Finite Group Databasebeta

← C2×#10613114 #12975845

Subgroups — C2×#10613114 #12975845

Order 1280.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65943C211yesmaximal, characteristic
2C2×#65863C211yesmaximal, characteristic, complemented
3C2×C5×#482C211yesmaximal, characteristic, complemented
4C2×#65331C211yesmaximal, characteristic, complemented
5C2×#65290C211yesmaximal, characteristic, complemented
6#10613114C2116yesmaximal, direct product factor
7C2×#65171C211yesmaximal, characteristic, complemented
8C2×#65178C211yesmaximal, characteristic, complemented
9C2×#65160C211yesmaximal, characteristic, complemented
10C2×#65153C211yesmaximal, characteristic, complemented
11C2×#65051C211yesmaximal, characteristic, complemented
12C2×#65065C211yesmaximal, characteristic, complemented
13C2×D5×#102C211yesmaximal, characteristic, complemented
14C2×#65053C211yesmaximal, characteristic, complemented
15C2×#65020C211yesmaximal, characteristic, complemented
16C2×#65017C211yesmaximal, characteristic, complemented
17C22×D4×D5—21no—
18C22×D4×D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic, complemented
22C2×#4086C2211yescharacteristic
23C2×#4083—21no—
24C22×#687C2211yescharacteristic, complemented
25C2×C4×C22⋊D5C2211yescharacteristic
26C2×#4070C2211yescharacteristic, complemented
27C22×#681C2211yescharacteristic, complemented
28C22×#677C2211yescharacteristic
29C22×#677C2211yescharacteristic, complemented
30C22×C8×D5C2211yescharacteristic, complemented
31#65943—24no—
32#65943C2218yes—
33#65863—24no—
34#65863C2218yescomplemented
35C2×#4043C2211yescharacteristic, complemented
36C2×#4041C2211yescharacteristic
37C2×#4039C2211yescharacteristic
38C2×D5×C4⋊C4C2211yescharacteristic, complemented
39C2×#4036C2211yescharacteristic, complemented
40C2×#4033C2211yescharacteristic, complemented
41C2×#4030—21no—
42C2×#4029—21no—
43C2×#4028—21no—
44C2×#4025—21no—
45C2×#4018—21no—
46C2×#4016—21no—
47C5×#482C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#106C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic, complemented
51C2×C5×#102C2211yescharacteristic, complemented
52C2×C5×C22⋊C8C2211yescharacteristic, complemented
53C2×#3964C2211yescharacteristic, complemented
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic, complemented
56C2×#3952C2211yescharacteristic, complemented
57C2×#3947C2211yescharacteristic, complemented
58C2×#3946C2211yescharacteristic, complemented
59#65331C2218yescomplemented
60#65290C2218yescomplemented
61C2×#3942C2211yescharacteristic, complemented
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic, complemented
65C2×#3941C2211yescharacteristic, complemented
66C2×#3939C2211yescharacteristic, complemented
67#65178C2218yescomplemented
68#65171C2218yescomplemented
69#65160C2218yescomplemented
70#65153C2218yescomplemented
71#65065C2218yescomplemented
72D5×#102C2218yescomplemented
73#65053C2218yescomplemented
74#65051C2218yescomplemented
75#65020C2218yescomplemented
76#65017C2218yescomplemented
77C2×#3310—51nomaximal, Sylow
78C24×D5—21no—
79C24×D5—21no—
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5D411yescharacteristic
87C2×D4×D5—28no—
88C2×D4×D5—24no—
89C2×D4×D5—22no—
90C2×D4×D5—42no—
91C2×D4×D5—48no—
92C2×D4×D5C2314yes—
93C22×D20—24no—
