Finite Group Databasebeta

← C2×#10612294 #12975993

Subgroups — C2×#10612294 #12975993

Order 1280.

2318 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×#66010C211yesmaximal, characteristic, complemented
2C2×#65897C211yesmaximal, characteristic, complemented
3C2×C5×#463C211yesmaximal, characteristic, complemented
4C2×#65463C211yesmaximal, characteristic, complemented
5C2×#65461C211yesmaximal, characteristic, complemented
6C2×#65446C211yesmaximal, characteristic, complemented
7C2×#65445C211yesmaximal, characteristic, complemented
8C2×#65344C211yesmaximal, characteristic, complemented
9C2×#65303C211yesmaximal, characteristic, complemented
10#10612294C2116yesmaximal, direct product factor
11C2×#65135C211yesmaximal, characteristic, complemented
12C2×#65125C211yesmaximal, characteristic, complemented
13C2×#65093C211yesmaximal, characteristic, complemented
14C2×#65103C211yesmaximal, characteristic, complemented
15C2×#65073C211yesmaximal, characteristic, complemented
16C2×#65059C211yesmaximal, characteristic, complemented
17C22×#713C2211yescharacteristic
18C22×D4×D5C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic, complemented
20C22×C5×D8C2211yescharacteristic
21C2×C5×#124C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic, complemented
23C2×#4092C2211yescharacteristic
24C2×#4084C2211yescharacteristic
25C2×#4084C2211yescharacteristic
26C2×#4084C2211yescharacteristic, complemented
27C22×#686C2211yescharacteristic
28C2×#4076—21no—
29C2×#4072—21no—
30C22×#676C2211yescharacteristic
31C22×C8×D5C2211yescharacteristic, complemented
32#66010—24no—
33#66010C2218yescomplemented
34#65897—24no—
35#65897C2218yescomplemented
36C2×#4038C2211yescharacteristic
37C2×#4038C2211yescharacteristic, complemented
38C2×#4031—21no—
39C2×#4031—21no—
40C2×#4030—21no—
41C2×#4029—21no—
42C2×#4028—21no—
43C2×D5×C22⋊C4—21no—
44C2×C4×D20C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×#4015C2211yescharacteristic, complemented
47C5×#463C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×#103C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic
51C2×#3967C2211yescharacteristic, complemented
52C2×#3967C2211yescharacteristic, complemented
53C2×#3964C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×#3964C2211yescharacteristic, complemented
56#65463C2218yescomplemented
57#65461C2218yescomplemented
58#65446C2218yescomplemented
59#65445C2218yescomplemented
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3952C2211yescharacteristic
63C2×#3952C2211yescharacteristic, complemented
64C2×#3950C2211yescharacteristic, complemented
65C2×#3950C2211yescharacteristic, complemented
66#65344C2218yescomplemented
67#65303C2218yescomplemented
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic, complemented
70C2×#3935C2211yescharacteristic, complemented
71#65135C2218yescomplemented
72#65125C2218yescomplemented
73#65103C2218yescomplemented
74#65093C2218yescomplemented
75#65073C2218yescomplemented
76#65059C2218yescomplemented
77C2×#3319—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C2×#713—22no—
88C2×#713—24no—
89C2×#713—42no—
90C2×#713C2314yes—
91C2×D4×D5—24no—
92C2×D4×D5—22no—
93C2×D4×D5—42no—
94C2×D4×D5C2314yes—
95C22×D20—21no—
96C22×D20D411yescharacteristic
97C22×D20C2311yescharacteristic
98C22×C4×D5—21no—
99C22×C4×D5—21no—
100C22×C4×D5C2311yescharacteristic
101C22×C4×D5C2311yescharacteristic
102C22×Dic10—21no—
103C2×C5×SD16—42no—
104C2×C5×SD16C2314yescomplemented
105C2×C5×D8—42no—
106C2×C5×D8C2314yes—
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C5×#124—22no—
110C5×#124C2314yes—
111C4×C5×D4—22no—
