Finite Group Databasebeta

← C2×#10606147 #12267129

Subgroups — C2×#10606147 #12267129

Order 1280.

3550 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×#4070C211yesmaximal, characteristic
2C23×#683C211yesmaximal, characteristic
3C22×#4034C211yesmaximal, characteristic, complemented
4C22×#4024C211yesmaximal, characteristic
5C2×C5×#385C211yesmaximal, characteristic
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×#65268C211yesmaximal, characteristic, complemented
8C2×#65265C211yesmaximal, characteristic, complemented
9C2×#65239C211yesmaximal, characteristic
10C2×#65231C211yesmaximal, characteristic
11C2×C22⋊C4×Dic5C211yesmaximal, characteristic
12#10606147C2116yesmaximal, direct product factor
13C2×#64946C211yesmaximal, characteristic, complemented
14C2×#64945C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64936C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C2×#4070—28no—
33C2×#4070C2218yes—
34C22×#683—28no—
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2218yes—
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4034—28no—
49C2×#4034C2218yescomplemented
50C2×#4024—28no—
51C2×#4024C2218yes—
52C5×#385C2218yes—
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65273C2218yescomplemented
62#65268C2218yescomplemented
63#65265C2218yescomplemented
64#65239C2218yes—
65#65231C2218yes—
66C22⋊C4×Dic5C2218yes—
67#64946C2218yescomplemented
68#64945C2218yescomplemented
69#64936C2218yescomplemented
70#64936C2218yescomplemented
71C2×#2440—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C23×C4×C5—24no—
74C23×C4×C5—24no—
75C23×C4×C5—42no—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2314yes—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×Dic5—24no—
84C23×Dic5—24no—
85C23×Dic5—24no—
86C23×Dic5—24no—
87C23×Dic5—42no—
88C23×Dic5Q818yescomplemented
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2314yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2314yes—
98C23×Dic5C2311yescharacteristic
99C22×Dic10—24no—
100C22×Dic10—24no—
101C22×Dic10—24no—
102C22×Dic10—24no—
103C22×Dic10—42no—
104C22×Dic10—42no—
105C22×Dic10C2314yes—
106C22×Dic10C2314yes—
107C2×C5×C4⋊C4—24no—
108C2×C5×C4⋊C4—42no—
109C2×C5×C4⋊C4C2314yes—
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4Q818yescomplemented
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5D418yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5—42no—
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×C4⋊Dic5C2314yes—
126C2×C4⋊Dic5C2314yes—
127#4070—232no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683—24no—
133C2×#683—24no—
134C2×#683—24no—
135C2×#683—24no—
136C2×#683—24no—
137C2×#683—232no—
138C2×#683D418yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×C4×Dic5—24no—
150C2×C4×Dic5—24no—
151C2×C4×Dic5C2314yes—
152C2×C4×Dic5C2314yes—
153#4034—232no—
154#4024—232no—
155C5×#95C2314yes—
156C5×#95C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163C22×C4⋊Q8—51no—
164C22×C22⋊Q8—51no—
165C22×C22⋊Q8—51no—
166C23×C4⋊C4—51no—
167#2440—516no—
168C2×#398—51no—
169C2×#398—51no—
170C2×#395—51no—
171C2×#395—51no—
172C2×#389—51no—
173C2×#389—51no—
174C2×#385—51no—
175C2×#385D511yescharacteristic
176C2×#384—51no—
177C2×#380—51no—
178C2×C4×C22⋊C4—51no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5C2×D414yes—
184C24×C5C2×Q814yes—
185C24×C5C2×Q814yes—
186C24×C5C2412yes—
187C24×C5C2411yescharacteristic
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—28no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—28no—
205C22×C4×C5—44no—
