Finite Group Databasebeta

← C2×#10611602 #12967410

Subgroups — C2×#10611602 #12967410

Order 1280.

2582 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65891C211yesmaximal, characteristic, complemented
2C2×C4×D4×D5C211yesmaximal, characteristic, complemented
3C2×C5×#442C211yesmaximal, characteristic, complemented
4C2×#65445C211yesmaximal, characteristic
5C2×#65442C211yesmaximal, characteristic, complemented
6C2×#65303C211yesmaximal, characteristic, complemented
7C2×#65307C211yesmaximal, characteristic, complemented
8#10611602C2116yesmaximal, direct product factor
9C2×#65160C211yesmaximal, characteristic, complemented
10C2×#65151C211yesmaximal, characteristic, complemented
11C2×#65076C211yesmaximal, characteristic, complemented
12C2×#65063C211yesmaximal, characteristic, complemented
13C2×#65065C211yesmaximal, characteristic, complemented
14C2×#65055C211yesmaximal, characteristic, complemented
15C2×#64999C211yesmaximal, characteristic, complemented
16C2×#64994C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C23×C4×D5—21no—
19C22×C5×D8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic, complemented
22C2×#4084C2211yescharacteristic
23C2×#4082C2211yescharacteristic, complemented
24C2×D4×Dic5C2211yescharacteristic
25C22×#687C2211yescharacteristic
26C22×#686C2211yescharacteristic
27C2×C4×C22⋊D5—21no—
28C2×C4×C22⋊D5—21no—
29C2×#4072—21no—
30C22×#677C2211yescharacteristic
31#65891—24no—
32#65891C2218yescomplemented
33C4×D4×D5—24no—
34C4×D4×D5C2218yescomplemented
35C2×#4043C2211yescharacteristic
36C2×#4039C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4036C2211yescharacteristic, complemented
39C2×#4029—21no—
40C2×#4027—21no—
41C2×D5×C22⋊C4—21no—
42C2×#4025—21no—
43C2×C4×D20C2211yescharacteristic
44C2×C42×D5C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic, complemented
46C5×#442C2218yescomplemented
47C2×C5×#106C2211yescharacteristic, complemented
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic, complemented
50C2×C5×#97C2211yescharacteristic, complemented
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic, complemented
53#65445C2218yes—
54#65442C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3950C2211yescharacteristic, complemented
59C2×#3948C2211yescharacteristic, complemented
60C2×#3946C2211yescharacteristic, complemented
61C2×#3946C2211yescharacteristic, complemented
62#65307C2218yescomplemented
63#65303C2218yescomplemented
64C2×#3942C2211yescharacteristic, complemented
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic, complemented
67C2×#3939C2211yescharacteristic, complemented
68C2×#3935C2211yescharacteristic, complemented
69#65160C2218yescomplemented
70#65151C2218yescomplemented
71#65076C2218yescomplemented
72#65065C2218yescomplemented
73#65063C2218yescomplemented
74#65055C2218yescomplemented
75#64999C2218yescomplemented
76#64994C2218yescomplemented
77C2×#3114—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—
85C23×Dic5—21no—
86C2×D4×D5—24no—
87C2×D4×D5—24no—
88C2×D4×D5—22no—
89C2×D4×D5C2314yes—
90C22×D20C2311yescharacteristic
