Finite Group Databasebeta

← D5×#1854 #12100014

Subgroups — D5×#1854 #12100014

Order 1280.

1662 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#117C211yesmaximal, characteristic
2C2×D5×#107C211yesmaximal, characteristic, complemented
3C2×D5×#106C211yesmaximal, characteristic, complemented
4C2×D5×C22⋊C8C211yesmaximal, characteristic
5D5×#380C211yesmaximal, characteristic
6C5×#1854C211yesmaximal, characteristic, complemented
7#10602369C211yesmaximal, characteristic, complemented
8#10601426C211yesmaximal, characteristic, complemented
9#10601373C211yesmaximal, characteristic, complemented
10#10600722C211yesmaximal, characteristic, complemented
11#10600299C211yesmaximal, characteristic, complemented
12#10599670C211yesmaximal, characteristic, complemented
13#10599669C211yesmaximal, characteristic, complemented
14D5×#340C211yesmaximal, characteristic, complemented
15D5×#340C211yesmaximal, characteristic, complemented
16C23×C4×D5C2211yescharacteristic
17C2×C5×#117C2211yescharacteristic
18C2×#4072C2211yescharacteristic
19C22×C8×D5C2211yescharacteristic
20C22×C8×D5C2211yescharacteristic
21D5×#117—24no—
22D5×#117—24no—
23C2×#4038C2211yescharacteristic
24C2×#4038C2211yescharacteristic
25C2×D5×C4⋊C4C2211yescharacteristic
26C2×D5×C4⋊C4C2211yescharacteristic
27C2×D5×C4⋊C4C2211yescharacteristic
28C2×D5×C4⋊C4C2211yescharacteristic
29C2×D5×C22⋊C4—21no—
30C2×D5×C22⋊C4—21no—
31C2×#4023—21no—
32C2×#4018—21no—
33C2×C42×D5—21no—
34C2×C5×#107C2211yescharacteristic, complemented
35C2×C5×#106C2211yescharacteristic, complemented
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#380C2211yescharacteristic
38#65501C2211yescharacteristic
39C2×C22⋊#168C2211yescharacteristic
40C2×#3952C2211yescharacteristic
41C2×#3952C2211yescharacteristic
42C2×#3950C2211yescharacteristic, complemented
43C2×#3949C2211yescharacteristic, complemented
44#65276C2211yescharacteristic
45#65276C2211yescharacteristic
46C2×#3940C2211yescharacteristic, complemented
47C2×#3940C2211yescharacteristic, complemented
48C2×#3939C2211yescharacteristic, complemented
49C2×#3939C2211yescharacteristic, complemented
50#65231—21no—
51D5×#107—24no—
52D5×#106—24no—
53D5×C22⋊C8C418yescomplemented
54#64956—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
64C2×#1854—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×D5—21no—
75C22×C4×D5—21no—
76C22×C4×D5C2×C414yes—
77C22×C4×D5D411yescharacteristic
78C22×C4×D5D411yescharacteristic
79C22×C4×D5Q814yes—
80C22×C4×D5C2311yescharacteristic
81C22×C4×D5C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C22×C5×C8C2311yescharacteristic
84C5×#117—22no—
85C5×#117—22no—
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C42×C5—21no—
93C2×C22⋊Dic5—21no—
94C2×C22⋊Dic5—21no—
95C2×#685—21no—
96C2×#685—21no—
