Finite Group Databasebeta

← #12021249

Subgroups — #12021249

Order 1280.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65276C211yesmaximal, characteristic
2C2×#65276C211yesmaximal, characteristic
3C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
4C2×#65224C211yesmaximal, characteristic, complemented
5C2×C4×#685C211yesmaximal, characteristic
6C2×#64959C212yesmaximal
7C5×C4⋊#95C211yesmaximal, characteristic, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10600220C212yesmaximal
10#10600208C212yesmaximal, complemented
11#10600200C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×#685C2212yes—
17C22×#685C2212yes—
18C22×#685C2211yescharacteristic
19C22×#685C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2212yes—
22C22×C4⋊Dic5C2212yes—
23C22×C4⋊Dic5C2211yescharacteristic
24C22×C4×Dic5C2212yes—
25C22×C4×Dic5C2211yescharacteristic
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35#65276—24no—
36#65276—24no—
37C4⋊C4×Dic5—24no—
38C4×#685C418yescomplemented
39#65224—24no—
40#64959—28no—
41#13876—51nomaximal, Sylow
42C24×D5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2312yes—
52C23×Dic5C2311yescharacteristic
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5C2×C414yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4D414yes—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5C2×C414yes—
69C2×#685—22no—
70C2×#685—22no—
71C2×#685—24no—
72C2×#685—24no—
73C2×#685—24no—
74C2×#685—24no—
75C2×#685—42no—
76C2×#685—42no—
77C2×#685C2×C414yes—
78C2×#685C2×C414yes—
79C2×#685D414yes—
80C2×#685Q814yes—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5—24no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—24no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—24no—
89C2×C4⋊Dic5—24no—
90C2×C4⋊Dic5—42no—
91C2×C4⋊Dic5—42no—
92C2×C4⋊Dic5D414yes—
93C2×C4×Dic5—22no—
94C2×C4×Dic5—22no—
95C2×C4×Dic5—24no—
96C2×C4×Dic5—24no—
97C2×C4×Dic5—42no—
98C2×C4×Dic5C2×C414yes—
99C5×#95—24no—
100C5×#95—24no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—24no—
105#3963—42no—
106#3963C2×C414yes—
107#3963C2×C414yes—
108C2×#388—52no—
109C2×#384—51no—
110C2×#380—51no—
111C2×#380—51no—
112C2×C4×C4⋊C4—51no—
113C2×C4×C22⋊C4—51no—
114#1442—52no—
115#1439—52no—
116#1436—52no—
117C4⋊#95—51no—
118C4⋊#95D511yescharacteristic, complemented
119C24×C5C2411yescharacteristic
120C23×D5—21no—
121C23×D5—21no—
122C23×D5—21no—
123C23×D5—21no—
124C23×D5—21no—
125C23×D5—21no—
126C23×D5—21no—
127C23×D5—21no—
128C23×D5—21no—
129C23×D5—21no—
130C23×D5—21no—
131C23×D5—21no—
132C23×D5C22×C412yes—
133C23×D5C2×D412yes—
134C23×D5C2×Q812yes—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
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×C5C22×C412yes—
157C22×C4×C5C22×C412yes—
158C22×C4×C5C22×C412yes—
159C22×C4×C5C2×D414yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5C2×D412yes—
163C22×C4×C5C2×Q812yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C22×C4×C5#4112yes—
167C22×C4×C5#4112yes—
168C22×C4×C5#4112yes—
169C22×C4×C5#4112yes—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—21no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5C22×C412yes—
200C22×Dic5C22×C412yes—
201C22×Dic5C22×C412yes—
202C22×Dic5C2×D414yes—
203C22×Dic5C2×D412yes—
204C22×Dic5C2×Q812yes—
205C2×C4×D5—28no—
206C2×C4×D5—28no—
207C2×C4×D5—28no—
208C2×C4×D5—44no—
209C2×C4×D5—44no—
210C2×C4×D5—44no—
211C2×C4×D5—44no—
212C5×C4⋊C4—28no—
213C5×C4⋊C4—44no—
214C42×C5—28no—
215#685—28no—
216#685—48no—
217#685—48no—
218#685C4⋊C4116yescomplemented
219C4⋊Dic5—28no—
220C4⋊Dic5—48no—
221C4⋊Dic5—48no—
222C4⋊Dic5—44no—
223C4×Dic5—28no—
224C4×Dic5—48no—
225C24×C4—51no—
