Finite Group Databasebeta

← C2×#10611230 #12975812

Subgroups — C2×#10611230 #12975812

Order 1280.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65884C211yesmaximal, characteristic, complemented
2C2×#65889C211yesmaximal, characteristic, complemented
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65424C211yesmaximal, characteristic, complemented
5C2×#65422C211yesmaximal, characteristic, complemented
6C2×#65403C211yesmaximal, characteristic, complemented
7C22×#3953C211yesmaximal, characteristic, complemented
8#10611230C2116yesmaximal, direct product factor
9C2×#65131C211yesmaximal, characteristic, complemented
10C2×#65133C211yesmaximal, characteristic, complemented
11C2×#65023C211yesmaximal, characteristic, complemented
12C2×#65021C211yesmaximal, characteristic, complemented
13C2×#65024C211yesmaximal, characteristic, complemented
14C2×#65010C211yesmaximal, characteristic, complemented
15C2×#65003C211yesmaximal, characteristic, complemented
16C2×#65000C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×#709C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic, complemented
21C23×C5×C8C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C2×#4083—21no—
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4076C2211yescharacteristic, complemented
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic, complemented
29C2×#4070C2211yescharacteristic
30C22×D40C2211yescharacteristic
31C22×D40C2211yescharacteristic
32C22×#677C2211yescharacteristic, complemented
33#65889—24no—
34#65889C2218yescomplemented
35#65884—24no—
36#65884C2218yescomplemented
37C2×#4043—21no—
38C2×#4040—21no—
39C2×#4032—21no—
40C2×#4032—21no—
41C2×#4030—21no—
42C2×D5×C22⋊C4—21no—
43C2×#4021C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic, complemented
46C2×#4015C2211yescharacteristic, complemented
47C5×#435C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic, complemented
51C2×C5×#97C2211yescharacteristic, complemented
52#65424C2218yescomplemented
53#65422C2218yescomplemented
54#65403C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2218yescomplemented
62C2×#3953C2211yescharacteristic, complemented
63C2×#3949C2211yescharacteristic, complemented
64C2×#3949C2211yescharacteristic, complemented
65C2×#3949C2211yescharacteristic, complemented
66C2×#3948C2211yescharacteristic, complemented
67C2×#3948C2211yescharacteristic, complemented
68C2×#3948C2211yescharacteristic, complemented
69#65133C2218yescomplemented
70#65131C2218yescomplemented
71#65024C2218yescomplemented
72#65023C2218yescomplemented
73#65021C2218yescomplemented
74#65010C2218yescomplemented
75#65003C2218yescomplemented
76#65000C2218yescomplemented
77C2×#3306—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4D411yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C23×Dic5—21no—
87C23×Dic5—21no—
88C2×#711—28no—
89C2×#711—48no—
90C2×#709—22no—
91C2×#709—24no—
92C2×#709—42no—
93C2×#709C2314yes—
94C22×D20—24no—
95C22×D20—21no—
96C22×D20—22no—
97C22×D20—42no—
98C22×D20C2311yescharacteristic
99C22×D20C2311yescharacteristic
100C22×D20C2314yes—