97C2×#685—21no—
98C2×#685—21no—
99#4072—22no—
100#4072—22no—
101C2×C4⋊Dic5C2311yescharacteristic
102C2×C4⋊Dic5C2311yescharacteristic
103C2×C4⋊Dic5C2311yescharacteristic
104C2×C4⋊Dic5C2311yescharacteristic
105C2×#683—21no—
106C2×#683—21no—
107C2×#683—21no—
108C2×#683—21no—
109C2×C4×Dic5—21no—
110C2×C4×Dic5—21no—
111C2×C4×Dic5—21no—
112C22×#168C2311yescharacteristic
113C22×#168C2311yescharacteristic
114C2×C8×D5—22no—
115C2×C8×D5—22no—
116C2×C8×D5—22no—
117C2×C8×D5—22no—
118C2×C8×D5C2×C414yes—
119C2×C8×D5C2×C414yes—
120#4038—22no—
121#4038—22no—
122#4038—22no—
123#4038—22no—
124D5×C4⋊C4—22no—
125D5×C4⋊C4—22no—
126D5×C4⋊C4—22no—
127D5×C4⋊C4—22no—
128D5×C4⋊C4—22no—
129D5×C4⋊C4—22no—
130D5×C4⋊C4D414yes—
131D5×C4⋊C4D414yes—
132D5×C22⋊C4—28no—
133D5×C22⋊C4—44no—
134#4023—28no—
135#4018—28no—
136C42×D5—28no—
137C5×#107—22no—
138C5×#106—22no—
139C5×C22⋊C8C2×C414yescomplemented
140C5×#95—21no—
141#3963—21no—
142#3963—21no—
143#3963—21no—
144C22⋊#168C2×C414yescomplemented
145#3952C2×C414yescomplemented
146#3952C2×C414yescomplemented
147#3950—22no—
148#3949—22no—
149#3940—22no—
150#3940—22no—
151#3939—22no—
152#3939—22no—
153C22×#117—51no—
154C22×#107—51no—
155C22×#106—51no—
156C22×C22⋊C8—51no—
157C2×#380—51no—
158#1854—51no—
159#1854—51no—
160#1854—51no—
161#1854—51no—
162#1854—51no—
163#1854—51no—
164#1854—51no—
165#1854D511yescharacteristic, direct product factor
166C2×#340—51no—
167C2×#340—51no—
168C24×C5C2×D411yescharacteristic
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5C4⋊C414yes—
176C23×D5C2×D411yescharacteristic
177C23×D5C2×D411yescharacteristic
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5C22×C412yes—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×Q812yes—
189C22×C4×C5C2411yescharacteristic
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5C4⋊C414yes—
197C22×Dic5C2×D411yescharacteristic
198C22×Dic5C2×D411yescharacteristic
199C2×C4×D5—22no—
200C2×C4×D5—22no—
201C2×C4×D5—21no—
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—22no—
206C2×C4×D5—22no—
207C2×C4×D5—28no—
208C2×C4×D5—28no—
209C2×C4×D5—28no—
210C2×C4×D5—28no—
211C2×C4×D5—24no—
212C2×C4×D5—24no—
213C2×C4×D5—42no—
214C2×C4×D5—42no—
215C2×C4×D5—42no—
216C2×C4×D5—42no—
217C2×C4×D5—42no—
218C2×C4×D5—42no—
219C2×C4×D5—42no—
220C2×C4×D5—42no—
221C2×C4×D5—42no—
222C2×C4×D5—42no—
223C2×C4×D5C4⋊C414yes—
224C2×C4×D5C4⋊C414yes—
225C2×C4×D5C22×C412yes—
226C2×C4×D5C22×C412yes—
227C2×C4×D5C2×D412yes—
228C2×C4×D5C2×D412yes—
229C2×C4×D5C2×Q812yes—
230C2×C4×D5C2×Q812yes—
231C2×C4×D5#4112yes—
232C2×C4×D5#4112yes—
233C2×C5×C8—21no—
234C2×C5×C8—21no—
235C2×C5×C8—21no—
236C2×C5×C8—21no—
237C2×C5×C8C22×C412yes—
238C2×C5×C8C22×C412yes—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4C2×D412yes—
246C5×C4⋊C4C2×D412yes—
247C5×C22⋊C4—24no—
