Finite Group Databasebeta

← C2×#10612128 #12975849

Subgroups — C2×#10612128 #12975849

Order 1280.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66051C211yesmaximal, characteristic
2C2×#65915C211yesmaximal, characteristic, complemented
3C2×C5×#460C211yesmaximal, characteristic, complemented
4C2×#65463C211yesmaximal, characteristic, complemented
5C2×#65460C211yesmaximal, characteristic, complemented
6C2×#65458C211yesmaximal, characteristic, complemented
7C2×#65458C211yesmaximal, characteristic, complemented
8C2×#65360C211yesmaximal, characteristic, complemented
9C2×#65315C211yesmaximal, characteristic, complemented
10#10612128C2116yesmaximal, direct product factor
11C2×#65136C211yesmaximal, characteristic, complemented
12C2×#65125C211yesmaximal, characteristic, complemented
13C2×#65063C211yesmaximal, characteristic, complemented
14C2×#65059C211yesmaximal, characteristic, complemented
15C2×D5×#102C211yesmaximal, characteristic, complemented
16C2×#65068C211yesmaximal, characteristic, complemented
17C22×D4×D5—21no—
18C22×D4×D5C2211yescharacteristic
19C22×D4×D5C2211yescharacteristic
20C22×C5×SD16C2211yescharacteristic, complemented
21C22×C5×SD16C2211yescharacteristic, complemented
22C2×C5×#127C2211yescharacteristic
23C2×C4×C5×Q8C2211yescharacteristic, complemented
24C2×#4092C2211yescharacteristic, complemented
25C2×#4092C2211yescharacteristic, complemented
26C22×#688C2211yescharacteristic
27C2×#4084—21no—
28C2×#4084C2211yescharacteristic
29C2×#4084C2211yescharacteristic
30C2×#4083—21no—
31C2×#4083—21no—
32C22×#676C2211yescharacteristic, complemented
33C22×C8×D5C2211yescharacteristic, complemented
34#66051—24no—
35#66051C2218yes—
36#65915—24no—
37#65915C2218yescomplemented
38C2×#4040—21no—
39C2×#4038C2211yescharacteristic, complemented
40C2×D5×C4⋊C4C2211yescharacteristic, complemented
41C2×#4035—21no—
42C2×#4022—21no—
43C2×C4×D20C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×#4018—21no—
46C2×#4016C2211yescharacteristic, complemented
47C5×#460C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×#102C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic, complemented
51C2×#3967C2211yescharacteristic, complemented
52C2×#3964C2211yescharacteristic, complemented
53C2×#3964C2211yescharacteristic, complemented
54C2×#3964C2211yescharacteristic, complemented
55C2×#3964C2211yescharacteristic, complemented
56#65463C2218yescomplemented
57#65460C2218yescomplemented
58#65458C2218yescomplemented
59#65458C2218yescomplemented
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3952C2211yescharacteristic, complemented
63C2×#3952C2211yescharacteristic, complemented
64C2×#3950C2211yescharacteristic, complemented
65C2×#3949C2211yescharacteristic, complemented
66#65360C2218yescomplemented
67#65315C2218yescomplemented
68C2×#3941C2211yescharacteristic
69C2×#3939C2211yescharacteristic, complemented
70C2×#3935C2211yescharacteristic, complemented
71#65136C2218yescomplemented
72#65125C2218yescomplemented
73#65068C2218yescomplemented
74#65063C2218yescomplemented
75#65059C2218yescomplemented
76D5×#102C2218yescomplemented
77C2×#3310—51nomaximal, Sylow
78C24×D5—21no—
79C24×D5—21no—
80C22×C5×Q8C2311yescharacteristic
81C22×C5×D4—21no—
82C22×C5×D4—21no—
83C22×C5×D4C2311yescharacteristic
84C22×C5×D4C2311yescharacteristic
