Finite Group Databasebeta

← C2×#10611236 #12975860

Subgroups — C2×#10611236 #12975860

Order 1280.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D20C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic, complemented
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65424C211yesmaximal, characteristic, complemented
5C2×#65420C211yesmaximal, characteristic, complemented
6C2×#65404C211yesmaximal, characteristic, complemented
7C22×#3953C211yesmaximal, characteristic, complemented
8#10611236C2116yesmaximal, direct product factor
9C2×#65136C211yesmaximal, characteristic, complemented
10C2×#65132C211yesmaximal, characteristic, complemented
11C2×#65021C211yesmaximal, characteristic, complemented
12C2×#65021C211yesmaximal, characteristic, complemented
13C2×#65024C211yesmaximal, characteristic, complemented
14C2×#65026C211yesmaximal, characteristic, complemented
15C2×#65002C211yesmaximal, characteristic, complemented
16C2×#65000C211yesmaximal, characteristic, complemented
17C22×D4×D5—21no—
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic, complemented
21C23×C5×C8C2211yescharacteristic, complemented
22C2×C4×C5×D4C2211yescharacteristic
23C2×#4085—21no—
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4076C2211yescharacteristic, complemented
27C2×#4076C2211yescharacteristic, complemented
28C2×#4072C2211yescharacteristic, complemented
29C22×C4⋊Dic5C2211yescharacteristic, complemented
30C22×D40C2211yescharacteristic
31C22×D40C2211yescharacteristic, complemented
32C22×D40C2211yescharacteristic, complemented
33#65899—24no—
34#65899C2218yescomplemented
35D4×D20—24no—
36D4×D20C2218yescomplemented
37C2×#4044—21no—
38C2×#4041—21no—
39C2×#4029—21no—
40C2×#4028—21no—
41C2×#4028—21no—
42C2×#4027—21no—
43C2×#4020C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic, complemented
46C2×#4016C2211yescharacteristic, complemented
47C5×#435C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×C22⋊C8C2211yescharacteristic, complemented
50C2×C5×C22⋊C8C2211yescharacteristic, complemented
51C2×C5×#97C2211yescharacteristic, complemented
52#65424C2218yescomplemented
53#65420C2218yescomplemented
54#65404C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic, complemented
59C2×#3953C2211yescharacteristic, complemented
60C2×#3953C2211yescharacteristic, complemented
61C2×#3953C2211yescharacteristic, complemented
62C2×#3953C2211yescharacteristic, complemented
63C2×#3953C2211yescharacteristic, complemented
64C2×#3953C2211yescharacteristic, complemented
65C2×#3953C2218yescomplemented
66C2×#3950C2211yescharacteristic, complemented
67C2×#3949C2211yescharacteristic, complemented
68C2×#3949C2211yescharacteristic, complemented
69#65136C2218yescomplemented
70#65132C2218yescomplemented
71#65026C2218yescomplemented
72#65024C2218yescomplemented
73#65021C2218yescomplemented
74#65021C2218yescomplemented
75#65002C2218yescomplemented
76#65000C2218yescomplemented
77C2×#3318—51nomaximal, Sylow
78C24×D5—21no—
79C24×D5—21no—
80C22×C5×D4D411yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C23×Dic5—21no—
88C2×D4×D5—28no—
89C2×D4×D5—48no—
90C22×D20—24no—
91C22×D20—24no—
92C22×D20—21no—
93C22×D20—21no—
94C22×D20—21no—
95C22×D20—22no—
96C22×D20—22no—
97C22×D20—21no—
98C22×D20—42no—
99C22×D20—42no—
100C22×D20C2311yescharacteristic
