Finite Group Databasebeta

← C2×#10611232 #12975844

Subgroups — C2×#10611232 #12975844

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×D4×D20C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic, complemented
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65423C211yesmaximal, characteristic, complemented
5C2×#65420C211yesmaximal, characteristic, complemented
6C2×#65403C211yesmaximal, characteristic, complemented
7C22×#3953C211yesmaximal, characteristic, complemented
8#10611232C2116yesmaximal, direct product factor
9C2×#65137C211yesmaximal, characteristic, complemented
10C2×#65136C211yesmaximal, characteristic, complemented
11C2×#65020C211yesmaximal, characteristic, complemented
12C2×#65020C211yesmaximal, characteristic, complemented
13C2×#65026C211yesmaximal, characteristic, complemented
14C2×#65025C211yesmaximal, characteristic, complemented
15C2×#65002C211yesmaximal, characteristic, complemented
16C2×#64999C211yesmaximal, characteristic, complemented
17C22×D4×D5—21no—
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic, complemented
21C23×C5×C8C2211yescharacteristic, complemented
22C2×C4×C5×D4C2211yescharacteristic
23C2×#4081—21no—
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4072C2211yescharacteristic, complemented
27C22×C4⋊Dic5C2211yescharacteristic, complemented
28C2×#4070C2211yescharacteristic, complemented
29C2×#4070C2211yescharacteristic, complemented
30C22×#677C2211yescharacteristic
31C22×#677C2211yescharacteristic, complemented
32C22×#677C2211yescharacteristic, complemented
33D4×D20—24no—
34D4×D20C2218yes—
35#65875—24no—
36#65875C2218yescomplemented
37C2×#4041—21no—
38C2×#4035—21no—
39C2×#4028—21no—
40C2×#4028—21no—
41C2×#4025—21no—
42C2×#4023—21no—
43C2×#4020C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×#4016C2211yescharacteristic, complemented
46C2×C4×Dic10C2211yescharacteristic, complemented
47C5×#435C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×C22⋊C8C2211yescharacteristic, complemented
50C2×C5×C22⋊C8C2211yescharacteristic, complemented
51C2×C5×#97C2211yescharacteristic, complemented
52#65423C2218yescomplemented
53#65420C2218yescomplemented
54#65403C2218yescomplemented
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×#3953C2218yescomplemented
65C2×#3950C2211yescharacteristic, complemented
66C2×#3950C2211yescharacteristic, complemented
67C2×#3949C2211yescharacteristic, complemented
68C2×#3948C2211yescharacteristic, complemented
69#65137C2218yescomplemented
70#65136C2218yescomplemented
71#65026C2218yescomplemented
72#65025C2218yescomplemented
73#65020C2218yescomplemented
74#65020C2218yescomplemented
75#65002C2218yescomplemented
76#64999C2218yescomplemented
77C2×#3310—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—
85C23×Dic5—21no—
86C2×D4×D5—28no—
87C2×D4×D5—48no—
88C22×D20—24no—
89C22×D20—24no—
90C22×D20—21no—
91C22×D20—21no—
92C22×D20—21no—
93C22×D20—22no—
94C22×D20—22no—
95C22×D20—21no—
96C22×D20—42no—
97C22×D20—42no—
98C22×D20C2311yescharacteristic
99C22×D20C2311yescharacteristic
100C22×D20C2314yes—
101C22×D20C2314yes—
102C22×D20C2311yescharacteristic
103C22×C4×D5—21no—
104C22×Dic10C2311yescharacteristic
105C2×C5×M16—42no—
106C2×C5×M16C2314yescomplemented
107C22×C5×C8—42no—
108C22×C5×C8C2311yescharacteristic
109C22×C5×C8C2311yescharacteristic
110C22×C5×C8C2311yescharacteristic
111C22×C5×C8C2311yescharacteristic
112C22×C5×C8C2314yescomplemented
113C4×C5×D4D414yes—
114C4×C5×D4C2314yes—
115C2×C5×C4⋊C4D411yescharacteristic
116C2×C5×C22⋊C4D411yescharacteristic
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C42×C5C2311yescharacteristic