94C22×D20—21no—
95C22×D20—21no—
96C22×D20—22no—
97C22×D20—42no—
98C22×D20C2311yescharacteristic
99C22×D20C2314yes—
100C22×D20C2311yescharacteristic
101C22×C4×D5—21no—
102C22×C4×D5—21no—
103C22×C4×D5C2311yescharacteristic
104C22×Dic10C2311yescharacteristic
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C5×#121—22no—
108C5×#121C2314yes—
109C5×#117—22no—
110C5×#117C2314yescomplemented
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C42×C5—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5D411yescharacteristic
119#4086—22no—
120#4086C2314yes—
121#4083—28no—
122C2×#687—42no—
123C2×#687C2314yescomplemented
124C4×C22⋊D5D414yes—
125C4×C22⋊D5C2314yes—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685—21no—
129C2×#685D411yescharacteristic
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5C2311yescharacteristic
133#4070—22no—
134#4070C2314yescomplemented
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683D411yescharacteristic
140C2×C4×Dic5—21no—
141C2×C4×Dic5C2311yescharacteristic
142C2×#681—42no—
143C2×#681C2314yescomplemented
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146C2×#677—24no—
147C2×#677—42no—
148C2×#677C2314yes—
149C2×#677C2314yescomplemented
150C2×C8×D5—42no—
151C2×C8×D5C2314yescomplemented
152#4043—22no—
153#4043C2314yescomplemented
154#4041—22no—
155#4041C2314yes—
156#4039—22no—
157#4039C2314yes—
158D5×C4⋊C4—22no—
159D5×C4⋊C4C2314yescomplemented
160#4036—22no—
161#4036C2314yescomplemented
162#4033—22no—
163#4033C2314yescomplemented
164#4030—28no—
165#4029—28no—
166#4028—28no—
167#4025—28no—
168#4018—28no—
169#4016—28no—
170C5×#107C2314yescomplemented
171C5×#106C2314yescomplemented
172C5×#102C2314yescomplemented
173C5×#102C2314yescomplemented
174C5×C22⋊C8C2314yescomplemented
175#3964C2314yescomplemented
176#3953C2314yes—
177#3953C2314yescomplemented
178#3952C2314yescomplemented
179#3947C2314yescomplemented
180#3946C2314yescomplemented
181#3942C2314yescomplemented
182#3941C2314yes—
183#3941C2314yes—
184#3941C2314yescomplemented
185#3941C2314yescomplemented
186#3939C2314yescomplemented
187C2×#552—51no—
188C2×D42—51no—
189#3310—516no—
190C2×#490—51no—
191C2×#482D511yescharacteristic, complemented
192C2×#480—51no—
193C2×#478—51no—
194C2×#468—51no—
195C2×#465—51no—
196C2×#460—51no—
197C2×#450—51no—
198C2×#450—51no—
199C2×#440—51no—
200C2×#435—51no—
201C2×#418—51no—
202C22×#102—51no—
203C24×C5—21no—
204C24×C5C2×D411yescharacteristic
205C23×D5—21no—
206C23×D5—21no—
207C23×D5—24no—
208C23×D5—24no—
209C23×D5—44no—
210C23×D5—44no—
211C23×D5—44no—
212C23×D5—44no—
213C23×D5—82no—
214C23×D5—82no—
215C23×D5C2×D411yescharacteristic
216C2×C5×D4—24no—
217C2×C5×D4—21no—
218C2×C5×D4—22no—
219C2×C5×D4—22no—
220C2×C5×D4—44no—
221C2×C5×D4C2412yes—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C2×C22⋊D5—24no—
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—24no—
235C2×C22⋊D5—44no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—82no—
238C2×C22⋊D5C2×D414yes—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5C2×D411yescharacteristic
242C22×Dic5C2×D411yescharacteristic
243C22×Dic5C2×D411yescharacteristic
244D4×D5—28no—
245D4×D5—44no—
246D4×D5—48no—
247D4×D5—432no—
248C2×D20—21no—
249C2×D20—22no—
250C2×D20—22no—
251C2×D20—22no—