248C5×C22⋊C4—42no—
249C42×C5—24no—
250C22⋊Dic5—24no—
251C22⋊Dic5—42no—
252#685—24no—
253#685—24no—
254#685—42no—
255#685—42no—
256C4⋊Dic5—21no—
257C4⋊Dic5—21no—
258C4⋊Dic5—21no—
259C4⋊Dic5—21no—
260C4⋊Dic5—21no—
261C4⋊Dic5—21no—
262C4⋊Dic5C2×D412yes—
263C4⋊Dic5C2×D412yes—
264#683—24no—
265#683—24no—
266#683—42no—
267#683—42no—
268C4×Dic5—24no—
269C4×Dic5—24no—
270C4×Dic5—24no—
271C2×#168—21no—
272C2×#168—21no—
273C2×#168—21no—
274C2×#168—21no—
275C2×#168C22×C412yes—
276C2×#168C22×C412yes—
277C8×D5—28no—
278C8×D5—28no—
279C24×C4—51no—
280C23×C8—51no—
281C23×C8—51no—
282C2×#117—51no—
283C2×#117—51no—
284C2×#117—51no—
285C2×#117—101no—
286C2×#117—101no—
287C2×#117—104no—
288C2×#117—104no—
289C2×#117C2×D511yescharacteristic
290C22×C4⋊C4—51no—
291C22×C4⋊C4—51no—
292C22×C4⋊C4—51no—
293C22×C4⋊C4—51no—
294C22×C22⋊C4—101no—
295C22×C22⋊C4—101no—
296C22×C42—101no—
297C2×#107—51no—
298C2×#107—51no—
299C2×#107—51no—
300C2×#107—104no—
301C2×#107C2×D511yescharacteristic, complemented
302C2×#106—51no—
303C2×#106—51no—
304C2×#106—51no—
305C2×#106—104no—
306C2×#106C2×D511yescharacteristic, complemented
307C2×C22⋊C8—51no—
308C2×C22⋊C8—51no—
309C2×C22⋊C8—51no—
310C2×C22⋊C8—58no—
311C2×C22⋊C8C2×D511yescharacteristic
312#380—51no—
313#380—51no—
314#380—51no—
315#380—101no—
316#380—101no—
317#380C2×D511yescharacteristic
318C2×#95—101no—
319#340—51no—
320#340—51no—
321#340—51no—
322#340—51no—
323#340—51no—
324#340—51no—
325#340C2×D511yescharacteristic, complemented
326#340C2×D511yescharacteristic, complemented
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5C2×C4⋊C412yes—
334C23×C5C22×D411yescharacteristic
335C22×D5—21no—
336C22×D5—21no—
337C22×D5—21no—
338C22×D5—21no—
339C22×D5—21no—
340C22×D5—21no—
341C22×D5—28no—
342C22×D5—28no—
343C22×D5—28no—
344C22×D5—44no—
345C22×D5—44no—
346C22×D5—44no—
347C22×D5—44no—
348C22×D5C2×C4⋊C412yes—
349C22×D5C2×C4⋊C412yes—
350C22×D5#12012yes—
351C22×D5#12312yes—
352C22×D5#13512yes—
353C22×D5#13512yes—
354C22×D5AGL(1,ℤ/8)12yes—
355C22×D5#13712yes—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5C2×C4⋊C412yes—
375C2×C4×C5C23×C411yescharacteristic
376C2×C4×C5C22×D411yescharacteristic
377C2×C4×C5C22×D411yescharacteristic
378C2×C4×C5C22×Q811yescharacteristic
379C2×C4×C5C2×#4111yescharacteristic
380C2×C4×C5C2×#4111yescharacteristic
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—41no—
387C2×Dic5—41no—
388C2×Dic5—41no—
389C2×Dic5—41no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—41no—
394C2×Dic5—41no—
395C2×Dic5—41no—
396C2×Dic5C2×C4⋊C412yes—
397C2×Dic5C2×C4⋊C412yes—
398C2×Dic5#12012yes—
399C2×Dic5#12312yes—
400C4×D5—28no—
401C4×D5—22no—
402C4×D5—22no—
403C4×D5—22no—
404C4×D5—22no—
405C4×D5—28no—
406C4×D5—48no—
407C4×D5—48no—
408C4×D5—84no—
409C4×D5—84no—
