Finite Group Databasebeta

← #12022430

Subgroups — #12022430

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×C5×#380C211yesmaximal, characteristic
3C2×C4×C22⋊Dic5C211yesmaximal, characteristic
4C2×#65263C211yesmaximal, characteristic, complemented
5C2×#65263C211yesmaximal, characteristic, complemented
6C2×#65262C211yesmaximal, 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×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2212yes—
17C22×C22⋊Dic5C2211yescharacteristic
18C22×C22⋊Dic5C2212yes—
19C22×C22⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C2×#4070—24no—
22C2×#4070—24no—
23C2×#4070C418yescomplemented
24C22×#683C2212yes—
25C22×#683C2212yes—
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2212yes—
28C22×C4×Dic5C2211yescharacteristic
29C5×#380—24no—
30C2×C5×#95C2212yes—
31C4×C22⋊Dic5—24no—
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2211yescharacteristic
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40C4⋊C4×Dic5—24no—
41#65263—24no—
42#65263—24no—
43#65262—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×C5C2312yes—
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2312yes—
56C23×C4×C5C2311yescharacteristic
57C23×Dic5C2312yes—
58C23×Dic5C2311yescharacteristic
59C23×Dic5C2311yescharacteristic
60C23×Dic5C2311yescharacteristic
61C23×Dic5C2312yes—
62C23×Dic5C2311yescharacteristic
63C22×Dic10—22no—
64C22×Dic10—22no—
65C22×Dic10—22no—
66C22×Dic10—22no—
67C22×Dic10—22no—
68C22×Dic10—22no—
69C22×Dic10C2×C414yes—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4D414yes—
76C2×C5×C22⋊C4—24no—
77C2×C5×C22⋊C4—24no—
78C2×C5×C22⋊C4—42no—
79C2×C22⋊Dic5—22no—
80C2×C22⋊Dic5—24no—
81C2×C22⋊Dic5—24no—
82C2×C22⋊Dic5—22no—
83C2×C22⋊Dic5—22no—
84C2×C22⋊Dic5—22no—
85C2×C22⋊Dic5—22no—
86C2×C22⋊Dic5C2×C418yes—
87C2×C22⋊Dic5Q814yescomplemented
88C2×C4⋊Dic5C2×C414yes—
89C2×C4⋊Dic5D414yes—
90C2×C4⋊Dic5D414yes—
91#4070—232no—
92C2×#683—24no—
93C2×#683—24no—
94C2×#683—24no—
95C2×#683—24no—
96C2×#683—42no—
97C2×#683C2×C418yes—
98C2×C4×Dic5—22no—
99C2×C4×Dic5—22no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5—22no—
103C2×C4×Dic5—24no—
104C2×C4×Dic5—24no—
105C2×C4×Dic5—42no—
106C2×C4×Dic5D414yes—
107C5×#95—24no—
108#3963—24no—
109#3963—24no—
110#3963—22no—
111#3963—22no—
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×#380D511yescharacteristic
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
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—28no—
156C22×C4×C5—28no—
157C22×C4×C5—28no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—44no—
166C22×C4×C5—44no—
167C22×C4×C5—44no—
168C22×C4×C5—44no—
169C22×C4×C5C22×C412yes—
170C22×C4×C5C22×C412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D414yes—
175C22×C4×C5C2×D412yes—
176C22×C4×C5#4112yes—
177C22×C4×C5#4112yes—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—21no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—21no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—21no—
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5C22×C414yes—
211C22×Dic5C22×C414yes—
212C22×Dic5C2×D412yes—
213C22×Dic5C2×D414yes—
214C22×Dic5C2×D414yes—
215C22×Dic5C2×D412yes—
216C22×Dic5C2×Q812yes—
217C22×Dic5C2×Q812yes—
218C22×Dic5#4112yes—
219C22×Dic5#4112yes—
220C2×Dic10—28no—
221C2×Dic10—28no—
222C2×Dic10—28no—
223C2×Dic10—44no—
224C2×Dic10—44no—
225C2×Dic10—44no—
226C2×Dic10—44no—
227C5×C4⋊C4—28no—
228C5×C4⋊C4—44no—
229C5×C22⋊C4—48no—
230C22⋊Dic5—28no—
231C22⋊Dic5—216no—
232C22⋊Dic5—28no—
233C4⋊Dic5C22⋊C4116yescomplemented
234#683—216no—
235#683—48no—
236C4×Dic5—28no—
