Finite Group Databasebeta

← #12098882

Subgroups — #12098882

Order 1280.

1590 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×M16C211yesmaximal, characteristic
2C2×#65170C211yesmaximal, characteristic, complemented
3C2×#65150C211yesmaximal, characteristic, complemented
4D5×#380C211yesmaximal, characteristic
5#10605593C211yesmaximal, characteristic
6C5×#1809C211yesmaximal, characteristic, complemented
7#10602781C211yesmaximal, characteristic, complemented
8#10601423C211yesmaximal, characteristic, complemented
9#10601370C211yesmaximal, characteristic, complemented
10#10600306C211yesmaximal, characteristic, complemented
11#10600306C211yesmaximal, characteristic, complemented
12#10599662C211yesmaximal, characteristic, complemented
13#10599661C211yesmaximal, characteristic, complemented
14#10599660C211yesmaximal, characteristic, complemented
15#10599660C211yesmaximal, characteristic, complemented
16C23×C4×D5C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C22×#681C2211yescharacteristic
19C2×D5×M16—24no—
20C2×D5×M16—24no—
21C2×D5×M16C418yescomplemented
22C22×#676C2211yescharacteristic
23C22×#676C2211yescharacteristic
24C22×C8×D5C2211yescharacteristic
25C22×C8×D5C2211yescharacteristic
26C2×#4038C2211yescharacteristic
27C2×#4038C2211yescharacteristic
28C2×D5×C4⋊C4C2211yescharacteristic
29C2×D5×C4⋊C4C2211yescharacteristic
30C2×D5×C22⋊C4—21no—
31C2×C5×#107C2211yescharacteristic, complemented
32C2×C5×#106C2211yescharacteristic, complemented
33C5×#380C2211yescharacteristic
34C5×#380C2211yescharacteristic
35#65501C2211yescharacteristic
36#65501C2211yescharacteristic
37C2×#3950C2211yescharacteristic, complemented
38C2×#3949C2211yescharacteristic, complemented
39#65276C2211yescharacteristic
40#65276C2211yescharacteristic
41#65276C2211yescharacteristic
42#65276C2211yescharacteristic
43C2×#3940C2211yescharacteristic, complemented
44C2×#3940C2211yescharacteristic, complemented
45C2×#3939C2211yescharacteristic, complemented
46C2×#3939C2211yescharacteristic, complemented
47#65244—21no—
48#65231—21no—
49C22⋊C4×Dic5—21no—
50#65170—24no—
51#65150—24no—
52#64956—21no—
53#64955—21no—
54#64953—21no—
55D5×#95—21no—
56C5×#340C2211yescharacteristic, complemented
57C5×#340C2211yescharacteristic, complemented
58#64771C2211yescharacteristic, complemented
59#64771C2211yescharacteristic, complemented
60#64749C2211yescharacteristic, complemented
61#64749C2211yescharacteristic, complemented
62#64749C2211yescharacteristic, complemented
63#64749C2211yescharacteristic, complemented
64#20661—51nomaximal, Sylow
65C24×D5D411yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×Dic5D411yescharacteristic
68C22×C4×D5—22no—
69C22×C4×D5—22no—
70C22×C4×D5—22no—
71C22×C4×D5—22no—
72C22×C4×D5—21no—
73C22×C4×D5—21no—
74C22×C4×D5C2×C414yes—
75C22×C4×D5D411yescharacteristic
76C22×C4×D5D411yescharacteristic
77C22×C4×D5Q814yes—
78C22×C4×D5C2311yescharacteristic
79C22×C4×D5C2311yescharacteristic
80C2×C5×M16—22no—
81C2×C5×M16—22no—
82C2×C5×M16C2×C414yescomplemented
83C22×C5×C8C2311yescharacteristic
84C22×C5×C8C2311yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C22⋊Dic5—21no—
92C2×C22⋊Dic5—21no—
93C2×#685—21no—
94C2×#685—21no—
95C2×#685—21no—
96C2×#685—21no—
97C2×#685—21no—
98C2×#685—21no—
99C2×C4⋊Dic5C2311yescharacteristic
100C2×C4⋊Dic5C2311yescharacteristic
101C2×C4⋊Dic5C2311yescharacteristic
