Finite Group Databasebeta

← #12022434

Subgroups — #12022434

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×#4070C211yesmaximal, characteristic
2C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
3C2×#65501C211yesmaximal, characteristic
4C2×#65218C211yesmaximal, characteristic, complemented
5C2×#65218C211yesmaximal, characteristic, complemented
6C2×#65217C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
8#10602340C212yesmaximal
9#10602338C212yesmaximal
10#10600214C212yesmaximal, complemented
11#10600197C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C23×Dic10C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×C22⋊Dic5C2212yes—
19C22×C22⋊Dic5C2212yes—
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C2×#4070—24no—
24C2×#4070—24no—
25C2×#4070C418yescomplemented
26C22×#683C2212yes—
27C22×#683C2212yes—
28C22×C4×Dic5C2212yes—
29C4×C5×C22⋊C4—24no—
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32#65501—24no—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40C4×C4⋊Dic5—24no—
41#65218—24no—
42#65218—24no—
43#65217—24no—
44#13997—51nomaximal, Sylow
45C25×C5C2311yescharacteristic
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5—22no—
52C23×C4×C5C2×C414yes—
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×Dic5C2312yes—
60C23×Dic5C2312yes—
61C23×Dic5C2312yes—
62C23×Dic5C2312yes—
63C22×Dic10—22no—
64C22×Dic10—22no—
65C22×Dic10—22no—
66C22×Dic10—22no—
67C22×Dic10—22no—
68C22×Dic10—22no—
69C22×Dic10C2×C414yes—
70C2×C5×C22⋊C4—22no—
71C2×C5×C22⋊C4—22no—
72C2×C5×C22⋊C4—22no—
73C2×C5×C22⋊C4—22no—
74C2×C5×C22⋊C4—22no—
75C2×C5×C22⋊C4Q814yescomplemented
76C2×C42×C5—22no—
77C2×C42×C5—22no—
78C2×C42×C5—22no—
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×C42×C5D414yes—
82C2×C22⋊Dic5—24no—
83C2×C22⋊Dic5—24no—
84C2×C22⋊Dic5—24no—
85C2×C22⋊Dic5—24no—
86C2×C22⋊Dic5—42no—
87C2×C22⋊Dic5C2×C418yes—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5C2×C414yes—
94C2×C4⋊Dic5D414yes—
95C2×C4⋊Dic5D414yes—
96C2×C4⋊Dic5D414yes—
97#4070—232no—
98C2×#683—24no—
99C2×#683—24no—
100C2×#683—24no—
101C2×#683—24no—
102C2×#683—42no—
103C2×#683C2×C418yes—
104C2×C4×Dic5—24no—
105C2×C4×Dic5—24no—
106C2×C4×Dic5—42no—
107C5×#95—22no—
108C5×#95—22no—
109#3963—24no—
110#3963—24no—
111#3963—24no—
112#3963—24no—
113#3963—24no—
114#3963—24no—
115#3963—24no—
116C22×C22⋊Q8—51no—
117C2×#391—51no—
118C2×#391—51no—
119C2×#389—51no—
120C2×#380—51no—
121C2×C4×C4⋊C4—51no—
122C2×C4×C22⋊C4D511yescharacteristic
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
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—28no—
172C22×C4×C5—28no—
173C22×C4×C5—28no—
174C22×C4×C5—44no—
175C22×C4×C5—44no—
176C22×C4×C5—44no—
177C22×C4×C5—44no—
178C22×C4×C5C22×C412yes—
179C22×C4×C5C22×C412yes—
180C22×C4×C5C2×D412yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×D412yes—
186C22×C4×C5C2×Q812yes—
187C22×C4×C5C2×Q812yes—
188C22×C4×C5#4112yes—
189C22×C4×C5#4112yes—
190C22×C4×C5#4112yes—
191C22×C4×C5#4112yes—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5C22×C414yes—
216C22×Dic5C22×C414yes—
217C22×Dic5C2×D414yes—
218C22×Dic5C2×D414yes—
219C22×Dic5C2×D414yes—
220C2×Dic10—28no—
221C2×Dic10—28no—
222C2×Dic10—28no—
223C2×Dic10—44no—
224C2×Dic10—44no—
225C2×Dic10—44no—
226C2×Dic10—44no—
227C5×C22⋊C4—28no—
228C5×C22⋊C4—28no—
229C42×C5—28no—
230C42×C5—44no—
231C22⋊Dic5—216no—
232C22⋊Dic5—48no—
233C4⋊Dic5—28no—
234C4⋊Dic5—44no—
235C4⋊Dic5C22⋊C4116yescomplemented
236#683—216no—
237#683—48no—
238C4×Dic5—48no—
239C23×Q8—51no—
240C24×C4C2×D511yescharacteristic
241C2×C22⋊Q8—58no—
242C2×C22⋊Q8—104no—
243C2×C22⋊Q8—104no—
244C22×C4⋊C4—51no—
245C22×C4⋊C4—52no—
246C22×C4⋊C4—51no—
