Finite Group Databasebeta

← #12022741

Subgroups — #12022741

Order 1280.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#65279C212yesmaximal, complemented
3C2×#65228C211yesmaximal, characteristic
4C2×#65228C211yesmaximal, characteristic
5C2×#65228C211yesmaximal, characteristic
6C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
7#10602363C212yesmaximal, complemented
8#10602328C211yesmaximal, characteristic, complemented
9#10602328C211yesmaximal, characteristic, complemented
10#10600222C212yesmaximal, complemented
11#10600201C212yesmaximal, complemented
12C23×D20C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×#685C2212yes—
22C22×#685C2212yes—
23C22×#685C2212yes—
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×C4×Dic5C2212yes—
28C4×C5×C4⋊C4—24no—
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2211yescharacteristic
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36#65279—28no—
37#65228—24no—
38#65228—24no—
39#65228C418yescomplemented
40C4×C4⋊Dic5—24no—
41#14022—51nomaximal, Sylow
42C24×D5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2312yes—
52C23×Dic5C2312yes—
53C22×D20—22no—
54C22×D20—22no—
55C22×D20—22no—
56C22×D20—22no—
57C22×D20—22no—
58C22×D20—22no—
59C22×D20C2×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⋊C4D414yescomplemented
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5—22no—
69C2×C42×C5—22no—
70C2×C42×C5—22no—
71C2×C42×C5—22no—
72C2×C42×C5—22no—
73C2×C42×C5C2×C414yes—
74C2×C42×C5D414yes—
75C2×#685—24no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—24no—
79C2×#685—24no—
80C2×#685—24no—
81C2×#685—24no—
82C2×#685—24no—
83C2×#685—24no—
84C2×#685—24no—
85C2×#685—42no—
86C2×#685—42no—
87C2×#685—42no—
88C2×#685—42no—
89C2×#685—42no—
90C2×#685—42no—
91C2×#685C2×C418yes—
92C2×#685C2×C418yes—
93C2×C4⋊Dic5—22no—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—22no—
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5—22no—
98C2×C4⋊Dic5—22no—
99C2×C4⋊Dic5—22no—
100C2×C4⋊Dic5C2×C414yes—
101C2×C4⋊Dic5D414yes—
102C2×C4×Dic5—24no—
103C2×C4×Dic5—24no—
104C2×C4×Dic5—42no—
105C5×#95—22no—
106C5×#95—22no—
107#3963—24no—
108#3963—24no—
109#3963—24no—
110#3963—42no—
111#3963—42no—
112C2×#390—51no—
113C2×#390—51no—
114C2×#390—51no—
115C2×#388—52no—
116C2×C4×C4⋊C4—51no—
117C2×C4×C4⋊C4D511yescharacteristic, complemented
118#1440—52no—
119#1439—52no—
120#1437—52no—
121C4⋊#95—51no—
122C4⋊#95—51no—
123C24×C5C2411yescharacteristic
124C23×D5—22no—
125C23×D5—22no—
126C23×D5—22no—
127C23×D5—22no—
128C23×D5—22no—
129C23×D5—22no—
130C23×D5—22no—
131C23×D5—22no—
132C23×D5—22no—
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—22no—
136C23×D5—22no—
137C23×D5—22no—
138C23×D5C22×C414yes—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
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×C5C22×C412yes—
172C22×C4×C5C22×C412yes—
173C22×C4×C5C22×C412yes—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D412yes—
176C22×C4×C5C2×D412yes—
177C22×C4×C5C2×D412yes—
178C22×C4×C5C2×D412yes—
179C22×C4×C5C2×D412yes—
180C22×C4×C5C2×D412yes—
181C22×C4×C5#4112yes—
182C22×C4×C5#4112yes—
183C22×C4×C5#4112yes—
184C22×C4×C5#4112yes—
185C22×C4×C5#4112yes—
186C22×C4×C5#4112yes—
187C22×C4×C5#4112yes—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—22no—
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×Dic5C22×C414yes—
208C22×Dic5C2×D414yes—
209C2×D20—28no—
210C2×D20—28no—
211C2×D20—28no—
212C2×D20—44no—
213C2×D20—44no—
214C2×D20—44no—
215C2×D20—44no—
216C5×C4⋊C4—28no—
217C5×C4⋊C4—28no—
218C42×C5—28no—
219C42×C5—28no—
220C42×C5—44no—
221#685—216no—
222#685—48no—
223#685—48no—
224#685—48no—
225#685—48no—
226#685—48no—
227C4⋊Dic5—28no—