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5—21no—
94C22×C4×D5—28no—
95C22×C4×D5—48no—
96C22×C4×D5D411yescharacteristic
97C22×C4×D5D411yescharacteristic
98C22×C4×D5C2311yescharacteristic
99C22×Dic10C2311yescharacteristic
100C2×C5×D8—24no—
101C2×C5×D8C2314yes—
102C22×C5×C8C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C4×C5×D4—22no—
105C4×C5×D4—22no—
106C4×C5×D4C2314yes—
107C4×C5×D4C2314yescomplemented
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C42×C5C2311yescharacteristic
113C2×C22⋊Dic5—21no—
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5—21no—
117#4084—22no—
118#4084C2314yes—
119#4082—22no—
120#4082C2314yescomplemented
121D4×Dic5—22no—
122D4×Dic5C2314yes—
123C2×#687—24no—
124C2×#687C2314yes—
125C2×#686—24no—
126C2×#686C2314yes—
127C4×C22⋊D5—28no—
128C4×C22⋊D5—28no—
129C2×#685—21no—
130C2×#685—21no—
131C2×#685—21no—
132#4072—28no—
133C2×C4⋊Dic5—21no—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137C2×#683—21no—
138C2×#683—21no—
139C2×#683—21no—
140C2×C4×Dic5—21no—
141C2×C4×Dic5D411yescharacteristic
142C2×C4×Dic5D411yescharacteristic
143C2×C4×Dic5C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146C2×#677—24no—
147C2×#677C2314yes—
148#4043—22no—
149#4043C2314yes—
150#4039—22no—
151#4039C2314yes—
152D5×C4⋊C4—22no—
153D5×C4⋊C4C2314yes—
154#4036—22no—
155#4036C2314yescomplemented
156#4029—28no—
157#4027—28no—
158D5×C22⋊C4—28no—
159#4025—28no—
160C4×D20—22no—
161C4×D20C2314yes—
162C42×D5D414yes—
163C42×D5C2314yes—
164C4×Dic10—22no—
165C4×Dic10C2314yescomplemented
166C5×#106C2314yescomplemented
167C5×#102C2314yes—
168C5×#102C2314yescomplemented
169C5×#97C2314yescomplemented
170#3964C2314yes—
171#3964C2314yescomplemented
172#3953C2314yes—
173#3952C2314yes—
174#3952C2314yes—
175#3950C2314yescomplemented
176#3948C2314yescomplemented
177#3946C2314yescomplemented
178#3946C2314yescomplemented
179#3942C2314yescomplemented
180#3941C2314yes—
181#3940C2314yescomplemented
182#3939C2314yescomplemented
183#3935C2314yescomplemented
184C2×#529—51no—
185C22×C4×D4—51no—
186#3114—516no—
187C2×#483—51no—
188C2×#480—51no—
189C2×#478—51no—
190C2×#478—51no—
191C2×#463—51no—
192C2×#463—51no—
193C2×#450—51no—
194C2×#447—51no—
195C2×#442—51no—
196C2×#442D511yescharacteristic, complemented
197C2×#440—51no—
198C2×#440—51no—
199C2×#432—51no—
200C24×C5—21no—
201C24×C5—21no—
202C23×D5—28no—
203C23×D5—21no—
204C23×D5—24no—
205C23×D5—44no—
206C23×D5—44no—
207C23×D5C2×D411yescharacteristic
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4#4114yes—
214C2×C5×D4C2412yes—
215C2×C5×D4C2412yes—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—24no—
219C22×C4×C5—24no—
220C22×C4×C5—44no—
221C22×C4×C5—44no—
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2411yescharacteristic
225C2×C22⋊D5—28no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—24no—
228C2×C22⋊D5—44no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—24no—
233C22×Dic5—44no—
234C22×Dic5C2×D411yescharacteristic
235C22×Dic5C2×D411yescharacteristic
236C22×Dic5C2×D411yescharacteristic
237D4×D5—216no—
