Finite Group Databasebeta

← C2×#10611202 #12977865

Subgroups — C2×#10611202 #12977865

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65899C211yesmaximal, characteristic, complemented
2C2×#65889C211yesmaximal, characteristic, complemented
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65424C211yesmaximal, characteristic, complemented
5C2×#65410C211yesmaximal, characteristic, complemented
6C2×#65404C211yesmaximal, characteristic, complemented
7C22×#3949C211yesmaximal, characteristic, complemented
8#10611202C2116yesmaximal, direct product factor
9C2×#65136C211yesmaximal, characteristic, complemented
10C2×#65131C211yesmaximal, characteristic, complemented
11C2×#65024C211yesmaximal, characteristic, complemented
12C2×#65024C211yesmaximal, characteristic, complemented
13C2×#65026C211yesmaximal, characteristic, complemented
14C2×#65025C211yesmaximal, characteristic, complemented
15C2×#65000C211yesmaximal, characteristic, complemented
16C2×#64991C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×M16C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×#4085—21no—
22C2×#4076C2211yescharacteristic
23C2×#4076C2211yescharacteristic
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4072C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×D40C2211yescharacteristic
31#65899—24no—
32#65899C2218yescomplemented
33#65889—24no—
34#65889C2218yescomplemented
35C2×#4044—21no—
36C2×#4043—21no—
37C2×#4032—21no—
38C2×#4032—21no—
39C2×#4029—21no—
40C2×#4027—21no—
41C2×C4×D20C2211yescharacteristic
42C2×C4×D20C2211yescharacteristic
43C2×#4016C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C5×#435C2218yescomplemented
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C5×#97C2211yescharacteristic
50#65424C2218yescomplemented
51#65410C2218yescomplemented
52#65404C2218yescomplemented
53C2×#3953C2211yescharacteristic
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3950C2211yescharacteristic
61C2×#3950C2211yescharacteristic
62C2×#3949C2211yescharacteristic
63C2×#3949C2211yescharacteristic
64C2×#3949C2211yescharacteristic
65C2×#3949C2211yescharacteristic
66C2×#3949C2211yescharacteristic
67C2×#3949C2211yescharacteristic
68C2×#3949C2218yescomplemented
69#65136C2218yescomplemented
70#65131C2218yescomplemented
71#65026C2218yescomplemented
72#65025C2218yescomplemented
73#65024C2218yescomplemented
74#65024C2218yescomplemented
75#65000C2218yescomplemented
76#64991C2218yescomplemented
77C2×#3345—51nomaximal, Sylow
78C22×C5×D4D411yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C23×Dic5—21no—
87C23×Dic5—21no—
88C2×#711—28no—
89C2×#711—48no—
90C22×D20C2311yescharacteristic
91C22×D20C2311yescharacteristic
92C22×C4×D5—21no—
93C22×C4×D5—21no—
94C22×Dic10—21no—
95C2×C5×M16—24no—
96C2×C5×M16C2314yes—
97C22×C5×C8—24no—
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C22×C5×C8C2314yes—
102C22×C5×C8C2311yescharacteristic
103C4×C5×D4D414yes—
104C4×C5×D4C2314yes—
105C2×C5×C4⋊C4D411yescharacteristic
106C2×C5×C22⋊C4D411yescharacteristic
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C42×C5C2311yescharacteristic
109C2×C22⋊Dic5—21no—
110#4085—28no—
111#4076—22no—
112#4076—22no—
113#4076—22no—
114#4076—22no—
115#4076C2314yes—
116#4076C2314yes—
117#4076C2314yes—
118#4076C2314yes—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125#4072—22no—
126#4072C2314yes—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—22no—
132C2×C4⋊Dic5—22no—
133C2×C4⋊Dic5—22no—
134C2×C4⋊Dic5C2314yes—
135C2×C4⋊Dic5C2314yes—
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2311yescharacteristic
138C2×C4⋊Dic5C2311yescharacteristic
139C2×C4⋊Dic5C2311yescharacteristic
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×#683—21no—
144C2×#683—21no—
145C2×C4×Dic5—21no—
146C2×D40—24no—
147C2×D40C2314yes—
148#4044—28no—
149#4043—28no—