247C22×C4⋊C4—51no—
248C22×C4⋊C4—52no—
249C22×C22⋊C4—52no—
250C22×C22⋊C4—52no—
251C22×C22⋊C4C2×D511yescharacteristic
252C22×C22⋊C4C2×D511yescharacteristic
253C22×C42—52no—
254C22×C42C2×D511yescharacteristic
255C22×C42C2×D511yescharacteristic
256#391—104no—
257#391—104no—
258#389—104no—
259#380—104no—
260C4×C4⋊C4—104no—
261C4×C22⋊C4—24no—
262C2×#95—52no—
263C2×#95—52no—
264C2×#95—52no—
265C2×#95—52no—
266C2×#95—52no—
267C2×#95—52no—
268C2×#95—52no—
269C2×#95C2×D511yescharacteristic
270C2×#95C2×D511yescharacteristic
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
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—416no—
356C2×C4×C5C2×C22⋊C414yes—
357C2×C4×C5C4×D414yes—
358C2×C4×C5C4×D414yes—
359C2×C4×C5#12114yes—
360C2×C4×C5#12114yes—
361C2×C4×C5C22⋊Q814yescomplemented
362C2×C4×C5#12414yes—
363C2×C4×C5#12714yes—
364C2×Dic5—24no—
365C2×Dic5—24no—
366C2×Dic5—24no—
367C2×Dic5—24no—
368C2×Dic5—24no—
369C2×Dic5—24no—
370C2×Dic5—24no—
371C2×Dic5—24no—
372C2×Dic5—24no—
373C2×Dic5—24no—
374C2×Dic5—24no—
375C2×Dic5—24no—
376C2×Dic5—42no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5—42no—
380C2×Dic5—42no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5—42no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5C2×C22⋊C418yes—
392Dic10—416no—
393C25C22×D511yescharacteristic
394C22×Q8—54no—
395C22×Q8—102no—
396C22×Q8—102no—
397C22×Q8—102no—
398C22×Q8—102no—
399C22×Q8—102no—
400C22×Q8—102no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—52no—
408C23×C4—52no—
409C23×C4—52no—
410C23×C4—52no—
411C23×C4C4×D514yes—
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C22⋊Q8—1032no—
419C2×C4⋊C4—54no—
420C2×C4⋊C4—54no—
421C2×C4⋊C4—54no—
422C2×C4⋊C4—58no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—104no—
425C2×C4⋊C4—104no—
426C2×C4⋊C4—102no—
427C2×C4⋊C4—102no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—102no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—102no—
433C2×C4⋊C4—202no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—58no—
440C2×C22⋊C4—104no—
441C2×C22⋊C4—104no—
442C2×C22⋊C4—104no—
443C2×C22⋊C4—104no—
444C2×C22⋊C4—202no—
445C2×C22⋊C4Dic1014yescomplemented
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—104no—
452C2×C42—104no—
453C2×C42—202no—
454C2×C42C22⋊D514yes—
455#95—22no—
456#95—22no—
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—24no—
515C4×C5—42no—
516C4×C5—42no—
517C4×C5—42no—
518C4×C5—42no—
519C4×C5#39018yes—
520Dic5—28no—
521Dic5—44no—
522Dic5—44no—
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—
536C24C2×Dic1012yes—
537C24C2×C4×D512yes—
538C24#70912yes—
539C24C23×D511yescharacteristic
540C2×Q8—108no—
541C2×Q8—108no—
542C2×Q8—108no—
543C2×Q8—204no—
544C2×Q8—204no—
545C2×Q8—204no—
546C2×Q8—204no—
547C22×C4—21no—
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—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
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—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—54no—
583C22×C4—54no—
584C22×C4—54no—
585C22×C4—54no—
586C22×C4—54no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4C2×Dic1012yes—
611C22×C4C2×Dic1012yes—
612C22×C4C2×C4×D512yes—
613C22×C4C2×C4×D512yes—
614C22×C4#70912yes—
615C22×C4#70912yes—
616C22×C4#70912yes—
617C22×C4D4×D512yes—
618C22×C4D4×D512yes—
619C22×C4D4×D512yes—
620C22×C4#71112yes—
621C22×C4C2×C22⋊D512yes—
622C22×C4C2×C22⋊D512yes—
623C22×C4C2×C22⋊D512yes—
624C4⋊C4—516no—
625C4⋊C4—1016no—
626C4⋊C4—108no—
627C4⋊C4—208no—
628C4⋊C4—204no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—1016no—
632C22⋊C4—208no—
633C42—28no—
634C42—44no—
635C42—208no—
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—
