Finite Group Databasebeta

← #12030539

Subgroups — #12030539

Order 1280.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D5C211yesmaximal, characteristic
2C2×C5×#389C211yesmaximal, characteristic, complemented
3C2×#65278C212yesmaximal
4C2×#65276C211yesmaximal, characteristic
5C2×#65276C211yesmaximal, characteristic
6C2×#65262C211yesmaximal, characteristic, complemented
7#10602357C212yesmaximal, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602328C211yesmaximal, characteristic, complemented
10#10600218C212yesmaximal
11#10600199C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C23×C4×D5C2211yescharacteristic
14C23×C4×D5C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×#683C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C2×C42×D5—24no—
28C2×C42×D5—24no—
29C2×C42×D5—24no—
30C5×#389—24no—
31C2×C5×#95C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39#65278—28no—
40#65276—24no—
41#65276C418yescomplemented
42#65262—24no—
43#14697—51nomaximal, Sylow
44C24×D5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2312yes—
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2311yescharacteristic
54C23×Dic5C2311yescharacteristic
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—22no—
60C22×C4×D5—22no—
61C22×C4×D5—22no—
62C22×C4×D5—22no—
63C22×C4×D5—22no—
64C22×C4×D5—22no—
65C22×C4×D5—22no—
66C22×C4×D5—22no—
67C22×C4×D5—22no—
68C22×C4×D5—22no—
69C22×C4×D5—22no—
70C22×C4×D5—22no—
71C22×C4×D5C2×C414yes—
72C22×C4×D5D414yes—
73C22×C4×D5D414yes—
74C22×C4×D5Q814yes—
75C22×C4×D5Q814yes—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—24no—
83C2×C5×C4⋊C4—24no—
84C2×C5×C4⋊C4C2×C414yescomplemented
85C2×C42×C5—22no—
86C2×C42×C5—22no—
87C2×C42×C5D414yes—
88C2×#685—24no—
89C2×#685—24no—
90C2×#685—24no—
91C2×#685—24no—
92C2×#685—24no—
93C2×#685C2×C418yes—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—22no—
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5—22no—
98C2×C4⋊Dic5—22no—
99C2×C4⋊Dic5C2×C414yescomplemented
100C2×#683—24no—
101C2×#683—24no—
102C2×#683—24no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—22no—
105C2×C4×Dic5—22no—
106C2×C4×Dic5—22no—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5—22no—
111C2×C4×Dic5D414yes—
112C42×D5—232no—
113C5×#95—24no—
114#3963—24no—
115#3963—24no—
116#3963—24no—
117#3963—24no—
118#3963—24no—
119#3963—24no—
120#3963C2×C418yescomplemented
121C23×C42—51no—
122C2×#389—51no—
123C2×#389D511yescharacteristic, complemented
124C2×#385—52no—
125C2×#380—51no—
126C2×#380—51no—
127#1436—52no—
128#1436—52no—
129C4⋊#95—51no—
130C4⋊#95—51no—
131C22⋊#95—52no—
132C24×C5C2411yescharacteristic
133C23×D5—21no—
134C23×D5—21no—
135C23×D5—21no—
136C23×D5—21no—
137C23×D5—21no—
138C23×D5—21no—
139C23×D5—21no—
140C23×D5—21no—
141C23×D5C22×C412yes—
142C23×D5C2×D412yes—
143C23×D5C2×D412yes—
144C23×D5C2×Q812yes—
145C23×D5C2×Q812yes—
146C23×D5#4112yes—
147C23×D5#4112yes—
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—22no—
157C22×C4×C5—22no—
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—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5C22×C414yes—
170C22×C4×C5C22×C412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D412yes—
