Finite Group Databasebeta

← #12005950

Subgroups — #12005950

Order 1280.

1350 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#536C211yesmaximal, characteristic
2C22×#3969C211yesmaximal, characteristic
3C2×#65521C211yesmaximal, characteristic
4C2×#65519C211yesmaximal, characteristic, complemented
5C22×#3968C211yesmaximal, characteristic, complemented
6#10602374C211yesmaximal, characteristic, complemented
7C2×#64752C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C23×C5×Q8C2211yescharacteristic
10C5×#536—22no—
11C5×#536—22no—
12C5×#536—22no—
13C5×#536C414yescomplemented
14C2×C5×C4⋊Q8—21no—
15C2×C5×#124—21no—
16C2×C5×#123—22no—
17C2×C5×C22⋊Q8—22no—
18C2×C5×#117C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4×Dic5C2211yescharacteristic
21C22×#681C2211yescharacteristic
22C22×#681C2211yescharacteristic
23C2×#3969—22no—
24C2×#3969—22no—
25C2×#3969—22no—
26#65521—22no—
27#65521—22no—
28#65519—22no—
29#65519—22no—
30C2×#3968—22no—
31C2×#3968—22no—
32C2×#3968—22no—
33C2×#3967—21no—
34C2×#3964—21no—
35C2×#3963—22no—
36#64752—22no—
37#64749—22no—
38#10998—51nomaximal, Sylow
39C2×C5×#41—21no—
40C2×C5×#41—21no—
41C2×C5×#41—21no—
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41C2×C412yes—
50C2×C5×#41D412yes—
51C22×C5×Q8—21no—
52C22×C5×Q8—21no—
53C22×C5×Q8—21no—
54C22×C5×Q8—21no—
55C22×C5×Q8—21no—
56C22×C5×Q8—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8—21no—
59C22×C5×Q8—21no—
60C22×C5×Q8—21no—
61C22×C5×Q8—21no—
62C22×C5×Q8—21no—
63C22×C5×Q8C2×C412yes—
64C22×C5×Q8D411yescharacteristic
65C22×C5×Q8D412yes—
66C22×C5×D4—21no—
67C22×C5×D4D411yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5D412yes—
70C23×C4×C5C2311yescharacteristic
71C23×Dic5—21no—
72C23×Dic5—21no—
73C5×C4⋊Q8—24no—
74C5×C4⋊Q8—24no—
75C5×#124—24no—
76C5×#124—24no—
77C5×#123—28no—
78C5×#123—28no—
79C5×C22⋊Q8—28no—
80C5×C22⋊Q8—28no—
81C5×#117—21no—
82C5×#117—21no—
83C5×#117C2×C412yes—
84C5×#117D412yes—
85C2×C5×C4⋊C4—24no—
86C2×C5×C4⋊C4D412yes—
87C2×C5×C22⋊C4—24no—
88C2×C5×C22⋊C4—21no—
89C2×C42×C5—21no—
90C2×C4⋊Dic5—21no—
91C2×C4⋊Dic5—21no—
92C2×C4⋊Dic5—21no—
93C2×C4⋊Dic5—21no—
94C2×C4⋊Dic5—21no—
95C2×C4⋊Dic5D412yes—
96C2×C4×Dic5—21no—
97C2×C4×Dic5—21no—
98C2×C4×Dic5—21no—
99C2×C4×Dic5—21no—
100C2×C4×Dic5—21no—
101C2×C4×Dic5D412yes—
102C2×#681—21no—
103C2×#681—21no—
104C2×#681—21no—
105C2×#681—21no—
106C2×#681—21no—
107C2×#681—21no—
108C2×#681—21no—
109C2×#681—21no—
110C2×#681—21no—
111C2×#681—21no—
112C2×#681D412yes—
113C2×#681D412yes—
114C22×#168—21no—
115C22×#168—21no—
116#3969—28no—
117#3968—28no—
118#3967—24no—
119#3964—24no—
120#3963—28no—
121C2×#536D511yescharacteristic
122C22×#104—51no—
123C2×#417—51no—
124C22×#101—51no—
125C2×#391—51no—
126#1736—51no—
127C2×#339—51no—
128C24×C5—21no—
129C24×C5C2×D411yescharacteristic
130C5×#41—22no—
131C5×#41—22no—
132C5×#41—22no—
133C5×#41—22no—
134C5×#41—22no—
