Finite Group Databasebeta

← C2×#10611510 #12967467

Subgroups — C2×#10611510 #12967467

Order 1280.

2550 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65912C211yesmaximal, characteristic, complemented
2C2×C4×D4×D5C211yesmaximal, characteristic
3C2×C5×#440C211yesmaximal, characteristic, complemented
4C2×#65458C211yesmaximal, characteristic
5C2×#65451C211yesmaximal, characteristic, complemented
6C2×#65315C211yesmaximal, characteristic, complemented
7C2×#65307C211yesmaximal, characteristic, complemented
8#10611510C2116yesmaximal, direct product factor
9C2×#65179C211yesmaximal, characteristic, complemented
10C2×#65173C211yesmaximal, characteristic, complemented
11C2×#65107C211yesmaximal, characteristic, complemented
12C2×#65098C211yesmaximal, characteristic, complemented
13C2×#65065C211yesmaximal, characteristic
14C2×#65048C211yesmaximal, characteristic, complemented
15C2×#64999C211yesmaximal, characteristic, complemented
16C2×#64994C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C23×C4×D5—21no—
19C22×C5×SD16C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic, complemented
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4092C2211yescharacteristic
23C2×#4090C2211yescharacteristic, complemented
24C22×#688C2211yescharacteristic
25C2×D4×Dic5C2211yescharacteristic
26C22×#687C2211yescharacteristic
27C2×C4×C22⋊D5—21no—
28C22×#677C2211yescharacteristic
29#65912—24no—
30#65912C2218yescomplemented
31C4×D4×D5—24no—
32C4×D4×D5C2218yes—
33C2×#4043C2211yescharacteristic
34C2×#4042—21no—
35C2×#4039C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×#4035—21no—
38C2×#4034C2211yescharacteristic, complemented
39C2×#4027—21no—
40C2×D5×C22⋊C4—21no—
41C2×C4×D20C2211yescharacteristic
42C2×#4018—21no—
43C2×C42×D5C2211yescharacteristic
44C2×C4×Dic10—21no—
45C2×C4×Dic10C2211yescharacteristic, complemented
46C5×#440C2218yescomplemented
47C2×C5×#107C2211yescharacteristic, complemented
48C2×C5×#103C2211yescharacteristic, complemented
49C2×C5×#102C2211yescharacteristic
50C2×C5×#97C2211yescharacteristic, complemented
51C2×#3967C2211yescharacteristic, complemented
52C2×#3964C2211yescharacteristic
53#65458C2218yes—
54#65451C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3950C2211yescharacteristic, complemented
59C2×#3948C2211yescharacteristic, complemented
60C2×#3946C2211yescharacteristic, complemented
61C2×#3946C2211yescharacteristic, complemented
62#65315C2218yescomplemented
63#65307C2218yescomplemented
64C2×#3942C2211yescharacteristic, complemented
65C2×#3941C2211yescharacteristic
66C2×#3939C2211yescharacteristic, complemented
67C2×#3939C2211yescharacteristic, complemented
68C2×#3935C2211yescharacteristic, complemented
69#65179C2218yescomplemented
70#65173C2218yescomplemented
71#65107C2218yescomplemented
72#65098C2218yescomplemented
73#65065C2218yes—
74#65048C2218yescomplemented
75#64999C2218yescomplemented
76#64994C2218yescomplemented
77C2×#3110—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C2×D4×D5—24no—