228C4⋊Dic5—28no—
229C4⋊Dic5—44no—
230C4×Dic5—48no—
231C23×D4—51no—
232C22×C4⋊C4—51no—
233C22×C4⋊C4—51no—
234C22×C4⋊C4—51no—
235C22×C4⋊C4C2×D511yescharacteristic
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C22⋊C4—52no—
238C22×C22⋊C4—52no—
239C22×C22⋊C4—52no—
240C22×C22⋊C4—52no—
241C22×C22⋊C4—52no—
242C22×C22⋊C4—52no—
243C22×C42—52no—
244C22×C42C2×D511yescharacteristic
245C22×C42C2×D511yescharacteristic
246C22×C42C2×D511yescharacteristic
247#390—58no—
248#390—104no—
249#390—104no—
250#388—108no—
251C4×C4⋊C4—24no—
252C4×C4⋊C4—104no—
253C2×#95—52no—
254C2×#95—52no—
255C2×#95—52no—
256C2×#95—52no—
257C2×#95—52no—
258C2×#95C2×D511yescharacteristic
259C2×#95C2×D511yescharacteristic
260C23×C5C23×C411yescharacteristic
261C23×C5C22×D411yescharacteristic
262C23×C5C22×D411yescharacteristic
263C23×C5C22×D411yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5C2×#4111yescharacteristic
266C23×C5C2×#4111yescharacteristic
267C23×C5C2×#4111yescharacteristic
268C23×C5C2×#4111yescharacteristic
269C23×C5C2×#4111yescharacteristic
270C23×C5C2×#4111yescharacteristic
271C23×C5H(5,𝔽2)11yescharacteristic
272C23×C5H(5,𝔽2)11yescharacteristic
273C23×C5H(5,𝔽2)11yescharacteristic
274C23×C52−1+411yescharacteristic
275C22×D5—24no—
276C22×D5—24no—
277C22×D5—24no—
278C22×D5—24no—
279C22×D5—24no—
280C22×D5—24no—
281C22×D5—24no—
282C22×D5—42no—
283C22×D5—42no—
284C22×D5—42no—
285C22×D5—42no—
286C22×D5—42no—
287C22×D5—42no—
288C22×D5—42no—
289C22×D5—42no—
290C22×D5—42no—
291C22×D5—42no—
292C22×D5—42no—
293C22×D5—42no—
294C22×D5—42no—
295C22×D5—42no—
296C22×D5—42no—
297C22×D5—42no—
298C22×D5—42no—
299C22×D5—42no—
300C22×D5—42no—
301C22×D5—42no—
302C22×D5—42no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—42no—
306C22×D5—42no—
307C22×D5—42no—
308C22×D5—42no—
309C22×D5—42no—
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—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
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—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
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#11714yes—
351C2×C4×C5C4×D414yes—
352C2×C4×C5C4×D414yes—
353C2×C4×C5C4×D414yes—
354C2×C4×C5#12114yes—
355C2×C4×C5#12114yes—
356C2×C4×C5#12314yes—
357C2×C4×C5#12414yes—
358C2×C4×C5#12614yes—
359C2×Dic5—24no—
360C2×Dic5—24no—
361C2×Dic5—24no—
362C2×Dic5—24no—
363C2×Dic5—24no—
364C2×Dic5—24no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5—42no—
380D20—416no—
381C25—52no—
382C22×D4—54no—
383C22×D4—102no—
384C22×D4—102no—
385C22×D4—102no—
386C22×D4—102no—
387C22×D4—102no—
388C22×D4—102no—
389C23×C4—52no—
390C23×C4—52no—
391C23×C4—52no—
392C23×C4C22×D511yescharacteristic
393C23×C4C22×D511yescharacteristic
394C23×C4C22×D511yescharacteristic
395C23×C4C22×D511yescharacteristic
396C23×C4C22×D511yescharacteristic
397C23×C4C22×D511yescharacteristic
398C23×C4C22×D511yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—54no—
405C2×C4⋊C4—54no—
406C2×C4⋊C4—102no—
407C2×C4⋊C4—102no—
408C2×C4⋊C4—102no—
409C2×C4⋊C4—102no—
410C2×C4⋊C4—102no—
411C2×C4⋊C4—102no—
412C2×C4⋊C4—102no—
413C2×C4⋊C4D2014yescomplemented
414C2×C22⋊C4—58no—
415C2×C22⋊C4—58no—
416C2×C22⋊C4—104no—
417C2×C22⋊C4—104no—
418C2×C22⋊C4—104no—
419C2×C22⋊C4—104no—
420C2×C22⋊C4—104no—
421C2×C22⋊C4—104no—
422C2×C22⋊C4—104no—
423C2×C22⋊C4—104no—
424C2×C22⋊C4—104no—
425C2×C22⋊C4—104no—
426C2×C22⋊C4—202no—
427C2×C22⋊C4—202no—
428C2×C22⋊C4—202no—
429C2×C22⋊C4—202no—
430C2×C22⋊C4—202no—
431C2×C22⋊C4—202no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—104no—
440C2×C42—104no—
441C2×C42—202no—
442C2×C42C4×D514yes—
443C2×C42C22⋊D514yes—
444#95—22no—
445#95—22no—
446#95—104no—
447#95—104no—
448#95—104no—
449#95—202no—
450#95—202no—