135C5×#41—22no—
136C5×#41—22no—
137C5×#41—22no—
138C5×#41—41no—
139C5×#41—41no—
140C5×#41—41no—
141C5×#41—41no—
142C5×#41—41no—
143C5×#41—41no—
144C5×#41—41no—
145C5×#41—41no—
146C2×C5×Q8—22no—
147C2×C5×Q8—22no—
148C2×C5×Q8—22no—
149C2×C5×Q8—22no—
150C2×C5×Q8—22no—
151C2×C5×Q8—22no—
152C2×C5×Q8—22no—
153C2×C5×Q8—22no—
154C2×C5×Q8—21no—
155C2×C5×Q8—22no—
156C2×C5×Q8—22no—
157C2×C5×Q8—22no—
158C2×C5×Q8—22no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—41no—
164C2×C5×Q8—41no—
165C2×C5×Q8—41no—
166C2×C5×Q8—41no—
167C2×C5×Q8—41no—
168C2×C5×Q8—41no—
169C2×C5×Q8—41no—
170C2×C5×Q8—41no—
171C2×C5×Q8—41no—
172C2×C5×Q8—41no—
173C2×C5×Q8—41no—
174C2×C5×Q8—41no—
175C2×C5×Q8—41no—
176C2×C5×Q8—41no—
177C2×C5×Q8—41no—
178C2×C5×Q8—41no—
179C2×C5×Q8C22⋊C412yes—
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4—41no—
188C2×C5×D4—41no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4C22⋊C412yes—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—21no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—41no—
203C22×C4×C5—41no—
204C22×C4×C5—41no—
205C22×C4×C5—41no—
206C22×C4×C5C22⋊C414yes—
207C22×C4×C5C22×C411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5#4111yescharacteristic
218C22×C4×C5#4111yescharacteristic
219C22×C4×C5#4111yescharacteristic
220C22×C4×C5#4111yescharacteristic
221C22×Dic5—24no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—42no—
225C22×Dic5—41no—
226C22×Dic5—41no—
227C22×Dic5—44no—
228C22×Dic5—41no—
229C22×Dic5—41no—
230C5×C4⋊C4—216no—
231C5×C4⋊C4—22no—
232C5×C4⋊C4C22⋊C414yes—
233C5×C22⋊C4—216no—
234C5×C22⋊C4—22no—
235C5×C22⋊C4—22no—
236C42×C5—22no—
237C42×C5—22no—
238C4⋊Dic5—22no—
239C4⋊Dic5—22no—
240C4⋊Dic5—41no—
241C4⋊Dic5—41no—
242C4×Dic5—22no—
243C4×Dic5—22no—
244C4×Dic5—41no—
245C4×Dic5—41no—
246#681—22no—
247#681—22no—
248#681—22no—
249#681—22no—
250#681—41no—
251#681—41no—
252#681—41no—
253#681—41no—
254C2×#168—22no—
255C2×#168—22no—
256C2×#168—41no—
257C2×#168—41no—
258C2×#168—41no—
259C2×#168—41no—
260C22×#41C2×D511yescharacteristic
261C23×Q8C2×D511yescharacteristic
262C22×M16—51no—
263C22×M16—51no—
264#536—22no—
265#536—22no—
266#536—22no—
267#536Dic514yescomplemented
268C2×C4⋊Q8—21no—
269C2×#124—21no—
270C2×#123—22no—
271C2×C22⋊Q8—22no—
272C2×#117C2×D511yescharacteristic
273C22×C4⋊C4—51no—
274C22×C42—51no—
275C2×#104—102no—
276C2×#104—102no—
277C2×#104—102no—
278#417—102no—
279#417—102no—
280C2×#103—101no—
281C2×#102—101no—
282C2×#101—102no—
283C2×#101—102no—
284C2×#101—102no—
285#391—102no—
286#391—102no—
287C2×#95—102no—
288#340—102no—
289#339—102no—
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5C2×C22⋊C411yescharacteristic
298C23×C5#12011yescharacteristic
299C23×C5#12011yescharacteristic
300C23×C5#12011yescharacteristic
301C23×C5#12111yescharacteristic
302C23×C5#12111yescharacteristic
303C23×C5#12311yescharacteristic