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121C2×C22⋊Dic5—21no—
122#4081—28no—
123#4076—22no—
124#4076—22no—
125#4076C2314yes—
126#4076C2314yes—
127C2×#685—21no—
128C2×#685—21no—
129C2×#685—21no—
130#4072—22no—
131#4072C2314yescomplemented
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5—22no—
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137C2×C4⋊Dic5C2311yescharacteristic
138C2×C4⋊Dic5C2314yescomplemented
139#4070—22no—
140#4070—22no—
141#4070C2314yescomplemented
142#4070C2314yescomplemented
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×C4×Dic5—21no—
149C2×C4×Dic5—21no—
150C2×#677—24no—
151C2×#677—42no—
152C2×#677—42no—
153C2×#677C2314yes—
154C2×#677C2314yescomplemented
155C2×#677C2314yescomplemented
156#4041—28no—
157#4035—28no—
158#4028—28no—
159#4028—28no—
160#4025—28no—
161#4023—28no—
162#4020—22no—
163#4020C2314yes—
164C4×D20—22no—
165C4×D20C2314yes—
166#4016—22no—
167#4016C2314yescomplemented
168C4×Dic10—22no—
169C4×Dic10C2314yescomplemented
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#3950C2314yescomplemented
184#3950C2314yescomplemented
185#3949C2314yescomplemented
186#3948C2314yescomplemented
187C2×#552—51no—
188C2×D42—51no—
189#3310—516no—
190C2×#490—51no—
191C2×#482—51no—
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×#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—24no—
209C23×D5—24no—
210C23×D5—44no—
211C23×D5—44no—
212C23×D5—44no—
213C23×D5—44no—
214C23×D5—82no—
215C23×D5—82no—
216C2×C5×D4—24no—
217C2×C5×D4C2×D414yes—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C2×C22⋊D5—24no—
232C2×C22⋊D5—24no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—44no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—24no—
241C22×Dic5—44no—
242D4×D5—432no—
243C2×D20—21no—
244C2×D20—22no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—22no—
248C2×D20—22no—
249C2×D20—28no—
250C2×D20—28no—
251C2×D20—21no—
252C2×D20—21no—
253C2×D20—24no—
254C2×D20—24no—
255C2×D20—24no—
256C2×D20—24no—
257C2×D20—44no—
258C2×D20—44no—
259C2×D20—48no—
260C2×D20—48no—
261C2×D20—44no—
262C2×D20—44no—
263C2×D20—44no—
264C2×D20—82no—
265C2×D20#4114yes—
266C2×D20C2412yes—
267C2×D20C2412yes—
268C2×D20C2412yes—
269C2×C4×D5—24no—
270C2×C4×D5—44no—
271C2×Dic10—22no—
272C2×Dic10—22no—
273C2×Dic10—21no—
274C2×Dic10C2412yes—
275C5×M16—44no—
276C2×C5×C8—22no—
277C2×C5×C8—22no—
278C2×C5×C8—22no—
279C2×C5×C8—22no—
280C2×C5×C8—44no—
281C2×C5×C8C2412yes—
282C2×C5×C8C2412yes—
283C2×C5×C8C2412yes—
284C2×C5×C8C2412yes—
285C5×C4⋊C4C2×D414yes—
286C5×C22⋊C4C2×D414yes—
287C5×C22⋊C4C2×D414yes—
288C42×C5C2×D412yes—
289C42×C5C2412yes—
290C22⋊Dic5—24no—
291C22⋊Dic5—24no—
292C22⋊Dic5—24no—
293#685—24no—
294#685—24no—
295#685—24no—
296C4⋊Dic5—21no—
297C4⋊Dic5—21no—
298C4⋊Dic5—21no—
299C4⋊Dic5—21no—
300C4⋊Dic5—24no—
301C4⋊Dic5C2412yes—
302C4⋊Dic5C2412yes—
303C4⋊Dic5C2412yes—
304C4⋊Dic5C2412yes—
305#683—24no—
306#683—24no—
307#683—24no—
308#683—24no—
309#683—24no—
310C4×Dic5—24no—
311C4×Dic5—24no—
312#677—28no—
313#677—44no—
314#677—44no—
315C23×D4—51no—
316C23×D4—51no—
317C23×D4—101no—
318C22×SD16—51no—
319C22×SD16—51no—
320C22×SD16—51no—
321C22×M16C2×D511yescharacteristic, complemented
322C23×C8C2×D511yescharacteristic, complemented
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—51no—
336C2×#121—101no—
337C2×#120—101no—
338C2×#120—101no—
339C2×C4×Q8—51no—
340C2×C4×D4—51no—
341C2×C4×D4C2×D511yescharacteristic
342C2×#117—51no—
343C2×#117—101no—
344C22×C4⋊C4—51no—
345#490—58no—
346#482—58no—
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#435C2×D518yescomplemented
356C2×#107—51no—
357C2×#107—51no—
