Finite Group Databasebeta

← C2×#10611172 #12975669

Subgroups — C2×#10611172 #12975669

Order 1280.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65884C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic, complemented
3C2×C5×C8×D4C211yesmaximal, characteristic, complemented
4C2×#65404C211yesmaximal, characteristic, complemented
5C2×#65403C211yesmaximal, characteristic, complemented
6C2×#65402C211yesmaximal, characteristic, complemented
7C22×#3953C211yesmaximal, characteristic, complemented
8#10611172C2116yesmaximal, direct product factor
9C2×#65136C211yesmaximal, characteristic, complemented
10C2×#65133C211yesmaximal, characteristic, complemented
11C2×#65023C211yesmaximal, characteristic, complemented
12C2×#65021C211yesmaximal, characteristic, complemented
13C2×#65011C211yesmaximal, characteristic, complemented
14C2×#65026C211yesmaximal, characteristic, complemented
15C2×#64986C211yesmaximal, characteristic, complemented
16C2×C4×D40C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic, complemented
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4085—21no—
23C2×#4083—21no—
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4076C2211yescharacteristic, complemented
27C2×#4072C2211yescharacteristic, complemented
28C22×C4⋊Dic5C2211yescharacteristic
29C2×#4070C2211yescharacteristic
30C22×D40C2211yescharacteristic
31C22×D40C2211yescharacteristic
32C22×#677C2211yescharacteristic, complemented
33#65899—24no—
34#65899C2218yescomplemented
35#65884—24no—
36#65884C2218yescomplemented
37C2×#4044—21no—
38C2×#4040—21no—
39C2×#4030—21no—
40C2×#4029—21no—
41C2×#4027—21no—
42C2×D5×C22⋊C4—21no—
43C2×#4021C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic, complemented
46C2×#4016C2211yescharacteristic, complemented
47C5×C8×D4C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C5×C8C2211yescharacteristic, complemented
52#65404C2218yescomplemented
53#65403C2218yescomplemented
54#65402C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2218yescomplemented
62C2×#3953C2211yescharacteristic, complemented
63C2×#3950C2211yescharacteristic, complemented
64C2×#3950C2211yescharacteristic, complemented
65C2×#3949C2211yescharacteristic, complemented
66C2×#3948C2211yescharacteristic, complemented
67C2×#3948C2211yescharacteristic, complemented
68C2×#3948C2211yescharacteristic, complemented
69#65136C2218yescomplemented
70#65133C2218yescomplemented
71#65026C2218yescomplemented
72#65023C2218yescomplemented
73#65021C2218yescomplemented
74#65011C2218yescomplemented
75#64986C2218yescomplemented
76C4×D40C2218yescomplemented
77C2×#3297—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—
87C2×#709—22no—
88C2×#709—24no—
89C2×#709—42no—
90C2×#709C2314yes—
91C22×D20—24no—
92C22×D20—21no—
93C22×D20—22no—
94C22×D20—42no—
95C22×D20C2311yescharacteristic
96C22×D20C2311yescharacteristic
97C22×D20C2314yes—
98C22×D20C2311yescharacteristic
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×C4×D5—21no—
102C22×Dic10C2311yescharacteristic
103C22×C5×C8—42no—