410C4×D5C4×D414yes—
411C4×D5C4×D414yes—
412C4×D5C22⋊Q814yes—
413C4×D5C22⋊Q814yes—
414C5×C8—22no—
415C5×C8—22no—
416#168—22no—
417#168—22no—
418C25—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—54no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—54no—
425C23×C4—51no—
426C23×C4—102no—
427C23×C4—102no—
428C23×C4—102no—
429C23×C4—102no—
430C23×C4—101no—
431C23×C4—101no—
432C23×C4—101no—
433C23×C4—101no—
434C23×C4C22×D511yescharacteristic
435C22×C8—51no—
436C22×C8—51no—
437C22×C8—54no—
438C22×C8—54no—
439C22×C8—102no—
440C22×C8—102no—
441C22×C8—102no—
442C22×C8—102no—
443C22×C8C22×D511yescharacteristic
444C22×C8C22×D511yescharacteristic
445#117—22no—
446#117—22no—
447#117—108no—
448#117—108no—
449#117—102no—
450#117—102no—
451#117—102no—
452#117—102no—
453#117—102no—
454#117—102no—
455C2×C4⋊C4—51no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—54no—
459C2×C4⋊C4—51no—
460C2×C4⋊C4—51no—
461C2×C4⋊C4—102no—
462C2×C4⋊C4—102no—
463C2×C4⋊C4—102no—
464C2×C4⋊C4—102no—
465C2×C4⋊C4—102no—
466C2×C4⋊C4—102no—
467C2×C4⋊C4—101no—
468C2×C4⋊C4—101no—
469C2×C4⋊C4—101no—
470C2×C4⋊C4—101no—
471C2×C4⋊C4C22×D511yescharacteristic
472C2×C4⋊C4C22×D511yescharacteristic
473C2×C4⋊C4C22×D511yescharacteristic
474C2×C4⋊C4C22×D511yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—108no—
478C2×C22⋊C4—101no—
479C2×C22⋊C4—101no—
480C2×C22⋊C4—101no—
481C2×C22⋊C4—101no—
482C2×C22⋊C4—101no—
483C2×C22⋊C4—101no—
484C2×C22⋊C4—204no—
485C2×C42—21no—
486C2×C42—108no—
487C2×C42—101no—
488C2×C42—101no—
489C2×C42—101no—
490#107—22no—
491#107—102no—
492#107—102no—
493#107—102no—
494#106—22no—
495#106—102no—
496#106—102no—
497#106—102no—
498C22⋊C8—54no—
499C22⋊C8—54no—
500C22⋊C8—54no—
501C22⋊C8C4×D514yescomplemented
502#95—21no—
503#95—101no—
504#95—101no—
505#95—101no—
506C22×C5—22no—
507C22×C5—22no—
508C22×C5—22no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5C22×C4⋊C411yescharacteristic
514C22×C5C2×#12011yescharacteristic
515C22×C5C2×#12311yescharacteristic
516C22×C5C2×#13511yescharacteristic
517C22×C5C2×#13511yescharacteristic
518C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
519C22×C5C2×#13711yescharacteristic
520C2×D5—22no—
521C2×D5—22no—
522C2×D5—22no—
523C2×D5—41no—
524C2×D5—41no—
525C2×D5—41no—
526C2×D5—41no—
527C2×D5—416no—
528C2×D5#38514yes—
529C2×D5#42714yes—
530C2×D5#42814yes—
531C2×D5#44914yes—
532C2×D5#45214yes—
533C2×D5#48214yes—
534C2×D5#48514yes—
535C4×C5—22no—
536C4×C5—42no—
537C4×C5—42no—
538C4×C5—81no—
539C4×C5—81no—
540C4×C5C2×C4×D411yescharacteristic
541C4×C5C2×C4×D411yescharacteristic
542C4×C5C2×C22⋊Q811yescharacteristic
543C4×C5C2×C22⋊Q811yescharacteristic
544Dic5—22no—
545Dic5—42no—
546Dic5—42no—
547Dic5—81no—
548Dic5—81no—
549Dic5#38514yes—
550C24—51no—
551C24—51no—