451C22×C5C2×#11711yescharacteristic
452C22×C5C2×C4×D411yescharacteristic
453C22×C5C2×C4×D411yescharacteristic
454C22×C5C2×C4×D411yescharacteristic
455C22×C5C4×#4111yescharacteristic
456C22×C5#51811yescharacteristic
457C22×C5#52011yescharacteristic
458C22×C5C2×#12111yescharacteristic
459C22×C5C2×#12111yescharacteristic
460C22×C5C2×#12311yescharacteristic
461C22×C5#52511yescharacteristic
462C22×C5C2×#12411yescharacteristic
463C22×C5C2×#12611yescharacteristic
464C22×C5#52911yescharacteristic
465C22×C5#53211yescharacteristic
466C22×C5#53511yescharacteristic
467C22×C5#53711yescharacteristic
468C22×C5#54011yescharacteristic
469C22×C5#54211yescharacteristic
470C22×C5D4211yescharacteristic
471C22×C5#54611yescharacteristic
472C22×C5#54711yescharacteristic
473C22×C5#54811yescharacteristic
474C22×C5#55011yescharacteristic
475C22×C5#55011yescharacteristic
476C22×C5#55011yescharacteristic
477C22×C5#55311yescharacteristic
478C22×C5#55311yescharacteristic
479C22×C5#55511yescharacteristic
480C22×C5#55611yescharacteristic
481C22×C5#55611yescharacteristic
482C22×C5#55911yescharacteristic
483C22×C5#55911yescharacteristic
484C22×C5#55911yescharacteristic
485C22×C5#55911yescharacteristic
486C2×D5—44no—
487C2×D5—44no—
488C2×D5—44no—
489C2×D5—44no—
490C2×D5—44no—
491C2×D5—44no—
492C2×D5—44no—
493C2×D5—82no—
494C2×D5—82no—
495C2×D5—82no—
496C2×D5—82no—
497C2×D5—82no—
498C2×D5—82no—
499C2×D5—82no—
500C2×D5—82no—
501C4×C5—24no—
502C4×C5—24no—
503C4×C5—42no—
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—42no—
507C4×C5#38818yescomplemented
508Dic5—44no—
509Dic5—44no—
510Dic5—82no—
511C24—54no—
512C24—102no—
513C24—102no—
514C24—102no—
515C24—102no—
516C24—102no—
517C24—102no—
518C24—102no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24C23×D511yescharacteristic
527C2×D4—108no—
528C2×D4—108no—
529C2×D4—108no—
530C2×D4—204no—
531C2×D4—204no—
532C2×D4—204no—
533C2×D4—204no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
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—54no—
567C22×C4—54no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4C2×C4×D512yes—
588C22×C4C2×C4×D512yes—
589C22×C4C2×C4×D512yes—
590C22×C4C2×D2012yes—
591C22×C4C2×D2012yes—
592C22×C4C2×D2012yes—
593C22×C4#70912yes—
594C22×C4#70912yes—
595C22×C4#70912yes—
596C22×C4#70912yes—
597C22×C4D4×D512yes—
598C22×C4#71112yes—
599C22×C4#71312yes—
600C22×C4#71312yes—
601C22×C4C2×C22⋊D512yes—
602C22×C4C2×C22⋊D512yes—
603C22×C4C2×C22⋊D512yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—108no—
607C4⋊C4—108no—
608C4⋊C4—204no—
609C22⋊C4—1016no—
610C22⋊C4—208no—
611C22⋊C4—208no—
612C22⋊C4—208no—
613C22⋊C4—208no—
614C22⋊C4—208no—
615C42—28no—
616C42—28no—
617C42—44no—
618C42—208no—
619C2×C5C2×#38811yescharacteristic
620C2×C5C4×#12111yescharacteristic
621C2×C5#232411yescharacteristic
622C2×C5#235411yescharacteristic
623C2×C5#235711yescharacteristic
624C2×C5#236611yescharacteristic
625C2×C5#236711yescharacteristic
626C2×C5#241411yescharacteristic
627C2×C5#241611yescharacteristic
628C2×C5#244511yescharacteristic
629C2×C5#244811yescharacteristic
630C2×C5#251211yescharacteristic
631C2×C5#251311yescharacteristic
632C2×C5#254811yescharacteristic
633C2×C5#259211yescharacteristic
634D5—84no—
635C23—104no—
636C23—104no—
637C23—104no—
638C23—104no—
639C23—104no—
640C23—104no—
641C23—104no—
642C23—202no—
643C23—202no—
644C23—202no—
645C23—202no—
646C23—202no—
647C23—202no—
648C23—202no—
649C23—202no—
650C23—202no—
651C23—202no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23—202no—
656C23—202no—
657C23—202no—
658C23—202no—
659C23—202no—
660C23—202no—
661C23—202no—
662C23—202no—
663C23—202no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23—202no—