252C2×D20—28no—
253C2×D20—24no—
254C2×D20—24no—
255C2×D20—21no—
256C2×D20—44no—
257C2×D20—48no—
258C2×D20—44no—
259C2×D20—44no—
260C2×D20#4114yes—
261C2×D20C2412yes—
262C2×D20C2412yes—
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5—24no—
266C2×C4×D5—24no—
267C2×C4×D5—44no—
268C2×C4×D5—44no—
269C2×C4×D5C2×D412yes—
270C2×C4×D5C2412yes—
271C2×Dic10—22no—
272C2×Dic10—22no—
273C2×Dic10—21no—
274C2×Dic10C2412yes—
275C2×C5×C8—22no—
276C2×C5×C8—22no—
277C2×C5×C8C2412yes—
278C2×C5×C8C2412yes—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4C2412yes—
283C5×C4⋊C4C2412yes—
284C5×C4⋊C4C2412yes—
285C5×C22⋊C4—24no—
286C5×C22⋊C4—24no—
287C42×C5—24no—
288C22⋊Dic5—24no—
289C22⋊Dic5C2×D414yes—
290#687—44no—
291#685—24no—
292#685—24no—
293#685—24no—
294#685C2×D414yes—
295C4⋊Dic5—21no—
296C4⋊Dic5—24no—
297C4⋊Dic5—24no—
298C4⋊Dic5C2412yes—
299#683—24no—
300#683—24no—
301#683—24no—
302#683—24no—
303#683C2×D414yes—
304C4×Dic5—24no—
305C4×Dic5C2×D412yes—
306C4×Dic5C2412yes—
307#681—44no—
308C2×#168—22no—
309C2×#168—22no—
310C2×#168C2412yes—
311C2×#168C2412yes—
312#677—28no—
313#677—44no—
314C8×D5—44no—
315C23×D4—51no—
316C23×D4—51no—
317C23×D4—101no—
318C22×SD16—51no—
319C22×SD16—51no—
320C22×SD16—51no—
321C22×M16—51no—
322C23×C8—51no—
323#552—58no—
324#552—104no—
325D42—58no—
326D42—104no—
327C2×#127—51no—
328C2×#126—101no—
329C2×#125—51no—
330C2×#125—101no—
331C2×#123—101no—
332C2×C22⋊Q8—51no—
333C2×C22⋊Q8—51no—
334C2×#121—51no—
335C2×#121—101no—
336C2×#121C2×D511yescharacteristic
337C2×#120—101no—
338C2×#120—101no—
339C2×C4×Q8—51no—
340C2×C4×D4—51no—
341C2×C4×D4—51no—
342C2×#117—101no—
343C2×#117C2×D511yescharacteristic, complemented
344C22×C4⋊C4—51no—
345#490—58no—
346#482C2×D518yescomplemented
347#480—58no—
348#478—58no—
349#468—58no—
350#465—58no—
351#460—58no—
352#450—58no—
353#450—58no—
354#440—58no—
355#435—58no—
356C2×#107—51no—
357C2×#107C2×D511yescharacteristic, complemented
358C2×#106C2×D511yescharacteristic, complemented
359C2×C4⋊C8—51no—
360#418—58no—
361C2×#103—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—58no—
370C2×#102C2×D511yescharacteristic, complemented
371C2×#102C2×D511yescharacteristic, complemented
372C2×C22⋊C8—51no—
373C2×C22⋊C8C2×D511yescharacteristic, complemented
374C2×#97—51no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—42no—
380C23×C5—42no—
381C23×C5—42no—
382C23×C5C22×D412yes—
383C23×C5C22×D411yescharacteristic
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—24no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—48no—
390C22×D5—48no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—48no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—42no—
397C22×D5—48no—
398C22×D5—84no—
399C22×D5—816no—
400C22×D5—84no—
401C22×D5—816no—
402C22×D5AGL(1,ℤ/8)14yes—
403C22×D5C22×D412yes—
404C5×D4—22no—
405C5×D4—22no—
406C5×D4—48no—
407C5×D4—42no—
408C2×C4×C5—22no—
409C2×C4×C5—24no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—42no—
416C2×C4×C5—42no—
417C2×C4×C5—42no—
418C2×C4×C5C22×D412yes—
419C2×C4×C5C22×D411yescharacteristic
420C2×C4×C5C2×#4112yes—
421C2×C4×C5H(5,𝔽2)12yes—
422C2×C4×C5C2511yescharacteristic
423C22⋊D5—28no—
424C22⋊D5—48no—
425C22⋊D5—48no—
426C22⋊D5—84no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—42no—