85C2×D4×D5—24no—
86C2×D4×D5—22no—
87C2×D4×D5C2314yes—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—28no—
93C22×C4×D5—48no—
94C22×C4×D5D411yescharacteristic
95C22×C4×D5D411yescharacteristic
96C22×C4×D5C2311yescharacteristic
97C22×Dic10—21no—
98C22×Dic10C2311yescharacteristic
99C2×C5×SD16—24no—
100C2×C5×SD16C2314yes—
101C22×C5×C8C2311yescharacteristic
102C22×C5×C8C2311yescharacteristic
103C4×C5×Q8—22no—
104C4×C5×Q8C2314yescomplemented
105C4×C5×D4—22no—
106C4×C5×D4C2314yes—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C22⋊C4—21no—
111C2×C42×C5—21no—
112C2×C42×C5C2311yescharacteristic
113C2×C22⋊Dic5—21no—
114#4092—22no—
115#4092C2314yes—
116#4090—22no—
117#4090C2314yescomplemented
118C2×#688—24no—
119C2×#688C2314yes—
120D4×Dic5—22no—
121D4×Dic5C2314yes—
122C2×#687—24no—
123C2×#687C2314yes—
124C4×C22⋊D5—28no—
125C2×#685—21no—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5D411yescharacteristic
140C2×C4×Dic5D411yescharacteristic
141C2×C4×Dic5C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C2×#677—24no—
145C2×#677C2314yes—
146#4043—22no—
147#4043C2314yes—
148#4042—28no—
149#4039—22no—
150#4039C2314yes—
151D5×C4⋊C4—22no—
152D5×C4⋊C4C2314yes—
153#4035—28no—
154#4034—22no—
155#4034C2314yescomplemented
156#4027—28no—
157D5×C22⋊C4—28no—
158C4×D20—22no—
159C4×D20C2314yes—
160#4018—28no—
161C42×D5D414yes—
162C42×D5C2314yes—
163C4×Dic10—22no—
164C4×Dic10—28no—
165C4×Dic10C2314yescomplemented
166C5×#107C2314yescomplemented
167C5×#103C2314yescomplemented
168C5×#102C2314yes—
169C5×#97C2314yescomplemented
170#3967C2314yescomplemented
171#3964C2314yes—
172#3953C2314yes—
173#3952C2314yes—
174#3952C2314yes—
175#3950C2314yescomplemented
176#3948C2314yescomplemented
177#3946C2314yescomplemented
178#3946C2314yescomplemented
179#3942C2314yescomplemented
180#3941C2314yes—
181#3939C2314yescomplemented
182#3939C2314yescomplemented
183#3935C2314yescomplemented
184C2×#533—51no—
185C22×C4×D4—51no—
186#3110—516no—
187C2×#484—51no—
188C2×#484—51no—
189C2×#474—51no—
190C2×#474—51no—
191C2×#461—51no—
192C2×#461—51no—
193C2×#450—51no—
194C2×#450—51no—
195C2×#440—51no—
196C2×#440—51no—
197C2×#440—51no—
198C2×#440D511yescharacteristic, complemented
199C2×#432—51no—
200C24×C5—21no—
201C23×D5—28no—
202C23×D5—21no—
203C23×D5—24no—
204C23×D5—44no—
205C23×D5—44no—
206C23×D5C2×D411yescharacteristic
207C2×C5×Q8—21no—
208C2×C5×Q8—22no—
209C2×C5×Q8—22no—
210C2×C5×Q8C2412yes—
211C2×C5×D4—21no—
212C2×C5×D4—22no—
213C2×C5×D4#4114yes—
214C2×C5×D4C2412yes—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—24no—
219C22×C4×C5—44no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2411yescharacteristic
223C2×C22⋊D5—28no—
224C2×C22⋊D5—24no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—24no—
229C22×Dic5—44no—
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232C22×Dic5C2×D411yescharacteristic
233D4×D5—216no—
234D4×D5—28no—
235D4×D5—28no—
236C2×D20—21no—
237C2×D20—22no—
238C2×D20#4114yes—