304C5×Q8—22no—
305C5×Q8—22no—
306C5×Q8—42no—
307C5×Q8—42no—
308C5×Q8—42no—
309C5×Q8—42no—
310C5×Q8—42no—
311C5×Q8—42no—
312C5×Q8—41no—
313C5×Q8—42no—
314C5×Q8—42no—
315C5×Q8—41no—
316C5×D4—22no—
317C5×D4—22no—
318C5×D4—42no—
319C5×D4—42no—
320C5×D4—42no—
321C5×D4—42no—
322C5×D4—41no—
323C5×D4—41no—
324C2×C4×C5—24no—
325C2×C4×C5—24no—
326C2×C4×C5—22no—
327C2×C4×C5—24no—
328C2×C4×C5—24no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—41no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—41no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5C2×C22⋊C411yescharacteristic
342C2×C4×C5C2×C22⋊C411yescharacteristic
343C2×C4×C5C4×D411yescharacteristic
344C2×C4×C5C4×D411yescharacteristic
345C2×C4×C5C4×D411yescharacteristic
346C2×C4×C5C4×D411yescharacteristic
347C2×C4×C5#12011yescharacteristic
348C2×C4×C5#12011yescharacteristic
349C2×C4×C5#12011yescharacteristic
350C2×C4×C5#12011yescharacteristic
351C2×C4×C5#12011yescharacteristic
352C2×C4×C5#12111yescharacteristic
353C2×C4×C5#12111yescharacteristic
354C2×C4×C5#12111yescharacteristic
355C2×C4×C5#12111yescharacteristic
356C2×C4×C5#12111yescharacteristic
357C2×C4×C5#12111yescharacteristic
358C2×C4×C5#12111yescharacteristic
359C2×C4×C5#12111yescharacteristic
360C2×C4×C5#12111yescharacteristic
361C2×C4×C5#12111yescharacteristic
362C2×C4×C5#12311yescharacteristic
363C2×C4×C5#12311yescharacteristic
364C2×C4×C5#12311yescharacteristic
365C2×C4×C5#12411yescharacteristic
366C2×C4×C5#12411yescharacteristic
367C2×C4×C5#12711yescharacteristic
368C2×C4×C5#12711yescharacteristic
369C2×Dic5—24no—
370C2×Dic5—44no—
371C2×Dic5—42no—
372C2×Dic5—44no—
373C2×Dic5—42no—
374C2×Dic5—44no—
375C2×Dic5—42no—
376C2×Dic5—82no—
377C2×Dic5—82no—
378#168—42no—
379#168—42no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—21no—
390C2×#41C2×Dic512yes—
391C2×#41C22⋊D512yes—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—21no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8C2×Dic512yes—
405C22×Q8C22⋊D511yescharacteristic
406C22×Q8C22⋊D512yes—
407C22×D4—21no—
408C22×D4C22⋊D511yescharacteristic
409C23×C4—21no—
410C23×C4—101no—
411C23×C4—101no—
412C23×C4C22⋊D512yes—
413C23×C4C22×D511yescharacteristic
414C2×M16—52no—
415C2×M16—52no—
416C2×M16—101no—
417C2×M16—101no—
418C2×M16—101no—
419C2×M16—101no—
420C2×M16—101no—
421C2×M16—101no—
422C2×M16—101no—
423C2×M16—101no—
424C2×M16—101no—
425C2×M16—101no—
426C22×C8—101no—
427C22×C8—101no—
428C4⋊Q8—24no—
429C4⋊Q8—24no—
430#124—24no—
431#124—24no—
432#123—28no—
433#123—28no—
434C22⋊Q8—28no—
435C22⋊Q8—28no—
436#117—21no—
437#117—21no—
438#117C2×Dic512yes—
439#117C22⋊D512yes—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—52no—
442C2×C4⋊C4—101no—
443C2×C4⋊C4—101no—
444C2×C4⋊C4—101no—
445C2×C4⋊C4—101no—
446C2×C4⋊C4—101no—
447C2×C4⋊C4C22⋊D512yes—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—21no—
450C2×C42—21no—