101C22×D20C2311yescharacteristic
102C22×D20C2311yescharacteristic
103C22×D20C2314yes—
104C22×D20C2314yes—
105C22×D20C2311yescharacteristic
106C22×C4×D5—21no—
107C22×C4×D5—21no—
108C2×C5×M16—42no—
109C2×C5×M16C2314yescomplemented
110C22×C5×C8—42no—
111C22×C5×C8C2311yescharacteristic
112C22×C5×C8C2311yescharacteristic
113C22×C5×C8C2311yescharacteristic
114C22×C5×C8C2311yescharacteristic
115C22×C5×C8C2314yescomplemented
116C4×C5×D4D414yes—
117C4×C5×D4C2314yes—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C42×C5C2311yescharacteristic
122C2×C22⋊Dic5—21no—
123#4085—28no—
124#4076—22no—
125#4076—22no—
126#4076—22no—
127#4076—22no—
128#4076C2314yes—
129#4076C2314yes—
130#4076C2314yescomplemented
131#4076C2314yescomplemented
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138#4072—22no—
139#4072C2314yescomplemented
140C2×C4⋊Dic5—21no—
141C2×C4⋊Dic5—22no—
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2311yescharacteristic
145C2×C4⋊Dic5C2311yescharacteristic
146C2×C4⋊Dic5C2314yescomplemented
147C2×#683—21no—
148C2×#683—21no—
149C2×C4×Dic5—21no—
150C2×D40—24no—
151C2×D40—42no—
152C2×D40—42no—
153C2×D40C2314yes—
154C2×D40C2314yescomplemented
155C2×D40C2314yescomplemented
156#4044—28no—
157#4041—28no—
158#4029—28no—
159#4028—28no—
160#4028—28no—
161#4027—28no—
162#4020—22no—
163#4020C2314yes—
164C4×D20—22no—
165C4×D20—22no—
166C4×D20C2314yes—
167C4×D20C2314yescomplemented
168#4016—22no—
169#4016C2314yescomplemented
170C5×C4⋊C8C2314yescomplemented
171C5×C22⋊C8C2314yescomplemented
172C5×C22⋊C8C2314yescomplemented
173C5×#97C2314yescomplemented
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yescomplemented
178#3953C2314yescomplemented
179#3953C2314yescomplemented
180#3953C2314yescomplemented
181#3953C2314yescomplemented
182#3953C2314yescomplemented
183#3953C2314yescomplemented
184#3950C2314yescomplemented
185#3949C2314yescomplemented
186#3949C2314yescomplemented
187C2×#553—51no—
188C2×D42—51no—
189#3318—516no—
190C2×#490—51no—
191C2×#481—51no—
192C2×#482—51no—
193C2×#478—51no—
194C2×#469—51no—
195C2×#466—51no—
196C2×#459—51no—
197C2×#447—51no—
198C2×#447—51no—
199C2×#442—51no—
200C2×#435D511yescharacteristic, complemented
201C2×#418—51no—
202C22×#102—51no—
203C24×C5C2×D411yescharacteristic
204C24×C5C2×D411yescharacteristic
205C23×D5—21no—
206C23×D5—21no—
207C23×D5—21no—
208C23×D5—21no—
209C23×D5—24no—
210C23×D5—24no—
211C23×D5—44no—
212C23×D5—44no—
213C23×D5—44no—
214C23×D5—44no—
215C23×D5—82no—
216C23×D5—82no—
217C2×C5×D4—24no—
218C2×C5×D4C2×D414yes—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2411yescharacteristic
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—24no—
235C2×C22⋊D5—24no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—44no—
238C2×C22⋊D5—44no—
239C2×C22⋊D5—82no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—24no—
245C22×Dic5—82no—
246D4×D5—432no—
247C2×D20—21no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—22no—
251C2×D20—22no—
252C2×D20—22no—
253C2×D20—22no—
254C2×D20—22no—
255C2×D20—28no—
256C2×D20—28no—
257C2×D20—21no—
258C2×D20—21no—
259C2×D20—24no—
260C2×D20—24no—
261C2×D20—24no—
262C2×D20—21no—
263C2×D20—24no—
264C2×D20—44no—
265C2×D20—44no—
266C2×D20—48no—
267C2×D20—48no—
268C2×D20—44no—
269C2×D20—44no—
270C2×D20—44no—
271C2×D20—82no—
272C2×D20#4114yes—