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C22×C22⋊D5—21no—
88C22×C22⋊D5—21no—
89C2×D4×D5—28no—
90C2×D4×D5—24no—
91C2×D4×D5—24no—
92C2×D4×D5—22no—
93C2×D4×D5—22no—
94C2×D4×D5—42no—
95C2×D4×D5—42no—
96C2×D4×D5—48no—
97C2×D4×D5C2314yes—
98C2×D4×D5C2314yes—
99C22×D20D411yescharacteristic
100C22×D20C2311yescharacteristic
101C22×C4×D5—21no—
102C22×C4×D5—21no—
103C22×C4×D5C2311yescharacteristic
104C22×C4×D5C2311yescharacteristic
105C2×C5×SD16—42no—
106C2×C5×SD16—42no—
107C2×C5×SD16C2314yescomplemented
108C2×C5×SD16C2314yescomplemented
109C22×C5×C8C2311yescharacteristic
110C22×C5×C8C2311yescharacteristic
111C5×#127—22no—
112C5×#127C2314yes—
113C4×C5×Q8—22no—
114C4×C5×Q8C2314yescomplemented
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C42×C5—21no—
118C2×C42×C5C2311yescharacteristic
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121#4092—22no—
122#4092—22no—
123#4092C2314yescomplemented
124#4092C2314yescomplemented
125C2×#688—24no—
126C2×#688C2314yes—
127#4084—22no—
128#4084—22no—
129#4084—28no—
130#4084C2314yes—
131#4084C2314yes—
132#4083—28no—
133#4083—28no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685D411yescharacteristic
139C2×#685D411yescharacteristic
140C2×C4⋊Dic5D411yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×#683—21no—
149C2×C4×Dic5—21no—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C2×#676—42no—
153C2×#676C2314yescomplemented
154C2×C8×D5—42no—
155C2×C8×D5C2314yescomplemented
156#4040—28no—
157#4038—22no—
158#4038C2314yescomplemented
159D5×C4⋊C4—22no—
160D5×C4⋊C4C2314yescomplemented
161#4035—28no—
162#4022—28no—
163C4×D20—22no—
164C4×D20D414yes—
165C4×D20C2314yes—
166C4×D20C2314yes—
167#4018—28no—
168#4016—22no—
169#4016C2314yescomplemented
170C5×C4⋊C8C2314yescomplemented
171C5×#102C2314yescomplemented
172C5×#102C2314yescomplemented
173#3967C2314yescomplemented
174#3964C2314yescomplemented
175#3964C2314yescomplemented
176#3964C2314yescomplemented
177#3964C2314yescomplemented
178#3953C2314yes—
179#3953C2314yes—
180#3952C2314yescomplemented
181#3952C2314yescomplemented
182#3950C2314yescomplemented
183#3949C2314yescomplemented
184#3941C2314yes—
185#3939C2314yescomplemented
186#3935C2314yescomplemented
187C2×#552—51no—
188C2×D42—51no—
189#3310—516no—
190C2×#490—51no—
191C2×#482—51no—
192C2×#480—51no—
193C2×#478—51no—
194C2×#468—51no—
195C2×#465—51no—
196C2×#460D511yescharacteristic, complemented
197C2×#450—51no—
198C2×#450—51no—
199C2×#440—51no—
200C2×#435—51no—
201C2×#418—51no—
202C22×#102—51no—
203C24×C5—21no—
204C24×C5—21no—
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—24no—
208C23×D5—44no—
209C23×D5—44no—
210C23×D5—44no—
211C23×D5—44no—
212C23×D5—82no—
213C23×D5—82no—
214C23×D5C2×D411yescharacteristic
215C23×D5C2×D411yescharacteristic
216C2×C5×Q8—21no—
217C2×C5×Q8—22no—
218C2×C5×Q8—22no—
219C2×C5×Q8C2412yes—
220C2×C5×D4—21no—
221C2×C5×D4—21no—
222C2×C5×D4—24no—
223C2×C5×D4—24no—
224C2×C5×D4—22no—
225C2×C5×D4—22no—
226C2×C5×D4—22no—
227C2×C5×D4—22no—
228C2×C5×D4—44no—
229C2×C5×D4—82no—
230C2×C5×D4C2412yes—
231C2×C5×D4C2412yes—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2411yescharacteristic
237C2×C22⋊D5—24no—
238C2×C22⋊D5—24no—
239C2×C22⋊D5—24no—
240C2×C22⋊D5—24no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—44no—
