Finite Group Databasebeta

← C2×#10613069 #12978009

Subgroups — C2×#10613069 #12978009

Order 1280.

2146 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×#65950C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic, complemented
3C2×C5×#481C211yesmaximal, characteristic, complemented
4C2×#65328C211yesmaximal, characteristic, complemented
5C2×#65253C211yesmaximal, characteristic, complemented
6#10613069C2116yesmaximal, direct product factor
7C2×#65159C211yesmaximal, characteristic, complemented
8C2×#65155C211yesmaximal, characteristic, complemented
9C2×#65150C211yesmaximal, characteristic, complemented
10C2×#65144C211yesmaximal, characteristic, complemented
11C2×#65066C211yesmaximal, characteristic, complemented
12C2×#65071C211yesmaximal, characteristic, complemented
13C2×#65048C211yesmaximal, characteristic, complemented
14C2×#65045C211yesmaximal, characteristic, complemented
15C2×#65018C211yesmaximal, characteristic, complemented
16C2×#65026C211yesmaximal, characteristic, complemented
17C22×#709—21no—
18C2×C5×#121C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C2×#4085—21no—
21C2×#4084C2211yescharacteristic
22C2×#4082—21no—
23C2×D4×Dic5C2211yescharacteristic
24C22×#686C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4075—21no—
27C2×C4×C22⋊D5C2211yescharacteristic
28C2×#4072C2211yescharacteristic
29C22×#681C2211yescharacteristic
30C22×#676C2211yescharacteristic
31#65950—24no—
32#65950C2218yescomplemented
33C2×#4042—21no—
34#65841—24no—
35#65841C2218yescomplemented
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4039C2211yescharacteristic
39C2×#4038C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4031—21no—
44C2×#4023—21no—
45C5×#481C2218yescomplemented
46C2×C5×#106C2211yescharacteristic
47C2×C5×#106C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3950C2211yescharacteristic
56C2×#3949C2211yescharacteristic
57C2×#3946C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65328C2218yescomplemented
60C2×#3941C2211yescharacteristic
61#65253C2218yescomplemented
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3940C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67#65159C2218yescomplemented
68#65155C2218yescomplemented
69#65150C2218yescomplemented
70#65144C2218yescomplemented
71#65071C2218yescomplemented
72#65066C2218yescomplemented
73#65048C2218yescomplemented
74#65045C2218yescomplemented
75#65026C2218yescomplemented
76#65018C2218yescomplemented
77C2×#3354—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5D411yescharacteristic
85C23×Dic5—21no—
86C2×#709—28no—
87C2×#709—48no—
88C22×D20—21no—
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5C2311yescharacteristic
93C22×Dic10—21no—
94C22×Dic10—21no—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C5×#121—22no—
98C5×#121C2314yes—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C22⋊C4—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5D411yescharacteristic
110#4085—28no—
111#4084—22no—
112#4084C2314yes—
113#4082—28no—
114D4×Dic5—22no—
115D4×Dic5C2314yes—
116C2×#686—24no—
117C2×#686C2314yes—
118#4076—22no—
119#4076C2314yes—
120#4075—28no—
121C4×C22⋊D5D414yes—
122C4×C22⋊D5C2314yes—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685—21no—
127C2×#685D411yescharacteristic
128#4072—22no—
129#4072C2314yes—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683D411yescharacteristic
137C2×C4×Dic5—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5C2311yescharacteristic
140C2×#681—24no—
141C2×#681C2314yes—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C2×#676—24no—
145C2×#676C2314yes—
146#4042—28no—
147#4041—22no—