226C22×C4⋊C4—51no—
227C22×C4⋊C4—51no—
228C22×C4⋊C4—52no—
229C22×C4⋊C4—52no—
230C22×C4⋊C4C2×D511yescharacteristic
231C22×C4⋊C4C2×D511yescharacteristic
232C22×C22⋊C4—51no—
233C22×C22⋊C4—51no—
234C22×C22⋊C4—52no—
235C22×C22⋊C4—52no—
236C22×C42—51no—
237C22×C42—52no—
238C22×C42C2×D511yescharacteristic
239#388—108no—
240#384—104no—
241#380—104no—
242#380—104no—
243C4×C4⋊C4—104no—
244C4×C22⋊C4—58no—
245C2×#95—51no—
246C2×#95—51no—
247C2×#95—52no—
248C2×#95—52no—
249C2×#95—52no—
250C2×#95—52no—
251C2×#95—52no—
252C2×#95C2×D512yes—
253C2×#95C2×D512yes—
254C23×C5C23×C411yescharacteristic
255C23×C5C22×D411yescharacteristic
256C23×C5C22×D411yescharacteristic
257C23×C5C22×D411yescharacteristic
258C23×C5C22×Q811yescharacteristic
259C23×C5C2×#4111yescharacteristic
260C23×C5C2×#4111yescharacteristic
261C23×C5C2×#4111yescharacteristic
262C23×C5C2×#4111yescharacteristic
263C23×C5C2×#4111yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5H(5,𝔽2)11yescharacteristic
266C23×C5H(5,𝔽2)11yescharacteristic
267C23×C52−1+411yescharacteristic
268C23×C52−1+411yescharacteristic
269C22×D5—22no—
270C22×D5—22no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5—22no—
275C22×D5—22no—
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—22no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5—22no—
285C22×D5—22no—
286C22×D5—22no—
287C22×D5—41no—
288C22×D5—41no—
289C22×D5—41no—
290C22×D5—41no—
291C22×D5—41no—
292C22×D5—41no—
293C22×D5—41no—
294C22×D5—41no—
295C22×D5—41no—
296C22×D5—41no—
297C22×D5—41no—
298C22×D5—41no—
299C22×D5—41no—
300C22×D5—41no—
301C22×D5—41no—
302C22×D5—41no—
303C22×D5C2×C4⋊C414yes—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—24no—
317C2×C4×C5—24no—
318C2×C4×C5—24no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5C2×C4⋊C414yes—
331C2×C4×C5#11714yes—
332C2×C4×C5#11714yes—
333C2×C4×C5C4×D414yes—
334C2×C4×C5C4×D414yes—
335C2×C4×C5#12114yes—
336C2×C4×C5#12314yes—
337C2×C4×C5#12414yes—
338C2×C4×C5#12614yes—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—24no—
352C2×Dic5—24no—
353C2×Dic5—24no—
354C2×Dic5—41no—
355C2×Dic5—41no—
356C2×Dic5—41no—
357C2×Dic5—41no—
358C2×Dic5—42no—
359C2×Dic5—42no—
360C2×Dic5—42no—
361C2×Dic5—41no—
362C2×Dic5—41no—
363C2×Dic5—42no—
364C2×Dic5—41no—
365C2×Dic5—41no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5C2×C4⋊C414yes—
374C4×D5—416no—
375C25—51no—
376C23×C4—51no—
377C23×C4—52no—
378C23×C4—51no—
379C23×C4—51no—
380C23×C4—54no—
381C23×C4—52no—
382C23×C4—102no—
383C23×C4—102no—
384C23×C4—102no—
385C23×C4—102no—
386C23×C4—102no—
387C23×C4—102no—
388C23×C4C22×D512yes—
389C23×C4C22×D512yes—
390C23×C4C22×D511yescharacteristic
391C23×C4C22×D511yescharacteristic
392C23×C4C22×D511yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—54no—
399C2×C4⋊C4—102no—
400C2×C4⋊C4—102no—
401C2×C4⋊C4—104no—
402C2×C4⋊C4—104no—
403C2×C4⋊C4—102no—
404C2×C4⋊C4—102no—
405C2×C4⋊C4—104no—
406C2×C4⋊C4—104no—
407C2×C4⋊C4—102no—
408C2×C4⋊C4—202no—
409C2×C4⋊C4—202no—
410C2×C4⋊C4D2014yes—
411C2×C22⋊C4—54no—
412C2×C22⋊C4—54no—
413C2×C22⋊C4—54no—
414C2×C22⋊C4—54no—
415C2×C22⋊C4—102no—
416C2×C22⋊C4—102no—
417C2×C22⋊C4—104no—
418C2×C22⋊C4—104no—
419C2×C22⋊C4—104no—
420C2×C22⋊C4—104no—
421C2×C22⋊C4—202no—
422C2×C22⋊C4—202no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—54no—
426C2×C42—102no—
427C2×C42—102no—
428C2×C42—104no—
429C2×C42—104no—
430C2×C42—202no—
431C2×C42C4×D514yes—
432#95—24no—
433#95—24no—
434#95—54no—
435#95—54no—
436#95—104no—
437#95—104no—
438#95—104no—
439#95—104no—
440#95—202no—
441C22×C5C22×C4⋊C411yescharacteristic
442C22×C5C2×#11711yescharacteristic
443C22×C5C2×#11711yescharacteristic