243C2×C22⋊D5—44no—
244C2×C22⋊D5—44no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5C2×D411yescharacteristic
249C22×Dic5C2×D411yescharacteristic
250D4×D5—28no—
251D4×D5—28no—
252D4×D5—44no—
253D4×D5—44no—
254D4×D5—48no—
255D4×D5—48no—
256D4×D5—432no—
257C2×D20—24no—
258C2×D20—21no—
259C2×D20—22no—
260C2×D20C2×D414yes—
261C2×D20#4114yes—
262C2×D20C2412yes—
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5—22no—
266C2×C4×D5—22no—
267C2×C4×D5—24no—
268C2×C4×D5—24no—
269C2×C4×D5—44no—
270C2×C4×D5—44no—
271C2×C4×D5C2×D412yes—
272C2×C4×D5C2×D412yes—
273C2×C4×D5C2412yes—
274C2×C4×D5C2412yes—
275C5×SD16—44no—
276C5×SD16—44no—
277C2×C5×C8—22no—
278C2×C5×C8—22no—
279C2×C5×C8C2412yes—
280C2×C5×C8C2412yes—
281C5×C4⋊C4—24no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4C2412yes—
284C42×C5—24no—
285C42×C5C2×D412yes—
286C42×C5C2412yes—
287C22⋊Dic5—24no—
288C22⋊Dic5—24no—
289#688—28no—
290#685—24no—
291#685—24no—
292#685—24no—
293#685—24no—
294#685C2×D414yes—
295#685C2×D414yes—
296C4⋊Dic5—21no—
297C4⋊Dic5—21no—
298C4⋊Dic5—21no—
299C4⋊Dic5C2×D414yes—
300C4⋊Dic5C2412yes—
301C4⋊Dic5C2412yes—
302C4⋊Dic5C2412yes—
303#683—24no—
304#683—24no—
305#683—24no—
306#683—24no—
307#683—24no—
308C4×Dic5—24no—
309C2×#168—22no—
310C2×#168—22no—
311C2×#168C2412yes—
312C2×#168C2412yes—
313#676—44no—
314C8×D5—44no—
315C23×D4—51no—
316C23×D4—51no—
317C23×D4—101no—
318C22×SD16—51no—
319C22×SD16C2×D511yescharacteristic, complemented
320C22×SD16C2×D511yescharacteristic, complemented
321C22×M16—51no—
322C23×C8—51no—
323#552—58no—
324#552—104no—
325D42—58no—
326D42—104no—
327C2×#127C2×D511yescharacteristic
328C2×#126—101no—
329C2×#125—51no—
330C2×#125—101no—
331C2×#123—101no—
332C2×C22⋊Q8—51no—
333C2×C22⋊Q8—51no—
334C2×#121—51no—
335C2×#121—51no—
336C2×#121—101no—
337C2×#120—101no—
338C2×#120—101no—
339C2×C4×Q8C2×D511yescharacteristic, complemented
340C2×C4×D4—51no—
341C2×C4×D4—51no—
342C2×#117—51no—
343C2×#117—101no—
344C22×C4⋊C4—51no—
345#490—58no—
346#482—58no—
347#480—58no—
348#478—58no—
349#468—58no—
350#465—58no—
351#460C2×D518yescomplemented
352#450—58no—
353#450—58no—
354#440—58no—
355#435—58no—
356C2×#107—51no—
357C2×#107—51no—
358C2×#106—51no—
359C2×C4⋊C8C2×D511yescharacteristic, complemented
360#418—58no—
361C2×#103—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—58no—
370C2×#102C2×D511yescharacteristic, complemented
371C2×#102C2×D511yescharacteristic, complemented
372C2×C22⋊C8—51no—
373C2×C22⋊C8—51no—
374C2×#97—51no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—42no—
378C23×C5—42no—
379C23×C5—42no—
380C23×C5—42no—
381C23×C5—42no—
382C23×C5—42no—
383C23×C5C22×D411yescharacteristic
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—24no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—48no—
392C22×D5—48no—
393C22×D5—48no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—48no—
397C22×D5—84no—
398C22×D5—84no—
399C22×D5—816no—
400C22×D5—816no—
401C22×D5AGL(1,ℤ/8)14yes—
402C22×D5C22×D412yes—
403C22×D5C22×D412yes—
404C5×Q8—22no—
405C5×Q8—22no—
406C5×Q8—42no—
407C5×D4—22no—
408C5×D4—22no—
409C5×D4—22no—
410C5×D4—22no—
411C5×D4—48no—
412C5×D4—42no—
413C5×D4—42no—
414C5×D4—84no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—42no—
420C2×C4×C5—42no—
421C2×C4×C5C22×D412yes—
422C2×C4×C5C22×D412yes—
