Finite Group Databasebeta

← #12022436

Subgroups — #12022436

Order 1280.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×#65519C211yesmaximal, characteristic, complemented
3C2×#65519C211yesmaximal, characteristic, complemented
4C2×#65501C211yesmaximal, characteristic
5C2×C4×C22⋊Dic5C211yesmaximal, characteristic
6C2×#65274C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8#10602362C212yesmaximal, complemented
9#10602356C212yesmaximal, complemented
10#10602339C212yesmaximal
11#10602338C212yesmaximal
12C23×C5×Q8C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C2×C5×C22⋊Q8—24no—
15C2×C5×C22⋊Q8—24no—
16C2×C5×C22⋊Q8C418yescomplemented
17C22×C5×C4⋊C4C2212yes—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2212yes—
20C22×C22⋊Dic5C2211yescharacteristic
21C22×C22⋊Dic5C2212yes—
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C4⋊Dic5C2211yescharacteristic
24C22×C4⋊Dic5C2212yes—
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2212yes—
28C22×C4×Dic5C2211yescharacteristic
29#65519—24no—
30#65519—24no—
31#65501—24no—
32C4×C22⋊Dic5—24no—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2211yescharacteristic
40C2×#3963C2212yes—
41C2×#3963C2211yescharacteristic
42#65274—24no—
43C4⋊C4×Dic5—24no—
44#13997—51nomaximal, Sylow
45C25×C5C2311yescharacteristic
46C22×C5×Q8—22no—
47C22×C5×Q8—22no—
48C22×C5×Q8—22no—
49C22×C5×Q8—22no—
50C22×C5×Q8—22no—
51C22×C5×Q8—22no—
52C22×C5×Q8C2×C414yes—
53C23×C4×C5—22no—
54C23×C4×C5—22no—
55C23×C4×C5—22no—
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5C2×C414yes—
60C23×C4×C5C2312yes—
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2312yes—
63C23×C4×C5C2311yescharacteristic
64C23×Dic5C2312yes—
65C23×Dic5C2312yes—
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C5×C22⋊Q8—232no—
71C2×C5×C4⋊C4—24no—
72C2×C5×C4⋊C4—24no—
73C2×C5×C4⋊C4C2×C418yes—
74C2×C5×C4⋊C4C2×C414yes—
75C2×C5×C4⋊C4D414yes—
76C2×C5×C4⋊C4D414yes—
77C2×C5×C22⋊C4—24no—
78C2×C5×C22⋊C4—24no—
79C2×C5×C22⋊C4C2×C418yes—
80C2×C22⋊Dic5—22no—
81C2×C22⋊Dic5—22no—
82C2×C22⋊Dic5—22no—
83C2×C22⋊Dic5—22no—
84C2×C22⋊Dic5—22no—
85C2×C22⋊Dic5—24no—
86C2×C22⋊Dic5—24no—
87C2×C22⋊Dic5—42no—
88C2×C22⋊Dic5Q814yescomplemented
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5—24no—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—24no—
96C2×C4⋊Dic5—42no—
97C2×C4⋊Dic5D414yes—
98C2×C4×Dic5—22no—
99C2×C4×Dic5—22no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5—24no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—24no—
105C2×C4×Dic5—42no—
106C2×C4×Dic5D414yes—
107#3963—24no—
108#3963—24no—
109#3963—22no—
110#3963—22no—
111#3963—24no—
112#3963—24no—
113#3963—24no—
114#3963—24no—
115#3963—24no—
116C22×C22⋊Q8D511yescharacteristic
117C2×#391—51no—
118C2×#391—51no—
119C2×#389—51no—
120C2×#380—51no—
121C2×C4×C4⋊C4—51no—
122C2×C4×C22⋊C4—51no—
123#1445—52no—
124#1439—52no—
125#1437—52no—
126C4⋊#95—52no—
127C24×C5—21no—
128C24×C5—21no—
129C24×C5—21no—
130C24×C5—21no—
131C24×C5—21no—
132C24×C5—21no—
133C24×C5—21no—
134C24×C5—21no—
135C24×C5—21no—
136C24×C5—21no—
137C24×C5—21no—
138C24×C5—21no—