358C2×#106—51no—
359C2×C4⋊C8C2×D511yescharacteristic, complemented
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—51no—
370C2×#102—51no—
371C2×#102—58no—
372C2×C22⋊C8C2×D511yescharacteristic, complemented
373C2×C22⋊C8C2×D511yescharacteristic, complemented
374C2×#97C2×D511yescharacteristic, complemented
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5AGL(1,ℤ/8)14yes—
381C23×C5C22×D412yes—
382C23×C5C22×D412yes—
383C23×C5C22×D411yescharacteristic
384C22×D5—24no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—48no—
389C22×D5—48no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—48no—
393C22×D5—42no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—42no—
397C22×D5—48no—
398C22×D5—42no—
399C22×D5—42no—
400C22×D5—84no—
401C22×D5—84no—
402C22×D5—816no—
403C22×D5—816no—
404C5×D4—28no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—24no—
410C2×C4×C5—24no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5C22×D412yes—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D412yes—
418C2×C4×C5C22×D412yes—
419C2×C4×C5C22×D411yescharacteristic
420C2×C4×C5C2×#4112yes—
421C2×C4×C5H(5,𝔽2)12yes—
422C2×C4×C5C2511yescharacteristic
423C22⋊D5—48no—
424C22⋊D5—48no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—42no—
431C2×Dic5—42no—
432C2×Dic5—48no—
433C2×Dic5—42no—
434C2×Dic5—42no—
435C2×Dic5—42no—
436D20—24no—
437D20—22no—
438D20—22no—
439D20—22no—
440D20—22no—
441D20—22no—
442D20—48no—
443D20—48no—
444D20—48no—
445D20—42no—
446D20—42no—
447D20—84no—
448D20C2×#4114yes—
449C4×D5—48no—
450Dic10—22no—
451Dic10—22no—
452Dic10—42no—
453C5×C8—22no—
454C5×C8—22no—
455C5×C8—22no—
456C5×C8—22no—
457C25—101no—
458C25—101no—
459C22×Q8—51no—
460C22×D4—51no—
461C22×D4—51no—
462C22×D4—51no—
463C22×D4—54no—
464C22×D4—54no—
465C22×D4—104no—
466C22×D4—104no—
467C22×D4—101no—
468C22×D4—101no—
469C22×D4—108no—
470C22×D4—101no—
471C22×D4—101no—
472C22×D4—101no—
473C22×D4—102no—
474C22×D4—102no—
475C22×D4—101no—
476C22×D4—202no—
477C22×D4—202no—
478C22×D4—208no—
479C22×D4D2011yescharacteristic
480C23×C4—101no—
481C23×C4—101no—
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C2×SD16—54no—
485C2×SD16—54no—
486C2×SD16—54no—
487C2×SD16—104no—
488C2×SD16—202no—
489C2×SD16—202no—
490C2×M16—42no—
491C2×M16C22×D514yescomplemented
492C22×C8—42no—
493C22×C8C22×D511yescharacteristic
494C22×C8C22×D511yescharacteristic
495C22×C8C22×D511yescharacteristic
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D514yescomplemented
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—54no—
510#121—54no—
511#121—102no—
512#121—102no—
513#121—108no—
514#120—108no—
515#120—108no—
516C4×Q8—54no—
517C4×Q8—102no—
518C4×D4—54no—
519C4×D4—102no—
520C4×D4D2014yes—
521C4×D4C22×D514yes—
522#117—54no—
523#117—102no—
524#117—108no—
525C2×C4⋊C4—51no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—54no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—101no—
531C2×C4⋊C4—102no—
532C2×C4⋊C4—101no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4—101no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4D2011yescharacteristic
538C2×C22⋊C4—101no—
539C2×C22⋊C4—101no—
540C2×C22⋊C4—101no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4D2011yescharacteristic
545C2×C22⋊C4D2011yescharacteristic
546C2×C42—101no—
547C2×C42—101no—
548C2×C42C22×D511yescharacteristic
549#107—54no—
550#107—54no—
551#106—54no—
552C4⋊C8C22×D514yescomplemented
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#102—54no—
562#102—54no—
563C22⋊C8C22×D514yescomplemented
564C22⋊C8C22×D514yescomplemented
565#97C22×D514yescomplemented
566C22×C5—22no—