102C2×C4⋊Dic5C2311yescharacteristic
103C2×#683—21no—
104C2×#683—21no—
105C2×C4×Dic5—21no—
106C2×C4×Dic5—21no—
107C2×#681—22no—
108C2×#681—22no—
109C2×#681C2×C414yescomplemented
110C22×#168C2311yescharacteristic
111C22×#168C2311yescharacteristic
112D5×M16—232no—
113C2×#676—22no—
114C2×#676—22no—
115C2×#676C2×C414yes—
116C2×#676C2×C414yes—
117C2×#676D414yes—
118C2×#676D414yes—
119C2×C8×D5—22no—
120C2×C8×D5—22no—
121C2×C8×D5—22no—
122C2×C8×D5—22no—
123C2×C8×D5C2×C414yescomplemented
124C2×C8×D5C2×C414yescomplemented
125#4038—22no—
126#4038—22no—
127#4038—22no—
128#4038—22no—
129D5×C4⋊C4—22no—
130D5×C4⋊C4—22no—
131D5×C4⋊C4—22no—
132D5×C4⋊C4—22no—
133D5×C22⋊C4—44no—
134C5×#107—22no—
135C5×#106—22no—
136C5×#95—21no—
137C5×#95—21no—
138#3963—21no—
139#3963—21no—
140#3963—21no—
141#3963—21no—
142#3963—21no—
143#3963—21no—
144#3950—22no—
145#3949—22no—
146#3940—22no—
147#3940—22no—
148#3939—22no—
149#3939—22no—
150C23×M16—51no—
151C2×#428—51no—
152C2×#428—51no—
153#2280—51no—
154C2×#380—51no—
155#1809—51no—
156#1809—51no—
157#1809—51no—
158#1809D511yescharacteristic, complemented
159#1808—51no—
160#1808—51no—
161#1807—51no—
162#1807—51no—
163#1736—51no—
164#1736—51no—
165C24×C5C2×D411yescharacteristic
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—41no—
171C23×D5—41no—
172C23×D5C4⋊C414yes—
173C23×D5C2×D411yescharacteristic
174C23×D5C2×D411yescharacteristic
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5C22×C412yes—
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×Q812yes—
186C22×C4×C5C2411yescharacteristic
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5C4⋊C414yes—
194C22×Dic5C2×D411yescharacteristic
195C22×Dic5C2×D411yescharacteristic
196C2×C4×D5—22no—
197C2×C4×D5—22no—
198C2×C4×D5—21no—
199C2×C4×D5—21no—
200C2×C4×D5—21no—
201C2×C4×D5—21no—
202C2×C4×D5—22no—
203C2×C4×D5—22no—
204C2×C4×D5—28no—
205C2×C4×D5—28no—
206C2×C4×D5—28no—
207C2×C4×D5—28no—
208C2×C4×D5—42no—
209C2×C4×D5—42no—
210C2×C4×D5—42no—
211C2×C4×D5—42no—
212C2×C4×D5—42no—
213C2×C4×D5—42no—
214C2×C4×D5C4⋊C414yes—
215C2×C4×D5C4⋊C414yes—
216C2×C4×D5C22×C412yes—
217C2×C4×D5C22×C412yes—
218C2×C4×D5C2×D412yes—
219C2×C4×D5C2×D412yes—
220C2×C4×D5C2×Q812yes—
221C2×C4×D5C2×Q812yes—
222C2×C4×D5#4112yes—
223C2×C4×D5#4112yes—
224C5×M16—28no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8C22×C412yes—
228C2×C5×C8C22×C412yes—
229C2×C5×C8C2×D412yes—
230C2×C5×C8C2×D412yes—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C22⋊C4—42no—
240C5×C22⋊C4—42no—
241C22⋊Dic5—42no—
242C22⋊Dic5—42no—
243#685—42no—
244#685—42no—
245#685—42no—
246#685—42no—
247#685—42no—
248#685—42no—
249C4⋊Dic5—21no—
250C4⋊Dic5—21no—
251C4⋊Dic5—21no—
252C4⋊Dic5—21no—
253C4⋊Dic5—21no—
254C4⋊Dic5—21no—
255C4⋊Dic5—21no—
256C4⋊Dic5—21no—
257#683—42no—
258#683—42no—
259C4×Dic5—42no—
260C4×Dic5—42no—
261#681—28no—
262C2×#168—21no—
263C2×#168—21no—
264C2×#168C22×C412yes—
265C2×#168C22×C412yes—
266C2×#168C2×D412yes—
267C2×#168C2×D412yes—
268#676—28no—
269#676C22⋊C4116yescomplemented
270C8×D5—28no—
271C8×D5—28no—
272C24×C4—51no—
273C22×M16—51no—
274C22×M16—58no—
275C22×M16—51no—
276C22×M16—51no—
277C22×M16—104no—
278C22×M16—104no—
279C22×M16C2×D511yescharacteristic
280C23×C8—51no—
281C23×C8—51no—
282C2×#117—51no—
283C2×#117—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C22⋊C4—101no—
287#428—104no—
288#428—104no—