238D4×D5—28no—
239D4×D5—28no—
240C2×D20—21no—
241C2×D20—22no—
242C2×D20#4114yes—
243C2×D20C2412yes—
244C2×C4×D5—24no—
245C2×C4×D5—22no—
246C2×C4×D5—22no—
247C2×C4×D5—24no—
248C2×C4×D5—24no—
249C2×C4×D5—24no—
250C2×C4×D5—432no—
251C2×C4×D5—42no—
252C2×C4×D5—44no—
253C2×C4×D5—44no—
254C2×C4×D5—44no—
255C2×C4×D5C2×D414yes—
256C2×C4×D5C2×D412yes—
257C2×C4×D5C2×D414yes—
258C2×C4×D5C2412yes—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—21no—
262C2×Dic10C2412yes—
263C5×D8—28no—
264C2×C5×C8—22no—
265C2×C5×C8—22no—
266C2×C5×C8C2412yes—
267C2×C5×C8C2412yes—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4C2412yes—
271C5×C4⋊C4C2412yes—
272C5×C22⋊C4—24no—
273C5×C22⋊C4—24no—
274C42×C5C2×D412yes—
275C42×C5C2412yes—
276C22⋊Dic5—24no—
277C22⋊Dic5—24no—
278C22⋊Dic5—24no—
279C22⋊Dic5—24no—
280#687—28no—
281#686—28no—
282#685—24no—
283#685—24no—
284#685—24no—
285C4⋊Dic5—21no—
286C4⋊Dic5—21no—
287C4⋊Dic5—24no—
288C4⋊Dic5—24no—
289C4⋊Dic5C2412yes—
290C4⋊Dic5C2412yes—
291#683—24no—
292#683—24no—
293#683—24no—
294C4×Dic5—24no—
295C4×Dic5C2×D412yes—
296C4×Dic5C2×D414yes—
297C4×Dic5C2×D414yes—
298C4×Dic5C2412yes—
299C2×#168—22no—
300C2×#168—22no—
301C2×#168C2412yes—
302C2×#168C2412yes—
303#677—28no—
304C23×D4—51no—
305C24×C4—101no—
306C22×SD16—51no—
307C22×SD16—51no—
308C22×D8—51no—
309C22×D8C2×D511yescharacteristic
310#529—58no—
311#529—104no—
312C2×#126—101no—
313C2×#125—51no—
314C2×#124—51no—
315C2×#123—101no—
316C2×C22⋊Q8—51no—
317C2×#121—51no—
318C2×C4×Q8—51no—
319C2×C4×D4—51no—
320C2×C4×D4—58no—
321C2×C4×D4—51no—
322C2×C4×D4—51no—
323C2×C4×D4—101no—
324C2×C4×D4—104no—
325C2×C4×D4—101no—
326C2×C4×D4—101no—
327C2×C4×D4C2×D511yescharacteristic
328C2×C4×D4C2×D511yescharacteristic, complemented
329C2×#117—101no—
330C22×C4⋊C4—51no—
331C22×C22⋊C4—101no—
332C22×C42—51no—
333#483—58no—
334#480—58no—
335#478—58no—
336#478—58no—
337#463—58no—
338#463—58no—
339#450—58no—
340#447—58no—
341#442—58no—
342#442C2×D518yescomplemented
343#440—58no—
344#440—58no—
345#432—58no—
346C2×#107—51no—
347C2×#107—51no—
348C2×#106—51no—
349C2×#106C2×D511yescharacteristic, complemented
350C2×C4⋊C8—51no—
351C2×C4⋊C8—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#102—51no—
355C2×#102—51no—
356C2×#102—51no—
357C2×#102—51no—
358C2×#102C2×D511yescharacteristic
359C2×#102C2×D511yescharacteristic, complemented
360C2×C22⋊C8—51no—
361C2×C22⋊C8—51no—
362C2×#97—51no—
363C2×#97C2×D511yescharacteristic, complemented
364C23×C5—24no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—42no—
368C23×C5—42no—
369C23×C5—42no—
370C23×C5—42no—
371C23×C5—42no—
372C23×C5C22×D411yescharacteristic
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—216no—
376C22×D5—24no—
377C22×D5—22no—
378C22×D5—432no—
379C22×D5—48no—
380C22×D5—42no—
381C22×D5—42no—
382C22×D5—48no—
383C22×D5AGL(1,ℤ/8)14yes—
384C22×D5C22×D412yes—
385C5×D4—24no—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—22no—
389C5×D4—42no—
390C5×D4C2×#4114yes—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—48no—
396C2×C4×C5—48no—
397C2×C4×C5—42no—