206C22×C4×C5—416no—
207C22×C4×C5C2×D414yes—
208C22×C4×C5C2×Q814yes—
209C22×C4×C5C2×Q814yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2412yes—
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—232no—
225C22×Dic5—28no—
226C22×Dic5—28no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—28no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—28no—
238C22×Dic5—44no—
239C22×Dic5—416no—
240C22×Dic5C2×D414yes—
241C22×Dic5C2×D414yes—
242C22×Dic5C2×D414yes—
243C22×Dic5C2×D414yes—
244C22×Dic5C2×Q814yes—
245C22×Dic5C2×Q814yes—
246C22×Dic5C2×Q8116yescomplemented
247C22×Dic5#4114yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×Dic10—28no—
257C2×Dic10—28no—
258C2×Dic10—28no—
259C2×Dic10—28no—
260C2×Dic10—44no—
261C2×Dic10—44no—
262C2×Dic10—416no—
263C2×Dic10—416no—
264C5×C4⋊C4—28no—
265C5×C4⋊C4—44no—
266C5×C22⋊C4—28no—
267C5×C22⋊C4C2×Q8116yescomplemented
268C22⋊Dic5—28no—
269C22⋊Dic5C2×D4116yes—
270C4⋊Dic5—28no—
271C4⋊Dic5—28no—
272C4⋊Dic5—28no—
273C4⋊Dic5—44no—
274#683—28no—
275#683—28no—
276#683—28no—
277#683—28no—
278#683—28no—
279#683—28no—
280#683—28no—
281#683—28no—
282#683—28no—
283#683C2×D4116yes—
284C4×Dic5—28no—
285C4×Dic5—28no—
286C23×Q8—51no—
287C23×Q8—51no—
288C24×C4—51no—
289C24×C4—51no—
290C24×C4C2×D511yescharacteristic
291C2×C4⋊Q8—58no—
292C2×C4⋊Q8—108no—
293C2×C22⋊Q8—58no—
294C2×C22⋊Q8—58no—
295C2×C22⋊Q8—108no—
296C2×C22⋊Q8—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—58no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4—51no—
307C22×C4⋊C4—51no—
308C22×C4⋊C4—51no—
309C22×C4⋊C4—51no—
310C22×C4⋊C4—51no—
311C22×C4⋊C4—51no—
312C22×C4⋊C4—108no—
313C22×C4⋊C4C2×D511yescharacteristic
314C22×C4⋊C4C2×D511yescharacteristic
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C22⋊C4C2×D511yescharacteristic
319C22×C42—51no—
320C22×C42—51no—
321#398—58no—
322#398—58no—
323#395—58no—
324#395—58no—
325#389—58no—
326#389—58no—
327#385—58no—
328#385C2×D518yes—
329#384—58no—
330#380—58no—
331C4×C22⋊C4—58no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95C2×D511yescharacteristic
339C2×#95C2×D511yescharacteristic
340C23×C5—28no—
341C23×C5—28no—
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5C4⋊Q8116yescomplemented
351C23×C5C22×D414yes—
352C23×C5C22×D412yes—
353C23×C5C22×D412yes—
354C23×C5C22×Q814yes—
355C23×C5C22×Q812yes—
356C23×C5C22×Q814yes—
357C23×C5C22×Q812yes—
358C23×C5C2×#4112yes—
359C23×C5H(5,𝔽2)12yes—
360C23×C52−1+412yes—
361C23×C5C2511yescharacteristic
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—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—416no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5C22×D414yes—
385C2×C4×C5C22×Q814yes—
386C2×C4×C5C22×Q814yes—
387C2×Dic5—28no—
388C2×Dic5—28no—
389C2×Dic5—28no—
390C2×Dic5—28no—
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—232no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—416no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5C22⋊Q8116yescomplemented
414C2×Dic5C22×D414yes—
415C2×Dic5C22×D414yes—
416C2×Dic5C22×D414yes—
417C2×Dic5C22×D414yes—
418C2×Dic5C22×Q814yes—
419C2×Dic5C22×Q814yes—
420C2×Dic5C2×#4114yes—
421Dic10—416no—
422Dic10—416no—
423C25C22×D511yescharacteristic
424C22×Q8—54no—
425C22×Q8—54no—
426C22×Q8—104no—
427C22×Q8—104no—
428C22×Q8—104no—
429C22×Q8—104no—
430C22×Q8—202no—
431C22×Q8—202no—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—42no—
435C23×C4—51no—
436C23×C4—58no—
437C23×C4—54no—
438C23×C4—51no—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4—51no—
442C23×C4—51no—