104C22×C5×C8—42no—
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C22×C5×C8C2314yes—
110C22×C5×C8C2314yescomplemented
111C4×C5×D4D414yes—
112C4×C5×D4C2314yes—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C22⋊C4D411yescharacteristic
115C2×C5×C22⋊C4D411yescharacteristic
116C2×C42×C5C2311yescharacteristic
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5—21no—
119#4085—28no—
120#4083—28no—
121#4076—22no—
122#4076—22no—
123#4076—22no—
124#4076C2314yes—
125#4076C2314yes—
126#4076C2314yescomplemented
127C2×#685—21no—
128C2×#685—21no—
129C2×#685—21no—
130C2×#685—21no—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134#4072—22no—
135#4072C2314yescomplemented
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5—22no—
138C2×C4⋊Dic5C2311yescharacteristic
139C2×C4⋊Dic5C2311yescharacteristic
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2314yes—
143#4070—22no—
144#4070C2314yes—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×C4×Dic5—21no—
149C2×D40—24no—
150C2×D40—42no—
151C2×D40C2314yes—
152C2×D40C2314yes—
153C2×#677—42no—
154C2×#677C2314yescomplemented
155#4044—28no—
156#4040—28no—
157#4030—28no—
158#4029—28no—
159#4027—28no—
160D5×C22⋊C4—28no—
161#4021—22no—
162#4021C2314yes—
163C4×D20—22no—
164C4×D20—22no—
165C4×D20C2314yes—
166C4×D20C2314yescomplemented
167#4016—22no—
168#4016C2314yescomplemented
169C5×C4⋊C8C2314yescomplemented
170C5×C22⋊C8C2314yes—
171C5×C22⋊C8C2314yescomplemented
172C4×C5×C8C2314yescomplemented
173#3953C2314yes—
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3953C2314yescomplemented
180#3950C2314yescomplemented
181#3950C2314yescomplemented
182#3949C2314yescomplemented
183#3948C2314yescomplemented
184#3948C2314yescomplemented
185#3948C2314yescomplemented
186C2×#553—51no—
187C2×#546—51no—
188#3297—516no—
189C2×#488—51no—
190C2×#484—51no—
191C2×#482—51no—
192C2×#478—51no—
193C2×#466—51no—
194C2×#465—51no—
195C2×#463—51no—
196C2×#449—51no—
197C2×#447—51no—
198C2×C4×D8—51no—
199C2×C8×D4D511yescharacteristic, complemented
200C2×#416—51no—
201C22×#102—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—21no—
207C23×D5—24no—
208C23×D5—44no—
209C23×D5—44no—
210C23×D5—82no—
211C2×C5×D4—24no—
212C2×C5×D4C2×D414yes—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2×D412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2411yescharacteristic
226C2×C22⋊D5—24no—
227C2×C22⋊D5—24no—
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—44no—
231C2×C22⋊D5—44no—
232C2×C22⋊D5—82no—
233C2×C22⋊D5—82no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—24no—
240C22×Dic5—82no—
241#709—28no—
242#709—44no—
243#709—48no—
244C2×D20—21no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—22no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—28no—
251C2×D20—21no—
252C2×D20—24no—
253C2×D20—21no—
254C2×D20—44no—
255C2×D20—48no—
256C2×D20—44no—
257C2×D20#4114yes—
258C2×D20C2412yes—
259C2×D20C2412yes—
260C2×D20C2412yes—
261C2×C4×D5—24no—
262C2×C4×D5—24no—
263C2×C4×D5—24no—
264C2×C4×D5—44no—
265C2×C4×D5—82no—