433C2×Dic5—42no—
434C2×Dic5C22×D412yes—
435C2×Dic5C22×D412yes—
436C2×Dic5C22×D412yes—
437D20—24no—
438D20—22no—
439D20—22no—
440D20—22no—
441D20—48no—
442D20—48no—
443D20—42no—
444D20C2×#4114yes—
445C4×D5—24no—
446C4×D5—22no—
447C4×D5—22no—
448C4×D5—48no—
449C4×D5—48no—
450Dic10—22no—
451Dic10—22no—
452Dic10—42no—
453C5×C8—22no—
454C5×C8—22no—
455#168—22no—
456#168—22no—
457C25—101no—
458C25—101no—
459C22×Q8—51no—
460C22×D4—21no—
461C22×D4—51no—
462C22×D4—54no—
463C22×D4—51no—
464C22×D4—51no—
465C22×D4—54no—
466C22×D4—104no—
467C22×D4—101no—
468C22×D4—102no—
469C22×D4—101no—
470C22×D4—101no—
471C22×D4—101no—
472C22×D4—104no—
473C22×D4—108no—
474C22×D4—101no—
475C22×D4—102no—
476C22×D4—202no—
477C22×D4—202no—
478C22×D4—208no—
479C22×D4C22×D511yescharacteristic
480C23×C4—51no—
481C23×C4—101no—
482C23×C4—101no—
483C23×C4C22×D511yescharacteristic
484C2×SD16—54no—
485C2×SD16—54no—
486C2×SD16—54no—
487C2×SD16—104no—
488C2×SD16—202no—
489C2×SD16—202no—
490C2×M16—54no—
491C2×M16—202no—
492C22×C8—51no—
493C22×C8—51no—
494C22×C8—54no—
495C22×C8—202no—
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D511yescharacteristic
498#127—54no—
499#127—102no—
500#126—108no—
501#125—54no—
502#125—108no—
503#125—102no—
504#123—108no—
505C22⋊Q8—54no—
506C22⋊Q8—54no—
507C22⋊Q8—102no—
508C22⋊Q8—102no—
509#121—22no—
510#121—54no—
511#121—108no—
512#121—102no—
513#121C22×D514yes—
514#120—108no—
515#120—108no—
516C4×Q8—54no—
517C4×Q8—102no—
518C4×D4—54no—
519C4×D4—54no—
520C4×D4—54no—
521C4×D4—102no—
522#117—22no—
523#117—108no—
524#117C22×D514yescomplemented
525C2×C4⋊C4—51no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—54no—
528C2×C4⋊C4—102no—
529C2×C4⋊C4—101no—
530C2×C4⋊C4—101no—
531C2×C4⋊C4—101no—
532C2×C4⋊C4—101no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4C22×D511yescharacteristic
536C2×C4⋊C4C22×D511yescharacteristic
537C2×C4⋊C4C22×D511yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—51no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C42—21no—
547C2×C42—51no—
548C2×C42—101no—
549#107—54no—
550#107C22×D514yescomplemented
551#106C22×D514yescomplemented
552C4⋊C8—54no—
553#103—54no—
554#102—54no—
555#102—54no—
556#102—54no—
557#102—54no—
558#102—54no—
559#102—54no—
560#102—54no—
561#102C22×D514yescomplemented
562#102C22×D514yescomplemented
563C22⋊C8—54no—
564C22⋊C8C22×D514yescomplemented
565#97—54no—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—44no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—84no—
574C22×C5#54612yes—
575C22×C5C2×AGL(1,ℤ/8)12yes—
576C22×C5#57712yes—
577C22×C5C23×D411yescharacteristic
578C2×D5—22no—
579C2×D5—28no—
580C2×D5—22no—
581C2×D5—24no—
582C2×D5—48no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—816no—
589C2×D5—816no—
590C2×D5—84no—
591C2×D5C2×AGL(1,ℤ/8)14yes—
592C4×C5—22no—
593C4×C5—42no—
594C4×C5—42no—
595C4×C5—42no—
596C4×C5#54612yes—
597C4×C5C22×#4111yescharacteristic
598C4×C5C2×H(5,𝔽2)11yescharacteristic
599Dic5—22no—
600Dic5—22no—
601Dic5—22no—
602Dic5—42no—
603Dic5—42no—
604C24—21no—
605C24—51no—
606C24—104no—
607C24—101no—
608C24—101no—
609C24—104no—
610C24—204no—
611C24—204no—
612C24—204no—
613C24—204no—
614C24—402no—
615C24—402no—
616C24D4×D511yescharacteristic
617C2×Q8—52no—
618C2×Q8—101no—
