Finite Group Databasebeta

← #12022140

Subgroups — #12022140

Order 1280.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#380C211yesmaximal, characteristic
2C2×#65501C211yesmaximal, characteristic
3C2×C4×C22⋊Dic5C211yesmaximal, characteristic
4C2×#65274C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6#10602356C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10602339C212yesmaximal
9#10602338C212yesmaximal
10#10600205C212yesmaximal, complemented
11#10600194C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2212yes—
16C22×C22⋊Dic5C2211yescharacteristic
17C22×C22⋊Dic5C2212yes—
18C22×C22⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C22×C4×Dic5C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C5×#380C418yescomplemented
26C2×C5×#95C2212yes—
27#65501—24no—
28C4×C22⋊Dic5—24no—
29C2×#3963C2211yescharacteristic
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#65274—24no—
39C4⋊C4×Dic5—24no—
40#13973—51nomaximal, Sylow
41C25×C5C2311yescharacteristic
42C23×C4×C5—22no—
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5C2×C414yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2312yes—
51C23×C4×C5C2312yes—
52C23×C4×C5C2311yescharacteristic
53C23×Dic5C2312yes—
54C23×Dic5C2311yescharacteristic
55C23×Dic5C2312yes—
56C23×Dic5C2311yescharacteristic
57C23×Dic5C2311yescharacteristic
58C23×Dic5C2311yescharacteristic
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4C2×C414yes—
64C2×C5×C4⋊C4C2×C414yes—
65C2×C5×C22⋊C4—42no—
66C2×C5×C22⋊C4—42no—
67C2×C5×C22⋊C4C2×C418yes—
68C2×C22⋊Dic5—22no—
69C2×C22⋊Dic5—22no—
70C2×C22⋊Dic5—22no—
71C2×C22⋊Dic5—22no—
72C2×C22⋊Dic5—22no—
73C2×C22⋊Dic5—24no—
74C2×C22⋊Dic5—24no—
75C2×C22⋊Dic5—42no—
76C2×C22⋊Dic5Q814yes—
77C2×C4⋊Dic5—22no—
78C2×C4⋊Dic5—22no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—24no—
83C2×C4⋊Dic5—42no—
84C2×C4⋊Dic5—42no—
85C2×C4⋊Dic5D414yes—
86C2×C4×Dic5—22no—
87C2×C4×Dic5—22no—
88C2×C4×Dic5—22no—
89C2×C4×Dic5—22no—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—24no—
92C2×C4×Dic5—24no—
93C2×C4×Dic5—42no—
94C2×C4×Dic5D414yes—
95C5×#95C2×C418yes—
96#3963—22no—
97#3963—22no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101#3963—24no—
102#3963—42no—
103#3963—42no—
104#3963—42no—
105C2×#389—51no—
106C2×#380—51no—
107C2×#380D511yescharacteristic
108C2×C4×C4⋊C4—51no—
109C2×C4×C22⋊C4—51no—
110#1442—52no—
111#1439—52no—
112#1437—52no—
113C4⋊#95—51no—
114C4⋊#95—51no—
115#1434—52no—
116C24×C5—21no—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—21no—
120C24×C5—21no—
121C24×C5—21no—
122C24×C5—21no—
123C24×C5—21no—
124C24×C5—21no—
125C24×C5—21no—
126C24×C5—21no—
127C24×C5—21no—
128C24×C5C22×C412yes—
129C24×C5C2×Q812yes—
130C24×C5#4112yes—
131C24×C5C2411yescharacteristic
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
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—28no—
151C22×C4×C5—28no—
152C22×C4×C5—28no—
153C22×C4×C5—44no—
154C22×C4×C5—44no—
155C22×C4×C5—44no—
156C22×C4×C5—44no—
157C22×C4×C5C22×C414yes—
158C22×C4×C5C22×C414yes—
159C22×C4×C5C22×C412yes—
160C22×C4×C5C22×C412yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5C2×D412yes—