139C24×C5C22×C412yes—
140C24×C5C2×Q812yes—
141C24×C5#4112yes—
142C24×C5C2411yescharacteristic
143C2×C5×Q8—28no—
144C2×C5×Q8—28no—
145C2×C5×Q8—28no—
146C2×C5×Q8—44no—
147C2×C5×Q8—44no—
148C2×C5×Q8—44no—
149C2×C5×Q8—44no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—28no—
167C22×C4×C5—28no—
168C22×C4×C5—28no—
169C22×C4×C5—44no—
170C22×C4×C5—44no—
171C22×C4×C5—44no—
172C22×C4×C5—44no—
173C22×C4×C5C22×C414yes—
174C22×C4×C5C22×C412yes—
175C22×C4×C5C22×C414yes—
176C22×C4×C5C22×C412yes—
177C22×C4×C5C2×D412yes—
178C22×C4×C5C2×D412yes—
179C22×C4×C5C2×D414yes—
180C22×C4×C5C2×D414yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5#4112yes—
184C22×C4×C5#4112yes—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—22no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—22no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—21no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—22no—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—21no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5C2×D412yes—
221C22×Dic5C2×D414yes—
222C22×Dic5C2×D412yes—
223C22×Dic5C2×Q812yes—
224C22×Dic5C2×Q812yes—
225C22×Dic5#4112yes—
226C22×Dic5#4112yes—
227C5×C4⋊C4—216no—
228C5×C4⋊C4C22⋊C4116yescomplemented
229C5×C22⋊C4—216no—
230C22⋊Dic5—28no—
231C22⋊Dic5—28no—
232C22⋊Dic5—48no—
233C4⋊Dic5—28no—
234C4⋊Dic5—48no—
235C4⋊Dic5—44no—
236C4×Dic5—28no—
237C4×Dic5—48no—
238C4×Dic5—44no—
239C23×Q8C2×D511yescharacteristic
240C24×C4C2×D511yescharacteristic
241C2×C22⋊Q8—24no—
242C2×C22⋊Q8—24no—
243C2×C22⋊Q8Dic518yescomplemented
244C22×C4⋊C4—51no—
245C22×C4⋊C4—51no—
246C22×C4⋊C4—52no—
247C22×C4⋊C4C2×D512yes—
248C22×C4⋊C4C2×D511yescharacteristic
249C22×C22⋊C4—51no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—52no—
252C22×C22⋊C4C2×D512yes—
253C22×C42—51no—
254C22×C42—51no—
255C22×C42—52no—
256#391—104no—
257#391—104no—
258#389—104no—
259#380—104no—
260C4×C4⋊C4—104no—
261C4×C22⋊C4—104no—
262C2×#95—51no—
263C2×#95—52no—
264C2×#95—52no—
265C2×#95—52no—
266C2×#95—52no—
267C2×#95—52no—
268C2×#95—52no—
269C2×#95—52no—
270C2×#95—51no—
271C23×C5—22no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—22no—
278C23×C5—22no—
279C23×C5—22no—
280C23×C5—22no—
281C23×C5—22no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5C4×Q814yes—
306C23×C5C23×C411yescharacteristic
307C23×C5C22×D411yescharacteristic
308C23×C5C22×D411yescharacteristic
309C23×C5C22×D411yescharacteristic
310C23×C5C22×D411yescharacteristic
311C23×C5C22×Q811yescharacteristic
312C23×C5C2×#4111yescharacteristic
313C23×C5C2×#4111yescharacteristic
314C23×C5C2×#4111yescharacteristic
315C23×C5C2×#4111yescharacteristic
316C23×C5C2×#4111yescharacteristic
317C23×C5H(5,𝔽2)11yescharacteristic
318C23×C52−1+411yescharacteristic
319C23×C52−1+411yescharacteristic
320C23×C52−1+411yescharacteristic
321C5×Q8—416no—
322C2×C4×C5—24no—
323C2×C4×C5—24no—
324C2×C4×C5—24no—
325C2×C4×C5—24no—
326C2×C4×C5—24no—
327C2×C4×C5—24no—
328C2×C4×C5—24no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—24no—
333C2×C4×C5—24no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—41no—