273C2×D20C2412yes—
274C2×D20C2412yes—
275C2×D20C2412yes—
276C2×D20C2412yes—
277C2×C4×D5—24no—
278C2×C4×D5—24no—
279C2×C4×D5—44no—
280C2×C4×D5—82no—
281C5×M16—44no—
282C2×C5×C8—22no—
283C2×C5×C8—22no—
284C2×C5×C8—22no—
285C2×C5×C8—22no—
286C2×C5×C8—44no—
287C2×C5×C8C2412yes—
288C2×C5×C8C2412yes—
289C2×C5×C8C2412yes—
290C2×C5×C8C2412yes—
291C5×C4⋊C4C2×D414yes—
292C5×C22⋊C4C2×D414yes—
293C5×C22⋊C4C2×D414yes—
294C42×C5C2×D412yes—
295C42×C5C2412yes—
296C22⋊Dic5—24no—
297#685—24no—
298#685—24no—
299#685—24no—
300#685—24no—
301#685—24no—
302#685—24no—
303C4⋊Dic5—21no—
304C4⋊Dic5—21no—
305C4⋊Dic5—21no—
306C4⋊Dic5—21no—
307C4⋊Dic5—24no—
308C4⋊Dic5C2412yes—
309C4⋊Dic5C2412yes—
310C4⋊Dic5C2412yes—
311C4⋊Dic5C2412yes—
312#683—24no—
313#683—24no—
314C4×Dic5—24no—
315D40—28no—
316D40—44no—
317D40—44no—
318C23×D4—51no—
319C23×D4—51no—
320C23×D4—101no—
321C22×D8—51no—
322C22×D8—51no—
323C22×D8—51no—
324C22×M16C2×D511yescharacteristic, complemented
325C23×C8C2×D511yescharacteristic, complemented
326#553—58no—
327#553—104no—
328D42—58no—
329D42—104no—
330C2×#127—51no—
331C2×#126—101no—
332C2×#125—51no—
333C2×#123—101no—
334C2×#121—51no—
335C2×#121—51no—
336C2×#121—51no—
337C2×#121—51no—
338C2×#121—101no—
339C2×#121—101no—
340C2×#120—101no—
341C2×#120—101no—
342C2×C4×D4—51no—
343C2×C4×D4—51no—
344C2×C4×D4—101no—
345C2×C4×D4C2×D511yescharacteristic
346C2×#117—51no—
347C22×C4⋊C4—51no—
348#490—58no—
349#482—58no—
350#481—58no—
351#478—58no—
352#469—58no—
353#466—58no—
354#459—58no—
355#447—58no—
356#447—58no—
357#442—58no—
358#435C2×D518yescomplemented
359C2×#107—51no—
360C2×#106—51no—
361C2×#106—51no—
362C2×C4⋊C8C2×D511yescharacteristic, complemented
363#418—58no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—51no—
370C2×#102—51no—
371C2×#102—51no—
372C2×#102—51no—
373C2×#102—51no—
374C2×#102—58no—
375C2×C22⋊C8C2×D511yescharacteristic, complemented
376C2×C22⋊C8C2×D511yescharacteristic, complemented
377C2×#97C2×D511yescharacteristic, complemented
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5AGL(1,ℤ/8)14yes—
384C23×C5C22×D412yes—
385C23×C5C22×D412yes—
386C23×C5C22×D411yescharacteristic
387C22×D5—24no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—48no—
393C22×D5—48no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—48no—
397C22×D5—42no—
398C22×D5—42no—
399C22×D5—42no—
400C22×D5—42no—
401C22×D5—42no—
402C22×D5—48no—
403C22×D5—42no—
404C22×D5—42no—
405C22×D5—42no—
406C22×D5—42no—
407C22×D5—84no—
408C22×D5—84no—
409C22×D5—816no—
410C22×D5—816no—
411C5×D4—28no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—24no—
417C2×C4×C5—24no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5C22×D412yes—
423C2×C4×C5C22×D412yes—
424C2×C4×C5C22×D412yes—
425C2×C4×C5C22×D412yes—
426C2×C4×C5C22×D411yescharacteristic
427C2×C4×C5C2×#4112yes—
428C2×C4×C5H(5,𝔽2)12yes—
429C2×C4×C5C2511yescharacteristic
430C22⋊D5—48no—
431C22⋊D5—48no—
432C22⋊D5—48no—
433C22⋊D5—84no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—42no—
439C2×Dic5—42no—
440C2×Dic5—42no—
441C2×Dic5—42no—
442C2×Dic5—84no—
443D20—24no—
444D20—22no—
445D20—22no—
446D20—22no—
447D20—22no—
448D20—22no—
449D20—22no—
450D20—22no—
451D20—48no—
452D20—48no—
453D20—48no—
454D20—42no—
455D20—42no—
456D20—42no—
457D20—84no—
458D20C2×#4114yes—
459C4×D5—48no—
460C4×D5—84no—
461C5×C8—22no—
