Finite Group Databasebeta

← C2×#10611600 #12967458

Subgroups — C2×#10611600 #12967458

Order 1280.

2830 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65882C211yesmaximal, characteristic, complemented
2C2×C4×D4×D5C211yesmaximal, characteristic, complemented
3C2×C5×#442C211yesmaximal, characteristic, complemented
4C2×#65445C211yesmaximal, characteristic, complemented
5C2×#65439C211yesmaximal, characteristic, complemented
6C2×#65303C211yesmaximal, characteristic, complemented
7C2×#65303C211yesmaximal, characteristic, complemented
8#10611600C2116yesmaximal, direct product factor
9C2×#65159C211yesmaximal, characteristic, complemented
10C2×#65152C211yesmaximal, characteristic, complemented
11C2×#65075C211yesmaximal, characteristic, complemented
12C2×#65066C211yesmaximal, characteristic, complemented
13C2×#65062C211yesmaximal, characteristic, complemented
14C2×#65050C211yesmaximal, characteristic, complemented
15C2×#65000C211yesmaximal, characteristic, complemented
16C2×#64994C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C22×#709—21no—
19C23×C4×D5—21no—
20C22×C5×D8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic, complemented
23C2×#4086C2211yescharacteristic, complemented
24C2×#4084C2211yescharacteristic
25C2×D4×Dic5C2211yescharacteristic
26C22×#686C2211yescharacteristic
27C22×#686C2211yescharacteristic
28C2×C4×C22⋊D5—21no—
29C2×C4×C22⋊D5—21no—
30C22×D40C2211yescharacteristic
31#65882—24no—
32#65882C2218yescomplemented
33C4×D4×D5—24no—
34C4×D4×D5C2218yescomplemented
35C2×#4041C2211yescharacteristic
36C2×#4039C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4034C2211yescharacteristic, complemented
39C2×#4031—21no—
40C2×#4030—21no—
41C2×#4027—21no—
42C2×D5×C22⋊C4—21no—
43C2×C4×D20C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic, complemented
45C2×C42×D5C2211yescharacteristic
46C5×#442C2218yescomplemented
47C2×C5×#106C2211yescharacteristic, complemented
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic, complemented
50C2×C5×#97C2211yescharacteristic, complemented
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic, complemented
53#65445C2218yescomplemented
54#65439C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic, complemented
57C2×#3952C2211yescharacteristic
58C2×#3952C2211yescharacteristic
59C2×#3949C2211yescharacteristic, complemented
60C2×#3946C2211yescharacteristic, complemented
61C2×#3946C2211yescharacteristic, complemented
62#65303C2218yescomplemented
63#65303C2218yescomplemented
64C2×#3941C2211yescharacteristic
65C2×#3941C2211yescharacteristic, complemented
66C2×#3940C2211yescharacteristic, complemented
67C2×#3940C2211yescharacteristic, complemented
68C2×#3935C2211yescharacteristic, complemented
69#65159C2218yescomplemented
70#65152C2218yescomplemented
71#65075C2218yescomplemented
72#65066C2218yescomplemented
73#65062C2218yescomplemented
74#65050C2218yescomplemented
75#65000C2218yescomplemented
76#64994C2218yescomplemented
77C2×#3109—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C23×Dic5—21no—
88C2×D4×D5—24no—
89C2×D4×D5—24no—
90C2×D4×D5—22no—
91C2×D4×D5C2314yes—
92C2×#709—28no—
93C2×#709—48no—
94C22×D20—21no—