176C22×C4×C5C2×D412yes—
177C22×C4×C5C2×Q812yes—
178C22×C4×C5C2×Q812yes—
179C22×C4×C5#4112yes—
180C22×C4×C5#4112yes—
181C22×C4×C5#4112yes—
182C22×C4×C5#4112yes—
183C22×Dic5—21no—
184C22×Dic5—21no—
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—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×Dic5C22×C414yes—
209C22×Dic5C22×C412yes—
210C22×Dic5C2×D412yes—
211C22×Dic5C2×D412yes—
212C22×Dic5C2×D412yes—
213C22×Dic5C2×D412yes—
214C22×Dic5C2×Q812yes—
215C22×Dic5C2×Q812yes—
216C22×Dic5#4112yes—
217C22×Dic5#4112yes—
218C2×C4×D5—28no—
219C2×C4×D5—28no—
220C2×C4×D5—28no—
221C2×C4×D5—28no—
222C2×C4×D5—28no—
223C2×C4×D5—28no—
224C2×C4×D5—28no—
225C2×C4×D5—28no—
226C2×C4×D5—28no—
227C2×C4×D5—28no—
228C2×C4×D5—28no—
229C2×C4×D5—28no—
230C2×C4×D5—28no—
231C2×C4×D5—28no—
232C2×C4×D5—28no—
233C2×C4×D5—28no—
234C2×C4×D5—28no—
235C2×C4×D5—28no—
236C2×C4×D5—28no—
237C2×C4×D5—28no—
238C2×C4×D5C4⋊C4116yescomplemented
239C5×C4⋊C4—28no—
240C5×C4⋊C4—44no—
241C5×C4⋊C4—48no—
242C42×C5—28no—
243#685—216no—
244#685—48no—
245C4⋊Dic5—28no—
246C4⋊Dic5—44no—
247#683—48no—
248C4×Dic5—28no—
249C4×Dic5—28no—
250C4×Dic5—28no—
251C24×C4—51no—
252C24×C4—51no—
253C24×C4—51no—
254C22×C4⋊C4—51no—
255C22×C4⋊C4—52no—
256C22×C4⋊C4—51no—
257C22×C4⋊C4C2×D512yes—
258C22×C4⋊C4C2×D511yescharacteristic
259C22×C4⋊C4C2×D511yescharacteristic
260C22×C22⋊C4—52no—
261C22×C22⋊C4—52no—
262C22×C42—51no—
263C22×C42—51no—
264C22×C42—51no—
265C22×C42—104no—
266C22×C42—104no—
267C22×C42—104no—
268C22×C42C2×D511yescharacteristic
269#389—24no—
270#389—104no—
271#385—108no—
272#380—58no—
273#380—104no—
274C2×#95—52no—
275C2×#95—52no—
276C2×#95—52no—
277C2×#95—52no—
278C2×#95—52no—
279C2×#95—52no—
280C2×#95—52no—
281C2×#95C2×D512yes—
282C23×C5C23×C411yescharacteristic
283C23×C5C22×D411yescharacteristic
284C23×C5C22×D411yescharacteristic
285C23×C5C22×D411yescharacteristic
286C23×C5C22×D411yescharacteristic
287C23×C5C22×Q811yescharacteristic
288C23×C5C22×Q811yescharacteristic
289C23×C5C2×#4111yescharacteristic
290C23×C5C2×#4111yescharacteristic
291C23×C5C2×#4111yescharacteristic
292C23×C5C2×#4111yescharacteristic
293C23×C5C2×#4111yescharacteristic
294C23×C5C2×#4111yescharacteristic
295C23×C5C2×#4111yescharacteristic
296C23×C5C2×#4111yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5—22no—
308C22×D5—22no—
309C22×D5—22no—
310C22×D5—22no—
311C22×D5—22no—
312C22×D5—22no—
313C22×D5—22no—
314C22×D5—22no—
315C22×D5—22no—
316C22×D5—22no—
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—22no—
324C22×D5—22no—
325C22×D5C2×C4⋊C414yes—
326C22×D5C4×D414yes—
327C22×D5C4×Q814yes—
328C22×D5#12114yes—
329C22×D5C22⋊Q814yes—
330C22×D5#12514yes—
331C22×D5C4⋊Q814yes—
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—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—24no—
345C2×C4×C5—24no—
346C2×C4×C5—24no—
347C2×C4×C5—42no—
348C2×C4×C5—42no—
349C2×C4×C5—42no—
350C2×C4×C5—42no—
351C2×C4×C5—42no—
352C2×C4×C5—42no—
353C2×C4×C5—42no—
354C2×C4×C5—42no—
355C2×C4×C5—42no—
356C2×C4×C5—42no—
357C2×C4×C5—42no—
358C2×C4×C5C2×C4⋊C414yes—
359C2×C4×C5C4×D414yes—
360C2×C4×C5C4×D414yes—
361C2×C4×C5#12014yes—
362C2×C4×C5#12114yes—
363C2×C4×C5C22⋊Q814yes—