150#4032—28no—
151#4032—28no—
152#4029—28no—
153#4027—28no—
154C4×D20—22no—
155C4×D20—22no—
156C4×D20C2314yes—
157C4×D20C2314yes—
158#4016—22no—
159#4016C2314yes—
160#4015—22no—
161#4015C2314yes—
162C5×C4⋊C8C2314yes—
163C5×C22⋊C8C2314yes—
164C5×C22⋊C8C2314yes—
165C5×#97C2314yes—
166#3953C2314yes—
167#3953C2314yes—
168#3953C2314yes—
169#3953C2314yes—
170#3953C2314yes—
171#3953C2314yes—
172#3950C2314yes—
173#3950C2314yes—
174#3950C2314yes—
175#3949C2314yes—
176#3949C2314yes—
177#3949C2314yes—
178#3949C2314yes—
179#3949C2314yes—
180#3949C2314yes—
181C2×#553—51no—
182C2×#547—51no—
183#3345—516no—
184C2×#501—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#482—51no—
188C2×#480—51no—
189C2×#478—51no—
190C2×#476—51no—
191C2×#469—51no—
192C2×#466—51no—
193C2×#442—51no—
194C2×#435D511yescharacteristic, complemented
195C2×#428—51no—
196C22×#106—51no—
197C24×C5C2×D411yescharacteristic
198C24×C5C2×D411yescharacteristic
199C23×D5—21no—
200C23×D5—21no—
201C2×C5×D4—24no—
202C2×C5×D4C2×D414yes—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D412yes—
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2411yescharacteristic
216C2×C22⋊D5—24no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—44no—
221C2×C22⋊D5—44no—
222C2×C22⋊D5—44no—
223C2×C22⋊D5—82no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—24no—
230C22×Dic5—24no—
231C22×Dic5—21no—
232C22×Dic5—24no—
233C22×Dic5—44no—
234C22×Dic5—44no—
235C22×Dic5—82no—
236#711—432no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—22no—
240C2×D20—22no—
241C2×D20—21no—
242C2×D20—21no—
243C2×D20C2412yes—
244C2×D20C2412yes—
245C2×C4×D5—24no—
246C2×C4×D5—24no—
247C2×C4×D5—44no—
248C2×C4×D5—82no—
249C2×Dic10—24no—
250C2×Dic10—44no—
251C5×M16—28no—
252C2×C5×C8—22no—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8—28no—
256C2×C5×C8#4114yescomplemented
257C2×C5×C8C2412yes—
258C2×C5×C8C2412yes—
259C2×C5×C8C2412yes—
260C2×C5×C8C2412yes—
261C5×C4⋊C4C2×D414yes—
262C5×C22⋊C4C2×D414yes—
263C5×C22⋊C4C2×D414yes—
264C42×C5C2×D412yes—
265C42×C5C2412yes—
266C22⋊Dic5—24no—
267#685—24no—
268#685—24no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—24no—
276C4⋊Dic5—21no—
277C4⋊Dic5—21no—
278C4⋊Dic5—21no—
279C4⋊Dic5—21no—
280C4⋊Dic5—24no—
281C4⋊Dic5—24no—
282C4⋊Dic5—24no—
283C4⋊Dic5C2412yes—
284C4⋊Dic5C2412yes—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287C4⋊Dic5C2412yes—
288C4⋊Dic5C2412yes—
289#683—24no—
290#683—24no—
291C4×Dic5—24no—
292D40—28no—
293C22×#41—101no—
294C22×D8—51no—
295C22×M16C2×D511yescharacteristic
296C23×C8C2×D511yescharacteristic
297#553—58no—
298#553—104no—
299#547—58no—
300#547—104no—
301C2×C4⋊Q8—51no—
302C2×#126—101no—
303C2×#125—51no—
304C2×#123—101no—
305C2×#123—101no—
306C2×#123—101no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—51no—
311C2×#121—51no—
312C2×#121—101no—
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—101no—
316C2×C4×D4C2×D511yescharacteristic
317C2×#117—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321#501—58no—
322#482—58no—
323#481—58no—
324#481—58no—
325#480—58no—
326#478—58no—
327#476—58no—
328#469—58no—
329#466—58no—
330#442—58no—
331#435C2×D518yescomplemented
332#428—58no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—58no—
341C2×#106—51no—
342C2×#106—51no—
343C2×C4⋊C8C2×D511yescharacteristic
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×C22⋊C8C2×D511yescharacteristic
351C2×C22⋊C8C2×D511yescharacteristic
352C2×#97C2×D511yescharacteristic
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5AGL(1,ℤ/8)14yes—
359C23×C5C22×D412yes—
360C23×C5C22×D412yes—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C5×D4—28no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
376C2×C4×C5—24no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D411yescharacteristic
386C2×C4×C5C2×#4112yes—