101C22×D20C2311yescharacteristic
102C22×C4×D5—21no—
103C22×C4×D5—21no—
104C22×C4×D5—21no—
105C22×Dic10—21no—
106C22×Dic10C2311yescharacteristic
107C2×C5×M16—42no—
108C2×C5×M16C2314yescomplemented
109C22×C5×C8—42no—
110C22×C5×C8C2311yescharacteristic
111C22×C5×C8C2311yescharacteristic
112C22×C5×C8C2311yescharacteristic
113C22×C5×C8C2311yescharacteristic
114C22×C5×C8C2314yes—
115C4×C5×D4D414yes—
116C4×C5×D4C2314yes—
117C2×C5×C4⋊C4D411yescharacteristic
118C2×C5×C22⋊C4D411yescharacteristic
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C42×C5C2311yescharacteristic
121C2×C22⋊Dic5—21no—
122#4083—28no—
123#4076—22no—
124#4076—22no—
125#4076—22no—
126#4076C2314yes—
127#4076C2314yes—
128#4076C2314yescomplemented
129C2×#685—21no—
130C2×#685—21no—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—22no—
140C2×C4⋊Dic5—22no—
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2311yescharacteristic
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2314yescomplemented
147#4070—22no—
148#4070C2314yes—
149C2×#683—21no—
150C2×D40—24no—
151C2×D40—42no—
152C2×D40C2314yes—
153C2×D40C2314yes—
154C2×#677—42no—
155C2×#677C2314yescomplemented
156#4043—28no—
157#4040—28no—
158#4032—28no—
159#4032—28no—
160#4030—28no—
161D5×C22⋊C4—28no—
162#4021—22no—
163#4021C2314yes—
164C4×D20—22no—
165C4×D20—22no—
166C4×D20C2314yes—
167C4×D20C2314yescomplemented
168#4015—22no—
169#4015C2314yescomplemented
170C5×C4⋊C8C2314yescomplemented
171C5×C22⋊C8C2314yes—
172C5×C22⋊C8C2314yescomplemented
173C5×#97C2314yescomplemented
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3953C2314yes—
180#3953C2314yescomplemented
181#3949C2314yescomplemented
182#3949C2314yescomplemented
183#3949C2314yescomplemented
184#3948C2314yescomplemented
185#3948C2314yescomplemented
186#3948C2314yescomplemented
187C2×#547—51no—
188C2×#546—51no—
189#3306—516no—
190C2×#489—51no—
191C2×#481—51no—
192C2×#483—51no—
193C2×#476—51no—
194C2×#469—51no—
195C2×#465—51no—
196C2×#463—51no—
197C2×#449—51no—
198C2×#447—51no—
199C2×#442—51no—
200C2×#435D511yescharacteristic, complemented
201C2×#417—51no—
202C22×#102—51no—
203C24×C5C2×D411yescharacteristic
204C24×C5C2×D411yescharacteristic
205C23×D5—21no—
206C23×D5—21no—
207C23×D5—21no—
208C23×D5—24no—
209C23×D5—44no—
210C23×D5—44no—
211C23×D5—82no—
212C2×C5×D4—24no—
213C2×C5×D4C2×D414yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D412yes—
223C22×C4×C5C2×D412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2411yescharacteristic
227C2×C22⋊D5—24no—
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—24no—
231C2×C22⋊D5—44no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—82no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—24no—
241C22×Dic5—24no—
242C22×Dic5—44no—
243C22×Dic5—44no—
244#711—432no—
245#709—28no—
246#709—44no—
247#709—48no—
248C2×D20—21no—
249C2×D20—22no—
250C2×D20—22no—
251C2×D20—22no—
252C2×D20—22no—
253C2×D20—22no—
254C2×D20—28no—
255C2×D20—21no—
256C2×D20—24no—
257C2×D20—21no—
258C2×D20—44no—
259C2×D20—48no—
260C2×D20—44no—
261C2×D20#4114yescomplemented
262C2×D20C2412yes—
263C2×D20C2412yes—