462C5×C8—22no—
463C5×C8—22no—
464C5×C8—22no—
465C25—101no—
466C25—101no—
467C22×D4—51no—
468C22×D4—51no—
469C22×D4—51no—
470C22×D4—51no—
471C22×D4—54no—
472C22×D4—54no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—101no—
476C22×D4—101no—
477C22×D4—101no—
478C22×D4—101no—
479C22×D4—108no—
480C22×D4—101no—
481C22×D4—101no—
482C22×D4—101no—
483C22×D4—102no—
484C22×D4—102no—
485C22×D4—101no—
486C22×D4—202no—
487C22×D4—202no—
488C22×D4—208no—
489C22×D4D2011yescharacteristic
490C23×C4—101no—
491C23×C4—101no—
492C23×C4—101no—
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C2×D8—54no—
496C2×D8—54no—
497C2×D8—54no—
498C2×D8—104no—
499C2×D8—202no—
500C2×D8—202no—
501C2×M16—42no—
502C2×M16C22×D514yescomplemented
503C22×C8—42no—
504C22×C8C22×D511yescharacteristic
505C22×C8C22×D511yescharacteristic
506C22×C8C22×D511yescharacteristic
507C22×C8C22×D511yescharacteristic
508C22×C8C22×D514yescomplemented
509#127—54no—
510#127—102no—
511#126—108no—
512#125—54no—
513#125—102no—
514#123—108no—
515#121—54no—
516#121—54no—
517#121—54no—
518#121—54no—
519#121—108no—
520#121—102no—
521#121—102no—
522#121—102no—
523#121—102no—
524#121—108no—
525#120—108no—
526#120—108no—
527C4×D4—54no—
528C4×D4—54no—
529C4×D4—108no—
530C4×D4—102no—
531C4×D4—102no—
532C4×D4D2014yes—
533C4×D4C22×D514yes—
534#117—54no—
535#117—102no—
536C2×C4⋊C4—51no—
537C2×C4⋊C4—51no—
538C2×C4⋊C4—54no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—101no—
542C2×C4⋊C4—102no—
543C2×C4⋊C4—101no—
544C2×C4⋊C4—101no—
545C2×C4⋊C4D2011yescharacteristic
546C2×C22⋊C4—101no—
547C2×C22⋊C4—101no—
548C2×C22⋊C4—101no—
549C2×C22⋊C4—101no—
550C2×C22⋊C4—101no—
551C2×C22⋊C4—101no—
552C2×C22⋊C4—101no—
553C2×C22⋊C4D2011yescharacteristic
554C2×C22⋊C4D2011yescharacteristic
555C2×C42—101no—
556C2×C42C22×D511yescharacteristic
557#107—54no—
558#106—54no—
559#106—54no—
560C4⋊C8C22×D514yescomplemented
561#102—54no—
562#102—54no—
563#102—54no—
564#102—54no—
565#102—54no—
566#102—54no—
567#102—54no—
568#102—54no—
569#102—54no—
570#102—54no—
571C22⋊C8C22×D514yescomplemented
572C22⋊C8C22×D514yescomplemented
573#97C22×D514yescomplemented
574C22×C5—22no—
575C22×C5—28no—
576C22×C5—22no—
577C22×C5—22no—
578C22×C5—22no—
579C22×C5—22no—
580C22×C5—44no—
581C22×C5#54612yes—
582C22×C5C2×AGL(1,ℤ/8)14yes—
583C22×C5C2×AGL(1,ℤ/8)12yes—
584C22×C5#57612yes—
585C22×C5C23×D411yescharacteristic
586C2×D5—24no—
587C2×D5—48no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—42no—
596C2×D5—42no—
597C2×D5—42no—
598C2×D5—42no—
599C2×D5—816no—
600C2×D5—816no—
601C2×D5—84no—
602C2×D5—84no—
603C2×D5—84no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—22no—
607C4×C5—22no—
608C4×C5#54612yes—
609C4×C5C22×#4111yescharacteristic
610C4×C5C2×H(5,𝔽2)11yescharacteristic
611Dic5—42no—
612Dic5—42no—
613Dic5—42no—
614Dic5—42no—
615C24—101no—
616C24—101no—
617C24—101no—
618C24—101no—
619C24—104no—
620C24—104no—
621C24—204no—
622C24—204no—
623C24—204no—
624C24—204no—
625C24—402no—
626C24—402no—
627C24C2×D2011yescharacteristic
628C24C2×D2011yescharacteristic
629C2×D4—24no—
630C2×D4—54no—
631C2×D4—52no—
632C2×D4—52no—
633C2×D4—52no—
634C2×D4—52no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—104no—
638C2×D4—104no—
639C2×D4—104no—
640C2×D4—104no—
641C2×D4—101no—
642C2×D4—101no—
643C2×D4—104no—
644C2×D4—104no—