95C22×D20C2311yescharacteristic
96C22×D20C2311yescharacteristic
97C22×C4×D5—21no—
98C22×C4×D5—21no—
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×C4×D5—28no—
102C22×C4×D5—48no—
103C22×C4×D5D411yescharacteristic
104C22×C4×D5D411yescharacteristic
105C22×C4×D5C2311yescharacteristic
106C22×Dic10—21no—
107C2×C5×D8—24no—
108C2×C5×D8C2314yes—
109C22×C5×C8C2311yescharacteristic
110C22×C5×C8C2311yescharacteristic
111C4×C5×D4—22no—
112C4×C5×D4—22no—
113C4×C5×D4C2314yes—
114C4×C5×D4C2314yescomplemented
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C42×C5C2311yescharacteristic
120C2×C22⋊Dic5—21no—
121C2×C22⋊Dic5—21no—
122#4086—22no—
123#4086C2314yescomplemented
124#4084—22no—
125#4084C2314yes—
126D4×Dic5—22no—
127D4×Dic5C2314yes—
128C2×#686—24no—
129C2×#686—24no—
130C2×#686C2314yes—
131C2×#686C2314yes—
132C4×C22⋊D5—28no—
133C4×C22⋊D5—28no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×C4⋊Dic5C2311yescharacteristic
139C2×C4⋊Dic5C2311yescharacteristic
140C2×#683—21no—
141C2×#683—21no—
142C2×C4×Dic5D411yescharacteristic
143C2×C4×Dic5D411yescharacteristic
144C2×C4×Dic5C2311yescharacteristic
145C22×#168C2311yescharacteristic
146C22×#168C2311yescharacteristic
147C2×D40—24no—
148C2×D40C2314yes—
149#4041—22no—
150#4041C2314yes—
151#4039—22no—
152#4039C2314yes—
153D5×C4⋊C4—22no—
154D5×C4⋊C4C2314yes—
155#4034—22no—
156#4034C2314yescomplemented
157#4031—28no—
158#4030—28no—
159#4027—28no—
160D5×C22⋊C4—28no—
161C4×D20—22no—
162C4×D20—22no—
163C4×D20C2314yes—
164C4×D20C2314yescomplemented
165C42×D5D414yes—
166C42×D5C2314yes—
167C5×#106C2314yescomplemented
168C5×#102C2314yes—
169C5×#102C2314yescomplemented
170C5×#97C2314yescomplemented
171#3964C2314yes—
172#3964C2314yescomplemented
173#3953C2314yes—
174#3953C2314yescomplemented
175#3952C2314yes—
176#3952C2314yes—
177#3949C2314yescomplemented
178#3946C2314yescomplemented
179#3946C2314yescomplemented
180#3941C2314yes—
181#3941C2314yescomplemented
182#3940C2314yescomplemented
183#3940C2314yescomplemented
184#3935C2314yescomplemented
185C2×#532—51no—
186C22×C4×D4—51no—
187#3109—516no—
188C2×#481—51no—
189C2×#481—51no—
190C2×#476—51no—
191C2×#476—51no—
192C2×#459—51no—
193C2×#459—51no—
194C2×#447—51no—
195C2×#447—51no—
196C2×#442—51no—
197C2×#442—51no—
198C2×#442—51no—
199C2×#442D511yescharacteristic, complemented
200C2×#432—51no—
201C24×C5—21no—
202C24×C5—21no—
203C23×D5—28no—
204C23×D5—21no—
205C23×D5—24no—
206C23×D5—21no—
207C23×D5—44no—
208C23×D5—44no—
209C23×D5C2×D411yescharacteristic
210C2×C5×D4—21no—
211C2×C5×D4—21no—
212C2×C5×D4—22no—
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4#4114yescomplemented
216C2×C5×D4C2412yes—
217C2×C5×D4C2412yes—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—24no—
221C22×C4×C5—24no—
222C22×C4×C5—44no—
223C22×C4×C5—44no—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2411yescharacteristic
227C2×C22⋊D5—28no—
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—44no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—24no—
238C22×Dic5—44no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242D4×D5—216no—
243D4×D5—28no—
244D4×D5—28no—
245#709—432no—
246C2×D20—21no—