668C23—202no—
669C23—202no—
670C23C22×C4×D511yescharacteristic
671C23C22×D2011yescharacteristic
672C23C2×#70911yescharacteristic
673C23C2×#70911yescharacteristic
674C23C2×#70911yescharacteristic
675C23C2×#70911yescharacteristic
676C23C2×D4×D511yescharacteristic
677C23C2×#71111yescharacteristic
678C23C2×#71311yescharacteristic
679C23C2×#71311yescharacteristic
680C23#414911yescharacteristic
681C23#414911yescharacteristic
682C23#414911yescharacteristic
683C23#415011yescharacteristic
684C23C22×C22⋊D511yescharacteristic
685D4—2016no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—104no—
727C2×C4—104no—
728C2×C4—104no—
729C2×C4—104no—
730C2×C4—104no—
731C2×C4—104no—
732C2×C4—202no—
733C2×C4—202no—
734C2×C4—202no—
735C2×C4—202no—
736C2×C4—202no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4C4×D2014yes—
748C2×C4#403814yes—
749C2×C4#403914yes—
750C2×C4#404014yes—
751C2×C4#404414yes—
752C2×C4C4×C22⋊D514yes—
753C2×C4#407614yes—
754C2×C4#408514yes—
755C2×C4#409314yes—
756C5#1402211yescharacteristic, complemented, Sylow
757C22—204no—
758C22—204no—
759C22—204no—
760C22—204no—
761C22—204no—
762C22—204no—
763C22—204no—
764C22—402no—
765C22—402no—
766C22—402no—
767C22—402no—
768C22—402no—
769C22—402no—
770C22—402no—
771C22—402no—
772C22C2×C4×D2011yescharacteristic
773C22C4×#70911yescharacteristic
774C22#6581111yescharacteristic
775C22#6581311yescharacteristic
776C22C2×#403811yescharacteristic
777C22C2×#403911yescharacteristic
778C22C2×#404011yescharacteristic
779C22C2×#404411yescharacteristic
780C22#6585511yescharacteristic
781C22#6585711yescharacteristic
782C22#6586811yescharacteristic
783C22#6586911yescharacteristic
784C22D4×D2011yescharacteristic
785C22#6588411yescharacteristic
786C22#6588611yescharacteristic
787C22#6588711yescharacteristic
788C22#6588911yescharacteristic
789C22#6589711yescharacteristic
790C22#6589911yescharacteristic
791C22#6589911yescharacteristic
792C22#6591111yescharacteristic
793C22#6591111yescharacteristic
794C22#6591811yescharacteristic
795C22#6591811yescharacteristic
796C22#6591911yescharacteristic
797C22#6591911yescharacteristic
798C22#6591911yescharacteristic
799C22#6591911yescharacteristic
800C22C2×C4×C22⋊D511yescharacteristic
801C22C2×#407611yescharacteristic
802C22#6612511yescharacteristic
803C22C2×#408511yescharacteristic
804C22C2×#409311yescharacteristic
805C22#6616411yescharacteristic
806C22#6616711yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—204no—
814C4—204no—
815C4—402no—
816C4#6527918yescomplemented
817C2—404no—
818C2#1060536911yescharacteristic
819C2#1060537611yescharacteristic
820C2#1060538411yescharacteristic
821C2#1060538611yescharacteristic
822C2#1060540411yescharacteristic
823C2#1060542311yescharacteristic
824C2#1060542511yescharacteristic
825C2#1060551111yescharacteristic
826C2C4×#407611yescharacteristic
827C2C2×#6527911yescharacteristic
828C2#1061396711yescharacteristic
829C2#1061408111yescharacteristic
830C2#1061408311yescharacteristic
831C2#1061420711yescharacteristic
832C2#1061421511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#14022
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×C4⋊C4C2semidirect
2. C2×#65279C2semidirect
6. C2×C4×C4⋊Dic5C2semidirect
7. #10602363C2semidirect
8. #10602328C2semidirect
9. #10602328C2semidirect
10. #10600222C2semidirect
11. #10600201C2semidirect
39. #65228C4semidirect
65. C2×C5×C4⋊C4D4semidirect
117. C2×C4×C4⋊C4D5semidirect
413. C2×C4⋊C4D20semidirect
507. C4×C5#388semidirect
756. C5#14022semidirect
816. C4#65279semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C4⋊C42
C2×#652792
C2×#652282
C2×C4×C4⋊Dic52
#106023632
#106023282
#106002222
#106002012
#140225