239C2×D20C2412yes—
240C2×C4×D5—24no—
241C2×C4×D5—22no—
242C2×C4×D5—22no—
243C2×C4×D5—24no—
244C2×C4×D5—24no—
245C2×C4×D5—24no—
246C2×C4×D5—24no—
247C2×C4×D5—432no—
248C2×C4×D5—44no—
249C2×C4×D5—44no—
250C2×C4×D5—44no—
251C2×C4×D5C2×D414yes—
252C2×C4×D5C2×D414yes—
253C2×C4×D5C2×D412yes—
254C2×C4×D5C2412yes—
255C2×Dic10—22no—
256C2×Dic10—22no—
257C2×Dic10—21no—
258C2×Dic10—24no—
259C2×Dic10—44no—
260C2×Dic10C2412yes—
261C5×SD16—28no—
262C2×C5×C8—22no—
263C2×C5×C8—22no—
264C2×C5×C8C2412yes—
265C2×C5×C8C2412yes—
266C5×C4⋊C4—24no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4C2412yes—
270C5×C4⋊C4C2412yes—
271C5×C22⋊C4—24no—
272C42×C5—24no—
273C42×C5C2×D412yes—
274C42×C5C2412yes—
275C22⋊Dic5—24no—
276#688—28no—
277#687—28no—
278#685—24no—
279#685—24no—
280#685—24no—
281#685—24no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—24no—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287#683—24no—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292#683—24no—
293C4×Dic5—24no—
294C4×Dic5C2×D414yes—
295C4×Dic5C2×D412yes—
296C4×Dic5C2×D414yes—
297C4×Dic5C2412yes—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168C2412yes—
301C2×#168C2412yes—
302#677—28no—
303C23×D4—51no—
304C24×C4—101no—
305C22×SD16—51no—
306C22×SD16—51no—
307C22×SD16—51no—
308C22×SD16C2×D511yescharacteristic
309#533—58no—
310#533—104no—
311C2×C4⋊Q8—51no—
312C2×C4⋊Q8—51no—
313C2×#125—101no—
314C2×C22⋊Q8—51no—
315C2×C22⋊Q8—51no—
316C2×C22⋊Q8—101no—
317C2×C4×Q8—51no—
318C2×C4×Q8—101no—
319C2×C4×Q8C2×D511yescharacteristic, complemented
320C2×C4×D4—51no—
321C2×C4×D4—58no—
322C2×C4×D4—51no—
323C2×C4×D4—51no—
324C2×C4×D4—101no—
325C2×C4×D4—104no—
326C2×C4×D4—101no—
327C2×C4×D4C2×D511yescharacteristic
328C2×#117—101no—
329C22×C4⋊C4—51no—
330C22×C22⋊C4—101no—
331C22×C42—51no—
332#484—58no—
333#484—58no—
334#474—58no—
335#474—58no—
336#461—58no—
337#461—58no—
338#450—58no—
339#450—58no—
340#440—58no—
341#440—58no—
342#440—58no—
343#440C2×D518yescomplemented
344#432—58no—
345C2×#107—51no—
346C2×#107—51no—
347C2×#107—51no—
348C2×#107C2×D511yescharacteristic, complemented
349C2×C4⋊C8—51no—
350C2×C4⋊C8—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103C2×D511yescharacteristic, complemented
355C2×#102—51no—
356C2×#102—51no—
357C2×#102—51no—
358C2×#102C2×D511yescharacteristic
359C2×C22⋊C8—51no—
360C2×C22⋊C8—51no—
361C2×#97—51no—
362C2×#97C2×D511yescharacteristic, complemented
363C23×C5—24no—
364C23×C5—22no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5C22×D411yescharacteristic
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—216no—
371C22×D5—24no—
372C22×D5—22no—
373C22×D5—48no—
374C22×D5—432no—
375C22×D5—42no—
376C22×D5—42no—
377C22×D5—48no—
378C22×D5#13714yes—
379C22×D5C22×D412yes—
380C5×Q8—22no—
381C5×Q8—22no—
382C5×Q8—42no—
383C5×D4—24no—
384C5×D4—22no—
385C5×D4C2×#4114yes—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—48no—
392C2×C4×C5—42no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5C22×D412yes—