423C2×C4×C5C22×D411yescharacteristic
424C2×C4×C5C2×#4112yes—
425C2×C4×C5H(5,𝔽2)12yes—
426C2×C4×C5C2511yescharacteristic
427C22⋊D5—48no—
428C22⋊D5—48no—
429C22⋊D5—48no—
430C22⋊D5—48no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—42no—
437C2×Dic5—42no—
438C2×Dic5—42no—
439C2×Dic5C22×D412yes—
440C2×Dic5C22×D412yes—
441D20—28no—
442D20—24no—
443D20—22no—
444D20C2×#4114yes—
445C4×D5—24no—
446C4×D5—24no—
447C4×D5—22no—
448C4×D5—22no—
449C4×D5—22no—
450C4×D5—22no—
451C4×D5—48no—
452C4×D5—48no—
453C5×C8—22no—
454C5×C8—22no—
455#168—22no—
456#168—22no—
457C25—101no—
458C25—101no—
459C22×Q8C22×D511yescharacteristic
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—54no—
463C22×D4—54no—
464C22×D4—51no—
465C22×D4—51no—
466C22×D4—102no—
467C22×D4—102no—
468C22×D4—101no—
469C22×D4—101no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—108no—
473C22×D4—101no—
474C22×D4—101no—
475C22×D4—202no—
476C22×D4—202no—
477C22×D4—208no—
478C22×D4C22×D511yescharacteristic
479C22×D4C22×D511yescharacteristic
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—101no—
483C23×C4—101no—
484C2×SD16—42no—
485C2×SD16—42no—
486C2×SD16—54no—
487C2×SD16—104no—
488C2×SD16C22×D514yescomplemented
489C2×SD16C22×D514yescomplemented
490C2×M16—54no—
491C2×M16—202no—
492C22×C8—51no—
493C22×C8—51no—
494C22×C8—54no—
495C22×C8—202no—
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D511yescharacteristic
498#127—22no—
499#127C22×D514yes—
500#126—108no—
501#125—54no—
502#125—108no—
503#125—102no—
504#123—108no—
505C22⋊Q8—54no—
506C22⋊Q8—54no—
507C22⋊Q8—102no—
508C22⋊Q8—102no—
509#121—54no—
510#121—54no—
511#121—108no—
512#121—102no—
513#121—102no—
514#120—108no—
515#120—108no—
516C4×Q8—22no—
517C4×Q8C22×D514yescomplemented
518C4×D4—54no—
519C4×D4—54no—
520C4×D4—54no—
521C4×D4—102no—
522#117—54no—
523#117—108no—
524#117—102no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—54no—
531C2×C4⋊C4—102no—
532C2×C4⋊C4—101no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4—101no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4C22×D511yescharacteristic
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—101no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C42—21no—
547C2×C42—101no—
548C2×C42C22×D511yescharacteristic
549#107—54no—
550#107—54no—
551#106—54no—
552C4⋊C8C22×D514yescomplemented
553#103—54no—
554#102—54no—
555#102—54no—
556#102—54no—
557#102—54no—
558#102—54no—
559#102—54no—
560#102—54no—
561#102C22×D514yescomplemented
562#102C22×D514yescomplemented
563C22⋊C8—54no—
564C22⋊C8—54no—
565#97—54no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—84no—
573C22×C5—84no—
574C22×C5#54612yes—
575C22×C5C2×AGL(1,ℤ/8)12yes—
576C22×C5#57712yes—
577C22×C5C23×D411yescharacteristic
578C2×D5—22no—
579C2×D5—28no—
580C2×D5—22no—
581C2×D5—22no—
582C2×D5—24no—
583C2×D5—22no—
584C2×D5—22no—
585C2×D5—44no—
586C2×D5—48no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—816no—
590C2×D5—816no—
591C2×D5C2×AGL(1,ℤ/8)14yes—
592C4×C5—22no—
593C4×C5—22no—
594C4×C5—42no—
595C4×C5—42no—
596C4×C5#54612yes—
597C4×C5C22×#4111yescharacteristic
598C4×C5C2×H(5,𝔽2)11yescharacteristic
599Dic5—22no—
600Dic5—22no—
601Dic5—42no—
602Dic5—42no—
603Dic5—42no—
604C24—21no—
605C24—21no—
606C24—51no—
607C24—51no—
608C24—104no—
609C24—104no—
610C24—101no—