552C24—54no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24—102no—
559C24D4×D511yescharacteristic
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—51no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—51no—
576C22×C4—54no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—54no—
580C22×C4—54no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—108no—
584C22×C4—108no—
585C22×C4—108no—
586C22×C4—108no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—104no—
590C22×C4—104no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—202no—
602C22×C4—202no—
603C22×C4—202no—
604C22×C4—202no—
605C22×C4—202no—
606C22×C4—202no—
607C22×C4—202no—
608C22×C4—202no—
609C22×C4—202no—
610C22×C4—202no—
611C22×C4C2×C4×D512yes—
612C22×C4D4×D511yescharacteristic
613C22×C4Q8×D512yes—
614C22×C4C23×D511yescharacteristic
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—52no—
620C2×C8—52no—
621C2×C8—108no—
622C2×C8—108no—
623C2×C8—101no—
624C2×C8—101no—
625C2×C8—101no—
626C2×C8—101no—
627C2×C8C2×C4×D512yes—
628C2×C8C2×C4×D512yes—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—52no—
636C4⋊C4—52no—
637C4⋊C4—104no—
638C4⋊C4—104no—
639C4⋊C4—101no—
640C4⋊C4—101no—
641C4⋊C4—101no—
642C4⋊C4—101no—
643C4⋊C4—101no—
644C4⋊C4—101no—
645C4⋊C4—202no—
646C4⋊C4—202no—
647C4⋊C4D4×D512yes—
648C4⋊C4D4×D512yes—
649C22⋊C4—24no—
650C22⋊C4—42no—
651C22⋊C4—104no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—202no—
655C22⋊C4—202no—
656C22⋊C4—202no—
657C42—24no—
658C42—104no—
659C42—104no—
660C42—104no—
661C2×C5—42no—
662C2×C5C2×#38511yescharacteristic
663C2×C5C2×#42711yescharacteristic
664C2×C5C2×#42811yescharacteristic
665C2×C5C2×#44911yescharacteristic
666C2×C5C2×#45211yescharacteristic
667C2×C5C2×#48211yescharacteristic
668C2×C5C2×#48511yescharacteristic
669D5—42no—
670D5#185418yesdirect product factor
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—52no—
678C23—52no—
679C23—52no—
680C23—52no—
681C23—52no—
682C23—52no—
683C23—52no—
684C23—52no—
685C23—108no—
686C23—108no—
687C23—108no—
688C23—101no—
689C23—101no—
690C23—101no—
691C23—101no—
692C23—101no—
693C23—101no—
694C23—204no—
695C23—204no—
696C23—204no—
697C23—204no—
698C23D5×C4⋊C412yes—
699C23C2×D4×D511yescharacteristic
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—52no—
719C2×C4—52no—
720C2×C4—52no—
721C2×C4—54no—
722C2×C4—54no—
723C2×C4—54no—
724C2×C4—54no—
725C2×C4—52no—
726C2×C4—108no—
727C2×C4—108no—
728C2×C4—108no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—208no—
738C2×C4—208no—
739C2×C4—201no—
740C2×C4—201no—
741C2×C4—201no—
742C2×C4—201no—
743C2×C4—201no—
744C2×C4—201no—
745C2×C4—201no—
746C2×C4—201no—
747C2×C4—201no—
748C2×C4—201no—
749C2×C4—404no—
750C2×C4—404no—
751C2×C4D5×C4⋊C412yes—
752C2×C4C22×C4×D511yescharacteristic
