
309#388—58no—
310#388—58no—
311#387—58no—
312#386—58no—
313#385—58no—
314C4×C4⋊C4—58no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95C2×D511yescharacteristic
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5C22×D412yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5H(5,𝔽2)12yes—
343C23×C52−1+412yes—
344C23×C5C2511yescharacteristic
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5C2×#4114yes—
359C2×C4×C5—28no—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
362C2×C4×C5—22no—
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—44no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5C22×D414yes—
381C2×C4×C5C2×#4114yes—
382C2×C4×C5C2×#4114yes—
383C22⋊D5—416no—
384C2×Dic5—28no—
385C2×Dic5—28no—
386C2×Dic5—28no—
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—44no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5C22×D414yes—
410C2×Dic5C22×D414yes—
411C2×Dic5C2×#4114yes—
412C4×D5—232no—
413C25—51no—
414C25C22×D511yescharacteristic
415C22×D4—54no—
416C22×D4—104no—
417C22×D4—104no—
418C22×D4—202no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—54no—
427C23×C4—104no—
428C23×C4—104no—
429C23×C4—104no—
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436#126—1032no—
437#117—1032no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—104no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—104no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—202no—
455C2×C4⋊C4C22×D514yes—
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—54no—
462C2×C22⋊C4—54no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—104no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—202no—
476C2×C22⋊C4—202no—
477C2×C22⋊C4C22×D514yes—
478C2×C22⋊C4C22×D514yes—
479C2×C22⋊C4C22×D514yes—
480C2×C42—58no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—54no—
485C2×C42—104no—
486C2×C42—202no—
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#95C22×D514yes—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—88no—
504C22×C5#52514yes—
505C22×C5#53214yes—
506C22×C5#53714yes—
507C22×C5#55114yes—
508C22×C5#55214yes—
509C22×C5#55314yes—
510C22×C5#55614yes—
511C22×C5C23×D411yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C22×#4111yescharacteristic
515C22×C5C22×#4111yescharacteristic
516C22×C5C2×H(5,𝔽2)11yescharacteristic
517C22×C5C2×2−1+411yescharacteristic
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—416no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—24no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532Dic5—24no—
533Dic5—24no—
534Dic5—24no—
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—54no—
547C24—52no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24C23×D512yes—
555C24C23×D511yescharacteristic
556C2×D4—108no—
557C2×D4—108no—
558C2×D4—204no—
559C2×D4—2016no—
560C22×C4—22no—
561C22×C4—22no—
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—22no—
574C22×C4—22no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—108no—
586C22×C4—108no—
587C22×C4—1032no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—108no—
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×C4D4×D514yes—
608C22×C4#71114yes—
609C22×C4#71114yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—108no—
622C4⋊C4—108no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C4⋊C4—204no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—204no—
636C22⋊C4—204no—
637C42—516no—
638C42—108no—
639C42—204no—
640C42—204no—
641C2×C5—82no—
642C2×C5#260118yescomplemented
643C2×C5C2×#52511yescharacteristic
644C2×C5C2×#53211yescharacteristic
645C2×C5C2×#53711yescharacteristic
646C2×C5C2×#55111yescharacteristic
647C2×C5C2×#55211yescharacteristic
648C2×C5C2×#55311yescharacteristic
649C2×C5C2×#55611yescharacteristic
650D5—44no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—54no—
666C23—108no—
667C23—108no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—108no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23C2×D4×D512yes—
680C23C2×#71112yes—
681C23C2×#71112yes—
682C23#414712yes—
683C23D5×#4112yes—
684C23D5×#4112yes—
685C23#414912yes—
686C23C24×D511yescharacteristic
687D4—2016no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—54no—
710C2×C4—54no—
711C2×C4—54no—
712C2×C4—1032no—
713C2×C4—108no—
714C2×C4—108no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—108no—
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×C4C2×D4×D514yes—
739C2×C4C2×#71114yes—
740C2×C4C2×#71114yes—
741C5C2×#260111yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—104no—
751C22—104no—
752C22—104no—
753C22—202no—
754C22—202no—
755C22—2016no—
756C22—202no—
757C22—202no—
758C22#6593014yes—
759C22#6594014yes—
760C22#6595214yes—
761C22#6596314yes—
762C22#6597314yes—
763C22#6597514yes—
764C22#6603914yes—
765C22C22×D4×D511yescharacteristic
766C22C22×#71111yescharacteristic
767C22C22×#71111yescharacteristic
768C22C2×#414711yescharacteristic
769C22C2×D5×#4111yescharacteristic
770C22C2×D5×#4111yescharacteristic
771C22C2×#414911yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—104no—
779C4—104no—
780C4—104no—
781C4—202no—
782C4—202no—
783C4—202no—
784C4—202no—
785C2—82no—
786C2—204no—
787C2#1060905918yesdirect product factor
788C2C2×#6594011yescharacteristic
789C2C2×#6593011yescharacteristic
790C2C2×#6595211yescharacteristic
791C2C2×#6597511yescharacteristic
792C2C2×#6596311yescharacteristic
793C2C2×#6597311yescharacteristic
794C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2601
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4038C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#396C2semidirect
4. C2×#65283C2semidirect
5. C2×#65278C2semidirect
6. C2×#65273C2semidirect
7. C2×#65274C2semidirect
8. C2×C4⋊C4×Dic5C2semidirect
12. C2×#65240C2semidirect
13. C2×#65240C2semidirect
14. #10609059C2direct (N × H)
15. C2×#64959C2semidirect
16. C2×#64941C2semidirect
45. C2×#4038C22semidirect
47. C2×#4025C22semidirect
48. C5×#396C22semidirect
57. #65283C22semidirect
58. #65278C22semidirect
59. #65274C22semidirect
60. #65273C22semidirect
61. C4⋊C4×Dic5C22semidirect
65. #65240C22semidirect
66. #65240C22semidirect
67. #64959C22semidirect
68. #64941C22semidirect
138. C2×C4×Dic5D4semidirect
158. C2×#396D5semidirect
270. C4×Dic5C2×D4semidirect
304. #396C2×D5semidirect
642. C2×C5#2601semidirect
741. C5C2×#2601semidirect
787. C2#10609059direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40382
C22×#40252
C2×C5×#3962
C2×#652832
C2×#652782
C2×#652732
C2×#652742
C2×C4⋊C4×Dic52
C2×#652452
C2×#652502
C2×#652462
C2×#652402
#106090592
C2×#649592
C2×#649412
C2×#26015