237C4×Dic5—48no—
238C4×Dic5—44no—
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—52no—
247C22×C4⋊C4C2×D511yescharacteristic
248C22×C4⋊C4C2×D511yescharacteristic
249C22×C22⋊C4—52no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4C2×D512yes—
253C22×C42—51no—
254C22×C42—51no—
255C22×C42—52no—
256#391—104no—
257#391—104no—
258#389—104no—
259#380—24no—
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—51no—
270C2×#95C2×D512yes—
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—24no—
325C2×C4×C5—24no—
326C2×C4×C5—24no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—42no—
331C2×C4×C5—41no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—416no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5C2×C22⋊C414yes—
344C2×C4×C5C4×D414yes—
345C2×C4×C5C4×D414yes—
346C2×C4×C5#12114yes—
347C2×C4×C5#12114yes—
348C2×C4×C5#12414yes—
349C2×C4×C5#12714yes—
350C2×Dic5—24no—
351C2×Dic5—24no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—24no—
356C2×Dic5—24no—
357C2×Dic5—24no—
358C2×Dic5—24no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—24no—
363C2×Dic5—24no—
364C2×Dic5—24no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—42no—
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×Dic5—41no—
390C2×Dic5C2×C22⋊C418yes—
391C2×Dic5C22⋊Q814yescomplemented
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—51no—
409C23×C4—51no—
410C23×C4—52no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4C4×D514yes—
414C23×C4C22×D512yes—
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D512yes—
417C23×C4C22×D511yescharacteristic
418C22⋊Q8—1032no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—58no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4—104no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4C22⋊D514yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—58no—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—102no—
440C2×C22⋊C4—102no—
441C2×C22⋊C4—104no—
442C2×C22⋊C4—104no—
443C2×C22⋊C4—102no—
444C2×C22⋊C4—102no—
445C2×C22⋊C4—102no—
446C2×C42—54no—
447C2×C42—102no—
448C2×C42—102no—
449C2×C42—104no—
450C2×C42—104no—
451C2×C42—102no—
452C2×C42—102no—
453C2×C42—102no—
454C2×C42—202no—
455#95—24no—
456#95—102no—
457#95—102no—
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—44no—
515C4×C5—42no—
516C4×C5—82no—
517C4×C5#39018yes—
518Dic5—28no—
519Dic5—24no—
520Dic5—42no—
521Dic5—42no—
522Dic5—42no—
523Dic5—44no—
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×C4×D512yes—
537C24#71112yes—
538C24Q8×D512yes—
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—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—54no—
574C22×C4—52no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—54no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—102no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—102no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—102no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—102no—
615C22×C4C2×C4×D512yes—
616C22×C4C2×C4×D512yes—
617C22×C4#70912yes—
618C22×C4D4×D512yes—
619C22×C4D4×D512yes—
620C22×C4D4×D512yes—
621C22×C4#71112yes—
622C22×C4C2×C22⋊D514yes—
623C22×C4C2×C22⋊D512yes—
624C4⋊C4—28no—
625C4⋊C4—44no—
626C4⋊C4—516no—
627C4⋊C4—1016no—
628C4⋊C4—208no—
629C22⋊C4—48no—
630C22⋊C4—1016no—
631C22⋊C4—108no—
632C22⋊C4—108no—
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—
686C23#403314yes—
687C23C22×C4×D511yescharacteristic
688C23C2×#70911yescharacteristic
689C23C2×D4×D511yescharacteristic
690C23C2×D4×D511yescharacteristic
691C23C2×D4×D511yescharacteristic
692C23C2×#71111yescharacteristic