264C2×D20C2412yes—
265C2×C4×D5—24no—
266C2×C4×D5—24no—
267C2×C4×D5—24no—
268C2×C4×D5—44no—
269C2×C4×D5—44no—
270C2×C4×D5—82no—
271C2×Dic10—22no—
272C2×Dic10—22no—
273C2×Dic10—24no—
274C2×Dic10—21no—
275C2×Dic10—44no—
276C2×Dic10C2412yes—
277C5×M16—44no—
278C2×C5×C8—22no—
279C2×C5×C8—22no—
280C2×C5×C8—22no—
281C2×C5×C8—22no—
282C2×C5×C8—44no—
283C2×C5×C8C2412yes—
284C2×C5×C8C2412yes—
285C2×C5×C8C2412yes—
286C2×C5×C8C2412yes—
287C5×C4⋊C4C2×D414yes—
288C5×C22⋊C4C2×D414yes—
289C5×C22⋊C4C2×D414yes—
290C42×C5C2×D412yes—
291C42×C5C2412yes—
292C22⋊Dic5—24no—
293#685—24no—
294#685—24no—
295#685—24no—
296#685—24no—
297#685—24no—
298#685—24no—
299#685—24no—
300C4⋊Dic5—21no—
301C4⋊Dic5—21no—
302C4⋊Dic5—24no—
303C4⋊Dic5—21no—
304C4⋊Dic5—21no—
305C4⋊Dic5—24no—
306C4⋊Dic5—24no—
307C4⋊Dic5C2412yes—
308C4⋊Dic5C2412yes—
309C4⋊Dic5C2412yes—
310C4⋊Dic5C2412yes—
311#683—24no—
312D40—28no—
313D40—44no—
314#677—44no—
315C22×#41—51no—
316C22×#41—101no—
317C23×D4—51no—
318C22×SD16—51no—
319C22×D8—51no—
320C22×D8—51no—
321C22×M16C2×D511yescharacteristic, complemented
322C23×C8C2×D511yescharacteristic
323#547—58no—
324#547—104no—
325#546—58no—
326#546—104no—
327C2×C4⋊Q8—51no—
328C2×#124—51no—
329C2×#123—101no—
330C2×#123—101no—
331C2×#123—101no—
332C2×C22⋊Q8—51no—
333C2×C22⋊Q8—101no—
334C2×#121—51no—
335C2×#121—51no—
336C2×#121—51no—
337C2×#121—101no—
338C2×#120—101no—
339C2×C4×D4—51no—
340C2×C4×D4—51no—
341C2×C4×D4C2×D511yescharacteristic
342C22×C4⋊C4—51no—
343C22×C4⋊C4—51no—
344C22×C22⋊C4—101no—
345#489—58no—
346#483—58no—
347#481—58no—
348#476—58no—
349#469—58no—
350#465—58no—
351#463—58no—
352#449—58no—
353#447—58no—
354#442—58no—
355#435C2×D518yescomplemented
356C2×#106—51no—
357C2×#106—51no—
358C2×#106—51no—
359C2×C4⋊C8C2×D511yescharacteristic, complemented
360#417—58no—
361C2×#103—51no—
362C2×#103—51no—
363C2×#103—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—58no—
370C2×#102—51no—
371C2×#102—51no—
372C2×C22⋊C8C2×D511yescharacteristic
373C2×C22⋊C8C2×D511yescharacteristic, complemented
374C2×#97C2×D511yescharacteristic, complemented
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5AGL(1,ℤ/8)14yes—
381C23×C5C22×D412yes—
382C23×C5C22×D412yes—
383C23×C5C22×D411yescharacteristic
384C22×D5—24no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—48no—
389C22×D5—42no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—48no—
395C22×D5—42no—
396C22×D5—42no—
397C22×D5—42no—
398C22×D5—84no—
399C22×D5—816no—
400C5×D4—28no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—24no—
406C2×C4×C5—24no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D412yes—
415C2×C4×C5C22×D411yescharacteristic
416C2×C4×C5C2×#4112yes—
417C2×C4×C5H(5,𝔽2)12yes—
418C2×C4×C5C2511yescharacteristic
419C22⋊D5—48no—
420C22⋊D5—48no—
421C22⋊D5—48no—
422C22⋊D5—84no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—48no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431C2×Dic5—42no—
432C2×Dic5—42no—
433C2×Dic5—48no—
434C2×Dic5—42no—
435D20—24no—
436D20—22no—
437D20—22no—
438D20—22no—
439D20—22no—
440D20—22no—
441D20—48no—
442D20—42no—