339C2×C4×C5—42no—
340C2×C4×C5—41no—
341C2×C4×C5—42no—
342C2×C4×C5—416no—
343C2×C4×C5C2×C22⋊C418yes—
344C2×C4×C5C2×C22⋊C414yes—
345C2×C4×C5C4×D414yes—
346C2×C4×C5C4×D414yes—
347C2×C4×C5#12114yes—
348C2×C4×C5#12114yes—
349C2×C4×C5#12414yes—
350C2×C4×C5#12714yes—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—24no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—24no—
365C2×Dic5—24no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—42no—
370C2×Dic5—41no—
371C2×Dic5—41no—
372C2×Dic5—41no—
373C2×Dic5—41no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—41no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—42no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5—42no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5C22⋊Q814yescomplemented
393C25C22×D511yescharacteristic
394C22×Q8—22no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8C2×Dic514yes—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—52no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—52no—
413C23×C4C2×Dic514yes—
414C23×C4C22×D512yes—
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D512yes—
417C23×C4C22×D511yescharacteristic
418C22⋊Q8—232no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—54no—
422C2×C4⋊C4—102no—
423C2×C4⋊C4—102no—
424C2×C4⋊C4—104no—
425C2×C4⋊C4—102no—
426C2×C4⋊C4—102no—
427C2×C4⋊C4—104no—
428C2×C4⋊C4—102no—
429C2×C4⋊C4—202no—
430C2×C4⋊C4C2×Dic518yes—
431C2×C4⋊C4C2×Dic514yes—
432C2×C4⋊C4C22⋊D514yes—
433C2×C4⋊C4C22⋊D514yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—54no—
437C2×C22⋊C4—102no—
438C2×C22⋊C4—102no—
439C2×C22⋊C4—102no—
440C2×C22⋊C4—102no—
441C2×C22⋊C4—102no—
442C2×C22⋊C4—104no—
443C2×C22⋊C4—104no—
444C2×C22⋊C4—202no—
445C2×C22⋊C4C2×Dic518yes—
446C2×C42—54no—
447C2×C42—102no—
448C2×C42—102no—
449C2×C42—104no—
450C2×C42—102no—
451C2×C42—102no—
452C2×C42—104no—
453C2×C42—102no—
454C2×C42—202no—
455#95—102no—
456#95—102no—
457#95—104no—
458#95—104no—
459#95—104no—
460#95—104no—
461#95—104no—
462#95—104no—
463#95—104no—
464C22×C5—24no—
465C22×C5—24no—
466C22×C5—24no—
467C22×C5—42no—
468C22×C5—42no—
469C22×C5—42no—
470C22×C5—42no—
471C22×C5—42no—
472C22×C5—42no—
473C22×C5—42no—
474C22×C5—42no—
475C22×C5—42no—
476C22×C5—42no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5C22×C22⋊C411yescharacteristic
480C22×C5C2×C4×D411yescharacteristic
481C22×C5C2×C4×D411yescharacteristic
482C22×C5C2×C4×Q811yescharacteristic
483C22×C5C4×#4111yescharacteristic
484C22×C5#51911yescharacteristic
485C22×C5#52011yescharacteristic
486C22×C5C2×#12111yescharacteristic
487C22×C5C2×#12111yescharacteristic
488C22×C5C2×C22⋊Q811yescharacteristic
489C22×C5#52511yescharacteristic
490C22×C5C2×#12411yescharacteristic
491C22×C5#52911yescharacteristic
492C22×C5C2×#12711yescharacteristic
493C22×C5#53311yescharacteristic
494C22×C5#53611yescharacteristic
495C22×C5#53711yescharacteristic
496C22×C5#54111yescharacteristic
497C22×C5#54211yescharacteristic
498C22×C5#54611yescharacteristic
499C22×C5#54611yescharacteristic
500C22×C5#54611yescharacteristic
501C22×C5#54711yescharacteristic
502C22×C5#54711yescharacteristic