387C2×C4×C52−1+412yes—
388C2×C4×C5C2511yescharacteristic
389C22⋊D5—48no—
390C22⋊D5—48no—
391C22⋊D5—48no—
392C22⋊D5—84no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—48no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5—48no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5—84no—
408D20—22no—
409D20—22no—
410D20—22no—
411D20—22no—
412D20—42no—
413D20—42no—
414C4×D5—48no—
415C4×D5—84no—
416Dic10—48no—
417C5×C8—22no—
418C5×C8—22no—
419C5×C8—22no—
420C5×C8C2×#4114yescomplemented
421C2×#41—108no—
422C2×#41—208no—
423C22×Q8—101no—
424C22×D4—51no—
425C22×D4—51no—
426C22×D4—101no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4—101no—
430C22×D4D2011yescharacteristic
431C23×C4—101no—
432C23×C4—101no—
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C2×D8—54no—
439C2×D8—104no—
440C2×M16—24no—
441C2×M16C22×D514yes—
442C22×C8—24no—
443C22×C8C22×D511yescharacteristic
444C22×C8C22×D514yes—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D511yescharacteristic
447C22×C8C22×D511yescharacteristic
448C4⋊Q8—54no—
449C4⋊Q8—102no—
450#126—108no—
451#125—54no—
452#125—102no—
453#123—108no—
454#123—108no—
455#123—108no—
456C22⋊Q8—108no—
457#121—54no—
458#121—54no—
459#121—54no—
460#121—54no—
461#121—108no—
462#121—102no—
463#121—102no—
464#121—102no—
465#121—102no—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—108no—
469C4×D4—102no—
470C4×D4—102no—
471C4×D4D2014yes—
472C4×D4C22×D514yes—
473#117—54no—
474#117—102no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—51no—
477C2×C4⋊C4—51no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—102no—
488C2×C4⋊C4—102no—
489C2×C4⋊C4—102no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4D2011yescharacteristic
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4D2011yescharacteristic
502C2×C22⋊C4D2011yescharacteristic
503C2×C42—101no—
504C2×C42C22×D511yescharacteristic
505#107—54no—
506#107—54no—
507#107—54no—
508#106—54no—
509#106—54no—
510#106—54no—
511#106—54no—
512#106—54no—
513#106—54no—
514C4⋊C8C22×D514yes—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#102—54no—
520#102—54no—
521C22⋊C8C22×D514yes—
522C22⋊C8C22×D514yes—
523#97C22×D514yes—
524C22×C5—28no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—22no—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—44no—
531C22×C5#54712yes—
532C22×C5C2×AGL(1,ℤ/8)14yes—
533C22×C5C2×AGL(1,ℤ/8)12yes—
534C22×C5#57712yes—
535C22×C5C23×D411yescharacteristic
536C2×D5—42no—
537C2×D5—42no—
538C2×D5—42no—
539C2×D5—42no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—84no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—22no—
546C4×C5—22no—
547C4×C5—22no—
548C4×C5#54712yes—
549C4×C5C22×#4111yescharacteristic
550C4×C5C2×2−1+411yescharacteristic
551Dic5—42no—
552Dic5—42no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557C24—101no—
558C24—101no—
559C24C2×D2011yescharacteristic
560C24C2×D2011yescharacteristic
561#41—2032no—
562C2×Q8—104no—
563C2×Q8—204no—
564C2×D4—24no—
565C2×D4—52no—
566C2×D4—52no—
567C2×D4—104no—
568C2×D4—104no—
569C2×D4—104no—
570C2×D4—104no—
571C2×D4—101no—
572C2×D4—101no—
573C2×D4—102no—
574C2×D4—102no—
575C2×D4—102no—
576C2×D4—102no—
577C2×D4—204no—
578C2×D4—204no—
579C2×D4—204no—
580C2×D4—402no—
581C2×D4C2×D2014yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—104no—
587C22×C4—104no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—104no—
597C22×C4—204no—
598C22×C4—204no—
599C22×C4—204no—
600C22×C4—402no—
601C22×C4—402no—
602C22×C4C2×D2012yes—
603C22×C4C2×D2012yes—
604C22×C4C2×D2011yescharacteristic
605C22×C4C2×D2011yescharacteristic
606C22×C4C2×D2011yescharacteristic
607C22×C4C2×D2011yescharacteristic
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C22×C4C23×D511yescharacteristic
611D8—108no—
612M16—28no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—28no—