396C2×C4×C5C22×D412yes—
397C2×C4×C5C22×D411yescharacteristic
398C2×C4×C5C2×#4112yes—
399C2×C4×C5C2×#4112yes—
400C2×C4×C5C2511yescharacteristic
401C22⋊D5—216no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—42no—
408C2×Dic5—42no—
409C2×Dic5—42no—
410C2×Dic5—48no—
411C2×Dic5AGL(1,ℤ/8)14yes—
412C2×Dic5C22×D412yes—
413C2×Dic5C22×D412yes—
414C2×Dic5C22×D412yes—
415D20—24no—
416D20—22no—
417D20C2×#4114yes—
418C4×D5—28no—
419C4×D5—24no—
420C4×D5—22no—
421C4×D5—22no—
422C4×D5—28no—
423C4×D5—48no—
424C4×D5—48no—
425C4×D5—48no—
426Dic10—22no—
427Dic10—22no—
428Dic10—42no—
429Dic10—48no—
430C5×C8—22no—
431C5×C8—22no—
432#168—22no—
433#168—22no—
434C25—101no—
435C22×Q8—51no—
436C22×Q8—101no—
437C22×Q8C22×D511yescharacteristic
438C22×D4—54no—
439C22×D4—51no—
440C22×D4—102no—
441C22×D4—101no—
442C22×D4—104no—
443C22×D4—104no—
444C22×D4C22×D511yescharacteristic
445C23×C4—21no—
446C23×C4—51no—
447C23×C4—51no—
448C23×C4—51no—
449C23×C4—101no—
450C23×C4—108no—
451C23×C4—101no—
452C23×C4—101no—
453C23×C4—101no—
454C23×C4—208no—
455C2×SD16—24no—
456C2×SD16—54no—
457C2×SD16—54no—
458C2×SD16—54no—
459C2×SD16—104no—
460C2×SD16—104no—
461C2×SD16—104no—
462C2×SD16C22×D514yes—
463C22×C8—51no—
464C22×C8—51no—
465C22×C8C22×D511yescharacteristic
466C22×C8C22×D511yescharacteristic
467C4⋊Q8—54no—
468C4⋊Q8—54no—
469C4⋊Q8—102no—
470C4⋊Q8—102no—
471#125—108no—
472C22⋊Q8—54no—
473C22⋊Q8—54no—
474C22⋊Q8—102no—
475C22⋊Q8—108no—
476C22⋊Q8—102no—
477C4×Q8—22no—
478C4×Q8—54no—
479C4×Q8—108no—
480C4×Q8—102no—
481C4×Q8C22×D514yescomplemented
482C4×D4—22no—
483C4×D4—54no—
484C4×D4—54no—
485C4×D4—54no—
486C4×D4—108no—
487C4×D4—102no—
488C4×D4—108no—
489C4×D4—102no—
490C4×D4—102no—
491C4×D4C22×D514yes—
492#117—108no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—102no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4C22×D511yescharacteristic
506C2×C4⋊C4C22×D511yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—108no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4—101no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C42—21no—
515C2×C42—51no—
516C2×C42—51no—
517C2×C42—51no—
518C2×C42—54no—
519C2×C42—54no—
520C2×C42—101no—
521C2×C42C22×D511yescharacteristic
522#107—54no—
523#107—54no—
524#107—54no—
525#107C22×D514yescomplemented
526C4⋊C8—54no—
527C4⋊C8—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#103C22×D514yescomplemented
532#102—54no—
533#102—54no—
534#102—54no—
535#102C22×D514yes—
536C22⋊C8—54no—
537C22⋊C8—54no—
538#97—54no—
539#97C22×D514yescomplemented
540C22×C5—24no—
541C22×C5—48no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5#52512yes—
545C22×C5C2×AGL(1,ℤ/8)12yes—
546C22×C5C2×#13712yes—
547C22×C5C23×D411yescharacteristic
548C2×D5—28no—
549C2×D5—22no—
550C2×D5—22no—
551C2×D5—24no—
552C2×D5—432no—
553C2×D5—48no—
554C2×D5—42no—
555C2×D5—42no—
556C2×D5C2×#13714yes—
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—42no—
560C4×C5—42no—
561C4×C5—42no—
562C4×C5#52512yes—
563C4×C5C22×#4111yescharacteristic