148#4041C2314yes—
149#4040—28no—
150#4039—22no—
151#4039C2314yes—
152#4038—22no—
153#4038C2314yes—
154D5×C4⋊C4—22no—
155D5×C4⋊C4C2314yes—
156#4034—22no—
157#4034—22no—
158#4034C2314yes—
159#4034C2314yes—
160#4031—28no—
161#4023—28no—
162C5×#106C2314yes—
163C5×#106C2314yes—
164C5×#102C2314yes—
165C5×#102C2314yes—
166C5×C22⋊C8C2314yes—
167#3964C2314yes—
168#3953C2314yes—
169#3953C2314yes—
170#3952C2314yes—
171#3950C2314yes—
172#3949C2314yes—
173#3946C2314yes—
174C8×Dic5C2314yes—
175#3941C2314yes—
176#3940C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181C2×#555—51no—
182C2×#547—51no—
183#3354—516no—
184C2×#498—51no—
185C2×#481—51no—
186C2×#481D511yescharacteristic, complemented
187C2×#482—51no—
188C2×#482—51no—
189C2×#476—51no—
190C2×#474—51no—
191C2×#469—51no—
192C2×#469—51no—
193C2×C4×D8—51no—
194C2×#436—51no—
195C2×#428—51no—
196C2×#428—51no—
197C24×C5—21no—
198C24×C5C2×D411yescharacteristic
199C23×D5—21no—
200C23×D5C2×D411yescharacteristic
201C2×C5×D4—24no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—82no—
206C2×C5×D4C2412yes—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—24no—
213C22×C4×C5—44no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—44no—
222C2×C22⋊D5—82no—
223C2×C22⋊D5C2×D414yes—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—44no—
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232#709—432no—
233C2×D20—22no—
234C2×D20—22no—
235C2×D20—24no—
236C2×D20—21no—
237C2×D20—44no—
238C2×D20C2412yes—
239C2×C4×D5—22no—
240C2×C4×D5—22no—
241C2×C4×D5—24no—
242C2×C4×D5—24no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×C4×D5C2×D412yes—
246C2×C4×D5C2412yes—
247C2×Dic10—24no—
248C2×Dic10—24no—
249C2×Dic10—44no—
250C2×Dic10—82no—
251C2×C5×C8—22no—
252C2×C5×C8—22no—
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C4⋊C4C2412yes—
262C5×C22⋊C4—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265C22⋊Dic5—24no—
266C22⋊Dic5C2×D414yes—
267#686—28no—
268#685—24no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685C2×D414yes—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279#683—24no—
280#683—24no—
281#683—24no—
282#683C2×D414yes—
283C4×Dic5—24no—
284C4×Dic5—24no—
285C4×Dic5C2×D412yes—
286C4×Dic5C2412yes—
287#681—28no—
288C2×#168—22no—
289C2×#168#4114yescomplemented
290C2×#168C2412yes—
291C2×#168C2412yes—
292#676—28no—
293C22×#41—101no—
294C22×D8—51no—
295C22×M16—51no—
296C22×M16—51no—
297#555—58no—
298#555—104no—
299#547—58no—
300#547—104no—
301C2×C4⋊Q8—51no—
302C2×C4⋊Q8—51no—
303C2×#124—101no—
304C2×#124—101no—
305C2×#123—101no—
306C2×#123—101no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—51no—
311C2×#121—101no—
312C2×#121C2×D511yescharacteristic
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—51no—
316C2×#117—51no—
317C2×#117—51no—
318C2×#117—101no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4C2×D511yescharacteristic
321#498—58no—
322#482—58no—
323#482—58no—
324#481—58no—
325#481C2×D518yescomplemented
326#476—58no—
327#474—58no—
328#469—58no—
329#469—58no—
330C4×D8—58no—
331#436—58no—
332#428—58no—
333#428—58no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#107—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—51no—
341C2×#106C2×D511yescharacteristic
342C2×#106C2×D511yescharacteristic
343C2×C4⋊C8—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349C2×#102C2×D511yescharacteristic
350C2×C22⋊C8—51no—
351C2×C22⋊C8C2×D511yescharacteristic
352C2×C4×C8—51no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5C22×D412yes—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5C22×D412yes—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—42no—