686C23C4×Dic1014yes—
687C23C22×Dic1011yescharacteristic
688C23C22×C4×D511yescharacteristic
689C23C2×#70911yescharacteristic
690C23C2×#70911yescharacteristic
691C23C2×#70911yescharacteristic
692C23C2×#70911yescharacteristic
693C23C2×D4×D511yescharacteristic
694C23C2×D4×D511yescharacteristic
695C23C2×D4×D511yescharacteristic
696C23C2×#71111yescharacteristic
697C23#414911yescharacteristic
698C23#415011yescharacteristic
699C23#415011yescharacteristic
700C23#415011yescharacteristic
701C23C22×C22⋊D511yescharacteristic
702Q8—2016no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—416no—
738C2×C4—58no—
739C2×C4—104no—
740C2×C4—104no—
741C2×C4—104no—
742C2×C4—104no—
743C2×C4—104no—
744C2×C4—104no—
745C2×C4—104no—
746C2×C4—104no—
747C2×C4—104no—
748C2×C4—104no—
749C2×C4—104no—
750C2×C4—104no—
751C2×C4—202no—
752C2×C4—202no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4—202no—
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×C4D5×C22⋊C414yes—
767C2×C4#402714yes—
768C2×C4#403014yes—
769C2×C4#403114yes—
770C2×C4#407014yescomplemented
771C2×C4C4×C22⋊D514yes—
772C2×C4#408514yes—
773C2×C4#408614yes—
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—
790C22C2×C4×Dic1011yescharacteristic
791C22#6580411yescharacteristic
792C22C4×#70911yescharacteristic
793C22#6581311yescharacteristic
794C22C2×D5×C22⋊C411yescharacteristic
795C22C2×#402711yescharacteristic
796C22C2×#403011yescharacteristic
797C22C2×#403111yescharacteristic
798C22#6585011yescharacteristic
799C22#6585211yescharacteristic
800C22#6585711yescharacteristic
801C22#6586811yescharacteristic
802C22D4×Dic1011yescharacteristic
803C22D4×Dic1011yescharacteristic
804C22D4×Dic1011yescharacteristic
805C22#6587511yescharacteristic
806C22#6587511yescharacteristic
807C22#6587611yescharacteristic
808C22#6587711yescharacteristic
809C22#6588411yescharacteristic
810C22#6588411yescharacteristic
811C22#6588411yescharacteristic
812C22#6588511yescharacteristic
813C22#6588511yescharacteristic
814C22#6588511yescharacteristic
815C22#6588611yescharacteristic
816C22#6588611yescharacteristic
817C22#6588611yescharacteristic
818C22C2×#407011yescharacteristic
819C22C2×C4×C22⋊D511yescharacteristic
820C22#6612511yescharacteristic
821C22C2×#408511yescharacteristic
822C22C2×#408611yescharacteristic
823C22#6615911yescharacteristic
824C22#6616711yescharacteristic
825C4—24no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—108no—
831C4—204no—
832C4—204no—
833C4—402no—
834C4#6524618yes—
835C2—44no—
836C2C22⋊C4×Dic1011yescharacteristic
837C2#1060519611yescharacteristic
838C2#1060519911yescharacteristic
839C2#1060521711yescharacteristic
840C2#1060521911yescharacteristic
841C2#1060523611yescharacteristic
842C2#1060523911yescharacteristic
843C2#1060530411yescharacteristic
844C2C4×#407011yescharacteristic
845C2C2×#6524611yescharacteristic
846C2#1061396611yescharacteristic
847C2#1061408211yescharacteristic
848C2#1061408411yescharacteristic
849C2#1061410811yescharacteristic
850C2#1061411011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×C4×C22⋊C4D5
hypocenterC5#13997
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#65218C2semidirect
5. C2×#65218C2semidirect
6. C2×#65217C2semidirect
7. C2×C4×C4⋊Dic5C2semidirect
10. #10600214C2semidirect
11. #10600197C2semidirect
25. C2×#4070C4semidirect
75. C2×C5×C22⋊C4Q8semidirect
235. C4⋊Dic5C22⋊C4semidirect
361. C2×C4×C5C22⋊Q8semidirect
445. C2×C22⋊C4Dic10semidirect
770. C2×C4#4070semidirect
774. C5#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#40702
C2×C4×C5×C22⋊C42
C2×#655012
C2×#652182
C2×#652172
C2×C4×C4⋊Dic52
#106023402
#106023382
#106002142
#106001972
#139975