112C4×C5×D4C2314yescomplemented
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C42×C5C2311yescharacteristic
118C2×C22⋊Dic5—21no—
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121#4092—22no—
122#4092C2314yes—
123#4084—22no—
124#4084—22no—
125#4084—22no—
126#4084C2314yes—
127#4084C2314yes—
128#4084C2314yescomplemented
129C2×#686—24no—
130C2×#686C2314yes—
131#4076—28no—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685D411yescharacteristic
137C2×#685D411yescharacteristic
138#4072—28no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5D411yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×#683—21no—
145C2×C4×Dic5—21no—
146C2×C4×Dic5—21no—
147C22×#168C2311yescharacteristic
148C22×#168C2311yescharacteristic
149C2×#676—42no—
150C2×#676C2314yes—
151C2×C8×D5—42no—
152C2×C8×D5C2314yescomplemented
153#4038—22no—
154#4038—22no—
155#4038C2314yes—
156#4038C2314yescomplemented
157#4031—28no—
158#4031—28no—
159#4030—28no—
160#4029—28no—
161#4028—28no—
162D5×C22⋊C4—28no—
163C4×D20—22no—
164C4×D20D414yes—
165C4×D20C2314yes—
166C4×D20C2314yes—
167#4015—22no—
168#4015C2314yescomplemented
169C5×C4⋊C8C2314yescomplemented
170C5×#103C2314yescomplemented
171C5×#102C2314yes—
172#3967C2314yescomplemented
173#3967C2314yescomplemented
174#3964C2314yes—
175#3964C2314yes—
176#3964C2314yescomplemented
177#3953C2314yes—
178#3953C2314yes—
179#3952C2314yes—
180#3952C2314yescomplemented
181#3950C2314yescomplemented
182#3950C2314yescomplemented
183#3941C2314yes—
184#3940C2314yescomplemented
185#3935C2314yescomplemented
186C2×#555—51no—
187C2×#546—51no—
188#3319—516no—
189C2×#489—51no—
190C2×#485—51no—
191C2×#482—51no—
192C2×#474—51no—
193C2×#468—51no—
194C2×#466—51no—
195C2×#463D511yescharacteristic, complemented
196C2×#449—51no—
197C2×#447—51no—
198C2×#442—51no—
199C2×#435—51no—
200C2×#418—51no—
201C2×#416—51no—
202C24×C5—21no—
203C24×C5—21no—
204C23×D5—21no—
205C23×D5—24no—
206C23×D5—44no—
207C23×D5—44no—
208C23×D5—82no—
209C23×D5C2×D411yescharacteristic
210C23×D5C2×D411yescharacteristic
211C2×C5×Q8—21no—
212C2×C5×Q8—22no—
213C2×C5×Q8—22no—
214C2×C5×Q8C2412yes—
215C2×C5×D4—21no—
216C2×C5×D4—21no—
217C2×C5×D4—22no—
218C2×C5×D4—22no—
219C2×C5×D4—22no—
220C2×C5×D4—22no—
221C2×C5×D4C2412yes—
222C2×C5×D4C2412yes—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—24no—
226C22×C4×C5—44no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2411yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5—82no—
236C2×C22⋊D5—82no—
237C2×C22⋊D5—82no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5C2×D411yescharacteristic
242C22×Dic5C2×D411yescharacteristic
243#713—28no—
244#713—44no—
245#713—48no—
246D4×D5—28no—
247D4×D5—44no—
248D4×D5—48no—
249C2×D20—21no—
250C2×D20—22no—
251C2×D20—24no—
252C2×D20—42no—
253C2×D20—44no—
254C2×D20C2×D414yes—
255C2×D20#4114yes—
256C2×D20C2412yes—
257C2×C4×D5—22no—
258C2×C4×D5—22no—
259C2×C4×D5—22no—
260C2×C4×D5—22no—
261C2×C4×D5—24no—
262C2×C4×D5—24no—
263C2×C4×D5—44no—
264C2×C4×D5—82no—
265C2×C4×D5C2×D412yes—
266C2×C4×D5C2×D412yes—
267C2×C4×D5C2412yes—
268C2×C4×D5C2412yes—
269C2×Dic10—24no—
270C2×Dic10—82no—
271C5×SD16—44no—
272C5×D8—44no—
273C2×C5×C8—22no—
274C2×C5×C8—22no—
275C2×C5×C8C2412yes—
276C2×C5×C8C2412yes—
277C5×C4⋊C4—21no—
278C5×C4⋊C4C2412yes—
279C5×C22⋊C4—24no—
280C5×C22⋊C4—24no—
281C5×C22⋊C4—24no—
282C42×C5C2×D412yes—
283C42×C5C2412yes—
284C22⋊Dic5—24no—
285C22⋊Dic5—24no—
286C22⋊Dic5—24no—
287#686—28no—
288#685—24no—
289#685—24no—
290#685—24no—
291#685—24no—
292#685C2×D414yes—
293#685C2×D414yes—
294C4⋊Dic5—21no—
295C4⋊Dic5—21no—
296C4⋊Dic5—24no—
297C4⋊Dic5—21no—