443D20—42no—
444D20C2×#4114yescomplemented
445C4×D5—48no—
446C4×D5—48no—
447C4×D5—84no—
448Dic10—22no—
449Dic10—22no—
450Dic10—48no—
451Dic10—42no—
452C5×C8—22no—
453C5×C8—22no—
454C5×C8—22no—
455C5×C8—22no—
456C25—101no—
457C2×#41—54no—
458C2×#41—104no—
459C2×#41—108no—
460C2×#41—102no—
461C2×#41—202no—
462C2×#41—208no—
463C22×Q8—51no—
464C22×Q8—101no—
465C22×D4—51no—
466C22×D4—51no—
467C22×D4—51no—
468C22×D4—54no—
469C22×D4—104no—
470C22×D4—101no—
471C22×D4—101no—
472C22×D4—101no—
473C22×D4—101no—
474C22×D4—101no—
475C22×D4—102no—
476C22×D4—202no—
477C22×D4D2011yescharacteristic
478C23×C4—101no—
479C23×C4—101no—
480C23×C4—101no—
481C23×C4—101no—
482C23×C4—101no—
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C2×SD16—54no—
486C2×SD16—202no—
487C2×D8—54no—
488C2×D8—54no—
489C2×D8—104no—
490C2×D8—202no—
491C2×M16—42no—
492C2×M16C22×D514yescomplemented
493C22×C8—42no—
494C22×C8C22×D511yescharacteristic
495C22×C8C22×D511yescharacteristic
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D511yescharacteristic
498C22×C8C22×D514yes—
499C4⋊Q8—54no—
500C4⋊Q8—102no—
501#124—54no—
502#124—102no—
503#123—108no—
504#123—108no—
505#123—108no—
506C22⋊Q8—54no—
507C22⋊Q8—102no—
508C22⋊Q8—108no—
509#121—54no—
510#121—54no—
511#121—54no—
512#121—102no—
513#121—102no—
514#121—102no—
515#121—108no—
516#120—108no—
517C4×D4—54no—
518C4×D4—54no—
519C4×D4—102no—
520C4×D4—102no—
521C4×D4D2014yes—
522C4×D4C22×D514yes—
523C2×C4⋊C4—51no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—51no—
526C2×C4⋊C4—54no—
527C2×C4⋊C4—54no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—101no—
530C2×C4⋊C4—101no—
531C2×C4⋊C4—102no—
532C2×C4⋊C4—102no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4D2011yescharacteristic
536C2×C22⋊C4—101no—
537C2×C22⋊C4—101no—
538C2×C22⋊C4—101no—
539C2×C22⋊C4—101no—
540C2×C22⋊C4—101no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—108no—
545C2×C22⋊C4D2011yescharacteristic
546C2×C22⋊C4D2011yescharacteristic
547C2×C42C22×D511yescharacteristic
548#106—54no—
549#106—54no—
550#106—54no—
551C4⋊C8C22×D514yescomplemented
552#103—54no—
553#103—54no—
554#103—54no—
555#102—54no—
556#102—54no—
557#102—54no—
558#102—54no—
559#102—54no—
560#102—54no—
561#102—54no—
562C22⋊C8C22×D514yes—
563C22⋊C8C22×D514yescomplemented
564#97C22×D514yescomplemented
565C22×C5—22no—
566C22×C5—28no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—44no—
572C22×C5#54612yes—
573C22×C5C2×AGL(1,ℤ/8)14yes—
574C22×C5C2×AGL(1,ℤ/8)12yes—
575C22×C5#57712yes—
576C22×C5C23×D411yescharacteristic
577C2×D5—24no—
578C2×D5—48no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—816no—
588C2×D5—84no—
589C2×D5—84no—
590C4×C5—22no—
591C4×C5—22no—
592C4×C5—22no—
593C4×C5—22no—
594C4×C5#54612yes—
595C4×C5C22×#4111yescharacteristic
596C4×C5C2×H(5,𝔽2)11yescharacteristic
597Dic5—42no—
598Dic5—42no—
599Dic5—42no—
600Dic5—42no—
601Dic5—42no—
602C24—101no—
603C24—101no—
604C24—101no—
605C24—104no—
606C24—204no—
607C24—204no—
608C24—402no—
609C24C2×D2011yescharacteristic
610C24C2×D2011yescharacteristic
611#41—108no—
612#41—204no—
613#41—208no—
