Finite Group Databasebeta

← #12021245

Subgroups — #12021245

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×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#65276C211yesmaximal, characteristic
3C2×#65276C211yesmaximal, characteristic
4C2×#65265C211yesmaximal, characteristic, complemented
5C2×#65229C212yesmaximal
6C2×C4×#685C211yesmaximal, characteristic
7#10602356C211yesmaximal, characteristic, complemented
8#10602329C212yesmaximal, complemented
9#10602328C211yesmaximal, characteristic, complemented
10#10600221C212yesmaximal
11#10600206C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2212yes—
16C22×C42×C5C2211yescharacteristic
17C22×#685C2212yes—
18C22×#685C2212yes—
19C22×#685C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×#683C2212yes—
24C22×#683C2212yes—
25C22×C4×Dic5C2211yescharacteristic
26C4×C5×C4⋊C4—24no—
27C2×C5×#95C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36#65276—24no—
37#65276—24no—
38#65265—24no—
39#65229—28no—
40C4×#685C418yescomplemented
41#13876—51nomaximal, Sylow
42C24×D5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
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⋊C4D414yes—
65C2×C5×C4⋊C4D414yes—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5—24no—
69C2×C42×C5—24no—
70C2×C42×C5—42no—
71C2×C42×C5C2×C414yes—
72C2×#685—22no—
73C2×#685—22no—
74C2×#685—24no—
75C2×#685—24no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—42no—
79C2×#685—42no—
80C2×#685C2×C414yes—
81C2×#685C2×C414yes—
82C2×#685D414yes—
83C2×#685Q814yes—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×#683—24no—
91C2×#683—24no—
92C2×#683—24no—
93C2×#683—24no—
94C2×#683—42no—
95C2×#683—42no—
96C2×C4×Dic5—22no—
97C2×C4×Dic5—22no—
98C2×C4×Dic5C2×C414yes—
99C5×#95—24no—
100#3963—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⋊C4D511yescharacteristic, complemented
113C2×C4×C22⋊C4—51no—
114#1442—52no—
115#1439—52no—
116#1436—52no—
117C4⋊#95—51no—
118C4⋊#95—51no—
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—22no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—21no—
154C22×C4×C5—22no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5C22×C412yes—
158C22×C4×C5C22×C412yes—
159C22×C4×C5C22×C412yes—
160C22×C4×C5C2×D414yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5C2×D412yes—
163C22×C4×C5C2×D414yes—
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×Q812yes—
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—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—22no—
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×Dic5C22×C412yes—
199C22×Dic5C22×C412yes—
200C22×Dic5C22×C412yes—
201C22×Dic5C2×D412yes—
202C22×Dic5C2×Q812yes—
203C22×Dic5#4112yes—
204C22×Dic5#4112yes—
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—28no—
214C42×C5—28no—
215C42×C5—48no—
216#685—28no—
217#685—48no—
218#685—48no—
219#685C4⋊C4116yescomplemented
220C4⋊Dic5—44no—
221C4⋊Dic5—44no—
222#683—48no—
223#683—48no—
224C4×Dic5—28no—
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×C42C2×D512yes—
238C22×C42C2×D511yescharacteristic
239#388—108no—
240#384—104no—
241#380—104no—
242#380—104no—
243C4×C4⋊C4—24no—
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×#95—52no—
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—24no—
314C2×C4×C5—24no—
315C2×C4×C5—24no—
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—41no—
326C2×C4×C5—41no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5C2×C4⋊C414yes—
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—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—41no—
355C2×Dic5—41no—
356C2×Dic5—41no—
357C2×Dic5—41no—
358C2×Dic5—42no—
359C2×Dic5—42no—
360C2×Dic5—42no—
361C2×Dic5—42no—
362C2×Dic5—42no—
363C2×Dic5—42no—
364C2×Dic5—42no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5C2×C4⋊C414yes—
373C2×Dic5#11714yes—
374C4×D5—416no—
375C25—51no—
376C23×C4—51no—
377C23×C4—51no—
378C23×C4—51no—
379C23×C4—54no—
380C23×C4—52no—
381C23×C4—52no—
382C23×C4—102no—
383C23×C4—102no—
384C23×C4—102no—
385C23×C4—102no—
386C23×C4—102no—
387C23×C4—102no—
388C23×C4C22×D511yescharacteristic
389C23×C4C22×D512yes—
390C23×C4C22×D512yes—
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—104no—
398C2×C4⋊C4—104no—
399C2×C4⋊C4—102no—
400C2×C4⋊C4—104no—
401C2×C4⋊C4—104no—
402C2×C4⋊C4—102no—
403C2×C4⋊C4—102no—
404C2×C4⋊C4—102no—
405C2×C4⋊C4—102no—
406C2×C4⋊C4—102no—
407C2×C4⋊C4—202no—
408C2×C4⋊C4—202no—
409C2×C4⋊C4D2014yes—
410C2×C4⋊C4C22⋊D514yes—
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—24no—
426C2×C42—24no—
427C2×C42—42no—
428C2×C42—54no—
429C2×C42—102no—
430C2×C42—102no—
431C2×C42C4×D514yes—
432#95—24no—
433#95—54no—
434#95—54no—