398C2×C4×C5—42no—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D412yes—
401C2×C4×C5C22×D411yescharacteristic
402C2×C4×C5C2×#4112yes—
403C2×C4×C5C2×#4112yes—
404C2×C4×C5C2511yescharacteristic
405C22⋊D5—216no—
406C22⋊D5—48no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—48no—
414C2×Dic5—42no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5C22×D412yes—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420D20—24no—
421D20—22no—
422D20C2×#4114yes—
423C4×D5—28no—
424C4×D5—24no—
425C4×D5—22no—
426C4×D5—22no—
427C4×D5—44no—
428C4×D5—48no—
429C4×D5—48no—
430C4×D5—48no—
431Dic10—22no—
432Dic10—22no—
433Dic10—42no—
434C5×C8—22no—
435C5×C8—22no—
436#168—22no—
437#168—22no—
438C25—101no—
439C22×Q8—51no—
440C22×D4—54no—
441C22×D4—51no—
442C22×D4—102no—
443C22×D4—101no—
444C22×D4—104no—
445C22×D4—104no—
446C22×D4—101no—
447C22×D4C22×D511yescharacteristic
448C22×D4C22×D511yescharacteristic
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—51no—
452C23×C4—51no—
453C23×C4—51no—
454C23×C4—101no—
455C23×C4—108no—
456C23×C4—101no—
457C23×C4—101no—
458C23×C4—101no—
459C23×C4—208no—
460C2×SD16—54no—
461C2×SD16—54no—
462C2×SD16—104no—
463C2×SD16—104no—
464C2×D8—24no—
465C2×D8—54no—
466C2×D8—104no—
467C2×D8C22×D514yes—
468C22×C8—51no—
469C22×C8—51no—
470C22×C8C22×D511yescharacteristic
471C22×C8C22×D511yescharacteristic
472#126—108no—
473#125—54no—
474#125—102no—
475#124—54no—
476#124—102no—
477#123—108no—
478C22⋊Q8—54no—
479C22⋊Q8—102no—
480#121—54no—
481#121—102no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—54no—
487C4×D4—54no—
488C4×D4—54no—
489C4×D4—108no—
490C4×D4—102no—
491C4×D4—108no—
492C4×D4—102no—
493C4×D4—108no—
494C4×D4—102no—
495C4×D4C22×D514yes—
496C4×D4C22×D514yescomplemented
497#117—108no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—102no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4C22×D511yescharacteristic
508C2×C4⋊C4C22×D511yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—108no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C22⋊C4—101no—
517C2×C22⋊C4—101no—
518C2×C22⋊C4—101no—
519C2×C42—51no—
520C2×C42—51no—
521C2×C42—51no—
522C2×C42—54no—
523C2×C42—54no—
524C2×C42—101no—
525C2×C42C22×D511yescharacteristic
526#107—54no—
527#107—54no—
528#106—54no—
529#106C22×D514yescomplemented
530C4⋊C8—54no—
531C4⋊C8—54no—
532#103—54no—
533#103—54no—
534#102—54no—
535#102—54no—
536#102—54no—
537#102—54no—
538#102C22×D514yes—
539#102C22×D514yescomplemented
540C22⋊C8—54no—
541C22⋊C8—54no—
542#97—54no—
543#97C22×D514yescomplemented
544C22×C5—24no—
545C22×C5—48no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—84no—
552C22×C5#52512yes—
553C22×C5C2×AGL(1,ℤ/8)12yes—
554C22×C5#57512yes—
555C22×C5C23×D411yescharacteristic
556C2×D5—28no—
557C2×D5—22no—
558C2×D5—22no—
559C2×D5—24no—
560C2×D5—432no—
561C2×D5—48no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5C2×AGL(1,ℤ/8)14yes—
565C4×C5—22no—
566C4×C5—22no—
567C4×C5—42no—
568C4×C5—42no—
569C4×C5#52512yes—
570C4×C5C22×#4111yescharacteristic
571C4×C5C22×#4111yescharacteristic
572Dic5—22no—
573Dic5—22no—