298C4⋊Dic5C2×D414yes—
299C4⋊Dic5C2412yes—
300C4⋊Dic5C2412yes—
301C4⋊Dic5C2412yes—
302#683—24no—
303C4×Dic5—24no—
304C4×Dic5—24no—
305C2×#168—22no—
306C2×#168—22no—
307C2×#168C2412yes—
308C2×#168C2412yes—
309#676—44no—
310C8×D5—44no—
311C22×#41—51no—
312C23×D4—51no—
313C22×SD16C2×D511yescharacteristic, complemented
314C22×D8—51no—
315C22×D8C2×D511yescharacteristic
316C22×M16—51no—
317C23×C8—51no—
318#555—58no—
319#555—104no—
320#546—58no—
321#546—104no—
322C2×C4⋊Q8—51no—
323C2×#124—101no—
324C2×#124—101no—
325C2×#124C2×D511yescharacteristic
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×D4C2×D511yescharacteristic, complemented
337C2×#117—51no—
338C2×#117—51no—
339C2×#117—101no—
340C22×C22⋊C4—101no—
341#489—58no—
342#485—58no—
343#482—58no—
344#474—58no—
345#468—58no—
346#466—58no—
347#463C2×D518yescomplemented
348#449—58no—
349#447—58no—
350#442—58no—
351#435—58no—
352C2×#107—51no—
353C2×#107—51no—
354C2×#106—51no—
355C2×C4⋊C8C2×D511yescharacteristic, complemented
356#418—58no—
357#416—58no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103C2×D511yescharacteristic, complemented
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102C2×D511yescharacteristic
368C2×C22⋊C8—51no—
369C2×C22⋊C8—51no—
370C2×#97—51no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—42no—
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—24no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—48no—
389C22×D5—48no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—84no—
393C22×D5—816no—
394C22×D5C22×D412yes—
395C22×D5C22×D412yes—
396C5×Q8—22no—
397C5×Q8—22no—
398C5×Q8—42no—
399C5×D4—22no—
400C5×D4—22no—
401C5×D4—22no—
402C5×D4—22no—
403C5×D4—42no—
404C5×D4—42no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—48no—
410C2×C4×C5—42no—
411C2×C4×C5—42no—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D411yescharacteristic
415C2×C4×C5C2×#4112yes—
416C2×C4×C5H(5,𝔽2)12yes—
417C2×C4×C5C2511yescharacteristic
418C22⋊D5—48no—
419C22⋊D5—84no—
420C22⋊D5—84no—
421C22⋊D5—84no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—42no—
428C2×Dic5—42no—
429C2×Dic5—42no—
430C2×Dic5C22×D412yes—
431C2×Dic5C22×D412yes—
432D20—24no—
433D20—22no—
434D20—44no—
435D20—48no—
436D20C2×#4114yes—
437C4×D5—24no—
438C4×D5—24no—
439C4×D5—22no—
440C4×D5—22no—
441C4×D5—22no—
442C4×D5—22no—
443C4×D5—48no—
444C4×D5—84no—
445Dic10—84no—
446C5×C8—22no—
447C5×C8—22no—
448#168—22no—
449#168—22no—
450C25—101no—
451C2×#41—54no—
452C2×#41—102no—
453C2×#41—104no—
454C2×#41—202no—
455C22×Q8—101no—
456C22×Q8C22×D511yescharacteristic
457C22×D4—54no—
458C22×D4—51no—
459C22×D4—51no—
460C22×D4—101no—
461C22×D4—102no—
462C22×D4—101no—
463C22×D4—104no—
464C22×D4—101no—
465C22×D4—101no—
466C22×D4—101no—
467C22×D4—202no—
468C22×D4C22×D511yescharacteristic
469C22×D4C22×D511yescharacteristic
470C23×C4—21no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—101no—
474C23×C4—101no—
475C2×SD16—42no—
476C2×SD16C22×D514yescomplemented
477C2×D8—42no—
478C2×D8—54no—
479C2×D8—104no—
480C2×D8C22×D514yes—
481C2×M16—54no—
482C2×M16—202no—
483C22×C8—51no—
484C22×C8—51no—
485C22×C8—54no—
486C22×C8—202no—
487C22×C8C22×D511yescharacteristic
488C22×C8C22×D511yescharacteristic
489C4⋊Q8—54no—
490C4⋊Q8—102no—
491#124—22no—
492#124—108no—
493#124—108no—
494#124C22×D514yes—
495#123—108no—
496C22⋊Q8—54no—
497C22⋊Q8—102no—
498#121—54no—
499#121—54no—
500#121—54no—
501#121—108no—
502#121—108no—
503#121—102no—
504#121—102no—
505#121—102no—
506#120—108no—
507C4×D4—22no—
508C4×D4—54no—
509C4×D4—54no—
510C4×D4—54no—
511C4×D4—102no—
512C4×D4C22×D514yescomplemented