564C4×C5C22×#4111yescharacteristic
565Dic5—22no—
566Dic5—22no—
567Dic5—42no—
568Dic5—42no—
569Dic5—42no—
570Dic5C2×AGL(1,ℤ/8)14yes—
571C24—21no—
572C24—51no—
573C24—104no—
574C24—108no—
575C24—101no—
576C24—204no—
577C24—204no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—52no—
582C2×Q8—104no—
583C2×Q8—101no—
584C2×Q8—102no—
585C2×Q8—102no—
586C2×Q8—204no—
587C2×Q8C23×D512yes—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—54no—
591C2×D4—52no—
592C2×D4—104no—
593C2×D4—108no—
594C2×D4—1016no—
595C2×D4—108no—
596C2×D4—108no—
597C2×D4—102no—
598C2×D4—101no—
599C2×D4#70914yes—
600C2×D4C23×D512yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—44no—
606C22×C4—51no—
607C22×C4—51no—
608C22×C4—51no—
609C22×C4—54no—
610C22×C4—52no—
611C22×C4—54no—
612C22×C4—52no—
613C22×C4—104no—
614C22×C4—104no—
615C22×C4—104no—
616C22×C4—104no—
617C22×C4—104no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—104no—
624C22×C4—204no—
625C22×C4—204no—
626C22×C4—2032no—
627C22×C4—204no—
628C22×C4—204no—
629C22×C4D4×D511yescharacteristic
630C22×C4D4×D511yescharacteristic
631C22×C4C23×D511yescharacteristic
632SD16—28no—
633SD16—108no—
634SD16—108no—
635SD16—108no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—52no—
639C2×C8—52no—
640C2×C8—102no—
641C2×C8—102no—
642C2×C8C23×D512yes—
643C2×C8C23×D512yes—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—52no—
648C4⋊C4—52no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4—104no—
653C4⋊C4—104no—
654C4⋊C4—104no—
655C4⋊C4—101no—
656C4⋊C4—101no—
657C4⋊C4—104no—
658C4⋊C4C23×D512yes—
659C4⋊C4C23×D512yes—
660C22⋊C4—24no—
661C22⋊C4—104no—
662C22⋊C4—104no—
663C22⋊C4—104no—
664C22⋊C4—104no—
665C22⋊C4—104no—
666C42—24no—
667C42—54no—
668C42—54no—
669C42—52no—
670C42—52no—
671C42—104no—
672C42D4×D512yes—
673C42C23×D512yes—
674C2×C5—44no—
675C2×C5#311014yescomplemented
676C2×C5C2×#52511yescharacteristic
677C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
678C2×C5C22×#13711yescharacteristic
679D5—24no—
680D5—44no—
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—54no—
686C23—52no—
687C23—1016no—
688C23—102no—
689C23—102no—
690C23—104no—
691C23—102no—
692C23—208no—
693C23—208no—
694C23—2032no—
695C23—202no—
696C23—202no—
697C23C2×D4×D511yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—102no—
702Q8—102no—
703Q8—208no—
704Q8—202no—
705D4—24no—
706D4—22no—
707D4—54no—
708D4—1016no—
709D4—104no—
710D4—102no—
711D4C2×#70914yes—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—54no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—108no—
726C2×C4—108no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—104no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—208no—
736C2×C4—208no—
737C2×C4—208no—
738C2×C4—208no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4C2×#70912yes—
743C2×C4C2×D4×D512yes—
744C2×C4C2×D4×D512yes—
745C2×C4C2×D4×D511yescharacteristic
746C2×C4D5×#4112yes—
747C2×C4C24×D511yescharacteristic
748C8—22no—