645C2×D4—104no—
646C2×D4—101no—
647C2×D4—101no—
648C2×D4—104no—
649C2×D4—102no—
650C2×D4—102no—
651C2×D4—102no—
652C2×D4—102no—
653C2×D4—102no—
654C2×D4—102no—
655C2×D4—102no—
656C2×D4—204no—
657C2×D4—204no—
658C2×D4—208no—
659C2×D4—208no—
660C2×D4—204no—
661C2×D4—204no—
662C2×D4—204no—
663C2×D4—2032no—
664C2×D4—204no—
665C2×D4—204no—
666C2×D4—204no—
667C2×D4—402no—
668C2×D4—402no—
669C2×D4C2×D2014yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—101no—
675C22×C4—101no—
676C22×C4—101no—
677C22×C4—101no—
678C22×C4—104no—
679C22×C4—104no—
680C22×C4—104no—
681C22×C4—204no—
682C22×C4—402no—
683C22×C4—402no—
684C22×C4C2×D2012yes—
685C22×C4C2×D2012yes—
686C22×C4C2×D2011yescharacteristic
687C22×C4C2×D2011yescharacteristic
688C22×C4C2×D2011yescharacteristic
689C22×C4C2×D2011yescharacteristic
690C22×C4C23×D512yes—
691C22×C4C23×D512yes—
692C22×C4C23×D511yescharacteristic
693D8—108no—
694D8—204no—
695D8—204no—
696M16—44no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—44no—
702C2×C8C23×D512yes—
703C2×C8C23×D512yes—
704C2×C8C23×D512yes—
705C2×C8C23×D512yes—
706C4⋊C4—52no—
707C4⋊C4—52no—
708C4⋊C4—52no—
709C4⋊C4—52no—
710C4⋊C4—101no—
711C4⋊C4—101no—
712C4⋊C4—104no—
713C4⋊C4—101no—
714C4⋊C4—101no—
715C4⋊C4—104no—
716C4⋊C4—104no—
717C4⋊C4C2×D2014yes—
718C22⋊C4—104no—
719C22⋊C4—104no—
720C22⋊C4—104no—
721C22⋊C4—104no—
722C22⋊C4—104no—
723C22⋊C4—104no—
724C22⋊C4—104no—
725C22⋊C4C2×D2014yes—
726C22⋊C4C2×D2014yes—
727C42—104no—
728C42C2×D2012yes—
729C42C23×D512yes—
730C2×C5—24no—
731C2×C5—42no—
732C2×C5#331814yescomplemented
733C2×C5C2×#54611yescharacteristic
734C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
735C2×C5C2×#57611yescharacteristic
736D5—44no—
737D5—82no—
738D5—82no—
739D5—82no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—104no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—208no—
751C23—208no—
752C23—208no—
753C23—202no—
754C23—202no—
755C23—208no—
756C23—202no—
757C23—202no—
758C23—202no—
759C23—202no—
760C23—202no—
761C23—202no—
762C23—202no—
763C23—202no—
764C23—202no—
765C23—404no—
766C23—404no—
767C23—4016no—
768C23—4016no—
769C23#405414yes—
770C23C22×D2012yes—
771C23C22×D2012yes—
772C23C22×D2011yescharacteristic
773D4—28no—
774D4—54no—
775D4—104no—
776D4—102no—
777D4—102no—
778D4—102no—
779D4—102no—
780D4—102no—
781D4—102no—
782D4—102no—
783D4—208no—
784D4—208no—
785D4—208no—
786D4—208no—
787D4—208no—
788D4—208no—
789D4—202no—
790D4—202no—
791D4—202no—
792D4—404no—
793D4—404no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—208no—
809C2×C4—202no—
810C2×C4—202no—
811C2×C4—202no—
812C2×C4—202no—
813C2×C4—404no—
814C2×C4—404no—
815C2×C4C22×D2012yes—
816C2×C4C22×D2012yes—
817C2×C4C22×D2012yes—
818C2×C4C22×D2012yes—
819C2×C4C22×D2011yescharacteristic
820C2×C4#414412yes—
821C2×C4D5×#4112yes—
822C2×C4C24×D511yescharacteristic
823C8—22no—
824C8—22no—
825C8—22no—
826C8—22no—
827C5C2×#331811yescharacteristic, complemented, Sylow
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—104no—
836C22—208no—
837C22—202no—
838C22—202no—
839C22—202no—
840C22—202no—
841C22—202no—
842C22—202no—
843C22—202no—
844C22—202no—
845C22—202no—
846C22—202no—
847C22—202no—
848C22—4016no—
849C22—4016no—
850C22—404no—
851C22—404no—
852C22—404no—
853C22#6588812yes—
854C22C2×#405414yes—
855C22C2×#405412yes—