513#117—54no—
514#117—54no—
515#117—102no—
516#117—102no—
517#117—108no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—51no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—51no—
529C2×C22⋊C4—51no—
530C2×C22⋊C4—108no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—101no—
533C2×C22⋊C4—101no—
534C2×C22⋊C4—101no—
535C2×C22⋊C4—101no—
536C2×C22⋊C4—101no—
537C2×C22⋊C4—101no—
538C2×C42—101no—
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#103C22×D514yescomplemented
548#102—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553#102—54no—
554#102C22×D514yes—
555C22⋊C8—54no—
556C22⋊C8—54no—
557#97—54no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—84no—
565C22×C5—84no—
566C22×C5#54612yes—
567C22×C5#57512yes—
568C22×C5#57612yes—
569C22×C5C23×D411yescharacteristic
570C2×D5—22no—
571C2×D5—22no—
572C2×D5—24no—
573C2×D5—22no—
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—44no—
578C2×D5—44no—
579C2×D5—48no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—816no—
583C4×C5—22no—
584C4×C5—22no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5#54612yes—
588C4×C5C22×#4111yescharacteristic
589C4×C5C2×H(5,𝔽2)11yescharacteristic
590Dic5—22no—
591Dic5—22no—
592Dic5—42no—
593Dic5—42no—
594Dic5—42no—
595C24—21no—
596C24—21no—
597C24—51no—
598C24—51no—
599C24—104no—
600C24—101no—
601C24—204no—
602C24—204no—
603C24—402no—
604#41—108no—
605#41—204no—
606#41—208no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—104no—
611C2×Q8—402no—
612C2×Q8C23×D512yes—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—54no—
620C2×D4—54no—
621C2×D4—52no—
622C2×D4—104no—
623C2×D4—104no—
624C2×D4—108no—
625C2×D4—104no—
626C2×D4—104no—
627C2×D4—104no—
628C2×D4—101no—
629C2×D4—102no—
630C2×D4—202no—
631C2×D4—204no—
632C2×D4—204no—
633C2×D4—208no—
634C2×D4—204no—
635C2×D4—402no—
636C2×D4—402no—
637C2×D4—402no—
638C2×D4C23×D512yes—
639C2×D4C23×D512yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—104no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—104no—
659C22×C4—204no—
660C22×C4—402no—
661C22×C4D4×D511yescharacteristic
662C22×C4D4×D511yescharacteristic
663C22×C4C23×D511yescharacteristic
664SD16—44no—
665D8—44no—
666D8—108no—
667M16—204no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—52no—
671C2×C8—52no—
672C2×C8—102no—
673C2×C8—102no—
674C2×C8—204no—
675C2×C8C23×D512yes—
676C2×C8C23×D512yes—
677C4⋊C4—21no—
678C4⋊C4—54no—
679C4⋊C4—52no—
680C4⋊C4—52no—
681C4⋊C4—52no—
682C4⋊C4—104no—
683C4⋊C4—101no—
684C4⋊C4—101no—
685C4⋊C4—101no—
686C4⋊C4—104no—
687C4⋊C4C23×D512yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—54no—
692C22⋊C4—54no—
693C22⋊C4—104no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C42—104no—
701C42—104no—
702C42D4×D512yes—
703C42C23×D512yes—
704C2×C5—82no—
705C2×C5—82no—
706C2×C5#331914yescomplemented
707C2×C5C2×#54611yescharacteristic
708C2×C5C2×#57511yescharacteristic
709C2×C5C2×#57611yescharacteristic
710D5—42no—
711D5—42no—
712D5—44no—
713C23—22no—
714C23—22no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—52no—
722C23—52no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23—104no—
730C23—102no—
731C23—208no—
732C23—208no—
733C23—202no—
734C23—202no—
735C23—404no—
736C23—4016no—
737C23C2×D4×D511yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—42no—
741Q8—404no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—42no—
748D4—54no—
749D4—104no—
750D4—102no—
751D4—204no—
752D4—208no—
753D4—208no—
754D4—404no—
755D4—404no—
756D4—404no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—48no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—52no—