443C23×C4—51no—
444C23×C4—51no—
445C23×C4—54no—
446C23×C4—104no—
447C23×C4—104no—
448C23×C4—104no—
449C23×C4—104no—
450C23×C4—202no—
451C23×C4C22×D511yescharacteristic
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454C23×C4C22×D514yes—
455C23×C4C22×D511yescharacteristic
456C23×C4C22×D511yescharacteristic
457C23×C4C22×D511yescharacteristic
458C4⋊Q8—1032no—
459C22⋊Q8—1032no—
460C22⋊Q8—1032no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—58no—
464C2×C4⋊C4—54no—
465C2×C4⋊C4—54no—
466C2×C4⋊C4—54no—
467C2×C4⋊C4—54no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—1032no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—104no—
481C2×C4⋊C4—104no—
482C2×C4⋊C4—104no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—104no—
487C2×C4⋊C4—104no—
488C2×C4⋊C4—104no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—104no—
491C2×C4⋊C4—202no—
492C2×C4⋊C4C22×D514yes—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—58no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—104no—
499C2×C22⋊C4Dic1018yescomplemented
500C2×C22⋊C4C22×D514yes—
501C2×C22⋊C4C22×D514yes—
502C2×C42—54no—
503C2×C42—54no—
504C2×C42—104no—
505C2×C42—104no—
506#95—54no—
507#95—54no—
508#95—54no—
509#95—54no—
510#95—54no—
511#95—54no—
512#95C22×D514yes—
513#95C22×D514yes—
514C22×C5—24no—
515C22×C5—24no—
516C22×C5—24no—
517C22×C5—232no—
518C22×C5—24no—
519C22×C5—24no—
520C22×C5—24no—
521C22×C5C2×C22⋊Q814yes—
522C22×C5C2×C4⋊Q814yes—
523C22×C5C2×C4⋊Q818yescomplemented
524C22×C5#54414yes—
525C22×C5D4214yes—
526C22×C5#54714yes—
527C22×C5D4×Q814yes—
528C22×C5#55414yes—
529C22×C5C23×D411yescharacteristic
530C22×C5C23×D411yescharacteristic
531C22×C5C23×Q811yescharacteristic
532C22×C5C23×Q811yescharacteristic
533C22×C5C22×#4111yescharacteristic
534C22×C5C2×H(5,𝔽2)11yescharacteristic
535C22×C5C2×2−1+411yescharacteristic
536C4×C5—24no—
537C4×C5—24no—
538C4×C5—24no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5—42no—
542Dic5—24no—
543Dic5—24no—
544Dic5—24no—
545Dic5—24no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C2×C22⋊Q818yescomplemented
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24C2×Dic1014yes—
555C24D4×D514yes—
556C24Q8×D514yes—
557C24C23×D512yes—
558C24C23×D511yescharacteristic
559C2×Q8—108no—
560C2×Q8—108no—
561C2×Q8—108no—
562C2×Q8—108no—
563C2×Q8—204no—
564C2×Q8—204no—
565C2×Q8—2016no—
566C2×Q8—2016no—
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—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—416no—
586C22×C4—54no—
587C22×C4—54no—
588C22×C4—54no—
589C22×C4—52no—
590C22×C4—54no—
591C22×C4—54no—
592C22×C4—54no—
593C22×C4—54no—
594C22×C4—516no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—52no—
598C22×C4—52no—
599C22×C4—52no—
600C22×C4—52no—
601C22×C4—52no—
602C22×C4—108no—
603C22×C4—1032no—
604C22×C4—108no—
605C22×C4—108no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—108no—
620C22×C4—102no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—102no—
624C22×C4—204no—
625C22×C4—2016no—
626C22×C4C2×Dic1014yes—
627C22×C4C2×Dic1014yes—
628C22×C4D4×D514yes—
629C22×C4C23×D512yes—
630C22×C4C23×D512yes—
631C22×C4C23×D512yes—
632C22×C4C23×D512yes—
633C22×C4C23×D512yes—
634C22×C4C23×D512yes—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—516no—
638C4⋊C4—108no—
639C4⋊C4—108no—
640C4⋊C4—108no—
641C4⋊C4—108no—
642C4⋊C4—108no—
643C4⋊C4—108no—
644C4⋊C4—108no—
645C4⋊C4—108no—
646C4⋊C4—108no—
647C4⋊C4—108no—
648C4⋊C4—108no—
649C4⋊C4—108no—
650C4⋊C4—204no—
651C22⋊C4—28no—
652C22⋊C4—516no—
653C22⋊C4—108no—