289C2×#107—51no—
290C2×#107—51no—
291C2×#107—51no—
292C2×#107C2×D511yescharacteristic, complemented
293C2×#106—51no—
294C2×#106—51no—
295C2×#106—51no—
296C2×#106C2×D511yescharacteristic, complemented
297#381—101no—
298#380—51no—
299#380—51no—
300#380—51no—
301#380—51no—
302#380—51no—
303#380—51no—
304#380—101no—
305#380—101no—
306#380C2×D511yescharacteristic
307#380C2×D511yescharacteristic
308#379—101no—
309C4×C22⋊C4—101no—
310C4×C22⋊C4—101no—
311C2×#95—101no—
312#340—51no—
313#340—51no—
314#340—51no—
315#340—51no—
316#340—51no—
317#340—51no—
318#340C2×D511yescharacteristic, complemented
319#340C2×D511yescharacteristic, complemented
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5C2×C4⋊C412yes—
327C23×C5C22×D411yescharacteristic
328C22×D5—21no—
329C22×D5—21no—
330C22×D5—21no—
331C22×D5—21no—
332C22×D5—21no—
333C22×D5—21no—
334C22×D5—21no—
335C22×D5—21no—
336C22×D5—28no—
337C22×D5—28no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5C2×C4⋊C412yes—
344C22×D5C2×C4⋊C412yes—
345C22×D5#12112yes—
346C22×D5#12112yes—
347C22×D5AGL(1,ℤ/8)12yes—
348C22×D5#13712yes—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5C2×C4⋊C412yes—
368C2×C4×C5C23×C411yescharacteristic
369C2×C4×C5C22×D411yescharacteristic
370C2×C4×C5C22×D411yescharacteristic
371C2×C4×C5C22×Q811yescharacteristic
372C2×C4×C5C2×#4111yescharacteristic
373C2×C4×C5C2×#4111yescharacteristic
374C2×Dic5—21no—
375C2×Dic5—21no—
376C2×Dic5—28no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—41no—
386C2×Dic5—41no—
387C2×Dic5—41no—
388C2×Dic5—41no—
389C2×Dic5C2×C4⋊C412yes—
390C2×Dic5C2×C4⋊C412yes—
391C2×Dic5#12112yes—
392C2×Dic5#12112yes—
393C4×D5—28no—
394C4×D5—22no—
395C4×D5—22no—
396C4×D5—22no—
397C4×D5—22no—
398C4×D5—28no—
399C4×D5—84no—
400C4×D5—84no—
401C4×D5C2×C22⋊C414yes—
402C4×D5#11714yes—
403C4×D5C22⋊Q814yes—
404C4×D5C22⋊Q814yes—
405C5×C8—22no—
406C5×C8C2×C22⋊C414yescomplemented
407#168—22no—
408#168C2×C22⋊C414yescomplemented
409C25—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—54no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—54no—
416C23×C4—51no—
417C23×C4—102no—
418C23×C4—102no—
419C23×C4—102no—
420C23×C4—102no—
421C23×C4—101no—
422C23×C4—101no—
423C23×C4C22×D511yescharacteristic
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—54no—
427C2×M16—54no—
428C2×M16—54no—
429C2×M16—54no—
430C2×M16—54no—
431C2×M16—102no—
432C2×M16—102no—
433C2×M16—102no—
434C2×M16—102no—
435C2×M16—1032no—
436C2×M16C4×D514yescomplemented
437C22×C8—51no—
438C22×C8—51no—
439C22×C8—54no—
440C22×C8—54no—
441C22×C8—102no—
442C22×C8—102no—
443C22×C8—102no—
444C22×C8—102no—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D511yescharacteristic
447#117—102no—
448#117—102no—
449#117—102no—
450#117—102no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—102no—
456C2×C4⋊C4—102no—
457C2×C4⋊C4—102no—
458C2×C4⋊C4—102no—
459C2×C4⋊C4—101no—
460C2×C4⋊C4—101no—
461C2×C4⋊C4C22×D511yescharacteristic
462C2×C4⋊C4C22×D511yescharacteristic
463C2×C4⋊C4C22×D511yescharacteristic
464C2×C4⋊C4C22×D511yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—101no—
468C2×C22⋊C4—101no—
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471C2×C22⋊C4—101no—
472C2×C22⋊C4—101no—
473C2×C22⋊C4—101no—
474C2×C22⋊C4—101no—
475C2×C22⋊C4—204no—
476C2×C42—101no—
477C2×C42—101no—
478#107—22no—
479#107—102no—
480#107—102no—
481#107—102no—
