Finite Group Databasebeta

← #12022445

Subgroups — #12022445

Order 1280.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4076C211yesmaximal, characteristic
2C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#65501C211yesmaximal, characteristic, complemented
4C2×#65246C212yesmaximal, complemented
5C2×#65228C211yesmaximal, characteristic, complemented
6C2×#65228C211yesmaximal, characteristic, complemented
7C2×#65217C211yesmaximal, characteristic, complemented
8C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
9#10602343C212yesmaximal, complemented
10#10600221C212yesmaximal, complemented
11#10600201C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C23×C22⋊D5C2212yes—
14C23×D20C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×C22⋊Dic5C2212yes—
20C2×#4076—24no—
21C2×#4076—24no—
22C2×#4076C418yescomplemented
23C22×#685C2212yes—
24C22×#685C2212yes—
25C22×#685C2212yes—
26C22×#685C2212yes—
27C22×#685C2212yes—
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2212yes—
32C22×C4×Dic5C2212yes—
33C4×C5×C22⋊C4—24no—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36#65501—24no—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40#65246—28no—
41#65228—24no—
42#65228—24no—
43C4×C4⋊Dic5—24no—
44#65217—24no—
45#13998—51nomaximal, Sylow
46C25×C5C2311yescharacteristic
47C24×D5C2312yes—
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5—22no—
52C23×C4×C5—22no—
53C23×C4×C5—22no—
54C23×C4×C5C2×C414yes—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C22×C22⋊D5—24no—
62C22×C22⋊D5—24no—
63C22×C22⋊D5—24no—
64C22×C22⋊D5—24no—
65C22×C22⋊D5—42no—
66C22×C22⋊D5—42no—
67C22×C22⋊D5C2×C418yes—
68C23×Dic5C2312yes—
69C23×Dic5C2312yes—
70C23×Dic5C2312yes—
71C22×D20—22no—
72C22×D20—22no—
73C22×D20—22no—
74C22×D20—22no—
75C22×D20—22no—
76C22×D20—22no—
77C22×D20C2×C414yes—
78C2×C5×C22⋊C4—22no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4D414yescomplemented
84C2×C42×C5—22no—
85C2×C42×C5—22no—
86C2×C42×C5—22no—
87C2×C42×C5—22no—
88C2×C42×C5—22no—
89C2×C42×C5D414yescomplemented
90C2×C22⋊Dic5—24no—
91C2×C22⋊Dic5—24no—
92C2×C22⋊Dic5—42no—
93#4076—232no—
94C2×#685—24no—
95C2×#685—24no—
96C2×#685—24no—
97C2×#685—24no—
98C2×#685—24no—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—42no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685C2×C418yes—
109C2×C4⋊Dic5—22no—
110C2×C4⋊Dic5—22no—
111C2×C4⋊Dic5—22no—
112C2×C4⋊Dic5—22no—
113C2×C4⋊Dic5—22no—
114C2×C4⋊Dic5C2×C414yes—
115C2×C4⋊Dic5D414yes—
116C2×C4⋊Dic5D414yes—
117C2×C4⋊Dic5D414yescomplemented
118C2×#683—24no—
119C2×#683—24no—
120C2×#683—42no—
121C2×C4×Dic5—24no—
122C2×C4×Dic5—24no—
123C2×C4×Dic5—42no—
124C5×#95—22no—
125C5×#95—22no—
126#3963—24no—
127#3963—24no—
128#3963—24no—
129C22×#121—51no—
130C2×#390—51no—
131C2×#390—51no—
132C2×#390—52no—
133C2×#389—51no—
134C2×#380—51no—
135C2×C4×C4⋊C4—51no—
136C2×C4×C22⋊C4D511yescharacteristic, complemented
137#1439—52no—
138#1438—52no—
139#1437—52no—
140C24×C5—21no—
141C24×C5—21no—
142C24×C5—21no—
143C24×C5—21no—
144C24×C5—21no—
145C24×C5—21no—
146C24×C5—21no—
147C24×C5—21no—
148C24×C5—21no—
149C24×C5—21no—
150C24×C5—21no—
151C24×C5—21no—
152C24×C5C22×C412yes—
153C24×C5C2×D412yes—
154C24×C5#4112yes—
155C24×C5C2411yescharacteristic
156C23×D5—22no—
157C23×D5—22no—
158C23×D5—22no—
159C23×D5—22no—
160C23×D5—22no—
161C23×D5—22no—
162C23×D5—22no—
163C23×D5—22no—