765C2×C4—52no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—104no—
769C2×C4—104no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—208no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—404no—
782C2×C4C2×D4×D512yes—
783C2×C4C2×D4×D512yes—
784C2×C4C2×D4×D511yescharacteristic
785C2×C4#414412yes—
786C2×C4D5×#4112yes—
787C2×C4C24×D511yescharacteristic
788C8—22no—
789C8—22no—
790C8—102no—
791C8—102no—
792C5C2×#331911yescharacteristic, complemented, Sylow
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—84no—
800C22—84no—
801C22—102no—
802C22—102no—
803C22—102no—
804C22—102no—
805C22—102no—
806C22—102no—
807C22—104no—
808C22—204no—
809C22—204no—
810C22—208no—
811C22—202no—
812C22—202no—
813C22—4016no—
814C22#6594612yes—
815C22#6610312yes—
816C22#6610712yes—
817C22C22×D4×D511yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—102no—
823C4—102no—
824C4—202no—
825C4—202no—
826C4—202no—
827C4#6594612yes—
828C4C2×#414411yescharacteristic
829C4C2×D5×#4111yescharacteristic
830C2—82no—
831C2—82no—
832C2—202no—
833C2—202no—
834C2—204no—
835C2#1061229414yesdirect product factor
836C2C2×#6594611yescharacteristic
837C2C2×#6610311yescharacteristic
838C2C2×#6610711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#463C2
socleC23×C5C22×D4
hypercenterC2×#463D5
hypocenterC5C2×#3319
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#66010C2semidirect
2. C2×#65897C2semidirect
3. C2×C5×#463C2semidirect
4. C2×#65463C2semidirect
5. C2×#65461C2semidirect
6. C2×#65446C2semidirect
7. C2×#65445C2semidirect
8. C2×#65344C2semidirect
9. C2×#65303C2semidirect
10. #10612294C2direct (N × H)
11. C2×#65135C2semidirect
12. C2×#65125C2semidirect
13. C2×#65093C2semidirect
14. C2×#65103C2semidirect
15. C2×#65073C2semidirect
16. C2×#65059C2semidirect
19. C22×C5×SD16C22semidirect
22. C2×C4×C5×D4C22semidirect
26. C2×#4084C22semidirect
31. C22×C8×D5C22semidirect
33. #66010C22semidirect
35. #65897C22semidirect
37. C2×#4038C22semidirect
46. C2×#4015C22semidirect
47. C5×#463C22semidirect
48. C2×C5×C4⋊C8C22semidirect
49. C2×C5×#103C22semidirect
51. C2×#3967C22semidirect
52. C2×#3967C22semidirect
55. C2×#3964C22semidirect
56. #65463C22semidirect
57. #65461C22semidirect
58. #65446C22semidirect
59. #65445C22semidirect
63. C2×#3952C22semidirect
64. C2×#3950C22semidirect
65. C2×#3950C22semidirect
66. #65344C22semidirect
67. #65303C22semidirect
69. C2×#3940C22semidirect
70. C2×#3935C22semidirect
71. #65135C22semidirect
72. #65125C22semidirect
73. #65103C22semidirect
74. #65093C22semidirect
75. #65073C22semidirect
76. #65059C22semidirect
104. C2×C5×SD16C23semidirect
112. C4×C5×D4C23semidirect
128. #4084C23semidirect
152. C2×C8×D5C23semidirect
156. #4038C23semidirect
168. #4015C23semidirect
169. C5×C4⋊C8C23semidirect
170. C5×#103C23semidirect
172. #3967C23semidirect
173. #3967C23semidirect
176. #3964C23semidirect
180. #3952C23semidirect
181. #3950C23semidirect
182. #3950C23semidirect
184. #3940C23semidirect
185. #3935C23semidirect
195. C2×#463D5semidirect
313. C22×SD16C2×D5semidirect
336. C2×C4×D4C2×D5semidirect
347. #463C2×D5semidirect
355. C2×C4⋊C8C2×D5semidirect
360. C2×#103C2×D5semidirect
476. C2×SD16C22×D5semidirect
512. C4×D4C22×D5semidirect
544. C4⋊C8C22×D5semidirect
547. #103C22×D5semidirect
706. C2×C5#3319semidirect
792. C5C2×#3319semidirect
835. C2#10612294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660102
C2×#658972
C2×C5×#4632
C2×#654632
C2×#654612
C2×#654462
C2×#654452
C2×#653442
C2×#653032
#106122942
C2×#651352
C2×#651252
C2×#650932
C2×#651032
C2×#650732
C2×#650592
C2×#33195