567C22×C5—28no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—44no—
573C22×C5#54612yes—
574C22×C5C2×AGL(1,ℤ/8)14yes—
575C22×C5C2×AGL(1,ℤ/8)12yes—
576C22×C5#57712yes—
577C22×C5C23×D411yescharacteristic
578C2×D5—24no—
579C2×D5—48no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
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×D5—84no—
592C4×C5—22no—
593C4×C5—22no—
594C4×C5—22no—
595C4×C5—22no—
596C4×C5#54612yes—
597C4×C5C22×#4111yescharacteristic
598C4×C5C2×H(5,𝔽2)11yescharacteristic
599Dic5—42no—
600Dic5—42no—
601Dic5—42no—
602Dic5—42no—
603Dic5—42no—
604C24—101no—
605C24—101no—
606C24—101no—
607C24—104no—
608C24—104no—
609C24—204no—
610C24—204no—
611C24—204no—
612C24—204no—
613C24—402no—
614C24—402no—
615C24C2×D2011yescharacteristic
616C24C2×D2011yescharacteristic
617C2×Q8—52no—
618C2×Q8—101no—
619C2×Q8—102no—
620C2×Q8—102no—
621C2×D4—24no—
622C2×D4—54no—
623C2×D4—52no—
624C2×D4—52no—
625C2×D4—52no—
626C2×D4—108no—
627C2×D4—108no—
628C2×D4—104no—
629C2×D4—104no—
630C2×D4—101no—
631C2×D4—104no—
632C2×D4—104no—
633C2×D4—104no—
634C2×D4—101no—
635C2×D4—101no—
636C2×D4—104no—
637C2×D4—102no—
638C2×D4—102no—
639C2×D4—102no—
640C2×D4—102no—
641C2×D4—102no—
642C2×D4—204no—
643C2×D4—204no—
644C2×D4—208no—
645C2×D4—208no—
646C2×D4—204no—
647C2×D4—204no—
648C2×D4—204no—
649C2×D4—2032no—
650C2×D4—204no—
651C2×D4—204no—
652C2×D4—402no—
653C2×D4C2×D2014yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—104no—
659C22×C4—101no—
660C22×C4—101no—
661C22×C4—101no—
662C22×C4—101no—
663C22×C4—101no—
664C22×C4—104no—
665C22×C4—204no—
666C22×C4—204no—
667C22×C4C2×D2012yes—
668C22×C4C2×D2012yes—
669C22×C4C2×D2011yescharacteristic
670C22×C4C2×D2011yescharacteristic
671C22×C4C2×D2011yescharacteristic
672C22×C4C2×D2011yescharacteristic
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D511yescharacteristic
676SD16—108no—
677SD16—204no—
678SD16—204no—
679M16—44no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—44no—
685C2×C8C23×D512yes—
686C2×C8C23×D512yes—
687C2×C8C23×D512yes—
688C2×C8C23×D512yes—
689C4⋊C4—52no—
690C4⋊C4—52no—
691C4⋊C4—52no—
692C4⋊C4—52no—
693C4⋊C4—101no—
694C4⋊C4—101no—
695C4⋊C4—104no—
696C4⋊C4—101no—
697C4⋊C4—101no—
698C4⋊C4—104no—
699C4⋊C4—104no—
700C4⋊C4—104no—
701C4⋊C4—104no—
702C4⋊C4—104no—
703C4⋊C4C2×D2014yes—
704C22⋊C4—104no—
705C22⋊C4—104no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4C2×D2014yes—
711C22⋊C4C2×D2014yes—
712C42—104no—
713C42—104no—
714C42C2×D2012yes—
715C42C23×D512yes—
716C2×C5—24no—
717C2×C5—42no—
718C2×C5#331014yescomplemented
719C2×C5C2×#54611yescharacteristic
720C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
721C2×C5C2×#57711yescharacteristic
722D5—44no—
723D5—82no—
724D5—82no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—104no—
731C23—102no—
732C23—102no—
733C23—102no—
734C23—208no—
735C23—208no—
736C23—208no—
737C23—202no—
738C23—202no—
739C23—208no—
740C23—202no—
741C23—202no—
742C23—202no—
743C23—202no—
744C23—202no—
745C23—202no—
746C23—404no—
747C23—404no—
748C23—4016no—
749C23—4016no—
750C23#405414yes—
751C23C22×D2012yes—
752C23C22×D2012yes—
753C23C22×D2011yescharacteristic
754Q8—102no—
755Q8—102no—
756Q8—202no—
757D4—28no—
758D4—54no—
759D4—104no—
760D4—102no—
761D4—102no—
762D4—102no—
763D4—102no—
764D4—102no—
765D4—208no—
766D4—208no—
767D4—208no—
768D4—208no—
769D4—208no—
770D4—202no—
771D4—202no—
772D4—404no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—208no—
789C2×C4—202no—
790C2×C4—208no—
791C2×C4—202no—
792C2×C4—202no—
793C2×C4—202no—
794C2×C4—202no—
795C2×C4C22×D2012yes—
796C2×C4C22×D2012yes—
797C2×C4C22×D2012yes—
798C2×C4C22×D2012yes—