856C22#6608612yes—
857C22C23×D2011yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—202no—
863C4—202no—
864C4—202no—
865C4—202no—
866C4#6588812yes—
867C4C2×#414411yescharacteristic
868C4C2×D5×#4111yescharacteristic
869C2—24no—
870C2—42no—
871C2—204no—
872C2—402no—
873C2—402no—
874C2—402no—
875C2#1061123614yesdirect product factor
876C2C2×#6588811yescharacteristic
877C2C22×#405411yescharacteristic
878C2C2×#6608611yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
hypercenterC2×#435D5
hypocenterC5C2×#3318
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×D4×D20C2semidirect
2. C2×#65899C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65424C2semidirect
5. C2×#65420C2semidirect
6. C2×#65404C2semidirect
7. C22×#3953C2semidirect
8. #10611236C2direct (N × H)
9. C2×#65136C2semidirect
10. C2×#65132C2semidirect
11. C2×#65021C2semidirect
12. C2×#65021C2semidirect
13. C2×#65024C2semidirect
14. C2×#65026C2semidirect
15. C2×#65002C2semidirect
16. C2×#65000C2semidirect
20. C22×C5×M16C22semidirect
21. C23×C5×C8C22semidirect
26. C2×#4076C22semidirect
27. C2×#4076C22semidirect
28. C2×#4072C22semidirect
29. C22×C4⋊Dic5C22semidirect
31. C22×D40C22semidirect
32. C22×D40C22semidirect
34. #65899C22semidirect
36. D4×D20C22semidirect
45. C2×C4×D20C22semidirect
46. C2×#4016C22semidirect
47. C5×#435C22semidirect
48. C2×C5×C4⋊C8C22semidirect
49. C2×C5×C22⋊C8C22semidirect
50. C2×C5×C22⋊C8C22semidirect
51. C2×C5×#97C22semidirect
52. #65424C22semidirect
53. #65420C22semidirect
54. #65404C22semidirect
58. C2×#3953C22semidirect
59. C2×#3953C22semidirect
60. C2×#3953C22semidirect
61. C2×#3953C22semidirect
62. C2×#3953C22semidirect
63. C2×#3953C22semidirect
64. C2×#3953C22semidirect
65. C2×#3953C22semidirect
66. C2×#3950C22semidirect
67. C2×#3949C22semidirect
68. C2×#3949C22semidirect
69. #65136C22semidirect
70. #65132C22semidirect
71. #65026C22semidirect
72. #65024C22semidirect
73. #65021C22semidirect
74. #65021C22semidirect
75. #65002C22semidirect
76. #65000C22semidirect
109. C2×C5×M16C23semidirect
115. C22×C5×C8C23semidirect
130. #4076C23semidirect
131. #4076C23semidirect
139. #4072C23semidirect
146. C2×C4⋊Dic5C23semidirect
154. C2×D40C23semidirect
155. C2×D40C23semidirect
167. C4×D20C23semidirect
169. #4016C23semidirect
170. C5×C4⋊C8C23semidirect
171. C5×C22⋊C8C23semidirect
172. C5×C22⋊C8C23semidirect
173. C5×#97C23semidirect
177. #3953C23semidirect
178. #3953C23semidirect
179. #3953C23semidirect
180. #3953C23semidirect
181. #3953C23semidirect
182. #3953C23semidirect
183. #3953C23semidirect
184. #3950C23semidirect
185. #3949C23semidirect
186. #3949C23semidirect
200. C2×#435D5semidirect
324. C22×M16C2×D5semidirect
325. C23×C8C2×D5semidirect
358. #435C2×D5semidirect
362. C2×C4⋊C8C2×D5semidirect
375. C2×C22⋊C8C2×D5semidirect
376. C2×C22⋊C8C2×D5semidirect
377. C2×#97C2×D5semidirect
502. C2×M16C22×D5semidirect
508. C22×C8C22×D5semidirect
560. C4⋊C8C22×D5semidirect
571. C22⋊C8C22×D5semidirect
572. C22⋊C8C22×D5semidirect
573. #97C22×D5semidirect
732. C2×C5#3318semidirect
827. C5C2×#3318semidirect
875. C2#10611236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D202
C2×#658992
C2×C5×#4352
C2×#654242
C2×#654202
C2×#654042
C22×#39532
#106112362
C2×#651362
C2×#651322
C2×#650212
C2×#650242
C2×#650262
C2×#650022
C2×#650002
C2×#33185