503C22×C5#54711yescharacteristic
504C22×C5#54811yescharacteristic
505C22×C5#54811yescharacteristic
506C22×C5#54811yescharacteristic
507C22×C5D4×Q811yescharacteristic
508C22×C5D4×Q811yescharacteristic
509C22×C5D4×Q811yescharacteristic
510C22×C5#55211yescharacteristic
511C22×C5#55211yescharacteristic
512C22×C5#55411yescharacteristic
513C22×C5#55611yescharacteristic
514C4×C5—28no—
515C4×C5—42no—
516C4×C5—44no—
517C4×C5#39018yes—
518Dic5—24no—
519Dic5—42no—
520Dic5—44no—
521Dic5—42no—
522Dic5—42no—
523Dic5—82no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24Q8×D512yes—
537C24#71312yes—
538C24C22×Dic512yes—
539C24C23×D511yescharacteristic
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×Q8—44no—
546C2×Q8—44no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—54no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—102no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—102no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—102no—
593C22×C4—101no—
594C22×C4—102no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—102no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—102no—
604C22×C4—101no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4D4×D512yes—
613C22×C4D4×D512yes—
614C22×C4#71112yes—
615C22×C4#71112yes—
616C22×C4C22×Dic514yes—
617C22×C4C22×Dic512yes—
618C22×C4C22×Dic514yes—
619C22×C4C22×Dic512yes—
620C22×C4C2×C22⋊D514yes—
621C22×C4C2×C22⋊D514yes—
622C22×C4C2×C22⋊D512yes—
623C22×C4C2×C22⋊D512yes—
624C4⋊C4—216no—
625C4⋊C4—108no—
626C4⋊C4—208no—
627C4⋊C4—204no—
628C4⋊C4C22⋊Dic5116yescomplemented
629C22⋊C4—216no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—208no—
633C42—108no—
634C42—208no—
635C42—204no—
636C2×C5—44no—
637C2×C5C2×#39011yescharacteristic
638C2×C5C4×C22⋊Q811yescharacteristic
639C2×C5#232311yescharacteristic
640C2×C5#233911yescharacteristic
641C2×C5Q8×C22⋊C411yescharacteristic
642C2×C5#236011yescharacteristic
643C2×C5#236211yescharacteristic
644C2×C5#241511yescharacteristic
645C2×C5#241711yescharacteristic
646C2×C5#242711yescharacteristic
647C2×C5#242911yescharacteristic
648C2×C5#248911yescharacteristic
649C2×C5#249211yescharacteristic
650C2×C5#254011yescharacteristic
651C2×C5#254211yescharacteristic
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23Q8×Dic514yes—
687C23C2×D4×D511yescharacteristic
688C23C2×D4×D511yescharacteristic
689C23C2×#71111yescharacteristic
690C23C2×#71111yescharacteristic
691C23C2×Q8×D511yescharacteristic
692C23C2×#71311yescharacteristic
693C23#414711yescharacteristic
694C23#414711yescharacteristic
695C23D5×#4111yescharacteristic
696C23D5×#4111yescharacteristic
697C23#414911yescharacteristic
698C23#415011yescharacteristic
699C23C23×Dic511yescharacteristic
700C23C22×C22⋊D511yescharacteristic
701C23C22×C22⋊D511yescharacteristic
702Q8—416no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—416no—
724C2×C4—54no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—104no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—104no—
740C2×C4—104no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—201no—
744C2×C4—201no—