654C22⋊C4C2×Dic10116yescomplemented
655C42—108no—
656C42—108no—
657C2×C5—28no—
658C2×C5#244018yescomplemented
659C2×C5C22×C22⋊Q811yescharacteristic
660C2×C5C22×C4⋊Q811yescharacteristic
661C2×C5C2×#54411yescharacteristic
662C2×C5C2×D4211yescharacteristic
663C2×C5C2×#54711yescharacteristic
664C2×C5C2×D4×Q811yescharacteristic
665C2×C5C2×#55411yescharacteristic
666C23—28no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23#4034116yescomplemented
677C23C22×Dic1014yes—
678C23C22×Dic1012yes—
679C23C2×D4×D514yes—
680C23C2×D4×D512yes—
681C23C2×D4×D512yes—
682C23#414412yes—
683C23C2×Q8×D514yes—
684C23C2×Q8×D512yes—
685C23D5×#4112yes—
686C23#415012yes—
687C23C24×D511yescharacteristic
688Q8—2016no—
689Q8—2016no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
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—22no—
707C2×C4—22no—
708C2×C4—416no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—516no—
713C2×C4—54no—
714C2×C4—54no—
715C2×C4—54no—
716C2×C4—54no—
717C2×C4—54no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—1032no—
721C2×C4—108no—
722C2×C4—108no—
723C2×C4—108no—
724C2×C4—108no—
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—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—2016no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4C22×Dic1014yes—
747C2×C4C22×Dic1014yes—
748C2×C4C2×D4×D514yes—
749C5C2×#244011yescharacteristic, complemented, Sylow
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—232no—
756C22—24no—
757C22C2×#403414yes—
758C22C2×#403418yescomplemented
759C22D4×Dic1014yes—
760C22#6587314yes—
761C22#6592414yes—
762C22#6595714yes—
763C22D5×C22⋊Q814yes—
764C22#6598914yes—
765C22C23×Dic1011yescharacteristic
766C22C22×D4×D511yescharacteristic
767C22C22×D4×D511yescharacteristic
768C22C2×#414411yescharacteristic
769C22C22×Q8×D511yescharacteristic
770C22C2×D5×#4111yescharacteristic
771C22C2×#415011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—58no—
779C4—104no—
780C4—104no—
781C4—104no—
782C4—104no—
783C4—202no—
784C4—202no—
785C4—202no—
786C2—28no—
787C2#1060614718yesdirect product factor
788C2C22×#403411yescharacteristic
789C2C2×D4×Dic1011yescharacteristic
790C2C2×#6587311yescharacteristic
791C2C2×#6592411yescharacteristic
792C2C2×#6595711yescharacteristic
793C2C2×D5×C22⋊Q811yescharacteristic
794C2C2×#6598911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#385D5
hypocenterC5C2×#2440
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×#4034C2semidirect
6. C2×#65273C2semidirect
7. C2×#65268C2semidirect
8. C2×#65265C2semidirect
12. #10606147C2direct (N × H)
13. C2×#64946C2semidirect
14. C2×#64945C2semidirect
15. C2×#64936C2semidirect
16. C2×#64936C2semidirect
49. C2×#4034C22semidirect
61. #65273C22semidirect
62. #65268C22semidirect
63. #65265C22semidirect
67. #64946C22semidirect
68. #64945C22semidirect
69. #64936C22semidirect
70. #64936C22semidirect
88. C23×Dic5Q8semidirect
112. C2×C5×C22⋊C4Q8semidirect
246. C22×Dic5C2×Q8semidirect
267. C5×C22⋊C4C2×Q8semidirect
350. C23×C5C4⋊Q8semidirect
413. C2×Dic5C22⋊Q8semidirect
499. C2×C22⋊C4Dic10semidirect
523. C22×C5C2×C4⋊Q8semidirect
549. Dic5C2×C22⋊Q8semidirect
654. C22⋊C4C2×Dic10semidirect
658. C2×C5#2440semidirect
676. C23#4034semidirect
749. C5C2×#2440semidirect
758. C22C2×#4034semidirect
787. C2#10606147direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40702
C23×#6832
C22×#40342
C22×#40242
C2×C5×#3852
C2×#652732
C2×#652682
C2×#652652
C2×#652392
C2×#652312
C2×C22⋊C4×Dic52
#106061472
C2×#649462
C2×#649452
C2×#649362
C2×#24405