799C2×C4C22×D2011yescharacteristic
800C2×C4#414412yes—
801C2×C4D5×#4112yes—
802C2×C4C24×D511yescharacteristic
803C8—22no—
804C8—22no—
805C8—22no—
806C8—22no—
807C5C2×#331011yescharacteristic, complemented, Sylow
808C22—28no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—44no—
815C22—104no—
816C22—208no—
817C22—202no—
818C22—202no—
819C22—202no—
820C22—202no—
821C22—202no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—4016no—
826C22—4016no—
827C22—404no—
828C22—404no—
829C22#6588812yes—
830C22C2×#405414yes—
831C22C2×#405412yes—
832C22#6608512yes—
833C22C23×D2011yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—202no—
839C4—202no—
840C4—202no—
841C4—202no—
842C4—202no—
843C4#6588812yes—
844C4C2×#414411yescharacteristic
845C4C2×D5×#4111yescharacteristic
846C2—24no—
847C2—42no—
848C2—204no—
849C2—402no—
850C2—402no—
851C2#1061123214yesdirect product factor
852C2C2×#6588811yescharacteristic
853C2C22×#405411yescharacteristic
854C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
prime radicalC2×D4×D20C2
hypercenterC2×#435D5
hypocenterC5C2×#3310
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
2. C2×#65875C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65423C2semidirect
5. C2×#65420C2semidirect
6. C2×#65403C2semidirect
7. C22×#3953C2semidirect
8. #10611232C2direct (N × H)
9. C2×#65137C2semidirect
10. C2×#65136C2semidirect
11. C2×#65020C2semidirect
12. C2×#65020C2semidirect
13. C2×#65026C2semidirect
14. C2×#65025C2semidirect
15. C2×#65002C2semidirect
16. C2×#64999C2semidirect
20. C22×C5×M16C22semidirect
21. C23×C5×C8C22semidirect
26. C2×#4072C22semidirect
27. C22×C4⋊Dic5C22semidirect
28. C2×#4070C22semidirect
29. C2×#4070C22semidirect
31. C22×#677C22semidirect
32. C22×#677C22semidirect
36. #65875C22semidirect
45. C2×#4016C22semidirect
46. C2×C4×Dic10C22semidirect
47. C5×#435C22semidirect
48. C2×C5×C4⋊C8C22semidirect
49. C2×C5×C22⋊C8C22semidirect
50. C2×C5×C22⋊C8C22semidirect
51. C2×C5×#97C22semidirect
52. #65423C22semidirect
53. #65420C22semidirect
54. #65403C22semidirect
58. C2×#3953C22semidirect
59. C2×#3953C22semidirect
60. C2×#3953C22semidirect
61. C2×#3953C22semidirect
62. C2×#3953C22semidirect
63. C2×#3953C22semidirect
64. C2×#3953C22semidirect
65. C2×#3950C22semidirect
66. C2×#3950C22semidirect
67. C2×#3949C22semidirect
68. C2×#3948C22semidirect
69. #65137C22semidirect
70. #65136C22semidirect
71. #65026C22semidirect
72. #65025C22semidirect
73. #65020C22semidirect
74. #65020C22semidirect
75. #65002C22semidirect
76. #64999C22semidirect
106. C2×C5×M16C23semidirect
112. C22×C5×C8C23semidirect
131. #4072C23semidirect
138. C2×C4⋊Dic5C23semidirect
141. #4070C23semidirect
142. #4070C23semidirect
154. C2×#677C23semidirect
155. C2×#677C23semidirect
167. #4016C23semidirect
169. C4×Dic10C23semidirect
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. #3950C23semidirect
184. #3950C23semidirect
185. #3949C23semidirect
186. #3948C23semidirect
200. C2×#435D5semidirect
321. C22×M16C2×D5semidirect
322. C23×C8C2×D5semidirect
355. #435C2×D5semidirect
359. C2×C4⋊C8C2×D5semidirect
372. C2×C22⋊C8C2×D5semidirect
373. C2×C22⋊C8C2×D5semidirect
374. C2×#97C2×D5semidirect
491. C2×M16C22×D5semidirect
497. C22×C8C22×D5semidirect
552. C4⋊C8C22×D5semidirect
563. C22⋊C8C22×D5semidirect
564. C22⋊C8C22×D5semidirect
565. #97C22×D5semidirect
718. C2×C5#3310semidirect
807. C5C2×#3310semidirect
851. C2#10611232direct (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×#658752
C2×C5×#4352
C2×#654232
C2×#654202
C2×#654032
C22×#39532
#106112322
C2×#651372
C2×#651362
C2×#650202
C2×#650262
C2×#650252
C2×#650022
C2×#649992
C2×#33105