753C2×C4C2×D4×D511yescharacteristic
754C2×C4C2×D4×D511yescharacteristic
755C2×C4C2×Q8×D511yescharacteristic
756C2×C4D5×#4111yescharacteristic
757C2×C4D5×#4111yescharacteristic
758C8—22no—
759C8—22no—
760C8—102no—
761C8—102no—
762C5C2×#185411yescharacteristic, complemented, Sylow
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—54no—
771C22—54no—
772C22—54no—
773C22—54no—
774C22—54no—
775C22—54no—
776C22—54no—
777C22—102no—
778C22—102no—
779C22—102no—
780C22—2016no—
781C22—201no—
782C22—201no—
783C22—201no—
784C22—201no—
785C22C2×D5×C4⋊C411yescharacteristic
786C22D5×#12011yescharacteristic
787C22D5×#12311yescharacteristic
788C22D5×#13511yescharacteristic
789C22D5×#13511yescharacteristic
790C22D5×AGL(1,ℤ/8)11yescharacteristic
791C22D5×#13711yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—54no—
796C4—81no—
797C4—81no—
798C4—102no—
799C4—202no—
800C4—202no—
801C4—401no—
802C4—401no—
803C4C4×D4×D511yescharacteristic
804C4C4×D4×D511yescharacteristic
805C4D5×C22⋊Q811yescharacteristic
806C4D5×C22⋊Q811yescharacteristic
807C2—42no—
808C2—58no—
809C2—202no—
810C2D5×#38511yescharacteristic
811C2D5×#42711yescharacteristic
812C2D5×#42811yescharacteristic
813C2D5×#44911yescharacteristic
814C2D5×#45211yescharacteristic
815C2D5×#48211yescharacteristic
816C2D5×#48511yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1854C2
socleC23×C5C22×D4
prime radicalC24×D5D4
cosocleC22×C4×C5C24
hypercenter#1854D5
hypocenterC5C2×#1854
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×D5×#107C2semidirect
3. C2×D5×#106C2semidirect
6. C5×#1854C2semidirect
7. #10602369C2semidirect
8. #10601426C2semidirect
9. #10601373C2semidirect
10. #10600722C2semidirect
11. #10600299C2semidirect
12. #10599670C2semidirect
13. #10599669C2semidirect
14. D5×#340C2semidirect
15. D5×#340C2semidirect
34. C2×C5×#107C22semidirect
35. C2×C5×#106C22semidirect
42. C2×#3950C22semidirect
43. C2×#3949C22semidirect
46. C2×#3940C22semidirect
47. C2×#3940C22semidirect
48. C2×#3939C22semidirect
49. C2×#3939C22semidirect
53. D5×C22⋊C8C4semidirect
56. C5×#340C22semidirect
57. C5×#340C22semidirect
58. #64771C22semidirect
59. #64771C22semidirect
60. #64749C22semidirect
61. #64749C22semidirect
62. #64749C22semidirect
63. #64749C22semidirect
139. C5×C22⋊C8C2×C4semidirect
144. C22⋊#168C2×C4semidirect
145. #3952C2×C4semidirect
146. #3952C2×C4semidirect
165. #1854D5direct (N × H)
301. C2×#107C2×D5semidirect
306. C2×#106C2×D5semidirect
325. #340C2×D5semidirect
326. #340C2×D5semidirect
501. C22⋊C8C4×D5semidirect
670. D5#1854direct (N × H)
762. C5C2×#1854semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1172
C2×D5×#1072
C2×D5×#1062
C2×D5×C22⋊C82
D5×#3802
C5×#18542
#106023692
#106014262
#106013732
#106007222
#106002992
#105996702
#105996692
D5×#3402
C2×#18545