247C2×D20—22no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—24no—
251C2×D20—21no—
252C2×D20—44no—
253C2×D20#4114yescomplemented
254C2×D20C2412yes—
255C2×D20C2412yes—
256C2×C4×D5—24no—
257C2×C4×D5—22no—
258C2×C4×D5—22no—
259C2×C4×D5—24no—
260C2×C4×D5—24no—
261C2×C4×D5—24no—
262C2×C4×D5—24no—
263C2×C4×D5—24no—
264C2×C4×D5—432no—
265C2×C4×D5—44no—
266C2×C4×D5—44no—
267C2×C4×D5—44no—
268C2×C4×D5—44no—
269C2×C4×D5C2×D414yes—
270C2×C4×D5C2×D414yes—
271C2×C4×D5C2×D412yes—
272C2×C4×D5C2412yes—
273C2×Dic10—24no—
274C2×Dic10—44no—
275C5×D8—28no—
276C2×C5×C8—22no—
277C2×C5×C8—22no—
278C2×C5×C8C2412yes—
279C2×C5×C8C2412yes—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4C2412yes—
283C5×C4⋊C4C2412yes—
284C5×C22⋊C4—24no—
285C5×C22⋊C4—24no—
286C42×C5C2×D412yes—
287C42×C5C2412yes—
288C22⋊Dic5—24no—
289C22⋊Dic5—24no—
290#686—28no—
291#686—28no—
292#685—24no—
293#685—24no—
294#685—24no—
295#685—24no—
296C4⋊Dic5—21no—
297C4⋊Dic5—21no—
298C4⋊Dic5C2412yes—
299C4⋊Dic5C2412yes—
300#683—24no—
301#683—24no—
302C4×Dic5C2×D412yes—
303C4×Dic5C2×D414yes—
304C4×Dic5C2×D414yes—
305C4×Dic5C2412yes—
306C2×#168—22no—
307C2×#168—22no—
308C2×#168C2412yes—
309C2×#168C2412yes—
310D40—28no—
311C22×#41—101no—
312C23×D4—51no—
313C24×C4—101no—
314C22×D8—51no—
315C22×D8—51no—
316C22×D8—51no—
317C22×D8C2×D511yescharacteristic
318#532—58no—
319#532—104no—
320C2×C4⋊Q8—51no—
321C2×#127—51no—
322C2×#124—101no—
323C2×#121—51no—
324C2×#121—51no—
325C2×#121—101no—
326C2×C4×D4—51no—
327C2×C4×D4—58no—
328C2×C4×D4—51no—
329C2×C4×D4—51no—
330C2×C4×D4—51no—
331C2×C4×D4—101no—
332C2×C4×D4—104no—
333C2×C4×D4—101no—
334C2×C4×D4—101no—
335C2×C4×D4C2×D511yescharacteristic
336C2×C4×D4C2×D511yescharacteristic, complemented
337C22×C4⋊C4—51no—
338C22×C22⋊C4—101no—
339C22×C42—51no—
340#481—58no—
341#481—58no—
342#476—58no—
343#476—58no—
344#459—58no—
345#459—58no—
346#447—58no—
347#447—58no—
348#442—58no—
349#442—58no—
350#442—58no—
351#442C2×D518yescomplemented
352#432—58no—
353C2×#106—51no—
354C2×#106—51no—
355C2×#106—51no—
356C2×#106C2×D511yescharacteristic, complemented
357C2×C4⋊C8—51no—
358C2×C4⋊C8—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102C2×D511yescharacteristic
366C2×#102C2×D511yescharacteristic, complemented
367C2×C22⋊C8—51no—
368C2×C22⋊C8—51no—
369C2×#97—51no—
370C2×#97C2×D511yescharacteristic, complemented
371C23×C5—24no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—42no—
375C23×C5—42no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5—42no—
379C23×C5C22×D411yescharacteristic
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—216no—
383C22×D5—24no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—48no—
387C22×D5—432no—
388C22×D5—42no—
389C22×D5—42no—
390C22×D5—48no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5AGL(1,ℤ/8)14yes—
395C22×D5C22×D412yes—
396C5×D4—24no—
397C5×D4—22no—
398C5×D4—22no—
399C5×D4—22no—
400C5×D4—42no—
401C5×D4C2×#4114yescomplemented
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—48no—
407C2×C4×C5—48no—
408C2×C4×C5—42no—
409C2×C4×C5—42no—
410C2×C4×C5C22×D412yes—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D411yescharacteristic