444C22×C5C2×C4×D411yescharacteristic
445C22×C5C2×C4×D411yescharacteristic
446C22×C5#52011yescharacteristic
447C22×C5#52011yescharacteristic
448C22×C5C2×#12111yescharacteristic
449C22×C5C2×#12311yescharacteristic
450C22×C5C2×#12411yescharacteristic
451C22×C5C2×#12611yescharacteristic
452C22×C5#53211yescharacteristic
453C22×C5#53211yescharacteristic
454C22×C5#53311yescharacteristic
455C22×C5#53311yescharacteristic
456C22×C5#54011yescharacteristic
457C22×C5#54111yescharacteristic
458C22×C5#54211yescharacteristic
459C22×C5#54211yescharacteristic
460C22×C5D4211yescharacteristic
461C22×C5D4211yescharacteristic
462C22×C5#54611yescharacteristic
463C22×C5#54711yescharacteristic
464C22×C5#54711yescharacteristic
465C22×C5#54711yescharacteristic
466C22×C5#54811yescharacteristic
467C22×C5D4×Q811yescharacteristic
468C22×C5D4×Q811yescharacteristic
469C22×C5#55011yescharacteristic
470C22×C5#55211yescharacteristic
471C22×C5#55311yescharacteristic
472C22×C5#55411yescharacteristic
473C22×C5#55411yescharacteristic
474C22×C5#55511yescharacteristic
475C22×C5#55611yescharacteristic
476C2×D5—24no—
477C2×D5—24no—
478C2×D5—24no—
479C2×D5—42no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C2×D5—42no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5—42no—
489C2×D5—42no—
490C2×D5—42no—
491C4×C5—24no—
492C4×C5—24no—
493C4×C5—44no—
494C4×C5—82no—
495C4×C5#38818yescomplemented
496Dic5—24no—
497Dic5—42no—
498Dic5—44no—
499Dic5—42no—
500Dic5—82no—
501C24—52no—
502C24—52no—
503C24—52no—
504C24—101no—
505C24—101no—
506C24—101no—
507C24—101no—
508C24—101no—
509C24—101no—
510C24—101no—
511C24—101no—
512C24—101no—
513C24—101no—
514C24—101no—
515C24—101no—
516C24C23×D511yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—52no—
539C22×C4—52no—
540C22×C4—52no—
541C22×C4—52no—
542C22×C4—52no—
543C22×C4—54no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—102no—
551C22×C4—101no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—102no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—101no—
566C22×C4—108no—
567C22×C4—108no—
568C22×C4—108no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—204no—
577C22×C4—204no—
578C22×C4—204no—
579C22×C4—204no—
580C22×C4C2×C4×D512yes—
581C22×C4C2×C4×D512yes—
582C22×C4C2×C4×D512yes—
583C22×C4C2×D2014yes—
584C22×C4C2×D2012yes—
585C22×C4#70912yes—
586C22×C4D4×D512yes—
587C22×C4D4×D512yes—
588C22×C4#71112yes—
589C22×C4#71112yes—
590C22×C4#71112yes—
591C22×C4Q8×D512yes—
592C22×C4#71312yes—
593C22×C4#71312yes—
594C4⋊C4—28no—
595C4⋊C4—44no—
596C4⋊C4—108no—
597C4⋊C4—208no—
598C4⋊C4—208no—
599C4⋊C4—204no—
600C22⋊C4—516no—
601C22⋊C4—108no—
602C22⋊C4—208no—
603C22⋊C4—208no—
604C42—28no—
605C42—108no—
606C42—208no—
607C2×C5#228511yescharacteristic
608C2×C5C2×#38811yescharacteristic
609C2×C5#231411yescharacteristic
610C2×C5D4×C4⋊C411yescharacteristic
611C2×C5D4×C4⋊C411yescharacteristic
612C2×C5#235211yescharacteristic
613C2×C5#235411yescharacteristic
614C2×C5#242211yescharacteristic
615C2×C5#242311yescharacteristic
616C2×C5#242811yescharacteristic
617C2×C5#242911yescharacteristic
618C2×C5#249111yescharacteristic
619C2×C5#249211yescharacteristic
620C2×C5#249611yescharacteristic
621C2×C5#249711yescharacteristic
622D5—44no—
623C23—54no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—102no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—201no—
643C23—201no—
644C23—201no—
645C23—201no—
646C23—201no—
647C23—201no—
648C23—201no—
649C23—201no—
650C23—201no—
651C23—201no—
652C23—201no—
653C23—201no—
654C23—201no—
655C23—201no—
656C23—201no—
657C23—201no—
658C23C22×C4×D511yescharacteristic
659C23C22×D2011yescharacteristic
660C23C2×#70911yescharacteristic