619C2×Q8—102no—
620C2×Q8—102no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—54no—
627C2×D4—54no—
628C2×D4—52no—
629C2×D4—52no—
630C2×D4—108no—
631C2×D4—104no—
632C2×D4—104no—
633C2×D4—104no—
634C2×D4—104no—
635C2×D4—108no—
636C2×D4—104no—
637C2×D4—101no—
638C2×D4—104no—
639C2×D4—101no—
640C2×D4—102no—
641C2×D4—102no—
642C2×D4—102no—
643C2×D4—204no—
644C2×D4—208no—
645C2×D4—204no—
646C2×D4—204no—
647C2×D4—204no—
648C2×D4—208no—
649C2×D4—204no—
650C2×D4—204no—
651C2×D4—2032no—
652C2×D4—402no—
653C2×D4C23×D512yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—51no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—104no—
665C22×C4—104no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—101no—
669C22×C4—101no—
670C22×C4—204no—
671C22×C4—204no—
672C22×C4D4×D512yes—
673C22×C4D4×D511yescharacteristic
674C22×C4C23×D512yes—
675C22×C4C23×D511yescharacteristic
676SD16—108no—
677SD16—204no—
678SD16—204no—
679M16—204no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—52no—
683C2×C8—52no—
684C2×C8—102no—
685C2×C8—102no—
686C2×C8—204no—
687C2×C8C23×D512yes—
688C2×C8C23×D512yes—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—54no—
693C4⋊C4—52no—
694C4⋊C4—104no—
695C4⋊C4—104no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—104no—
699C4⋊C4—101no—
700C4⋊C4—104no—
701C4⋊C4C23×D512yes—
702C4⋊C4C23×D512yes—
703C4⋊C4C23×D512yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—54no—
707C22⋊C4—54no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C42—24no—
713C42—52no—
714C42—52no—
715C42—104no—
716C2×C5—42no—
717C2×C5—82no—
718C2×C5#331014yescomplemented
719C2×C5C2×#54611yescharacteristic
720C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
721C2×C5C2×#57711yescharacteristic
722D5—24no—
723D5—44no—
724D5—82no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—54no—
733C23—52no—
734C23—102no—
735C23—102no—
736C23—104no—
737C23—102no—
738C23—102no—
739C23—208no—
740C23—208no—
741C23—208no—
742C23—208no—
743C23—202no—
744C23—202no—
745C23—202no—
746C23—202no—
747C23—202no—
748C23—404no—
749C23—404no—
750C23—4016no—
751C23—4016no—
752C23C2×D4×D512yes—
753C23C2×D4×D511yescharacteristic
754Q8—102no—
755Q8—102no—
756Q8—202no—
757D4—22no—
758D4—22no—
759D4—48no—
760D4—42no—
761D4—54no—
762D4—108no—
763D4—104no—
764D4—102no—
765D4—102no—
766D4—102no—
767D4—208no—
768D4—208no—
769D4—208no—
770D4—208no—
771D4—202no—
772D4—404no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—52no—
784C2×C4—52no—
785C2×C4—52no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—104no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—208no—
795C2×C4—208no—
796C2×C4—202no—
797C2×C4—202no—
798C2×C4C2×D4×D512yes—
799C2×C4C2×D4×D511yescharacteristic
800C2×C4D5×#4112yes—
801C2×C4#414912yes—
802C2×C4C24×D511yescharacteristic
803C8—22no—
804C8—22no—
805C8—102no—
806C8—102no—
807C5C2×#331011yescharacteristic, complemented, Sylow
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—54no—
816C22—84no—
817C22—102no—
818C22—108no—
819C22—102no—
820C22—104no—
821C22—208no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—202no—
826C22—202no—
827C22—4016no—
828C22—4016no—
829C22—404no—
830C22#6598812yes—
831C22#6610412yes—
832C22D5×AGL(1,ℤ/8)12yes—
833C22C22×D4×D511yescharacteristic