164C23×D5—22no—
165C23×D5—22no—
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5C22×C414yes—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—28no—
200C22×C4×C5—28no—
201C22×C4×C5—28no—
202C22×C4×C5—44no—
203C22×C4×C5—44no—
204C22×C4×C5—44no—
205C22×C4×C5—44no—
206C22×C4×C5C22×C412yes—
207C22×C4×C5C22×C412yes—
208C22×C4×C5C2×D412yes—
209C22×C4×C5C2×D412yes—
210C22×C4×C5C2×D412yes—
211C22×C4×C5C2×D412yes—
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2×D412yes—
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2×D412yes—
216C22×C4×C5#4112yes—
217C22×C4×C5#4112yes—
218C22×C4×C5#4112yes—
219C22×C4×C5#4112yes—
220C2×C22⋊D5—216no—
221C2×C22⋊D5—216no—
222C2×C22⋊D5—48no—
223C2×C22⋊D5—48no—
224C2×C22⋊D5—48no—
225C2×C22⋊D5—48no—
226C2×C22⋊D5—48no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5C22×C414yes—
245C22×Dic5C2×D414yes—
246C22×Dic5C2×D414yes—
247C22×Dic5C2×D414yes—
248C2×D20—28no—
249C2×D20—28no—
250C2×D20—28no—
251C2×D20—44no—
252C2×D20—44no—
253C2×D20—44no—
254C2×D20—44no—
255C5×C22⋊C4—28no—
256C5×C22⋊C4—28no—
257C42×C5—28no—
258C42×C5—44no—
259C22⋊Dic5—48no—
260#685—216no—
261#685—48no—
262#685—48no—
263#685—48no—
264#685—48no—
265C4⋊Dic5—28no—
266C4⋊Dic5—44no—
267C4⋊Dic5C22⋊C4116yescomplemented
268#683—48no—
269C4×Dic5—48no—
270C23×D4—52no—
271C23×D4—51no—
272C24×C4C2×D511yescharacteristic
273C2×#121—58no—
274C2×#121—104no—
275C2×#121—104no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—52no—
280C22×C22⋊C4—52no—
281C22×C22⋊C4—52no—
282C22×C22⋊C4—52no—
283C22×C22⋊C4—52no—
284C22×C22⋊C4—52no—
285C22×C22⋊C4—52no—
286C22×C22⋊C4C2×D511yescharacteristic
287C22×C22⋊C4C2×D511yescharacteristic
288C22×C42—52no—
289C22×C42C2×D511yescharacteristic
290C22×C42C2×D511yescharacteristic
291#390—104no—
292#390—108no—
293#390—104no—
294#389—104no—
295#380—104no—
296C4×C4⋊C4—104no—
297C4×C22⋊C4—24no—
298C2×#95—52no—
299C2×#95—52no—
300C2×#95—52no—
301C2×#95C2×D511yescharacteristic
302C2×#95C2×D511yescharacteristic
303C23×C5—22no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—22no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—41no—
322C23×C5—41no—
323C23×C5—41no—
324C23×C5—41no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5C4×D414yes—
338C23×C5C23×C411yescharacteristic
339C23×C5C22×D411yescharacteristic
340C23×C5C22×D411yescharacteristic
341C23×C5C22×D411yescharacteristic
342C23×C5C22×D411yescharacteristic
343C23×C5C22×D411yescharacteristic
344C23×C5C2×#4111yescharacteristic
345C23×C5C2×#4111yescharacteristic
346C23×C5C2×#4111yescharacteristic
347C23×C5C2×#4111yescharacteristic
348C23×C5C2×#4111yescharacteristic
349C23×C5H(5,𝔽2)11yescharacteristic
350C23×C5H(5,𝔽2)11yescharacteristic
351C23×C5H(5,𝔽2)11yescharacteristic
352C23×C52−1+411yescharacteristic
353C22×D5—24no—
354C22×D5—24no—
355C22×D5—24no—
356C22×D5—24no—
357C22×D5—24no—
358C22×D5—24no—
359C22×D5—24no—
360C22×D5—42no—
361C22×D5—42no—
362C22×D5—42no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C22×D5—42no—
375C22×D5—42no—
376C22×D5—42no—
377C22×D5—42no—
378C22×D5—42no—
379C22×D5—42no—
380C22×D5—42no—
381C22×D5—42no—
382C22×D5—42no—
383C22×D5—42no—
384C22×D5—42no—
385C22×D5—42no—
386C22×D5—42no—
387C22×D5—42no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—41no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—416no—
423C2×C4×C5C2×C22⋊C414yes—
424C2×C4×C5C4×D414yes—