611C24—204no—
612C24—204no—
613C24—204no—
614C24—204no—
615C24—402no—
616C24—402no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D512yes—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—44no—
630C2×D4—54no—
631C2×D4—54no—
632C2×D4—52no—
633C2×D4—82no—
634C2×D4—104no—
635C2×D4—104no—
636C2×D4—104no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—104no—
640C2×D4—104no—
641C2×D4—101no—
642C2×D4—102no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—208no—
646C2×D4—208no—
647C2×D4—204no—
648C2×D4—204no—
649C2×D4—2032no—
650C2×D4—204no—
651C2×D4—204no—
652C2×D4C23×D512yes—
653C2×D4C23×D512yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—52no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—52no—
662C22×C4—104no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—101no—
668C22×C4—101no—
669C22×C4—101no—
670C22×C4—104no—
671C22×C4—204no—
672C22×C4—204no—
673C22×C4D4×D511yescharacteristic
674C22×C4D4×D511yescharacteristic
675C22×C4C23×D511yescharacteristic
676SD16—44no—
677SD16—44no—
678SD16—108no—
679M16—204no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—52no—
683C2×C8—52no—
684C2×C8—102no—
685C2×C8—102no—
686C2×C8—204no—
687C2×C8C23×D512yes—
688C2×C8C23×D512yes—
689C4⋊C4—24no—
690C4⋊C4—21no—
691C4⋊C4—54no—
692C4⋊C4—52no—
693C4⋊C4—52no—
694C4⋊C4—52no—
695C4⋊C4—104no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—101no—
699C4⋊C4—101no—
700C4⋊C4—101no—
701C4⋊C4—104no—
702C4⋊C4—104no—
703C4⋊C4C23×D512yes—
704C22⋊C4—54no—
705C22⋊C4—54no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C42—24no—
713C42—104no—
714C42D4×D512yes—
715C42C23×D512yes—
716C2×C5—82no—
717C2×C5—82no—
718C2×C5#331014yescomplemented
719C2×C5C2×#54611yescharacteristic
720C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
721C2×C5C2×#57711yescharacteristic
722D5—24no—
723D5—42no—
724D5—44no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—54no—
734C23—52no—
735C23—52no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—104no—
742C23—102no—
743C23—208no—
744C23—208no—
745C23—208no—
746C23—208no—
747C23—202no—
748C23—202no—
749C23—404no—
750C23—404no—
751C23—4016no—
752C23—4016no—
753C23C2×D4×D511yescharacteristic
754Q8—22no—
755Q8—22no—
756Q8—42no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—48no—
762D4—42no—
763D4—42no—
764D4—54no—
765D4—84no—
766D4—108no—
767D4—104no—
768D4—102no—
769D4—208no—
770D4—208no—
771D4—208no—
772D4—208no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—52no—
780C2×C4—52no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—104no—
784C2×C4—104no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—208no—
793C2×C4—208no—
794C2×C4—202no—
795C2×C4—202no—
796C2×C4—202no—
797C2×C4C2×D4×D512yes—
798C2×C4C2×D4×D512yes—
799C2×C4C2×D4×D511yescharacteristic
800C2×C4#414412yes—
801C2×C4D5×#4112yes—
802C2×C4C24×D511yescharacteristic
803C8—22no—
804C8—22no—
805C8—102no—
806C8—102no—
807C5C2×#331011yescharacteristic, complemented, Sylow
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—54no—
815C22—84no—
816C22—84no—
817C22—108no—
818C22—102no—
819C22—102no—
820C22—102no—
821C22—102no—
822C22—102no—
823C22—104no—
824C22—204no—
825C22—208no—
826C22—202no—
827C22—202no—
828C22—4016no—
829C22—4016no—
830C22#6594612yes—
831C22#6609612yes—
832C22D5×AGL(1,ℤ/8)12yes—