266C2×C4×D5—82no—
267C2×Dic10—22no—
268C2×Dic10—22no—
269C2×Dic10—21no—
270C2×Dic10C2412yes—
271C2×C5×C8—22no—
272C2×C5×C8—22no—
273C2×C5×C8—22no—
274C2×C5×C8—22no—
275C2×C5×C8—44no—
276C2×C5×C8—44no—
277C2×C5×C8C2412yes—
278C2×C5×C8C2412yes—
279C2×C5×C8C2412yes—
280C2×C5×C8C2412yes—
281C5×C4⋊C4C2×D414yes—
282C5×C22⋊C4C2×D414yes—
283C5×C22⋊C4C2×D414yes—
284C42×C5C2×D412yes—
285C42×C5C2412yes—
286C22⋊Dic5—24no—
287C22⋊Dic5—24no—
288#685—24no—
289#685—24no—
290#685—24no—
291#685—24no—
292#685—24no—
293#685—24no—
294#685—24no—
295C4⋊Dic5—21no—
296C4⋊Dic5—21no—
297C4⋊Dic5—21no—
298C4⋊Dic5—21no—
299C4⋊Dic5—24no—
300C4⋊Dic5C2412yes—
301C4⋊Dic5C2412yes—
302C4⋊Dic5C2412yes—
303C4⋊Dic5C2412yes—
304#683—24no—
305#683—24no—
306#683—24no—
307C4×Dic5—24no—
308D40—28no—
309D40—44no—
310#677—44no—
311C22×#41—51no—
312C23×D4—51no—
313C22×SD16—51no—
314C22×D8—51no—
315C22×D8—51no—
316C23×C8C2×D511yescharacteristic
317C23×C8C2×D511yescharacteristic, complemented
318#553—58no—
319#553—104no—
320#546—58no—
321#546—104no—
322C2×#126—101no—
323C2×#125—51no—
324C2×#124—51no—
325C2×#123—101no—
326C2×#123—101no—
327C2×C22⋊Q8—51no—
328C2×#121—51no—
329C2×#121—51no—
330C2×#121—51no—
331C2×#121—101no—
332C2×#121—101no—
333C2×#120—101no—
334C2×C4×D4—51no—
335C2×C4×D4—51no—
336C2×C4×D4—101no—
337C2×C4×D4C2×D511yescharacteristic
338C2×#117—51no—
339C22×C4⋊C4—51no—
340C22×C22⋊C4—101no—
341#488—58no—
342#484—58no—
343#482—58no—
344#478—58no—
345#466—58no—
346#465—58no—
347#463—58no—
348#449—58no—
349#447—58no—
350C4×D8—58no—
351C8×D4C2×D518yescomplemented
352C2×#107—51no—
353C2×#107—51no—
354C2×#106—51no—
355C2×C4⋊C8C2×D511yescharacteristic, complemented
356#416—58no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—58no—
367C2×#102—51no—
368C2×C22⋊C8C2×D511yescharacteristic
369C2×C22⋊C8C2×D511yescharacteristic, complemented
370C2×C4×C8C2×D511yescharacteristic, complemented
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5#13514yes—
377C23×C5C22×D412yes—
378C23×C5C22×D412yes—
379C23×C5C22×D411yescharacteristic
380C22×D5—24no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—48no—
385C22×D5—42no—
386C22×D5—42no—
387C22×D5—42no—
388C22×D5—42no—
389C22×D5—42no—
390C22×D5—48no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—84no—
395C22×D5—816no—
396C5×D4—28no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—24no—
402C2×C4×C5—24no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5C22×D412yes—
408C2×C4×C5C22×D412yes—
409C2×C4×C5C22×D412yes—
410C2×C4×C5C22×D412yes—
411C2×C4×C5C22×D411yescharacteristic
412C2×C4×C5C2×#4112yes—
413C2×C4×C5H(5,𝔽2)12yes—
414C2×C4×C5C2511yescharacteristic
415C22⋊D5—48no—
416C22⋊D5—48no—
417C22⋊D5—84no—
418C22⋊D5—84no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—42no—
425C2×Dic5—42no—
426C2×Dic5—42no—
427C2×Dic5—42no—
428C2×Dic5—42no—
429C2×Dic5—84no—
430D20—24no—
431D20—22no—
432D20—22no—
433D20—22no—
434D20—22no—
435D20—22no—
436D20—48no—
437D20—42no—
438D20—42no—
439D20C2×#4114yes—
440C4×D5—48no—
441C4×D5—84no—