749C8—22no—
750C8—102no—
751C8—102no—
752C5C2×#311011yescharacteristic, complemented, Sylow
753C22—24no—
754C22—48no—
755C22—42no—
756C22—42no—
757C22—54no—
758C22—108no—
759C22—102no—
760C22—102no—
761C22—104no—
762C22—2032no—
763C22—208no—
764C22—202no—
765C22—202no—
766C22#6588112yes—
767C22D5×AGL(1,ℤ/8)12yes—
768C22D5×#13712yes—
769C22C22×D4×D511yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—54no—
776C4—102no—
777C4—102no—
778C4—202no—
779C4—202no—
780C4—202no—
781C4#6588112yes—
782C4C22×#70911yescharacteristic
783C4C2×D5×#4111yescharacteristic
784C2—44no—
785C2—104no—
786C2—204no—
787C2#1061151014yesdirect product factor
788C2C2×#6588111yescharacteristic
789C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
790C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#440C2
socleC23×C5C22×D4
prime radicalC22×D4×D5C22
hypercenterC2×#440D5
hypocenterC5C2×#3110
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#65912C2semidirect
3. C2×C5×#440C2semidirect
5. C2×#65451C2semidirect
6. C2×#65315C2semidirect
7. C2×#65307C2semidirect
8. #10611510C2direct (N × H)
9. C2×#65179C2semidirect
10. C2×#65173C2semidirect
11. C2×#65107C2semidirect
12. C2×#65098C2semidirect
14. C2×#65048C2semidirect
15. C2×#64999C2semidirect
16. C2×#64994C2semidirect
20. C2×C4×C5×Q8C22semidirect
23. C2×#4090C22semidirect
30. #65912C22semidirect
38. C2×#4034C22semidirect
45. C2×C4×Dic10C22semidirect
46. C5×#440C22semidirect
47. C2×C5×#107C22semidirect
48. C2×C5×#103C22semidirect
50. C2×C5×#97C22semidirect
51. C2×#3967C22semidirect
54. #65451C22semidirect
58. C2×#3950C22semidirect
59. C2×#3948C22semidirect
60. C2×#3946C22semidirect
61. C2×#3946C22semidirect
62. #65315C22semidirect
63. #65307C22semidirect
64. C2×#3942C22semidirect
66. C2×#3939C22semidirect
67. C2×#3939C22semidirect
68. C2×#3935C22semidirect
69. #65179C22semidirect
70. #65173C22semidirect
71. #65107C22semidirect
72. #65098C22semidirect
74. #65048C22semidirect
75. #64999C22semidirect
76. #64994C22semidirect
104. C4×C5×Q8C23semidirect
117. #4090C23semidirect
155. #4034C23semidirect
165. C4×Dic10C23semidirect
166. C5×#107C23semidirect
167. C5×#103C23semidirect
169. C5×#97C23semidirect
170. #3967C23semidirect
175. #3950C23semidirect
176. #3948C23semidirect
177. #3946C23semidirect
178. #3946C23semidirect
179. #3942C23semidirect
181. #3939C23semidirect
182. #3939C23semidirect
183. #3935C23semidirect
198. C2×#440D5semidirect
319. C2×C4×Q8C2×D5semidirect
343. #440C2×D5semidirect
348. C2×#107C2×D5semidirect
354. C2×#103C2×D5semidirect
362. C2×#97C2×D5semidirect
481. C4×Q8C22×D5semidirect
525. #107C22×D5semidirect
531. #103C22×D5semidirect
539. #97C22×D5semidirect
675. C2×C5#3110semidirect
752. C5C2×#3110semidirect
787. C2#10611510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659122
C2×C4×D4×D52
C2×C5×#4402
C2×#654582
C2×#654512
C2×#653152
C2×#653072
#106115102
C2×#651792
C2×#651732
C2×#651072
C2×#650982
C2×#650652
C2×#650482
C2×#649992
C2×#649942
C2×#31105