661C23C2×D4×D511yescharacteristic
662C23C2×D4×D511yescharacteristic
663C23C2×#71111yescharacteristic
664C23C2×#71111yescharacteristic
665C23C2×#71111yescharacteristic
666C23C2×Q8×D511yescharacteristic
667C23C2×#71311yescharacteristic
668C23C2×#71311yescharacteristic
669C23#414911yescharacteristic
670C23#414911yescharacteristic
671C23#415011yescharacteristic
672C23#415011yescharacteristic
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—54no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—104no—
712C2×C4—102no—
713C2×C4—104no—
714C2×C4—104no—
715C2×C4—202no—
716C2×C4—201no—
717C2×C4—201no—
718C2×C4—201no—
719C2×C4—201no—
720C2×C4—202no—
721C2×C4—201no—
722C2×C4—201no—
723C2×C4—201no—
724C2×C4—202no—
725C2×C4—201no—
726C2×C4—202no—
727C2×C4—2016no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4—202no—
732C2×C4—202no—
733C2×C4—202no—
734C2×C4—202no—
735C2×C4C4×D2014yes—
736C2×C4#402714yes—
737C2×C4#403114yes—
738C2×C4#403214yes—
739C2×C4D5×C4⋊C414yes—
740C2×C4#403814yes—
741C2×C4#403814yes—
742C2×C4#404114yes—
743C2×C4#404414yes—
744C5#1387611yescharacteristic, complemented, Sylow
745C22—104no—
746C22—104no—
747C22—104no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22C2×C4×D2011yescharacteristic
761C22C2×#402711yescharacteristic
762C22C2×#403111yescharacteristic
763C22C2×#403211yescharacteristic
764C22C2×D5×C4⋊C411yescharacteristic
765C22C2×#403811yescharacteristic
766C22C2×#403811yescharacteristic
767C22C2×#404111yescharacteristic
768C22C2×#404411yescharacteristic
769C22#6585711yescharacteristic
770C22#6585711yescharacteristic
771C22D4×D2011yescharacteristic
772C22#6588511yescharacteristic
773C22#6588911yescharacteristic
774C22#6589711yescharacteristic
775C22Q8×D2011yescharacteristic
776C22#6591111yescharacteristic
777C22#6591311yescharacteristic
778C22#6591811yescharacteristic
779C22#6593211yescharacteristic
780C22#6594311yescharacteristic
781C22#6594511yescharacteristic
782C22#6595211yescharacteristic
783C22#6596411yescharacteristic
784C22#6596611yescharacteristic
785C22#6596911yescharacteristic
786C22#6597611yescharacteristic
787C22#6601611yescharacteristic
788C22#6601611yescharacteristic
789C22#6603111yescharacteristic
790C22#6603211yescharacteristic
791C22#6605011yescharacteristic
792C22#6605911yescharacteristic
793C22#6606211yescharacteristic
794C22#6606211yescharacteristic
795C4—24no—
796C4—24no—
797C4—44no—
798C4—82no—
799C4—104no—
800C4—202no—
801C4—202no—
802C4—204no—
803C4—402no—
804C4#6495918yescomplemented
805C2—204no—
806C2C2×#6495911yescharacteristic
807C2#1060536911yescharacteristic
808C2C4⋊C4×D2011yescharacteristic
809C2#1060561411yescharacteristic
810C2#1060574111yescharacteristic
811C2#1060595511yescharacteristic
812C2#1060604911yescharacteristic
813C2#1060795111yescharacteristic
814C2#1060795211yescharacteristic
815C2#1060796911yescharacteristic
816C2#1060797111yescharacteristic
817C2#1060817211yescharacteristic
818C2#1060818311yescharacteristic
819C2#1060835411yescharacteristic
820C2#1060836411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13876
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic5C2semidirect
4. C2×#65224C2semidirect
7. C5×C4⋊#95C2semidirect
8. #10602356C2semidirect
10. #10600208C2semidirect
11. #10600200C2semidirect
38. C4×#685C4semidirect
118. C4⋊#95D5semidirect
218. #685C4⋊C4semidirect
495. C4×C5#388semidirect
744. C5#13876semidirect
804. C4#64959semidirect

Maximal subgroups

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

subgroupindex
C2×#652762
C2×C4⋊C4×Dic52
C2×#652242
C2×C4×#6852
C2×#649592
C5×C4⋊#952
#106023562
#106002202
#106002082
#106002002
#138765