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—102no—
839C4—102no—
840C4—102no—
841C4—202no—
842C4—202no—
843C4#6598812yes—
844C4C2×D5×#4111yescharacteristic
845C4C2×#414911yescharacteristic
846C2—42no—
847C2—82no—
848C2—104no—
849C2—204no—
850C2—402no—
851C2#1061311414yesdirect product factor
852C2C2×#6598811yescharacteristic
853C2C2×#6610411yescharacteristic
854C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#482C2
socleC23×C5C22×D4
prime radicalC2×#65943C2
hypercenterC2×#482D5
hypocenterC5C2×#3310
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#65863C2semidirect
3. C2×C5×#482C2semidirect
4. C2×#65331C2semidirect
5. C2×#65290C2semidirect
6. #10613114C2direct (N × H)
7. C2×#65171C2semidirect
8. C2×#65178C2semidirect
9. C2×#65160C2semidirect
10. C2×#65153C2semidirect
11. C2×#65051C2semidirect
12. C2×#65065C2semidirect
13. C2×D5×#102C2semidirect
14. C2×#65053C2semidirect
15. C2×#65020C2semidirect
16. C2×#65017C2semidirect
21. C2×C5×#117C22semidirect
24. C22×#687C22semidirect
26. C2×#4070C22semidirect
27. C22×#681C22semidirect
29. C22×#677C22semidirect
30. C22×C8×D5C22semidirect
34. #65863C22semidirect
35. C2×#4043C22semidirect
38. C2×D5×C4⋊C4C22semidirect
39. C2×#4036C22semidirect
40. C2×#4033C22semidirect
47. C5×#482C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#106C22semidirect
50. C2×C5×#102C22semidirect
51. C2×C5×#102C22semidirect
52. C2×C5×C22⋊C8C22semidirect
53. C2×#3964C22semidirect
55. C2×#3953C22semidirect
56. C2×#3952C22semidirect
57. C2×#3947C22semidirect
58. C2×#3946C22semidirect
59. #65331C22semidirect
60. #65290C22semidirect
61. C2×#3942C22semidirect
64. C2×#3941C22semidirect
65. C2×#3941C22semidirect
66. C2×#3939C22semidirect
67. #65178C22semidirect
68. #65171C22semidirect
69. #65160C22semidirect
70. #65153C22semidirect
71. #65065C22semidirect
72. D5×#102C22semidirect
73. #65053C22semidirect
74. #65051C22semidirect
75. #65020C22semidirect
76. #65017C22semidirect
110. C5×#117C23semidirect
123. C2×#687C23semidirect
134. #4070C23semidirect
143. C2×#681C23semidirect
149. C2×#677C23semidirect
151. C2×C8×D5C23semidirect
153. #4043C23semidirect
159. D5×C4⋊C4C23semidirect
161. #4036C23semidirect
163. #4033C23semidirect
170. C5×#107C23semidirect
171. C5×#106C23semidirect
172. C5×#102C23semidirect
173. C5×#102C23semidirect
174. C5×C22⋊C8C23semidirect
175. #3964C23semidirect
177. #3953C23semidirect
178. #3952C23semidirect
179. #3947C23semidirect
180. #3946C23semidirect
181. #3942C23semidirect
184. #3941C23semidirect
185. #3941C23semidirect
186. #3939C23semidirect
191. C2×#482D5semidirect
343. C2×#117C2×D5semidirect
346. #482C2×D5semidirect
357. C2×#107C2×D5semidirect
358. C2×#106C2×D5semidirect
370. C2×#102C2×D5semidirect
371. C2×#102C2×D5semidirect
373. C2×C22⋊C8C2×D5semidirect
524. #117C22×D5semidirect
550. #107C22×D5semidirect
551. #106C22×D5semidirect
561. #102C22×D5semidirect
562. #102C22×D5semidirect
564. C22⋊C8C22×D5semidirect
718. C2×C5#3310semidirect
807. C5C2×#3310semidirect
851. C2#10613114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659432
C2×#658632
C2×C5×#4822
C2×#653312
C2×#652902
#106131142
C2×#651712
C2×#651782
C2×#651602
C2×#651532
C2×#650512
C2×#650652
C2×D5×#1022
C2×#650532
C2×#650202
C2×#650172
C2×#33105