413C2×C4×C5C2×#4112yes—
414C2×C4×C5C2×#4112yes—
415C2×C4×C5C2511yescharacteristic
416C22⋊D5—216no—
417C22⋊D5—48no—
418C22⋊D5—48no—
419C22⋊D5—48no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—42no—
425C2×Dic5—42no—
426C2×Dic5—48no—
427C2×Dic5AGL(1,ℤ/8)14yes—
428C2×Dic5C22×D412yes—
429C2×Dic5C22×D412yes—
430C2×Dic5C22×D412yes—
431D20—24no—
432D20—22no—
433D20—22no—
434D20—22no—
435D20—48no—
436D20—42no—
437D20C2×#4114yescomplemented
438C4×D5—28no—
439C4×D5—24no—
440C4×D5—22no—
441C4×D5—22no—
442C4×D5—28no—
443C4×D5—48no—
444C4×D5—48no—
445C4×D5—48no—
446C4×D5—48no—
447Dic10—48no—
448C5×C8—22no—
449C5×C8—22no—
450#168—22no—
451#168—22no—
452C25—101no—
453C2×#41—108no—
454C2×#41—208no—
455C22×Q8—101no—
456C22×D4—54no—
457C22×D4—51no—
458C22×D4—51no—
459C22×D4—101no—
460C22×D4—102no—
461C22×D4—101no—
462C22×D4—101no—
463C22×D4—101no—
464C22×D4—104no—
465C22×D4—104no—
466C22×D4—101no—
467C22×D4C22×D511yescharacteristic
468C22×D4C22×D511yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—101no—
475C23×C4—108no—
476C23×C4—101no—
477C23×C4—101no—
478C23×C4—101no—
479C23×C4—101no—
480C23×C4—208no—
481C2×D8—24no—
482C2×D8—54no—
483C2×D8—54no—
484C2×D8—54no—
485C2×D8—104no—
486C2×D8—104no—
487C2×D8—104no—
488C2×D8C22×D514yes—
489C22×C8—51no—
490C22×C8—51no—
491C22×C8C22×D511yescharacteristic
492C22×C8C22×D511yescharacteristic
493C4⋊Q8—54no—
494C4⋊Q8—102no—
495#127—54no—
496#127—102no—
497#124—108no—
498#121—54no—
499#121—54no—
500#121—108no—
501#121—102no—
502#121—102no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—54no—
506C4×D4—54no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—108no—
510C4×D4—102no—
511C4×D4—108no—
512C4×D4—108no—
513C4×D4—102no—
514C4×D4—102no—
515C4×D4—102no—
516C4×D4C22×D514yes—
517C4×D4C22×D514yescomplemented
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—54no—
521C2×C4⋊C4—102no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C4⋊C4C22×D511yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—108no—
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×C42—51no—
536C2×C42—51no—
537C2×C42—51no—
538C2×C42—54no—
539C2×C42—54no—
540C2×C42C22×D511yescharacteristic
541#106—54no—
542#106—54no—
543#106—54no—
544#106C22×D514yescomplemented
545C4⋊C8—54no—
546C4⋊C8—54no—
547#102—54no—
548#102—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553#102C22×D514yes—
554#102C22×D514yescomplemented
555C22⋊C8—54no—
556C22⋊C8—54no—
557#97—54no—
558#97C22×D514yescomplemented
559C22×C5—24no—
560C22×C5—48no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—84no—
567C22×C5#52512yes—
568C22×C5C2×AGL(1,ℤ/8)12yes—
569C22×C5C2×AGL(1,ℤ/8)12yes—
570C22×C5C23×D411yescharacteristic
571C2×D5—28no—
572C2×D5—22no—
573C2×D5—22no—
574C2×D5—24no—
575C2×D5—432no—
576C2×D5—48no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—84no—
583C2×D5C2×AGL(1,ℤ/8)14yes—
584C4×C5—22no—
585C4×C5—22no—
586C4×C5—42no—
587C4×C5—42no—
588C4×C5#52512yes—
589C4×C5C22×#4111yescharacteristic
590C4×C5C22×#4111yescharacteristic
591Dic5—22no—
592Dic5—22no—
593Dic5—42no—
594Dic5—42no—
595Dic5C2×AGL(1,ℤ/8)14yes—
596C24—21no—
597C24—21no—
598C24—51no—
599C24—104no—