442C4×D5—84no—
443Dic10—22no—
444Dic10—22no—
445Dic10—42no—
446C5×C8—22no—
447C5×C8—22no—
448C5×C8—22no—
449C5×C8—22no—
450C25—101no—
451C2×#41—54no—
452C2×#41—104no—
453C2×#41—102no—
454C2×#41—202no—
455C22×Q8—51no—
456C22×D4—51no—
457C22×D4—51no—
458C22×D4—51no—
459C22×D4—54no—
460C22×D4—104no—
461C22×D4—101no—
462C22×D4—101no—
463C22×D4—101no—
464C22×D4—101no—
465C22×D4—101no—
466C22×D4—102no—
467C22×D4—202no—
468C22×D4D2011yescharacteristic
469C23×C4—101no—
470C23×C4—101no—
471C23×C4—101no—
472C23×C4—101no—
473C23×C4C22×D511yescharacteristic
474C23×C4C22×D511yescharacteristic
475C2×SD16—54no—
476C2×SD16—202no—
477C2×D8—54no—
478C2×D8—54no—
479C2×D8—104no—
480C2×D8—202no—
481C22×C8—42no—
482C22×C8—42no—
483C22×C8C22×D511yescharacteristic
484C22×C8C22×D511yescharacteristic
485C22×C8C22×D511yescharacteristic
486C22×C8C22×D511yescharacteristic
487C22×C8C22×D514yes—
488C22×C8C22×D514yescomplemented
489#126—108no—
490#125—54no—
491#125—102no—
492#124—54no—
493#124—102no—
494#123—108no—
495#123—108no—
496C22⋊Q8—54no—
497C22⋊Q8—102no—
498#121—54no—
499#121—54no—
500#121—54no—
501#121—108no—
502#121—102no—
503#121—102no—
504#121—102no—
505#121—108no—
506#120—108no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—108no—
510C4×D4—102no—
511C4×D4—102no—
512C4×D4D2014yes—
513C4×D4C22×D514yes—
514#117—54no—
515#117—102no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—54no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4—102no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4—101no—
525C2×C4⋊C4—101no—
526C2×C4⋊C4D2011yescharacteristic
527C2×C22⋊C4—101no—
528C2×C22⋊C4—101no—
529C2×C22⋊C4—101no—
530C2×C22⋊C4—101no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—101no—
533C2×C22⋊C4—101no—
534C2×C22⋊C4—101no—
535C2×C22⋊C4—101no—
536C2×C22⋊C4—108no—
537C2×C22⋊C4D2011yescharacteristic
538C2×C22⋊C4D2011yescharacteristic
539C2×C42—101no—
540C2×C42C22×D511yescharacteristic
541#107—54no—
542#107—54no—
543#106—54no—
544C4⋊C8C22×D514yescomplemented
545#103—54no—
546#103—54no—
547#103—54no—
548#102—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553#102—54no—
554#102—54no—
555C22⋊C8C22×D514yes—
556C22⋊C8C22×D514yescomplemented
557C4×C8C22×D514yescomplemented
558C22×C5—22no—
559C22×C5—28no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—22no—
564C22×C5—44no—
565C22×C5#54612yes—
566C22×C5C2×#13514yes—
567C22×C5C2×#13512yes—
568C22×C5#57612yes—
569C22×C5C23×D411yescharacteristic
570C2×D5—24no—
571C2×D5—48no—
572C2×D5—42no—
573C2×D5—42no—
574C2×D5—42no—
575C2×D5—42no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—816no—
581C2×D5—84no—
582C2×D5—84no—
583C4×C5—22no—
584C4×C5—22no—
585C4×C5—22no—
586C4×C5—22no—
587C4×C5#54612yes—
588C4×C5C22×#4111yescharacteristic
589C4×C5C2×H(5,𝔽2)11yescharacteristic
590Dic5—42no—
591Dic5—42no—
592Dic5—42no—
593Dic5—42no—
594Dic5—42no—
595C24—101no—
596C24—101no—
597C24—101no—
598C24—104no—
599C24—204no—
600C24—204no—
601C24—402no—
602C24C2×D2011yescharacteristic
603C24C2×D2011yescharacteristic