574Dic5—22no—
575Dic5—42no—
576Dic5—42no—
577Dic5—42no—
578C24—21no—
579C24—21no—
580C24—51no—
581C24—104no—
582C24—108no—
583C24—101no—
584C24—204no—
585C24—204no—
586C2×Q8—52no—
587C2×Q8—101no—
588C2×Q8—102no—
589C2×Q8—102no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—54no—
596C2×D4—52no—
597C2×D4—104no—
598C2×D4—108no—
599C2×D4—1016no—
600C2×D4—108no—
601C2×D4—108no—
602C2×D4—104no—
603C2×D4—102no—
604C2×D4—101no—
605C2×D4—204no—
606C2×D4#70914yes—
607C2×D4C23×D512yes—
608C2×D4C23×D512yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—51no—
616C22×C4—51no—
617C22×C4—51no—
618C22×C4—52no—
619C22×C4—54no—
620C22×C4—52no—
621C22×C4—54no—
622C22×C4—104no—
623C22×C4—104no—
624C22×C4—104no—
625C22×C4—104no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—101no—
629C22×C4—101no—
630C22×C4—101no—
631C22×C4—104no—
632C22×C4—202no—
633C22×C4—204no—
634C22×C4—2032no—
635C22×C4—204no—
636C22×C4—204no—
637C22×C4—204no—
638C22×C4D4×D511yescharacteristic
639C22×C4D4×D511yescharacteristic
640C22×C4C23×D511yescharacteristic
641SD16—108no—
642SD16—108no—
643D8—28no—
644D8—108no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—52no—
648C2×C8—52no—
649C2×C8—102no—
650C2×C8—102no—
651C2×C8C23×D512yes—
652C2×C8C23×D512yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—52no—
656C4⋊C4—52no—
657C4⋊C4—104no—
658C4⋊C4—104no—
659C4⋊C4—104no—
660C4⋊C4—104no—
661C4⋊C4—101no—
662C4⋊C4—101no—
663C4⋊C4—104no—
664C4⋊C4C23×D512yes—
665C4⋊C4C23×D512yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—104no—
669C22⋊C4—104no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C22⋊C4—104no—
674C22⋊C4—104no—
675C42—54no—
676C42—52no—
677C42—54no—
678C42—52no—
679C42—104no—
680C42D4×D512yes—
681C42C23×D512yes—
682C2×C5—44no—
683C2×C5—82no—
684C2×C5#311414yescomplemented
685C2×C5C2×#52511yescharacteristic
686C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
687C2×C5C2×#57511yescharacteristic
688D5—24no—
689D5—44no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—54no—
699C23—52no—
700C23—1016no—
701C23—102no—
702C23—102no—
703C23—104no—
704C23—102no—
705C23—208no—
706C23—2032no—
707C23—208no—
708C23—202no—
709C23—202no—
710C23C2×D4×D511yescharacteristic
711Q8—102no—
712Q8—102no—
713Q8—202no—
714D4—24no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—42no—
719D4—54no—
720D4—1016no—
721D4—104no—
722D4—102no—
723D4—208no—
724D4C2×#70914yes—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—48no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—52no—
734C2×C4—52no—
735C2×C4—52no—
736C2×C4—108no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—104no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—204no—
747C2×C4—208no—
748C2×C4—208no—
749C2×C4—208no—
750C2×C4—208no—
751C2×C4—202no—
752C2×C4—202no—
753C2×C4—202no—
754C2×C4C2×#70912yes—
755C2×C4C2×D4×D512yes—
756C2×C4C2×D4×D512yes—
757C2×C4C2×D4×D511yescharacteristic
758C2×C4D5×#4112yes—
759C2×C4C24×D511yescharacteristic
760C8—22no—
761C8—22no—
762C8—102no—
763C8—102no—
764C5C2×#311411yescharacteristic, complemented, Sylow