364C2×C4×C5C22⋊Q814yes—
365C2×C4×C5C22⋊Q814yes—
366C2×C4×C5#12314yes—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—24no—
386C2×Dic5—24no—
387C2×Dic5—24no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5C2×C4⋊C414yes—
400C2×Dic5#12114yes—
401C2×Dic5C22⋊Q814yes—
402C4×D5—232no—
403C4×D5—232no—
404C4×D5—232no—
405C25—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—54no—
410C23×C4—54no—
411C23×C4—54no—
412C23×C4—52no—
413C23×C4—54no—
414C23×C4—54no—
415C23×C4—52no—
416C23×C4—102no—
417C23×C4—102no—
418C23×C4—102no—
419C23×C4—102no—
420C23×C4—102no—
421C23×C4—102no—
422C23×C4—102no—
423C23×C4—102no—
424C23×C4—102no—
425C23×C4—102no—
426C23×C4—102no—
427C23×C4—102no—
428C23×C4—102no—
429C23×C4—102no—
430C23×C4—102no—
431C23×C4—102no—
432C23×C4C22×D512yes—
433C23×C4C22×D512yes—
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—102no—
447C2×C4⋊C4—102no—
448C2×C4⋊C4—104no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—102no—
452C2×C4⋊C4—102no—
453C2×C4⋊C4—102no—
454C2×C4⋊C4C4×D514yescomplemented
455C2×C22⋊C4—58no—
456C2×C22⋊C4—104no—
457C2×C22⋊C4—104no—
458C2×C22⋊C4—104no—
459C2×C22⋊C4—104no—
460C2×C22⋊C4—104no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—54no—
464C2×C42—1032no—
465C2×C42—102no—
466C2×C42—102no—
467C2×C42—102no—
468C2×C42—102no—
469C2×C42—102no—
470C2×C42—102no—
471C2×C42—102no—
472C2×C42—102no—
473C2×C42C22⋊D514yes—
474#95—24no—
475#95—58no—
476#95—104no—
477#95—104no—
478#95—104no—
479#95—104no—
480#95—104no—
481#95—104no—
482C22×C5C22×C4⋊C411yescharacteristic
483C22×C5C2×C4×D411yescharacteristic
484C22×C5C2×C4×D411yescharacteristic
485C22×C5C2×C4×D411yescharacteristic
486C22×C5C2×C4×Q811yescharacteristic
487C22×C5C4×#4111yescharacteristic
488C22×C5C4×#4111yescharacteristic
489C22×C5C2×#12011yescharacteristic
490C22×C5C2×#12111yescharacteristic
491C22×C5C2×#12111yescharacteristic
492C22×C5C2×#12111yescharacteristic
493C22×C5C2×C22⋊Q811yescharacteristic
494C22×C5C2×C22⋊Q811yescharacteristic
495C22×C5C2×C22⋊Q811yescharacteristic
496C22×C5C2×C22⋊Q811yescharacteristic
497C22×C5C2×C22⋊Q811yescharacteristic
498C22×C5C2×#12311yescharacteristic
499C22×C5#52511yescharacteristic
500C22×C5#52511yescharacteristic
501C22×C5#52511yescharacteristic
502C22×C5#52511yescharacteristic
503C22×C5#52511yescharacteristic
504C22×C5#52511yescharacteristic
505C22×C5C2×#12511yescharacteristic
506C22×C5#52911yescharacteristic
507C22×C5#52911yescharacteristic
508C22×C5#52911yescharacteristic
509C22×C5#52911yescharacteristic
510C22×C5C2×C4⋊Q811yescharacteristic
511C22×C5#53211yescharacteristic
512C22×C5#53211yescharacteristic
513C22×C5#53311yescharacteristic
514C22×C5#53311yescharacteristic
515C22×C5#53311yescharacteristic
516C22×C5#53311yescharacteristic
517C2×D5—24no—
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—24no—
529C2×D5—24no—
530C2×D5—24no—
531C2×D5#38918yescomplemented
532C4×C5—24no—
533C4×C5—24no—
534C4×C5—44no—
535C4×C5—82no—
536C4×C5#38518yescomplemented
537Dic5—24no—
538Dic5—24no—
539Dic5—24no—
540Dic5—44no—
541Dic5—82no—
542C24—52no—
543C24—52no—
544C24—52no—
545C24—52no—
546C24—52no—
547C24—52no—
548C24—52no—
549C24—101no—
550C24—101no—