833C22C22×D4×D511yescharacteristic
834C4—22no—
835C4—22no—
836C4—42no—
837C4—42no—
838C4—102no—
839C4—102no—
840C4—202no—
841C4—202no—
842C4—202no—
843C4#6594612yes—
844C4C2×#414411yescharacteristic
845C4C2×D5×#4111yescharacteristic
846C2—82no—
847C2—82no—
848C2—104no—
849C2—202no—
850C2—204no—
851C2#1061212814yesdirect product factor
852C2C2×#6594611yescharacteristic
853C2C2×#6609611yescharacteristic
854C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#460C2
socleC23×C5C22×D4
prime radicalC2×#66051C2
hypercenterC2×#460D5
hypocenterC5C2×#3310
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×#65915C2semidirect
3. C2×C5×#460C2semidirect
4. C2×#65463C2semidirect
5. C2×#65460C2semidirect
6. C2×#65458C2semidirect
7. C2×#65458C2semidirect
8. C2×#65360C2semidirect
9. C2×#65315C2semidirect
10. #10612128C2direct (N × H)
11. C2×#65136C2semidirect
12. C2×#65125C2semidirect
13. C2×#65063C2semidirect
14. C2×#65059C2semidirect
15. C2×D5×#102C2semidirect
16. C2×#65068C2semidirect
20. C22×C5×SD16C22semidirect
21. C22×C5×SD16C22semidirect
23. C2×C4×C5×Q8C22semidirect
24. C2×#4092C22semidirect
25. C2×#4092C22semidirect
32. C22×#676C22semidirect
33. C22×C8×D5C22semidirect
37. #65915C22semidirect
39. C2×#4038C22semidirect
40. C2×D5×C4⋊C4C22semidirect
46. C2×#4016C22semidirect
47. C5×#460C22semidirect
48. C2×C5×C4⋊C8C22semidirect
49. C2×C5×#102C22semidirect
50. C2×C5×#102C22semidirect
51. C2×#3967C22semidirect
52. C2×#3964C22semidirect
53. C2×#3964C22semidirect
54. C2×#3964C22semidirect
55. C2×#3964C22semidirect
56. #65463C22semidirect
57. #65460C22semidirect
58. #65458C22semidirect
59. #65458C22semidirect
62. C2×#3952C22semidirect
63. C2×#3952C22semidirect
64. C2×#3950C22semidirect
65. C2×#3949C22semidirect
66. #65360C22semidirect
67. #65315C22semidirect
69. C2×#3939C22semidirect
70. C2×#3935C22semidirect
71. #65136C22semidirect
72. #65125C22semidirect
73. #65068C22semidirect
74. #65063C22semidirect
75. #65059C22semidirect
76. D5×#102C22semidirect
107. C2×C5×SD16C23semidirect
108. C2×C5×SD16C23semidirect
114. C4×C5×Q8C23semidirect
123. #4092C23semidirect
124. #4092C23semidirect
153. C2×#676C23semidirect
155. C2×C8×D5C23semidirect
158. #4038C23semidirect
160. D5×C4⋊C4C23semidirect
169. #4016C23semidirect
170. C5×C4⋊C8C23semidirect
171. C5×#102C23semidirect
172. C5×#102C23semidirect
173. #3967C23semidirect
174. #3964C23semidirect
175. #3964C23semidirect
176. #3964C23semidirect
177. #3964C23semidirect
180. #3952C23semidirect
181. #3952C23semidirect
182. #3950C23semidirect
183. #3949C23semidirect
185. #3939C23semidirect
186. #3935C23semidirect
196. C2×#460D5semidirect
319. C22×SD16C2×D5semidirect
320. C22×SD16C2×D5semidirect
339. C2×C4×Q8C2×D5semidirect
351. #460C2×D5semidirect
359. C2×C4⋊C8C2×D5semidirect
370. C2×#102C2×D5semidirect
371. C2×#102C2×D5semidirect
488. C2×SD16C22×D5semidirect
489. C2×SD16C22×D5semidirect
517. C4×Q8C22×D5semidirect
552. C4⋊C8C22×D5semidirect
561. #102C22×D5semidirect
562. #102C22×D5semidirect
718. C2×C5#3310semidirect
807. C5C2×#3310semidirect
851. C2#10612128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660512
C2×#659152
C2×C5×#4602
C2×#654632
C2×#654602
C2×#654582
C2×#653602
C2×#653152
#106121282
C2×#651362
C2×#651252
C2×#650632
C2×#650592
C2×D5×#1022
C2×#650682
C2×#33105