604#41—108no—
605#41—204no—
606#41—208no—
607C2×Q8—52no—
608C2×Q8—101no—
609C2×Q8—102no—
610C2×Q8—102no—
611C2×D4—24no—
612C2×D4—54no—
613C2×D4—52no—
614C2×D4—52no—
615C2×D4—52no—
616C2×D4—108no—
617C2×D4—104no—
618C2×D4—104no—
619C2×D4—104no—
620C2×D4—104no—
621C2×D4—101no—
622C2×D4—101no—
623C2×D4—104no—
624C2×D4—101no—
625C2×D4—102no—
626C2×D4—102no—
627C2×D4—102no—
628C2×D4—102no—
629C2×D4—102no—
630C2×D4—204no—
631C2×D4—208no—
632C2×D4—204no—
633C2×D4—204no—
634C2×D4—204no—
635C2×D4—402no—
636C2×D4—402no—
637C2×D4C2×D2014yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—101no—
643C22×C4—101no—
644C22×C4—101no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4—104no—
648C22×C4—104no—
649C22×C4—104no—
650C22×C4—104no—
651C22×C4—204no—
652C22×C4—402no—
653C22×C4—402no—
654C22×C4—402no—
655C22×C4C2×D2012yes—
656C22×C4C2×D2012yes—
657C22×C4C2×D2011yescharacteristic
658C22×C4C2×D2011yescharacteristic
659C22×C4C2×D2011yescharacteristic
660C22×C4C2×D2011yescharacteristic
661C22×C4C23×D512yes—
662C22×C4C23×D512yes—
663C22×C4C23×D511yescharacteristic
664SD16—204no—
665D8—108no—
666D8—204no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—44no—
672C2×C8—44no—
673C2×C8C23×D512yes—
674C2×C8C23×D512yes—
675C2×C8C23×D512yes—
676C2×C8C23×D512yes—
677C4⋊C4—52no—
678C4⋊C4—52no—
679C4⋊C4—52no—
680C4⋊C4—52no—
681C4⋊C4—101no—
682C4⋊C4—101no—
683C4⋊C4—104no—
684C4⋊C4—101no—
685C4⋊C4—101no—
686C4⋊C4—104no—
687C4⋊C4—104no—
688C4⋊C4—104no—
689C4⋊C4C2×D2014yes—
690C22⋊C4—104no—
691C22⋊C4—104no—
692C22⋊C4—104no—
693C22⋊C4—104no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4C2×D2014yes—
700C22⋊C4C2×D2014yes—
701C42—104no—
702C42C2×D2012yes—
703C42C23×D512yes—
704C2×C5—24no—
705C2×C5—42no—
706C2×C5#329714yescomplemented
707C2×C5C2×#54611yescharacteristic
708C2×C5C22×#13511yescharacteristic
709C2×C5C2×#57611yescharacteristic
710D5—44no—
711D5—82no—
712D5—82no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—104no—
719C23—102no—
720C23—102no—
721C23—102no—
722C23—208no—
723C23—202no—
724C23—202no—
725C23—202no—
726C23—208no—
727C23—202no—
728C23—202no—
729C23—202no—
730C23—202no—
731C23—202no—
732C23—404no—
733C23—4016no—
734C23#405014yes—
735C23C22×D2012yes—
736C23C22×D2012yes—
737C23C22×D2011yescharacteristic
738Q8—102no—
739Q8—102no—
740Q8—202no—
741D4—28no—
742D4—54no—
743D4—104no—
744D4—102no—
745D4—102no—
746D4—102no—
747D4—102no—
748D4—102no—
749D4—208no—
750D4—208no—
751D4—208no—
752D4—202no—
753D4—202no—
754D4—404no—
755D4—404no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—208no—
772C2×C4—202no—
773C2×C4—202no—
774C2×C4—202no—
775C2×C4—202no—
776C2×C4—202no—
777C2×C4—404no—
778C2×C4—404no—
779C2×C4—404no—
780C2×C4C22×D2012yes—
781C2×C4C22×D2012yes—
782C2×C4C22×D2012yes—
783C2×C4C22×D2012yes—
784C2×C4C22×D2011yescharacteristic
785C2×C4#414412yes—
786C2×C4D5×#4112yes—
787C2×C4C24×D511yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—22no—
792C5C2×#329711yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—104no—
801C22—202no—