482#106—22no—
483#106—102no—
484#106—102no—
485#106—102no—
486#95—21no—
487#95—21no—
488#95—101no—
489#95—101no—
490#95—101no—
491#95—101no—
492#95—101no—
493#95—101no—
494C22×C5—22no—
495C22×C5—22no—
496C22×C5—22no—
497C22×C5—41no—
498C22×C5—41no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5C22×C4⋊C411yescharacteristic
502C22×C5C2×#12111yescharacteristic
503C22×C5C2×#12111yescharacteristic
504C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
505C22×C5C2×#13711yescharacteristic
506C22×C5#57511yescharacteristic
507C22×C5#57511yescharacteristic
508C2×D5—22no—
509C2×D5—22no—
510C2×D5—22no—
511C2×D5—22no—
512C2×D5—22no—
513C2×D5—22no—
514C2×D5—22no—
515C2×D5—22no—
516C2×D5—22no—
517C2×D5—22no—
518C2×D5—22no—
519C2×D5—22no—
520C2×D5—416no—
521C2×D5#38014yes—
522C2×D5#42814yescomplemented
523C4×C5—22no—
524C4×C5—81no—
525C4×C5—81no—
526C4×C5—81no—
527C4×C5—81no—
528C4×C5C22×C22⋊C411yescharacteristic
529C4×C5C2×#11711yescharacteristic
530C4×C5C2×C22⋊Q811yescharacteristic
531C4×C5C2×C22⋊Q811yescharacteristic
532Dic5—22no—
533Dic5—81no—
534Dic5—81no—
535Dic5—81no—
536Dic5—81no—
537Dic5#38014yes—
538C24—51no—
539C24—51no—
540C24—54no—
541C24—102no—
542C24—102no—
543C24—102no—
544C24—102no—
545C24—201no—
546C24—201no—
547C24D4×D511yescharacteristic
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—51no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—51no—
564C22×C4—54no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—54no—
568C22×C4—54no—
569C22×C4—108no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—108no—
573C22×C4—108no—
574C22×C4—108no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—202no—
588C22×C4—202no—
589C22×C4—202no—
590C22×C4—202no—
591C22×C4—202no—
592C22×C4—202no—
593C22×C4C2×C4×D512yes—
594C22×C4D4×D511yescharacteristic
595C22×C4Q8×D512yes—
596C22×C4C23×D511yescharacteristic
597M16—28no—
598M16—516no—
599M16—108no—
600M16—108no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—52no—
604C2×C8—52no—
605C2×C8—52no—
606C2×C8—52no—
607C2×C8—108no—
608C2×C8—101no—
609C2×C8—101no—
610C2×C8—108no—
611C2×C8C2×C4×D512yes—
612C2×C8C2×C4×D512yes—
613C2×C8D4×D512yes—
614C2×C8D4×D512yes—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4—101no—
626C4⋊C4—101no—
627C4⋊C4—101no—
628C4⋊C4—101no—
629C4⋊C4—101no—
630C4⋊C4—101no—
631C4⋊C4—202no—
632C4⋊C4—202no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—202no—
636C22⋊C4—202no—
637C22⋊C4—202no—
638C22⋊C4—202no—
639C22⋊C4—202no—
640C22⋊C4—202no—
641C22⋊C4—202no—
642C22⋊C4—202no—
643C42—202no—
644C42—202no—
645C2×C5—42no—
646C2×C5C2×#38011yescharacteristic
647C2×C5C2×#42811yescharacteristic
648C2×C5#291111yescharacteristic
649C2×C5#305511yescharacteristic
650C2×C5#305511yescharacteristic
651C2×C5#305611yescharacteristic
652C2×C5#305611yescharacteristic
653D5—24no—
654D5—24no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—52no—
662C23—52no—
663C23—52no—
664C23—52no—
665C23—52no—
666C23—52no—
667C23—108no—
668C23—108no—
669C23—101no—
670C23—101no—
671C23—101no—
672C23—101no—
673C23—101no—
674C23—101no—
675C23—101no—
676C23—101no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23D5×C4⋊C412yes—
683C23C2×D4×D511yescharacteristic
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—54no—
706C2×C4—54no—
707C2×C4—54no—
708C2×C4—54no—
709C2×C4—52no—
710C2×C4—108no—