373C5×D4—84no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—48no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D411yescharacteristic
387C2×C4×C5C2×#4112yes—
388C2×C4×C52−1+412yes—
389C2×C4×C5C2511yescharacteristic
390C22⋊D5—28no—
391C22⋊D5—48no—
392C22⋊D5—84no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—48no—
402C2×Dic5AGL(1,ℤ/8)14yes—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406D20—22no—
407D20—22no—
408D20—48no—
409D20—42no—
410C4×D5—24no—
411C4×D5—22no—
412C4×D5—22no—
413C4×D5—48no—
414C4×D5—48no—
415Dic10—48no—
416Dic10—84no—
417C5×C8—22no—
418C5×C8—22no—
419#168—22no—
420#168C2×#4114yescomplemented
421C2×#41—108no—
422C2×#41—208no—
423C22×Q8—101no—
424C22×Q8—101no—
425C22×D4—21no—
426C22×D4—51no—
427C22×D4—51no—
428C22×D4—101no—
429C22×D4—101no—
430C22×D4—101no—
431C22×D4C22×D511yescharacteristic
432C23×C4—21no—
433C23×C4—51no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4C22×D511yescharacteristic
438C2×D8—54no—
439C2×D8—104no—
440C2×M16—54no—
441C2×M16—54no—
442C2×M16—104no—
443C2×M16—104no—
444C22×C8—51no—
445C22×C8—51no—
446C22×C8C22×D511yescharacteristic
447C22×C8C22×D511yescharacteristic
448C4⋊Q8—54no—
449C4⋊Q8—54no—
450C4⋊Q8—102no—
451C4⋊Q8—102no—
452#124—108no—
453#124—108no—
454#123—108no—
455#123—108no—
456C22⋊Q8—108no—
457#121—22no—
458#121—54no—
459#121—54no—
460#121—54no—
461#121—102no—
462#121—102no—
463#121—108no—
464#121—102no—
465#121C22×D514yes—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—102no—
471C4×D4—102no—
472#117—54no—
473#117—54no—
474#117—108no—
475#117—102no—
476#117—102no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—102no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D514yes—
491C2×C4⋊C4C22×D511yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—51no—
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⋊C4—101no—
502C2×C42—51no—
503C2×C42—101no—
504C2×C42—101no—
505#107—54no—
506#107—54no—
507#107—54no—
508#106—54no—
509#106—54no—
510#106—54no—
511#106—54no—
512#106C22×D514yes—
513#106C22×D514yes—
514C4⋊C8—54no—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#102C22×D514yes—
520#102C22×D514yes—
521C22⋊C8—54no—
522C22⋊C8C22×D514yes—
523C4×C8—54no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—44no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5—42no—
531C22×C5—84no—
532C22×C5#54712yes—
533C22×C5C2×AGL(1,ℤ/8)12yes—
534C22×C5#57712yes—
535C22×C5C23×D411yescharacteristic
536C2×D5—22no—
537C2×D5—22no—
538C2×D5—22no—
539C2×D5—44no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5#54712yes—
549C4×C5C22×#4111yescharacteristic
550C4×C5C2×2−1+411yescharacteristic
551Dic5—22no—
552Dic5—22no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556Dic5C2×AGL(1,ℤ/8)14yes—
557C24—21no—
558C24—51no—
559C24—101no—
560C24D4×D511yescharacteristic
561#41—2032no—
562C2×Q8—104no—
563C2×Q8—104no—
564C2×Q8—204no—
565C2×Q8—402no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—54no—
571C2×D4—52no—
572C2×D4—82no—
573C2×D4—104no—
574C2×D4—104no—
575C2×D4—104no—
576C2×D4—104no—
577C2×D4—101no—
578C2×D4—102no—
579C2×D4—102no—
580C2×D4—204no—
581C2×D4—204no—
582C2×D4—402no—
583C2×D4C23×D512yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—44no—
591C22×C4—51no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—52no—
595C22×C4—52no—
596C22×C4—104no—
597C22×C4—104no—
598C22×C4—104no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—204no—
605C22×C4—204no—
606C22×C4—204no—
607C22×C4D4×D512yes—
608C22×C4D4×D511yescharacteristic
609C22×C4C23×D512yes—
610C22×C4C23×D511yescharacteristic
611D8—108no—
612M16—108no—