451C2×C42—52no—
452C2×C42—101no—
453C2×C42—101no—
454C2×C42—101no—
455C2×C42—101no—
456C2×C42—101no—
457#104—108no—
458#103—104no—
459#102—104no—
460#101—108no—
461#95—108no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—21no—
465C22×C5—21no—
466C22×C5—21no—
467C22×C5—21no—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—44no—
471C22×C5—42no—
472C22×C5—81no—
473C22×C5—81no—
474C22×C5—82no—
475C22×C5#37911yescharacteristic
476C22×C5#38611yescharacteristic
477C22×C5#38611yescharacteristic
478C22×C5#39211yescharacteristic
479C22×C5#39211yescharacteristic
480C22×C5#39411yescharacteristic
481C22×C5#39411yescharacteristic
482C22×C5#45412yes—
483C22×C5#45612yes—
484C4×C5—44no—
485C4×C5—44no—
486C4×C5—42no—
487C4×C5#38611yescharacteristic
488C4×C5#38611yescharacteristic
489C4×C5#39011yescharacteristic
490C4×C5#39011yescharacteristic
491C4×C5#39211yescharacteristic
492C4×C5#39211yescharacteristic
493C4×C5#39411yescharacteristic
494C4×C5#39411yescharacteristic
495Dic5—44no—
496Dic5—82no—
497C24—21no—
498C24C2×C22⋊D511yescharacteristic
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C22⋊Dic512yes—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4C22⋊Dic512yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—104no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—202no—
579C22×C4—201no—
580C22×C4—201no—
581C22×C4—204no—
582C22×C4—201no—
583C22×C4—201no—
584C22×C4C22⋊Dic514yes—
585C22×C4D4×D511yescharacteristic
586C22×C4D4×D511yescharacteristic
587C22×C4D4×D511yescharacteristic
588C22×C4D4×D511yescharacteristic
589C22×C4#71111yescharacteristic
590C22×C4#71111yescharacteristic
591C22×C4#71111yescharacteristic
592C22×C4#71111yescharacteristic
593C22×C4C22×Dic511yescharacteristic
594C22×C4C2×C22⋊D511yescharacteristic
595C22×C4C2×C22⋊D511yescharacteristic
596C22×C4C2×C22⋊D511yescharacteristic
597C22×C4C2×C22⋊D511yescharacteristic
598C22×C4C2×C22⋊D511yescharacteristic
599M16—102no—
600M16—102no—
601M16—102no—
602M16—102no—
603M16—201no—
604M16—201no—
605M16—201no—
606M16—201no—
607C2×C8—102no—
608C2×C8—102no—
609C2×C8—201no—
610C2×C8—201no—
611C2×C8—201no—
612C2×C8—201no—
613C4⋊C4—216no—
614C4⋊C4—22no—
615C4⋊C4—102no—
616C4⋊C4—102no—
617C4⋊C4—201no—
618C4⋊C4—201no—
619C4⋊C4C22⋊Dic514yes—
620C22⋊C4—216no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C42—22no—
624C42—22no—
625C42—102no—
626C42—102no—
627C42—201no—
628C42—201no—
629C2×C5—21no—
630C2×C5—21no—
631C2×C5—21no—
632C2×C5—21no—
633C2×C5—82no—
634C2×C5#143811yescharacteristic
635C2×C5#179312yes—
636C2×C5#200311yescharacteristic
637C2×C5#200511yescharacteristic
638C2×C5#203812yes—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23#408111yescharacteristic
647C23#408311yescharacteristic
648C23#408511yescharacteristic
649C23#408511yescharacteristic
650C23C2×C22⋊Dic511yescharacteristic
651C23#409911yescharacteristic