711C2×C4—108no—
712C2×C4—108no—
713C2×C4—101no—
714C2×C4—101no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—201no—
720C2×C4—201no—
721C2×C4—201no—
722C2×C4—201no—
723C2×C4—201no—
724C2×C4—201no—
725C2×C4—201no—
726C2×C4—201no—
727C2×C4—201no—
728C2×C4—201no—
729C2×C4—201no—
730C2×C4—201no—
731C2×C4—404no—
732C2×C4—404no—
733C2×C4D5×C4⋊C412yes—
734C2×C4C22×C4×D511yescharacteristic
735C2×C4C2×D4×D511yescharacteristic
736C2×C4C2×D4×D511yescharacteristic
737C2×C4C2×Q8×D511yescharacteristic
738C2×C4D5×#4111yescharacteristic
739C2×C4D5×#4111yescharacteristic
740C8—22no—
741C8—54no—
742C8—102no—
743C8D5×C22⋊C414yescomplemented
744C5#2066111yescharacteristic, complemented, Sylow
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—54no—
753C22—54no—
754C22—102no—
755C22—102no—
756C22—102no—
757C22—102no—
758C22—102no—
759C22—102no—
760C22—102no—
761C22—102no—
762C22—102no—
763C22—102no—
764C22—102no—
765C22—102no—
766C22—2016no—
767C22C2×D5×C4⋊C411yescharacteristic
768C22D5×#12111yescharacteristic
769C22D5×#12111yescharacteristic
770C22D5×AGL(1,ℤ/8)11yescharacteristic
771C22#6610711yescharacteristic
772C22D5×#13711yescharacteristic
773C22#6611111yescharacteristic
774C4—22no—
775C4—54no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—102no—
781C4—401no—
782C4—401no—
783C4—401no—
784C4—401no—
785C4C2×D5×C22⋊C411yescharacteristic
786C4D5×#11711yescharacteristic
787C4D5×C22⋊Q811yescharacteristic
788C4D5×C22⋊Q811yescharacteristic
789C2—42no—
790C2—104no—
791C2—104no—
792C2D5×#38011yescharacteristic
793C2D5×#42811yescharacteristic
794C2#1061093911yescharacteristic
795C2#1061253611yescharacteristic
796C2#1061253711yescharacteristic
797C2#1061259511yescharacteristic
798C2#1061263511yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1809C2
socleC23×C5C22×D4
prime radicalC24×D5D4
cosocleC22×C4×C5C24
hypercenter#1809D5
hypocenterC5#20661
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#65170C2semidirect
3. C2×#65150C2semidirect
6. C5×#1809C2semidirect
7. #10602781C2semidirect
8. #10601423C2semidirect
9. #10601370C2semidirect
10. #10600306C2semidirect
11. #10600306C2semidirect
12. #10599662C2semidirect
13. #10599661C2semidirect
14. #10599660C2semidirect
15. #10599660C2semidirect
21. C2×D5×M16C4semidirect
31. C2×C5×#107C22semidirect
32. C2×C5×#106C22semidirect
37. C2×#3950C22semidirect
38. C2×#3949C22semidirect
43. C2×#3940C22semidirect
44. C2×#3940C22semidirect
45. C2×#3939C22semidirect
46. C2×#3939C22semidirect
56. C5×#340C22semidirect
57. C5×#340C22semidirect
58. #64771C22semidirect
59. #64771C22semidirect
60. #64749C22semidirect
61. #64749C22semidirect
62. #64749C22semidirect
63. #64749C22semidirect
82. C2×C5×M16C2×C4semidirect
109. C2×#681C2×C4semidirect
123. C2×C8×D5C2×C4semidirect
124. C2×C8×D5C2×C4semidirect
158. #1809D5semidirect
269. #676C22⋊C4semidirect
292. C2×#107C2×D5semidirect
296. C2×#106C2×D5semidirect
318. #340C2×D5semidirect
319. #340C2×D5semidirect
406. C5×C8C2×C22⋊C4semidirect
408. #168C2×C22⋊C4semidirect
436. C2×M16C4×D5semidirect
522. C2×D5#428semidirect
743. C8D5×C22⋊C4semidirect
744. C5#20661semidirect

Maximal subgroups

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

subgroupindex
C22×D5×M162
C2×#651702
C2×#651502
D5×#3802
#106055932
C5×#18092
#106027812
#106014232
#106013702
#106003062
#105996622
#105996612
#105996602
#206615