425C2×C4×C5C4×D414yes—
426C2×C4×C5#12114yes—
427C2×C4×C5#12114yes—
428C2×C4×C5#12114yescomplemented
429C2×C4×C5#12414yes—
430C2×C4×C5#12714yes—
431C22⋊D5—432no—
432C2×Dic5—24no—
433C2×Dic5—24no—
434C2×Dic5—24no—
435C2×Dic5—24no—
436C2×Dic5—24no—
437C2×Dic5—24no—
438C2×Dic5—24no—
439C2×Dic5—24no—
440C2×Dic5—24no—
441C2×Dic5—42no—
442C2×Dic5—42no—
443C2×Dic5—42no—
444C2×Dic5—42no—
445C2×Dic5—42no—
446C2×Dic5—42no—
447C2×Dic5—42no—
448C2×Dic5—42no—
449C2×Dic5—42no—
450C2×Dic5—42no—
451C2×Dic5—42no—
452C2×Dic5C2×C22⋊C418yes—
453D20—416no—
454C25—52no—
455C25C22×D511yescharacteristic
456C22×D4—58no—
457C22×D4—54no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—104no—
461C22×D4—104no—
462C22×D4—102no—
463C22×D4—102no—
464C22×D4—102no—
465C22×D4—102no—
466C22×D4—102no—
467C22×D4—102no—
468C22×D4—202no—
469C22×D4—202no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—52no—
477C23×C4—52no—
478C23×C4—52no—
479C23×C4C4×D514yes—
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486#121—1032no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—102no—
492C2×C4⋊C4—102no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—102no—
496C2×C4⋊C4—102no—
497C2×C4⋊C4—102no—
498C2×C4⋊C4—202no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—58no—
505C2×C22⋊C4—104no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4—202no—
520C2×C22⋊C4—202no—
521C2×C22⋊C4—202no—
522C2×C22⋊C4D2014yescomplemented
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—104no—
529C2×C42—104no—
530C2×C42—202no—
531C2×C42C22⋊D514yescomplemented
532#95—22no—
533#95—22no—
534#95—104no—
535#95—104no—
536#95—104no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5C22×C22⋊C411yescharacteristic
553C22×C5C2×C4×D411yescharacteristic
554C22×C5C2×C4×D411yescharacteristic
555C22×C5C2×C4×D411yescharacteristic
556C22×C5C4×#4111yescharacteristic
557C22×C5#51811yescharacteristic
558C22×C5#52011yescharacteristic
559C22×C5C2×#12111yescharacteristic
560C22×C5C2×#12111yescharacteristic
561C22×C5C2×#12111yescharacteristic
562C22×C5#52511yescharacteristic
563C22×C5C2×#12411yescharacteristic
564C22×C5#52911yescharacteristic
565C22×C5C2×#12711yescharacteristic
566C22×C5#53211yescharacteristic
567C22×C5#53511yescharacteristic
568C22×C5#53711yescharacteristic
569C22×C5#54011yescharacteristic
570C22×C5#54211yescharacteristic
571C22×C5D4211yescharacteristic
572C22×C5D4211yescharacteristic
573C22×C5D4211yescharacteristic
574C22×C5#54611yescharacteristic
575C22×C5#54611yescharacteristic
576C22×C5#54611yescharacteristic
577C22×C5#54711yescharacteristic
578C22×C5#54811yescharacteristic
579C22×C5#54811yescharacteristic
580C22×C5#54811yescharacteristic
581C22×C5#55011yescharacteristic
582C22×C5#55011yescharacteristic
583C22×C5#55011yescharacteristic
584C22×C5#55311yescharacteristic
585C22×C5#55311yescharacteristic
586C22×C5#55511yescharacteristic
587C2×D5—44no—
588C2×D5—44no—
589C2×D5—44no—
590C2×D5—44no—
591C2×D5—44no—
592C2×D5—44no—
593C2×D5—44no—
594C2×D5—82no—
595C2×D5—82no—
596C2×D5—82no—
597C2×D5—82no—
598C2×D5—82no—
599C2×D5—82no—
600C2×D5—82no—
601C2×D5—82no—
602C4×C5—24no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—42no—
606C4×C5—42no—
607C4×C5#39018yescomplemented
608Dic5—28no—
609Dic5—44no—
610Dic5—82no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—54no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24—102no—