435#95—104no—
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—42no—
493C4×C5—44no—
494C4×C5—44no—
495C4×C5#38818yescomplemented
496Dic5—24no—
497Dic5—24no—
498Dic5—42no—
499Dic5—82no—
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—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—52no—
540C22×C4—52no—
541C22×C4—52no—
542C22×C4—52no—
543C22×C4—52no—
544C22×C4—52no—
545C22×C4—52no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—108no—
561C22×C4—108no—
562C22×C4—108no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
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—204no—
578C22×C4—204no—
579C22×C4—204no—
580C22×C4—204no—
581C22×C4C2×C4×D512yes—
582C22×C4C2×C4×D512yes—
583C22×C4C2×C4×D512yes—
584C22×C4C2×D2014yes—
585C22×C4C2×D2012yes—
586C22×C4#70912yes—
587C22×C4#70912yes—
588C22×C4#70912yes—
589C22×C4#70912yes—
590C22×C4D4×D512yes—
591C22×C4Q8×D512yes—
592C22×C4C2×C22⋊D514yes—
593C22×C4C2×C22⋊D512yes—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—208no—
597C4⋊C4—208no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C22⋊C4—516no—
601C22⋊C4—108no—
602C22⋊C4—208no—
603C22⋊C4—208no—
604C42—28no—
605C42—48no—
606C42—108no—
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×#70911yescharacteristic
662C23C2×#70911yescharacteristic
663C23C2×#70911yescharacteristic
664C23C2×D4×D511yescharacteristic
665C23#414411yescharacteristic
666C23C2×Q8×D511yescharacteristic
667C23#414711yescharacteristic
668C23D5×#4111yescharacteristic
669C23D5×#4111yescharacteristic
670C23#414911yescharacteristic
671C23#415011yescharacteristic
672C23C22×C22⋊D511yescharacteristic
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—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—54no—
701C2×C4—54no—
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—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—201no—
718C2×C4—201no—
719C2×C4—201no—
720C2×C4—201no—
721C2×C4—2016no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4—202no—
732C2×C4—202no—
733C2×C4—202no—
734C2×C4—202no—
735C2×C4—202no—
736C2×C4#401814yes—
737C2×C4C4×D2014yes—
738C2×C4#402114yes—
739C2×C4#402214yes—
740C2×C4D5×C4⋊C414yes—
741C2×C4C4×C22⋊D514yes—
742C2×C4#407514yes—
743C2×C4#407614yes—
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×#401811yescharacteristic
761C22C2×C4×D2011yescharacteristic
762C22C2×#402111yescharacteristic
763C22C2×#402211yescharacteristic
764C22C2×D5×C4⋊C411yescharacteristic
765C22#6583811yescharacteristic
766C22#6584111yescharacteristic
767C22#6584511yescharacteristic
768C22D5×#11711yescharacteristic
769C22#6585711yescharacteristic
770C22#6586611yescharacteristic
771C22#6586711yescharacteristic
772C22#6588211yescharacteristic
773C22#6588211yescharacteristic
774C22D4×D2011yescharacteristic
775C22#6588511yescharacteristic
776C22#6588811yescharacteristic
777C22#6589211yescharacteristic
778C22#6589511yescharacteristic
779C22#6589611yescharacteristic
780C22Q8×D2011yescharacteristic
781C22#6591011yescharacteristic
782C22#6591211yescharacteristic
783C22#6591211yescharacteristic
784C22#6591311yescharacteristic
785C22#6591511yescharacteristic
786C22#6591611yescharacteristic
787C22#6591711yescharacteristic
788C22C2×C4×C22⋊D511yescharacteristic
789C22C2×#407511yescharacteristic
790C22C2×#407611yescharacteristic
791C22D4×C22⋊D511yescharacteristic
792C22Q8×C22⋊D511yescharacteristic
793C22#6615811yescharacteristic
794C22#6616811yescharacteristic
795C4—24no—
796C4—44no—
797C4—44no—
798C4—42no—
799C4—104no—
800C4—104no—
801C4—202no—
802C4—402no—
803C4—402no—
804C4#6522918yescomplemented
805C2—204no—
806C2#1060548411yescharacteristic
807C2#1060549111yescharacteristic
808C2C4⋊C4×D2011yescharacteristic
809C2#1060550211yescharacteristic
810C2#1060551911yescharacteristic
811C2#1060552011yescharacteristic
812C2#1060552311yescharacteristic
813C2#1060552411yescharacteristic
814C2C2×#6522911yescharacteristic
815C2C4⋊C4×C22⋊D511yescharacteristic
816C2#1061397211yescharacteristic
817C2#1061413711yescharacteristic
818C2#1061414011yescharacteristic
819C2#1061422511yescharacteristic
820C2#1061422711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#13876
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
4. C2×#65265C2semidirect
7. #10602356C2semidirect
8. #10602329C2semidirect
9. #10602328C2semidirect
11. #10600206C2semidirect
40. C4×#685C4semidirect
112. C2×C4×C4⋊C4D5semidirect
219. #685C4⋊C4semidirect
495. C4×C5#388semidirect
744. C5#13876semidirect
804. C4#65229semidirect

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×#652762
C2×#652652
C2×#652292
C2×C4×#6852
#106023562
#106023292
#106023282
#106002212
#106002062
#138765