600C24—108no—
601C24—101no—
602C24—101no—
603C24—204no—
604C24—204no—
605#41—2032no—
606C2×Q8—104no—
607C2×Q8—204no—
608C2×D4—22no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—54no—
614C2×D4—52no—
615C2×D4—52no—
616C2×D4—104no—
617C2×D4—104no—
618C2×D4—104no—
619C2×D4—104no—
620C2×D4—108no—
621C2×D4—1016no—
622C2×D4—108no—
623C2×D4—108no—
624C2×D4—104no—
625C2×D4—102no—
626C2×D4—102no—
627C2×D4—101no—
628C2×D4—101no—
629C2×D4—102no—
630C2×D4—204no—
631C2×D4—204no—
632C2×D4—204no—
633C2×D4—204no—
634C2×D4#70914yescomplemented
635C2×D4C23×D512yes—
636C2×D4C23×D512yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—54no—
647C22×C4—52no—
648C22×C4—54no—
649C22×C4—52no—
650C22×C4—104no—
651C22×C4—104no—
652C22×C4—104no—
653C22×C4—104no—
654C22×C4—104no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4—104no—
660C22×C4—104no—
661C22×C4—204no—
662C22×C4—204no—
663C22×C4—204no—
664C22×C4—2032no—
665C22×C4—204no—
666C22×C4—204no—
667C22×C4D4×D511yescharacteristic
668C22×C4D4×D511yescharacteristic
669C22×C4C23×D511yescharacteristic
670D8—28no—
671D8—108no—
672D8—108no—
673D8—108no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—52no—
677C2×C8—52no—
678C2×C8—102no—
679C2×C8—102no—
680C2×C8C23×D512yes—
681C2×C8C23×D512yes—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—52no—
685C4⋊C4—52no—
686C4⋊C4—104no—
687C4⋊C4—104no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4C23×D512yes—
691C4⋊C4C23×D512yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C42—54no—
701C42—54no—
702C42—52no—
703C42—52no—
704C42D4×D512yes—
705C42C23×D512yes—
706C2×C5—44no—
707C2×C5—82no—
708C2×C5#310914yescomplemented
709C2×C5C2×#52511yescharacteristic
710C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
711C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
712D5—24no—
713D5—44no—
714D5—82no—
715C23—24no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—54no—
724C23—52no—
725C23—1016no—
726C23—102no—
727C23—102no—
728C23—104no—
729C23—102no—
730C23—102no—
731C23—208no—
732C23—208no—
733C23—2032no—
734C23—202no—
735C23—202no—
736C23—202no—
737C23—202no—
738C23—202no—
739C23C2×D4×D511yescharacteristic
740Q8—208no—
741D4—24no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—42no—
746D4—54no—
747D4—1016no—
748D4—104no—
749D4—102no—
750D4—102no—
751D4—102no—
752D4—208no—
753D4—208no—
754D4—208no—
755D4—208no—
756D4—202no—
757D4C2×#70914yescomplemented
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—54no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—108no—
771C2×C4—108no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—104no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—208no—
780C2×C4—208no—
781C2×C4—208no—
782C2×C4—208no—
783C2×C4—208no—
784C2×C4—202no—
785C2×C4—202no—
786C2×C4C2×#70912yes—
787C2×C4C2×D4×D512yes—
788C2×C4C2×D4×D512yes—
789C2×C4C2×D4×D511yescharacteristic
790C2×C4D5×#4112yes—
791C2×C4C24×D511yescharacteristic
792C8—22no—
793C8—22no—
794C8—102no—
795C8—102no—
796C5C2×#310911yescharacteristic, complemented, Sylow
797C22—24no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—54no—
805C22—84no—
806C22—102no—
807C22—108no—