614#41—2032no—
615C2×Q8—52no—
616C2×Q8—101no—
617C2×Q8—104no—
618C2×Q8—102no—
619C2×Q8—102no—
620C2×Q8—204no—
621C2×D4—24no—
622C2×D4—54no—
623C2×D4—52no—
624C2×D4—52no—
625C2×D4—52no—
626C2×D4—108no—
627C2×D4—104no—
628C2×D4—104no—
629C2×D4—104no—
630C2×D4—104no—
631C2×D4—101no—
632C2×D4—101no—
633C2×D4—104no—
634C2×D4—101no—
635C2×D4—102no—
636C2×D4—102no—
637C2×D4—102no—
638C2×D4—102no—
639C2×D4—102no—
640C2×D4—204no—
641C2×D4—208no—
642C2×D4—204no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—204no—
646C2×D4—402no—
647C2×D4C2×D2014yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—104no—
653C22×C4—104no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4—104no—
660C22×C4—104no—
661C22×C4—104no—
662C22×C4—204no—
663C22×C4—204no—
664C22×C4—204no—
665C22×C4—204no—
666C22×C4—402no—
667C22×C4C2×D2012yes—
668C22×C4C2×D2012yes—
669C22×C4C2×D2011yescharacteristic
670C22×C4C2×D2011yescharacteristic
671C22×C4C2×D2011yescharacteristic
672C22×C4C2×D2011yescharacteristic
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D511yescharacteristic
676SD16—204no—
677D8—108no—
678D8—204no—
679M16—44no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—44no—
685C2×C8C23×D512yes—
686C2×C8C23×D512yes—
687C2×C8C23×D512yes—
688C2×C8C23×D512yes—
689C4⋊C4—52no—
690C4⋊C4—52no—
691C4⋊C4—52no—
692C4⋊C4—52no—
693C4⋊C4—101no—
694C4⋊C4—101no—
695C4⋊C4—101no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—101no—
699C4⋊C4—104no—
700C4⋊C4—104no—
701C4⋊C4C2×D2014yes—
702C22⋊C4—104no—
703C22⋊C4—104no—
704C22⋊C4—104no—
705C22⋊C4—104no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4C2×D2014yes—
711C22⋊C4C2×D2014yes—
712C42C2×D2012yes—
713C42C23×D512yes—
714C2×C5—24no—
715C2×C5—42no—
716C2×C5#330614yescomplemented
717C2×C5C2×#54611yescharacteristic
718C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
719C2×C5C2×#57711yescharacteristic
720D5—44no—
721D5—82no—
722D5—82no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—104no—
729C23—102no—
730C23—102no—
731C23—102no—
732C23—208no—
733C23—202no—
734C23—202no—
735C23—202no—
736C23—208no—
737C23—202no—
738C23—202no—
739C23—202no—
740C23—202no—
741C23—202no—
742C23—404no—
743C23—4016no—
744C23#405414yes—
745C23C22×D2012yes—
746C23C22×D2012yes—
747C23C22×D2011yescharacteristic
748Q8—102no—
749Q8—102no—
750Q8—208no—
751Q8—202no—
752D4—28no—
753D4—54no—
754D4—104no—
755D4—102no—
756D4—102no—
757D4—102no—
758D4—102no—
759D4—102no—
760D4—208no—
761D4—208no—
762D4—208no—
763D4—208no—
764D4—202no—
765D4—202no—
766D4—404no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—208no—
783C2×C4—208no—
784C2×C4—208no—
785C2×C4—202no—
786C2×C4—202no—
787C2×C4—202no—
788C2×C4—208no—
789C2×C4—202no—
790C2×C4—202no—
791C2×C4—404no—
792C2×C4C22×D2012yes—
793C2×C4C22×D2012yes—
794C2×C4C22×D2012yes—
795C2×C4C22×D2012yes—
796C2×C4C22×D2011yescharacteristic
797C2×C4#414412yes—
798C2×C4D5×#4112yes—
799C2×C4C24×D511yescharacteristic
800C8—22no—
801C8—22no—
802C8—22no—
803C8—22no—
804C5C2×#330611yescharacteristic, complemented, Sylow
805C22—28no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—104no—