765C22—24no—
766C22—48no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—54no—
773C22—84no—
774C22—102no—
775C22—108no—
776C22—102no—
777C22—104no—
778C22—2032no—
779C22—208no—
780C22—202no—
781C22—202no—
782C22#6588112yes—
783C22D5×AGL(1,ℤ/8)12yes—
784C22#6610712yes—
785C22C22×D4×D511yescharacteristic
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—102no—
791C4—102no—
792C4—102no—
793C4—202no—
794C4—202no—
795C4—202no—
796C4#6588112yes—
797C4C22×#70911yescharacteristic
798C4C2×D5×#4111yescharacteristic
799C2—44no—
800C2—82no—
801C2—104no—
802C2—204no—
803C2#1061160214yesdirect product factor
804C2C2×#6588111yescharacteristic
805C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
806C2C2×#6610711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#442C2
socleC23×C5C22×D4
prime radicalC2×#65445C2
hypercenterC2×#442D5
hypocenterC5C2×#3114
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×#65891C2semidirect
2. C2×C4×D4×D5C2semidirect
3. C2×C5×#442C2semidirect
5. C2×#65442C2semidirect
6. C2×#65303C2semidirect
7. C2×#65307C2semidirect
8. #10611602C2direct (N × H)
9. C2×#65160C2semidirect
10. C2×#65151C2semidirect
11. C2×#65076C2semidirect
12. C2×#65063C2semidirect
13. C2×#65065C2semidirect
14. C2×#65055C2semidirect
15. C2×#64999C2semidirect
16. C2×#64994C2semidirect
21. C2×C4×C5×D4C22semidirect
23. C2×#4082C22semidirect
32. #65891C22semidirect
34. C4×D4×D5C22semidirect
38. C2×#4036C22semidirect
45. C2×C4×Dic10C22semidirect
46. C5×#442C22semidirect
47. C2×C5×#106C22semidirect
49. C2×C5×#102C22semidirect
50. C2×C5×#97C22semidirect
52. C2×#3964C22semidirect
54. #65442C22semidirect
58. C2×#3950C22semidirect
59. C2×#3948C22semidirect
60. C2×#3946C22semidirect
61. C2×#3946C22semidirect
62. #65307C22semidirect
63. #65303C22semidirect
64. C2×#3942C22semidirect
66. C2×#3940C22semidirect
67. C2×#3939C22semidirect
68. C2×#3935C22semidirect
69. #65160C22semidirect
70. #65151C22semidirect
71. #65076C22semidirect
72. #65065C22semidirect
73. #65063C22semidirect
74. #65055C22semidirect
75. #64999C22semidirect
76. #64994C22semidirect
107. C4×C5×D4C23semidirect
120. #4082C23semidirect
155. #4036C23semidirect
165. C4×Dic10C23semidirect
166. C5×#106C23semidirect
168. C5×#102C23semidirect
169. C5×#97C23semidirect
171. #3964C23semidirect
175. #3950C23semidirect
176. #3948C23semidirect
177. #3946C23semidirect
178. #3946C23semidirect
179. #3942C23semidirect
181. #3940C23semidirect
182. #3939C23semidirect
183. #3935C23semidirect
196. C2×#442D5semidirect
328. C2×C4×D4C2×D5semidirect
342. #442C2×D5semidirect
349. C2×#106C2×D5semidirect
359. C2×#102C2×D5semidirect
363. C2×#97C2×D5semidirect
496. C4×D4C22×D5semidirect
529. #106C22×D5semidirect
539. #102C22×D5semidirect
543. #97C22×D5semidirect
684. C2×C5#3114semidirect
764. C5C2×#3114semidirect
803. C2#10611602direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658912
C2×C4×D4×D52
C2×C5×#4422
C2×#654452
C2×#654422
C2×#653032
C2×#653072
#106116022
C2×#651602
C2×#651512
C2×#650762
C2×#650632
C2×#650652
C2×#650552
C2×#649992
C2×#649942
C2×#31145