617C2×C8#71114yescomplemented
618C2×C8C23×D512yes—
619C2×C8C23×D512yes—
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—52no—
623C4⋊C4—52no—
624C4⋊C4—52no—
625C4⋊C4—52no—
626C4⋊C4—52no—
627C4⋊C4—52no—
628C4⋊C4—101no—
629C4⋊C4—101no—
630C4⋊C4—101no—
631C4⋊C4—101no—
632C4⋊C4—101no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4—101no—
637C4⋊C4—104no—
638C4⋊C4—104no—
639C4⋊C4—104no—
640C4⋊C4C2×D2014yes—
641C22⋊C4—104no—
642C22⋊C4—104no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4C2×D2014yes—
649C22⋊C4C2×D2014yes—
650C42—104no—
651C42C2×D2012yes—
652C42C23×D512yes—
653C2×C5—24no—
654C2×C5—42no—
655C2×C5#334514yescomplemented
656C2×C5C2×#54711yescharacteristic
657C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
658C2×C5C2×#57711yescharacteristic
659D5—82no—
660D5—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—102no—
667C23—102no—
668C23—202no—
669C23—202no—
670C23—202no—
671C23—202no—
672C23—202no—
673C23—202no—
674C23#405414yes—
675C23C22×D2012yes—
676C23C22×D2012yes—
677C23C22×D2011yescharacteristic
678Q8—208no—
679D4—28no—
680D4—102no—
681D4—102no—
682D4—102no—
683D4—102no—
684D4—208no—
685D4—208no—
686D4—208no—
687D4—202no—
688D4—202no—
689D4—404no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—208no—
707C2×C4—208no—
708C2×C4—202no—
709C2×C4—202no—
710C2×C4—202no—
711C2×C4—208no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—202no—
715C2×C4—404no—
716C2×C4—404no—
717C2×C4C22×D2012yes—
718C2×C4C22×D2012yes—
719C2×C4C22×D2012yes—
720C2×C4C22×D2012yes—
721C2×C4C22×D2011yescharacteristic
722C2×C4C2×#71112yes—
723C2×C4#415012yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8C2×#71114yescomplemented
729C5C2×#334511yescharacteristic, complemented, Sylow
730C22—28no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—202no—
738C22—202no—
739C22—202no—
740C22—202no—
741C22—202no—
742C22—202no—
743C22—404no—
744C22—404no—
745C22#6588912yes—
746C22C2×#405414yes—
747C22C2×#405412yes—
748C22#6608512yes—
749C22C23×D2011yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—202no—
755C4—202no—
756C4—202no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4#6588912yes—
761C4C22×#71111yescharacteristic
762C4C2×#415011yescharacteristic
763C2—24no—
764C2—42no—
765C2—402no—
766C2—402no—
767C2#1061120214yesdirect product factor
768C2C2×#6588911yescharacteristic
769C2C22×#405411yescharacteristic
770C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
hypercenterC2×#435D5
hypocenterC5C2×#3345
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×#65899C2semidirect
2. C2×#65889C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65424C2semidirect
5. C2×#65410C2semidirect
6. C2×#65404C2semidirect
7. C22×#3949C2semidirect
8. #10611202C2direct (N × H)
9. C2×#65136C2semidirect
10. C2×#65131C2semidirect
11. C2×#65024C2semidirect
12. C2×#65024C2semidirect
13. C2×#65026C2semidirect
14. C2×#65025C2semidirect
15. C2×#65000C2semidirect
16. C2×#64991C2semidirect
32. #65899C22semidirect
34. #65889C22semidirect
45. C5×#435C22semidirect
50. #65424C22semidirect
51. #65410C22semidirect
52. #65404C22semidirect
68. C2×#3949C22semidirect
69. #65136C22semidirect
70. #65131C22semidirect
71. #65026C22semidirect
72. #65025C22semidirect
73. #65024C22semidirect
74. #65024C22semidirect
75. #65000C22semidirect
76. #64991C22semidirect
194. C2×#435D5semidirect
256. C2×C5×C8#41semidirect
331. #435C2×D5semidirect
420. C5×C8C2×#41semidirect
617. C2×C8#711semidirect
655. C2×C5#3345semidirect
728. C8C2×#711semidirect
729. C5C2×#3345semidirect
767. C2#10611202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658992
C2×#658892
C2×C5×#4352
C2×#654242
C2×#654102
C2×#654042
C22×#39492
#106112022
C2×#651362
C2×#651312
C2×#650242
C2×#650262
C2×#650252
C2×#650002
C2×#649912
C2×#33455