652C23#409911yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—41no—
662Q8—42no—
663Q8—42no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—42no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—41no—
672D4—41no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—104no—
691C2×C4—204no—
692C2×C4—202no—
693C2×C4—204no—
694C2×C4—202no—
695C2×C4—204no—
696C2×C4—202no—
697C2×C4—402no—
698C2×C4—402no—
699C2×C4D4×Dic511yescharacteristic
700C2×C4D4×Dic511yescharacteristic
701C2×C4D4×Dic511yescharacteristic
702C2×C4D4×Dic511yescharacteristic
703C2×C4#408111yescharacteristic
704C2×C4#408111yescharacteristic
705C2×C4#408111yescharacteristic
706C2×C4#408211yescharacteristic
707C2×C4#408211yescharacteristic
708C2×C4#408311yescharacteristic
709C2×C4#408311yescharacteristic
710C2×C4#408311yescharacteristic
711C2×C4#408411yescharacteristic
712C2×C4#408411yescharacteristic
713C2×C4#408411yescharacteristic
714C2×C4#408411yescharacteristic
715C2×C4#408511yescharacteristic
716C2×C4#408511yescharacteristic
717C2×C4#408511yescharacteristic
718C2×C4#408511yescharacteristic
719C2×C4#408511yescharacteristic
720C2×C4#408511yescharacteristic
721C2×C4#408611yescharacteristic
722C2×C4#408611yescharacteristic
723C2×C4C2×C22⋊Dic511yescharacteristic
724C2×C4C2×C22⋊Dic511yescharacteristic
725C2×C4#409911yescharacteristic
726C2×C4#409911yescharacteristic
727C8—202no—
728C8—202no—
729C5#1099811yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—22no—
737C22—22no—
738C22—42no—
739C22—44no—
740C22—82no—
741C22—81no—
742C22—81no—
743C22#6550911yescharacteristic
744C22#6550911yescharacteristic
745C22#6551111yescharacteristic
746C22#6551111yescharacteristic
747C22#6551211yescharacteristic
748C22#6551211yescharacteristic
749C22#6553412yes—
750C22#6553512yes—
751C22#6553611yescharacteristic
752C4—44no—
753C4—42no—
754C4—44no—
755C4—204no—
756C4—402no—
757C4#6550911yescharacteristic
758C4#6550911yescharacteristic
759C4#6551011yescharacteristic
760C4#6551011yescharacteristic
761C4#6551111yescharacteristic
762C4#6551111yescharacteristic
763C4#6551211yescharacteristic
764C4#6551211yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—82no—
770C2#1060265612yes—
771C2#1060266011yescharacteristic
772C2#1060266111yescharacteristic
773C2#1060292411yescharacteristic
774C2#1060293612yes—
subgroupG/H
centerC23#4099
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#536C2
socleC23×C5#120
prime radicalC22×C5×#41C22
cosocleC23×C4×C5C23
hypercenterC2×#536D5
hypocenterC5#10998
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
4. C2×#65519C2semidirect
5. C22×#3968C2semidirect
6. #10602374C2semidirect
7. C2×#64752C2semidirect
13. C5×#536C4semidirect
267. #536Dic5semidirect
729. C5#10998semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5362
C22×#39692
C2×#655212
C2×#655192
C22×#39682
#106023742
C2×#647522
#109985