551C24—101no—
552C24—101no—
553C24—101no—
554C24—101no—
555C24—101no—
556C24—101no—
557C24C23×D511yescharacteristic
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—516no—
589C22×C4—54no—
590C22×C4—108no—
591C22×C4—108no—
592C22×C4—108no—
593C22×C4—108no—
594C22×C4—108no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—108no—
598C22×C4—108no—
599C22×C4—108no—
600C22×C4—108no—
601C22×C4—108no—
602C22×C4—101no—
603C22×C4—101no—
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—108no—
615C22×C4—108no—
616C22×C4—108no—
617C22×C4—108no—
618C22×C4—108no—
619C22×C4—108no—
620C22×C4—108no—
621C22×C4—108no—
622C22×C4—102no—
623C22×C4—102no—
624C22×C4—102no—
625C22×C4—102no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—102no—
630C22×C4—102no—
631C22×C4—102no—
632C22×C4—102no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4C2×C4×D514yes—
636C22×C4C2×C4×D512yes—
637C22×C4#70912yes—
638C22×C4D4×D512yes—
639C22×C4D4×D512yes—
640C22×C4D4×D512yes—
641C22×C4#71112yes—
642C22×C4Q8×D512yes—
643C22×C4Q8×D512yes—
644C22×C4#71312yes—
645C22×C4#71312yes—
646C22×C4C2×C22⋊D512yes—
647C22×C4C2×C22⋊D512yes—
648C22×C4C2×C22⋊D512yes—
649C4⋊C4—28no—
650C4⋊C4—44no—
651C4⋊C4—48no—
652C4⋊C4—108no—
653C4⋊C4—208no—
654C4⋊C4—204no—
655C22⋊C4—1016no—
656C22⋊C4—208no—
657C42—28no—
658C42—108no—
659C42—108no—
660C42—108no—
661C2×C5C2×#38511yescharacteristic
662C2×C5C2×#38911yescharacteristic
663C2×C5#229611yescharacteristic
664C2×C5C4×#12111yescharacteristic
665C2×C5C4×#12111yescharacteristic
666C2×C5C4×C22⋊Q811yescharacteristic
667C2×C5C4×C22⋊Q811yescharacteristic
668C2×C5#284711yescharacteristic
669C2×C5#284811yescharacteristic
670C2×C5#285111yescharacteristic
671C2×C5#285111yescharacteristic
672C2×C5#285411yescharacteristic
673C2×C5#285511yescharacteristic
674C2×C5#285711yescharacteristic
675C2×C5#285711yescharacteristic
676D5—28no—
677C23—54no—
678C23—54no—
679C23—54no—
680C23—54no—
681C23—54no—
682C23—54no—
683C23—54no—
684C23—102no—
685C23—102no—
686C23—102no—
687C23—102no—
688C23—102no—
689C23—102no—
690C23—102no—
691C23—102no—
692C23—102no—
693C23—102no—
694C23—102no—
695C23—102no—
696C23—102no—
697C23—102no—
698C23—102no—
699C23—102no—
700C23—102no—
701C23—102no—
702C23—102no—
703C23—102no—
704C23—102no—
705C23—102no—
706C23—102no—
707C23—102no—
708C23—102no—
709C23—102no—
710C23—102no—
711C23—102no—
712C23C22×C4×D511yescharacteristic
713C23C2×#70911yescharacteristic
714C23C2×D4×D511yescharacteristic
715C23C2×D4×D511yescharacteristic
716C23C2×D4×D511yescharacteristic
717C23C2×#71111yescharacteristic
718C23C2×Q8×D511yescharacteristic
719C23C2×Q8×D511yescharacteristic
720C23C2×#71311yescharacteristic
721C23C2×#71311yescharacteristic
722C23D5×#4111yescharacteristic
723C23D5×#4111yescharacteristic
724C23D5×#4111yescharacteristic
725C23D5×#4111yescharacteristic
726C23C22×C22⋊D511yescharacteristic
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—54no—
754C2×C4—54no—
755C2×C4—54no—
756C2×C4—1032no—
757C2×C4—1032no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—1032no—
777C2×C4—104no—
778C2×C4—104no—
779C2×C4—104no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4—202no—