630C24—102no—
631C24—102no—
632C24—102no—
633C24—102no—
634C24—102no—
635C24—102no—
636C24—102no—
637C24—102no—
638C24C2×C4×D512yes—
639C24C2×D2012yes—
640C24#70912yes—
641C24C23×D511yescharacteristic
642C2×D4—1016no—
643C2×D4—1016no—
644C2×D4—108no—
645C2×D4—108no—
646C2×D4—108no—
647C2×D4—208no—
648C2×D4—208no—
649C2×D4—208no—
650C2×D4—208no—
651C2×D4—208no—
652C2×D4—204no—
653C2×D4—204no—
654C2×D4—204no—
655C2×D4—204no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—54no—
692C22×C4—54no—
693C22×C4—54no—
694C22×C4—54no—
695C22×C4—102no—
696C22×C4—102no—
697C22×C4—102no—
698C22×C4—102no—
699C22×C4—102no—
700C22×C4—102no—
701C22×C4—102no—
702C22×C4—102no—
703C22×C4—102no—
704C22×C4—102no—
705C22×C4—102no—
706C22×C4—102no—
707C22×C4—102no—
708C22×C4—102no—
709C22×C4—102no—
710C22×C4—102no—
711C22×C4—102no—
712C22×C4C2×C4×D512yes—
713C22×C4C2×C4×D512yes—
714C22×C4C2×D2012yes—
715C22×C4C2×D2012yes—
716C22×C4#70912yes—
717C22×C4#70912yes—
718C22×C4#70912yes—
719C22×C4D4×D512yes—
720C22×C4D4×D512yes—
721C22×C4D4×D512yes—
722C22×C4#71112yes—
723C22×C4C2×C22⋊D512yes—
724C22×C4C2×C22⋊D512yes—
725C22×C4C2×C22⋊D512yes—
726C4⋊C4—516no—
727C4⋊C4—108no—
728C4⋊C4—208no—
729C4⋊C4—204no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—1016no—
733C22⋊C4—208no—
734C22⋊C4—208no—
735C22⋊C4—208no—
736C22⋊C4—208no—
737C22⋊C4—208no—
738C42—28no—
739C42—44no—
740C42—208no—
741C2×C5—44no—
742C2×C5C2×#39011yescharacteristic
743C2×C5C4×#12111yescharacteristic
744C2×C5#232411yescharacteristic
745C2×C5D4×C22⋊C411yescharacteristic
746C2×C5#234111yescharacteristic
747C2×C5#236111yescharacteristic
748C2×C5#236311yescharacteristic
749C2×C5#241411yescharacteristic
750C2×C5#241611yescharacteristic
751C2×C5#242611yescharacteristic
752C2×C5#242811yescharacteristic
753C2×C5#249011yescharacteristic
754C2×C5#249111yescharacteristic
755C2×C5#254011yescharacteristic
756C2×C5#254111yescharacteristic
757D5—84no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—104no—
793C23—104no—
794C23—104no—
795C23—104no—
796C23—104no—
797C23—104no—
798C23—104no—
799C23—202no—
800C23—202no—
801C23—202no—
802C23—202no—
803C23—202no—
804C23—202no—
805C23—202no—
806C23—202no—
807C23—202no—
808C23—202no—
809C23—202no—
810C23—202no—
811C23—202no—
812C23—202no—
813C23—202no—
814C23—202no—
815C23—202no—
816C23—202no—
817C23—202no—
818C23—202no—
819C23—202no—
820C23—202no—
821C23—202no—
822C23—202no—
823C23—202no—
824C23—202no—
825C23—202no—
826C23—202no—
827C23C4×D2014yes—
828C23C22×C4×D511yescharacteristic
829C23C22×D2011yescharacteristic
830C23C2×#70911yescharacteristic
831C23C2×#70911yescharacteristic
832C23C2×#70911yescharacteristic
833C23C2×#70911yescharacteristic
834C23C2×D4×D511yescharacteristic
835C23C2×D4×D511yescharacteristic
836C23C2×D4×D511yescharacteristic
837C23C2×#71111yescharacteristic
838C23#414911yescharacteristic
839C23#414911yescharacteristic
840C23#414911yescharacteristic
841C23#415011yescharacteristic
842C23C22×C22⋊D511yescharacteristic
843D4—2032no—
844D4—2016no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—416no—
880C2×C4—58no—
881C2×C4—104no—
882C2×C4—104no—
883C2×C4—104no—
884C2×C4—104no—
885C2×C4—104no—
886C2×C4—104no—
887C2×C4—104no—
888C2×C4—104no—
889C2×C4—104no—
890C2×C4—202no—
891C2×C4—202no—
892C2×C4—202no—
893C2×C4—202no—
894C2×C4—202no—