813C22—208no—
814C22—202no—
815C22—202no—
816C22—202no—
817C22—202no—
818C22—202no—
819C22—202no—
820C22—202no—
821C22—202no—
822C22—4016no—
823C22—404no—
824C22—404no—
825C22#6588812yes—
826C22C2×#405414yes—
827C22C2×#405412yes—
828C22#6608512yes—
829C22C23×D2011yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—202no—
835C4—202no—
836C4—202no—
837C4—202no—
838C4—202no—
839C4#6588812yes—
840C4C2×#414411yescharacteristic
841C4C2×D5×#4111yescharacteristic
842C2—24no—
843C2—42no—
844C2—204no—
845C2—402no—
846C2—402no—
847C2#1061123014yesdirect product factor
848C2C2×#6588811yescharacteristic
849C2C22×#405411yescharacteristic
850C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
hypercenterC2×#435D5
hypocenterC5C2×#3306
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#65884C2semidirect
2. C2×#65889C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65424C2semidirect
5. C2×#65422C2semidirect
6. C2×#65403C2semidirect
7. C22×#3953C2semidirect
8. #10611230C2direct (N × H)
9. C2×#65131C2semidirect
10. C2×#65133C2semidirect
11. C2×#65023C2semidirect
12. C2×#65021C2semidirect
13. C2×#65024C2semidirect
14. C2×#65010C2semidirect
15. C2×#65003C2semidirect
16. C2×#65000C2semidirect
20. C22×C5×M16C22semidirect
26. C2×#4076C22semidirect
28. C22×C4⋊Dic5C22semidirect
32. C22×#677C22semidirect
34. #65889C22semidirect
36. #65884C22semidirect
45. C2×C4×D20C22semidirect
46. C2×#4015C22semidirect
47. C5×#435C22semidirect
48. C2×C5×C4⋊C8C22semidirect
50. C2×C5×C22⋊C8C22semidirect
51. C2×C5×#97C22semidirect
52. #65424C22semidirect
53. #65422C22semidirect
54. #65403C22semidirect
61. C2×#3953C22semidirect
62. C2×#3953C22semidirect
63. C2×#3949C22semidirect
64. C2×#3949C22semidirect
65. C2×#3949C22semidirect
66. C2×#3948C22semidirect
67. C2×#3948C22semidirect
68. C2×#3948C22semidirect
69. #65133C22semidirect
70. #65131C22semidirect
71. #65024C22semidirect
72. #65023C22semidirect
73. #65021C22semidirect
74. #65010C22semidirect
75. #65003C22semidirect
76. #65000C22semidirect
108. C2×C5×M16C23semidirect
128. #4076C23semidirect
146. C2×C4⋊Dic5C23semidirect
155. C2×#677C23semidirect
167. C4×D20C23semidirect
169. #4015C23semidirect
170. C5×C4⋊C8C23semidirect
172. C5×C22⋊C8C23semidirect
173. C5×#97C23semidirect
180. #3953C23semidirect
181. #3949C23semidirect
182. #3949C23semidirect
183. #3949C23semidirect
184. #3948C23semidirect
185. #3948C23semidirect
186. #3948C23semidirect
200. C2×#435D5semidirect
261. C2×D20#41semidirect
321. C22×M16C2×D5semidirect
355. #435C2×D5semidirect
359. C2×C4⋊C8C2×D5semidirect
373. C2×C22⋊C8C2×D5semidirect
374. C2×#97C2×D5semidirect
444. D20C2×#41semidirect
492. C2×M16C22×D5semidirect
551. C4⋊C8C22×D5semidirect
563. C22⋊C8C22×D5semidirect
564. #97C22×D5semidirect
716. C2×C5#3306semidirect
804. C5C2×#3306semidirect
847. C2#10611230direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658842
C2×#658892
C2×C5×#4352
C2×#654242
C2×#654222
C2×#654032
C22×#39532
#106112302
C2×#651312
C2×#651332
C2×#650232
C2×#650212
C2×#650242
C2×#650102
C2×#650032
C2×#650002
C2×#33065