613M16—108no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—54no—
617C2×C8—52no—
618C2×C8—52no—
619C2×C8—102no—
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—54no—
627C4⋊C4—52no—
628C4⋊C4—52no—
629C4⋊C4—52no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—101no—
634C4⋊C4—101no—
635C4⋊C4—101no—
636C4⋊C4C23×D512yes—
637C4⋊C4C23×D512yes—
638C4⋊C4C23×D512yes—
639C22⋊C4—24no—
640C22⋊C4—54no—
641C22⋊C4—54no—
642C22⋊C4—104no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C42—52no—
650C42—52no—
651C42—104no—
652C42—104no—
653C2×C5—42no—
654C2×C5—82no—
655C2×C5#335414yescomplemented
656C2×C5C2×#54711yescharacteristic
657C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
658C2×C5C2×#57711yescharacteristic
659D5—42no—
660D5—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—52no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—202no—
674C23—202no—
675C23—202no—
676C23C2×D4×D512yes—
677C23C2×D4×D511yescharacteristic
678Q8—208no—
679Q8—404no—
680D4—22no—
681D4—22no—
682D4—42no—
683D4—84no—
684D4—108no—
685D4—102no—
686D4—102no—
687D4—208no—
688D4—208no—
689D4—202no—
690D4—404no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—48no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—54no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—104no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—208no—
715C2×C4—208no—
716C2×C4—208no—
717C2×C4—202no—
718C2×C4—202no—
719C2×C4—202no—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D511yescharacteristic
722C2×C4D5×#4112yes—
723C2×C4#415012yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—54no—
728C8—102no—
729C5C2×#335411yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—102no—
739C22—102no—
740C22—102no—
741C22—204no—
742C22—202no—
743C22—202no—
744C22—202no—
745C22—404no—
746C22#6598912yes—
747C22#6609612yes—
748C22D5×AGL(1,ℤ/8)12yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—54no—
755C4—102no—
756C4—102no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4#6598912yes—
761C4C2×D5×#4111yescharacteristic
762C4C2×#415011yescharacteristic
763C2—42no—
764C2—82no—
765C2—202no—
766C2—402no—
767C2#1061306914yesdirect product factor
768C2C2×#6598911yescharacteristic
769C2C2×#6609611yescharacteristic
770C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#481C2
socleC23×C5C22×D4
hypercenterC2×#481D5
hypocenterC5C2×#3354
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#65950C2semidirect
2. C2×#65841C2semidirect
3. C2×C5×#481C2semidirect
4. C2×#65328C2semidirect
5. C2×#65253C2semidirect
6. #10613069C2direct (N × H)
7. C2×#65159C2semidirect
8. C2×#65155C2semidirect
9. C2×#65150C2semidirect
10. C2×#65144C2semidirect
11. C2×#65066C2semidirect
12. C2×#65071C2semidirect
13. C2×#65048C2semidirect
14. C2×#65045C2semidirect
15. C2×#65018C2semidirect
16. C2×#65026C2semidirect
32. #65950C22semidirect
35. #65841C22semidirect
45. C5×#481C22semidirect
59. #65328C22semidirect
61. #65253C22semidirect
67. #65159C22semidirect
68. #65155C22semidirect
69. #65150C22semidirect
70. #65144C22semidirect
71. #65071C22semidirect
72. #65066C22semidirect
73. #65048C22semidirect
74. #65045C22semidirect
75. #65026C22semidirect
76. #65018C22semidirect
186. C2×#481D5semidirect
289. C2×#168#41semidirect
325. #481C2×D5semidirect
420. #168C2×#41semidirect
655. C2×C5#3354semidirect
729. C5C2×#3354semidirect
767. C2#10613069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659502
C2×#658412
C2×C5×#4812
C2×#653282
C2×#652532
#106130692
C2×#651592
C2×#651552
C2×#651502
C2×#651442
C2×#650662
C2×#650712
C2×#650482
C2×#650452
C2×#650182
C2×#650262
C2×#33545