895C2×C4—202no—
896C2×C4—202no—
897C2×C4—202no—
898C2×C4—202no—
899C2×C4—202no—
900C2×C4—202no—
901C2×C4D5×C22⋊C414yes—
902C2×C4#402714yes—
903C2×C4#403014yes—
904C2×C4#403114yes—
905C2×C4C4×C22⋊D514yes—
906C2×C4#407614yescomplemented
907C2×C4#408514yes—
908C2×C4#408614yes—
909C5#1399811yescharacteristic, complemented, Sylow
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—204no—
926C22—204no—
927C22—204no—
928C22—204no—
929C22—204no—
930C22—204no—
931C22—204no—
932C22—402no—
933C22—402no—
934C22—402no—
935C22—402no—
936C22—402no—
937C22—402no—
938C22—402no—
939C22—402no—
940C22C2×C4×D2011yescharacteristic
941C22C4×#70911yescharacteristic
942C22#6581111yescharacteristic
943C22#6581311yescharacteristic
944C22C2×D5×C22⋊C411yescharacteristic
945C22C2×#402711yescharacteristic
946C22C2×#403011yescharacteristic
947C22C2×#403111yescharacteristic
948C22#6585511yescharacteristic
949C22#6585711yescharacteristic
950C22#6586811yescharacteristic
951C22#6586911yescharacteristic
952C22D4×D2011yescharacteristic
953C22D4×D2011yescharacteristic
954C22D4×D2011yescharacteristic
955C22#6588411yescharacteristic
956C22#6588411yescharacteristic
957C22#6588411yescharacteristic
958C22#6588611yescharacteristic
959C22#6588611yescharacteristic
960C22#6588611yescharacteristic
961C22#6588711yescharacteristic
962C22#6588711yescharacteristic
963C22#6588711yescharacteristic
964C22#6588911yescharacteristic
965C22#6589711yescharacteristic
966C22#6589911yescharacteristic
967C22#6589911yescharacteristic
968C22C2×C4×C22⋊D511yescharacteristic
969C22C2×#407611yescharacteristic
970C22#6612511yescharacteristic
971C22C2×#408511yescharacteristic
972C22C2×#408611yescharacteristic
973C22#6616411yescharacteristic
974C22#6616711yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—108no—
981C4—204no—
982C4—402no—
983C4#6524618yescomplemented
984C2—44no—
985C2—404no—
986C2#1060518511yescharacteristic
987C2#1060519811yescharacteristic
988C2#1060520011yescharacteristic
989C2#1060521611yescharacteristic
990C2#1060521811yescharacteristic
991C2#1060523711yescharacteristic
992C2#1060523811yescharacteristic
993C2C22⋊C4×D2011yescharacteristic
994C2C4×#407611yescharacteristic
995C2C2×#6524611yescharacteristic
996C2#1061396711yescharacteristic
997C2#1061408111yescharacteristic
998C2#1061408311yescharacteristic
999C2#1061410811yescharacteristic
1000C2#1061410911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC22×#4076C2
hypercenterC2×C4×C22⋊C4D5
hypocenterC5#13998
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×C22⋊C4C2semidirect
3. C2×#65501C2semidirect
4. C2×#65246C2semidirect
5. C2×#65228C2semidirect
6. C2×#65228C2semidirect
7. C2×#65217C2semidirect
8. C2×C4×C4⋊Dic5C2semidirect
9. #10602343C2semidirect
10. #10600221C2semidirect
11. #10600201C2semidirect
22. C2×#4076C4semidirect
83. C2×C5×C22⋊C4D4semidirect
89. C2×C42×C5D4semidirect
117. C2×C4⋊Dic5D4semidirect
136. C2×C4×C22⋊C4D5semidirect
267. C4⋊Dic5C22⋊C4semidirect
428. C2×C4×C5#121semidirect
522. C2×C22⋊C4D20semidirect
531. C2×C42C22⋊D5semidirect
607. C4×C5#390semidirect
906. C2×C4#4076semidirect
909. C5#13998semidirect
983. C4#65246semidirect

Maximal subgroups

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

subgroupindex
C22×#40762
C2×C4×C5×C22⋊C42
C2×#655012
C2×#652462
C2×#652282
C2×#652172
C2×C4×C4⋊Dic52
#106023432
#106002212
#106002012
#139985