745C2×C4—201no—
746C2×C4—202no—
747C2×C4—201no—
748C2×C4—201no—
749C2×C4—201no—
750C2×C4—202no—
751C2×C4—202no—
752C2×C4—201no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—201no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4—202no—
765C2×C4—202no—
766C2×C4D4×Dic514yes—
767C2×C4D4×Dic514yes—
768C2×C4#408214yes—
769C2×C4#408414yes—
770C2×C4#408414yes—
771C2×C4#408614yes—
772C2×C4C2×C22⋊Dic518yes—
773C2×C4C2×C22⋊Dic514yes—
774C5#1399711yescharacteristic, complemented, Sylow
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22#6595611yescharacteristic
791C22#6595811yescharacteristic
792C22#6595911yescharacteristic
793C22D5×C22⋊Q811yescharacteristic
794C22#6596111yescharacteristic
795C22#6596211yescharacteristic
796C22#6596311yescharacteristic
797C22#6596411yescharacteristic
798C22#6596511yescharacteristic
799C22#6596611yescharacteristic
800C22#6596711yescharacteristic
801C22#6596911yescharacteristic
802C22#6597311yescharacteristic
803C22#6597511yescharacteristic
804C22#6597611yescharacteristic
805C22#6597711yescharacteristic
806C22C2×D4×Dic511yescharacteristic
807C22C2×D4×Dic511yescharacteristic
808C22C2×#408211yescharacteristic
809C22C2×#408411yescharacteristic
810C22C2×#408411yescharacteristic
811C22C2×#408611yescharacteristic
812C22C2×Q8×Dic511yescharacteristic
813C22#6614611yescharacteristic
814C22Q8×C22⋊D511yescharacteristic
815C22Q8×C22⋊D511yescharacteristic
816C22#6615111yescharacteristic
817C22#6615111yescharacteristic
818C22#6615811yescharacteristic
819C22#6615811yescharacteristic
820C22#41×Dic511yescharacteristic
821C22#6616111yescharacteristic
822C22#6616311yescharacteristic
823C22#6616311yescharacteristic
824C22C22×C22⋊Dic511yescharacteristic
825C4—28no—
826C4—42no—
827C4—44no—
828C4—104no—
829C4—202no—
830C4—204no—
831C4—202no—
832C4—202no—
833C4—402no—
834C4#6551018yes—
835C2—44no—
836C2Dic5×C22⋊Q811yescharacteristic
837C2#1061447511yescharacteristic
838C2#1061447811yescharacteristic
839C2#1061447911yescharacteristic
840C2#1061448311yescharacteristic
841C2#1061448711yescharacteristic
842C2#1061448811yescharacteristic
843C2#1061450311yescharacteristic
844C2#1061450411yescharacteristic
845C2#1061451011yescharacteristic
846C2#1061451111yescharacteristic
847C2#1061454411yescharacteristic
848C2C2×#6551011yescharacteristic
849C2Q8×C22⋊Dic511yescharacteristic
850C2#1061581911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC22×C5×C22⋊Q8C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22×C22⋊Q8D5
hypocenterC5#13997
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#65519C2semidirect
3. C2×#65519C2semidirect
6. C2×#65274C2semidirect
7. C2×C4⋊C4×Dic5C2semidirect
8. #10602362C2semidirect
9. #10602356C2semidirect
16. C2×C5×C22⋊Q8C4semidirect
88. C2×C22⋊Dic5Q8semidirect
228. C5×C4⋊C4C22⋊C4semidirect
243. C2×C22⋊Q8Dic5semidirect
392. C2×Dic5C22⋊Q8semidirect
628. C4⋊C4C22⋊Dic5semidirect
774. C5#13997semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×#655192
C2×#655012
C2×C4×C22⋊Dic52
C2×#652742
C2×C4⋊C4×Dic52
#106023622
#106023562
#106023392
#106023382
#139975