802C22—202no—
803C22—208no—
804C22—202no—
805C22—202no—
806C22—202no—
807C22—202no—
808C22—202no—
809C22—202no—
810C22—4016no—
811C22—404no—
812C22—404no—
813C22#6588812yes—
814C22C2×#405014yes—
815C22C2×#405012yes—
816C22#6608612yes—
817C22C23×D2011yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—202no—
823C4—202no—
824C4—202no—
825C4—202no—
826C4—202no—
827C4#6588812yes—
828C4C2×#414411yescharacteristic
829C4C2×D5×#4111yescharacteristic
830C2—24no—
831C2—42no—
832C2—204no—
833C2—402no—
834C2—402no—
835C2#1061117214yesdirect product factor
836C2C2×#6588811yescharacteristic
837C2C22×#405011yescharacteristic
838C2C2×#6608611yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×C8×D4C2
socleC23×C5C22×D4
hypercenterC2×C8×D4D5
hypocenterC5C2×#3297
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#65884C2semidirect
2. C2×#65899C2semidirect
3. C2×C5×C8×D4C2semidirect
4. C2×#65404C2semidirect
5. C2×#65403C2semidirect
6. C2×#65402C2semidirect
7. C22×#3953C2semidirect
8. #10611172C2direct (N × H)
9. C2×#65136C2semidirect
10. C2×#65133C2semidirect
11. C2×#65023C2semidirect
12. C2×#65021C2semidirect
13. C2×#65011C2semidirect
14. C2×#65026C2semidirect
15. C2×#64986C2semidirect
16. C2×C4×D40C2semidirect
20. C23×C5×C8C22semidirect
26. C2×#4076C22semidirect
27. C2×#4072C22semidirect
32. C22×#677C22semidirect
34. #65899C22semidirect
36. #65884C22semidirect
45. C2×C4×D20C22semidirect
46. C2×#4016C22semidirect
47. C5×C8×D4C22semidirect
48. C2×C5×C4⋊C8C22semidirect
50. C2×C5×C22⋊C8C22semidirect
51. C2×C4×C5×C8C22semidirect
52. #65404C22semidirect
53. #65403C22semidirect
54. #65402C22semidirect
61. C2×#3953C22semidirect
62. C2×#3953C22semidirect
63. C2×#3950C22semidirect
64. C2×#3950C22semidirect
65. C2×#3949C22semidirect
66. C2×#3948C22semidirect
67. C2×#3948C22semidirect
68. C2×#3948C22semidirect
69. #65136C22semidirect
70. #65133C22semidirect
71. #65026C22semidirect
72. #65023C22semidirect
73. #65021C22semidirect
74. #65011C22semidirect
75. #64986C22semidirect
76. C4×D40C22semidirect
110. C22×C5×C8C23semidirect
126. #4076C23semidirect
135. #4072C23semidirect
154. C2×#677C23semidirect
166. C4×D20C23semidirect
168. #4016C23semidirect
169. C5×C4⋊C8C23semidirect
171. C5×C22⋊C8C23semidirect
172. C4×C5×C8C23semidirect
179. #3953C23semidirect
180. #3950C23semidirect
181. #3950C23semidirect
182. #3949C23semidirect
183. #3948C23semidirect
184. #3948C23semidirect
185. #3948C23semidirect
199. C2×C8×D4D5semidirect
317. C23×C8C2×D5semidirect
351. C8×D4C2×D5semidirect
355. C2×C4⋊C8C2×D5semidirect
369. C2×C22⋊C8C2×D5semidirect
370. C2×C4×C8C2×D5semidirect
488. C22×C8C22×D5semidirect
544. C4⋊C8C22×D5semidirect
556. C22⋊C8C22×D5semidirect
557. C4×C8C22×D5semidirect
706. C2×C5#3297semidirect
792. C5C2×#3297semidirect
835. C2#10611172direct (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×#658992
C2×C5×C8×D42
C2×#654042
C2×#654032
C2×#654022
C22×#39532
#106111722
C2×#651362
C2×#651332
C2×#650232
C2×#650212
C2×#650112
C2×#650262
C2×#649862
C2×C4×D402
C2×#32975