783C2×C4—202no—
784C2×C4—202no—
785C2×C4—202no—
786C2×C4—202no—
787C2×C4—202no—
788C2×C4—202no—
789C2×C4—202no—
790C2×C4—202no—
791C2×C4D5×C4⋊C414yes—
792C2×C4#403914yes—
793C2×C4#404014yes—
794C2×C4#404214yes—
795C2×C4C4×C22⋊D514yes—
796C2×C4#408314yes—
797C2×C4#408414yes—
798C2×C4#409214yes—
799C2×C4#409214yes—
800C5#1469711yescharacteristic, complemented, Sylow
801C22—58no—
802C22—104no—
803C22—104no—
804C22—104no—
805C22—104no—
806C22—104no—
807C22—104no—
808C22—104no—
809C22—104no—
810C22—104no—
811C22—104no—
812C22—104no—
813C22—104no—
814C22—104no—
815C22—104no—
816C22C2×D5×C4⋊C411yescharacteristic
817C22C2×#403911yescharacteristic
818C22C2×#404011yescharacteristic
819C22C2×#404211yescharacteristic
820C22C4×#71111yescharacteristic
821C22C4×D4×D511yescharacteristic
822C22#6588211yescharacteristic
823C22#6589111yescharacteristic
824C22C4×Q8×D511yescharacteristic
825C22C4×#71311yescharacteristic
826C22#6591211yescharacteristic
827C22#6591411yescharacteristic
828C22D5×#12111yescharacteristic
829C22D5×#12111yescharacteristic
830C22#6594011yescharacteristic
831C22#6594011yescharacteristic
832C22D5×C22⋊Q811yescharacteristic
833C22D5×C22⋊Q811yescharacteristic
834C22#6596111yescharacteristic
835C22#6596111yescharacteristic
836C22D5×#12511yescharacteristic
837C22#6602211yescharacteristic
838C22#6602511yescharacteristic
839C22#6602511yescharacteristic
840C22D5×C4⋊Q811yescharacteristic
841C22#6605911yescharacteristic
842C22#6606211yescharacteristic
843C22#6606211yescharacteristic
844C22C2×C4×C22⋊D511yescharacteristic
845C22C2×#408311yescharacteristic
846C22C2×#408411yescharacteristic
847C22C2×#409211yescharacteristic
848C22C2×#409211yescharacteristic
849C22#6616211yescharacteristic
850C22#6616211yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—104no—
856C4—104no—
857C4—104no—
858C4—204no—
859C4—402no—
860C4#6527818yescomplemented
861C2—108no—
862C2#1060769411yescharacteristic
863C2#1060769511yescharacteristic
864C2#1060769611yescharacteristic
865C2D5×#38911yescharacteristic
866C2#1060801611yescharacteristic
867C2#1060801711yescharacteristic
868C2#1060801811yescharacteristic
869C2#1060801911yescharacteristic
870C2C2×#6527811yescharacteristic
871C2C4×#408411yescharacteristic
872C2C4×#409211yescharacteristic
873C2#1061445411yescharacteristic
874C2#1061456511yescharacteristic
875C2#1061480311yescharacteristic
876C2#1061500011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#389C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#389D5
hypocenterC5#14697
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×C5×#389C2semidirect
6. C2×#65262C2semidirect
7. #10602357C2semidirect
8. #10602356C2semidirect
9. #10602328C2semidirect
11. #10600199C2semidirect
41. #65276C4semidirect
84. C2×C5×C4⋊C4C2×C4semidirect
99. C2×C4⋊Dic5C2×C4semidirect
120. #3963C2×C4semidirect
123. C2×#389D5semidirect
238. C2×C4×D5C4⋊C4semidirect
454. C2×C4⋊C4C4×D5semidirect
531. C2×D5#389semidirect
536. C4×C5#385semidirect
800. C5#14697semidirect
860. C4#65278semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D52
C2×C5×#3892
C2×#652782
C2×#652762
C2×#652622
#106023572
#106023562
#106023282
#106002182
#106001992
#146975