808C22—102no—
809C22—104no—
810C22—2032no—
811C22—208no—
812C22—202no—
813C22—202no—
814C22—202no—
815C22—202no—
816C22—202no—
817C22—404no—
818C22#6588112yes—
819C22D5×AGL(1,ℤ/8)12yes—
820C22D5×AGL(1,ℤ/8)12yes—
821C22C22×D4×D511yescharacteristic
822C4—22no—
823C4—22no—
824C4—42no—
825C4—42no—
826C4—54no—
827C4—102no—
828C4—102no—
829C4—202no—
830C4—202no—
831C4#6588112yes—
832C4C22×#70911yescharacteristic
833C4C2×D5×#4111yescharacteristic
834C2—44no—
835C2—82no—
836C2—104no—
837C2—204no—
838C2—402no—
839C2#1061160014yesdirect product factor
840C2C2×#6588111yescharacteristic
841C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
842C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#442C2
socleC23×C5C22×D4
hypercenterC2×#442D5
hypocenterC5C2×#3109
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#65882C2semidirect
2. C2×C4×D4×D5C2semidirect
3. C2×C5×#442C2semidirect
4. C2×#65445C2semidirect
5. C2×#65439C2semidirect
6. C2×#65303C2semidirect
7. C2×#65303C2semidirect
8. #10611600C2direct (N × H)
9. C2×#65159C2semidirect
10. C2×#65152C2semidirect
11. C2×#65075C2semidirect
12. C2×#65066C2semidirect
13. C2×#65062C2semidirect
14. C2×#65050C2semidirect
15. C2×#65000C2semidirect
16. C2×#64994C2semidirect
22. C2×C4×C5×D4C22semidirect
23. C2×#4086C22semidirect
32. #65882C22semidirect
34. C4×D4×D5C22semidirect
38. C2×#4034C22semidirect
44. C2×C4×D20C22semidirect
46. C5×#442C22semidirect
47. C2×C5×#106C22semidirect
49. C2×C5×#102C22semidirect
50. C2×C5×#97C22semidirect
52. C2×#3964C22semidirect
53. #65445C22semidirect
54. #65439C22semidirect
56. C2×#3953C22semidirect
59. C2×#3949C22semidirect
60. C2×#3946C22semidirect
61. C2×#3946C22semidirect
62. #65303C22semidirect
63. #65303C22semidirect
65. C2×#3941C22semidirect
66. C2×#3940C22semidirect
67. C2×#3940C22semidirect
68. C2×#3935C22semidirect
69. #65159C22semidirect
70. #65152C22semidirect
71. #65075C22semidirect
72. #65066C22semidirect
73. #65062C22semidirect
74. #65050C22semidirect
75. #65000C22semidirect
76. #64994C22semidirect
114. C4×C5×D4C23semidirect
123. #4086C23semidirect
156. #4034C23semidirect
164. C4×D20C23semidirect
167. C5×#106C23semidirect
169. C5×#102C23semidirect
170. C5×#97C23semidirect
172. #3964C23semidirect
174. #3953C23semidirect
177. #3949C23semidirect
178. #3946C23semidirect
179. #3946C23semidirect
181. #3941C23semidirect
182. #3940C23semidirect
183. #3940C23semidirect
184. #3935C23semidirect
199. C2×#442D5semidirect
215. C2×C5×D4#41semidirect
253. C2×D20#41semidirect
336. C2×C4×D4C2×D5semidirect
351. #442C2×D5semidirect
356. C2×#106C2×D5semidirect
366. C2×#102C2×D5semidirect
370. C2×#97C2×D5semidirect
401. C5×D4C2×#41semidirect
437. D20C2×#41semidirect
517. C4×D4C22×D5semidirect
544. #106C22×D5semidirect
554. #102C22×D5semidirect
558. #97C22×D5semidirect
634. C2×D4#709semidirect
708. C2×C5#3109semidirect
757. D4C2×#709semidirect
796. C5C2×#3109semidirect
839. C2#10611600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658822
C2×C4×D4×D52
C2×C5×#4422
C2×#654452
C2×#654392
C2×#653032
#106116002
C2×#651592
C2×#651522
C2×#650752
C2×#650662
C2×#650622
C2×#650502
C2×#650002
C2×#649942
C2×#31095