693C23C2×#71111yescharacteristic
694C23#414411yescharacteristic
695C23C2×Q8×D511yescharacteristic
696C23#414711yescharacteristic
697C23D5×#4111yescharacteristic
698C23D5×#4111yescharacteristic
699C23#415011yescharacteristic
700C23#415011yescharacteristic
701C23C22×C22⋊D511yescharacteristic
702Q8—2016no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—416no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—58no—
726C2×C4—54no—
727C2×C4—102no—
728C2×C4—104no—
729C2×C4—102no—
730C2×C4—104no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—104no—
735C2×C4—104no—
736C2×C4—104no—
737C2×C4—104no—
738C2×C4—102no—
739C2×C4—104no—
740C2×C4—104no—
741C2×C4—102no—
742C2×C4—104no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—202no—
752C2×C4—202no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—202no—
756C2×C4—201no—
757C2×C4—201no—
758C2×C4—202no—
759C2×C4—201no—
760C2×C4—201no—
761C2×C4—201no—
762C2×C4—201no—
763C2×C4—201no—
764C2×C4—201no—
765C2×C4—201no—
766C2×C4—201no—
767C2×C4D5×C22⋊C414yes—
768C2×C4#402714yes—
769C2×C4#403014yes—
770C2×C4#403114yes—
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×D5×C22⋊C411yescharacteristic
791C22C2×#402711yescharacteristic
792C22C2×#403011yescharacteristic
793C22C2×#403111yescharacteristic
794C22C2×#403311yescharacteristic
795C22#6583811yescharacteristic
796C22#6584511yescharacteristic
797C22#6584711yescharacteristic
798C22#6585011yescharacteristic
799C22#6585611yescharacteristic
800C22#6586311yescharacteristic
801C22#6586711yescharacteristic
802C22#6593211yescharacteristic
803C22#6593211yescharacteristic
804C22#6593411yescharacteristic
805C22#6593711yescharacteristic
806C22#6594011yescharacteristic
807C22#6594211yescharacteristic
808C22#6594611yescharacteristic
809C22#6594611yescharacteristic
810C22#6595611yescharacteristic
811C22#6595911yescharacteristic
812C22D5×C22⋊Q811yescharacteristic
813C22#6596211yescharacteristic
814C22#6596511yescharacteristic
815C22#6596511yescharacteristic
816C22#6596611yescharacteristic
817C22#6596611yescharacteristic
818C22C2×C4×C22⋊D511yescharacteristic
819C22C2×#408511yescharacteristic
820C22C2×#408611yescharacteristic
821C22#6614011yescharacteristic
822C22Q8×C22⋊D511yescharacteristic
823C22#6615811yescharacteristic
824C22#6616511yescharacteristic
825C4—42no—
826C4—44no—
827C4—82no—
828C4—104no—
829C4—108no—
830C4—204no—
831C4—202no—
832C4—202no—
833C4—202no—
834C4#6524618yes—
835C2—44no—
836C2#1060559711yescharacteristic
837C2#1060560211yescharacteristic
838C2#1060560711yescharacteristic
839C2#1060561911yescharacteristic
840C2#1060564411yescharacteristic
841C2#1060564711yescharacteristic
842C2#1060573911yescharacteristic
843C2#1060575111yescharacteristic
844C2C2×#6524611yescharacteristic
845C2#1061389311yescharacteristic
846C2#1061397411yescharacteristic
847C2#1061437811yescharacteristic
848C2#1061439911yescharacteristic
849C2#1061448911yescharacteristic
850C2#1061451111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#380C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#380D5
hypocenterC5#13997
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#65263C2semidirect
5. C2×#65263C2semidirect
6. C2×#65262C2semidirect
7. C2×C4⋊C4×Dic5C2semidirect
10. #10600214C2semidirect
11. #10600197C2semidirect
23. C2×#4070C4semidirect
87. C2×C22⋊Dic5Q8semidirect
233. C4⋊Dic5C22⋊C4semidirect
391. C2×Dic5C22⋊Q8semidirect
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×C5×#3802
C2×C4×C22⋊Dic52
C2×#652632
C2×#652622
C2×C4⋊C4×Dic52
#106023402
#106023382
#106002142
#106001972
#139975