163C22×C4×C5#4112yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C22×C4×C5#4112yes—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—22no—
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—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—22no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5C2×D414yes—
203C22×Dic5C2×D412yes—
204C22×Dic5C2×D412yes—
205C22×Dic5C2×Q812yes—
206C22×Dic5C2×Q812yes—
207C22×Dic5#4112yes—
208C22×Dic5#4112yes—
209C5×C4⋊C4—28no—
210C5×C4⋊C4—28no—
211C5×C22⋊C4—48no—
212C22⋊Dic5—28no—
213C22⋊Dic5—28no—
214C22⋊Dic5—48no—
215C4⋊Dic5—28no—
216C4⋊Dic5—48no—
217C4⋊Dic5—44no—
218C4×Dic5—28no—
219C4×Dic5—48no—
220C4×Dic5—44no—
221C24×C4C2×D511yescharacteristic
222C22×C4⋊C4—51no—
223C22×C4⋊C4—51no—
224C22×C4⋊C4—52no—
225C22×C4⋊C4C2×D511yescharacteristic
226C22×C4⋊C4C2×D511yescharacteristic
227C22×C22⋊C4—51no—
228C22×C22⋊C4—51no—
229C22×C22⋊C4—52no—
230C22×C22⋊C4C2×D512yes—
231C22×C42—51no—
232C22×C42—51no—
233C22×C42—52no—
234#389—104no—
235#380—104no—
236#380Dic518yescomplemented
237C4×C4⋊C4—104no—
238C4×C22⋊C4—104no—
239C2×#95—51no—
240C2×#95—52no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—51no—
245C2×#95—52no—
246C2×#95—52no—
247C2×#95—52no—
248C2×#95C2×D512yes—
249C23×C5—22no—
250C23×C5—22no—
251C23×C5—22no—
252C23×C5—22no—
253C23×C5—22no—
254C23×C5—22no—
255C23×C5—22no—
256C23×C5—22no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—22no—
263C23×C5—22no—
264C23×C5—22no—
265C23×C5—22no—
266C23×C5—22no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5C4×Q814yes—
284C23×C5C23×C411yescharacteristic
285C23×C5C22×D411yescharacteristic
286C23×C5C22×D411yescharacteristic
287C23×C5C22×Q811yescharacteristic
288C23×C5C2×#4111yescharacteristic
289C23×C5C2×#4111yescharacteristic
290C23×C5C2×#4111yescharacteristic
291C23×C5C2×#4111yescharacteristic
292C23×C5C2×#4111yescharacteristic
293C23×C5C2×#4111yescharacteristic
294C23×C5C2×#4111yescharacteristic
295C23×C5H(5,𝔽2)11yescharacteristic
296C23×C5H(5,𝔽2)11yescharacteristic
297C23×C5H(5,𝔽2)11yescharacteristic
298C23×C52−1+411yescharacteristic
299C2×C4×C5—22no—
300C2×C4×C5—24no—
301C2×C4×C5—24no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—24no—
305C2×C4×C5—24no—
306C2×C4×C5—24no—
307C2×C4×C5—24no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—416no—
321C2×C4×C5#11714yes—
322C2×C4×C5C4×D414yes—
323C2×C4×C5C4×D414yes—
324C2×C4×C5#12114yes—
325C2×C4×C5#12314yes—
326C2×C4×C5#12414yes—
327C2×C4×C5#12614yes—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—22no—
332C2×Dic5—22no—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—24no—
337C2×Dic5—22no—
338C2×Dic5—22no—
339C2×Dic5—22no—
340C2×Dic5—24no—
341C2×Dic5—24no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—41no—
347C2×Dic5—41no—
348C2×Dic5—42no—
349C2×Dic5—41no—
350C2×Dic5—41no—
351C2×Dic5—42no—
352C2×Dic5—41no—
353C2×Dic5—41no—
354C2×Dic5—41no—
355C2×Dic5—41no—
356C2×Dic5—41no—
357C2×Dic5—42no—
358C2×Dic5—41no—
359C2×Dic5—41no—
360C2×Dic5—42no—
361C2×Dic5—41no—
362C2×Dic5—42no—
363C2×Dic5—42no—
364C2×Dic5—42no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5C22⋊Q814yes—
370C25C22×D511yescharacteristic
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—51no—
378C23×C4—51no—
379C23×C4—52no—
380C23×C4—51no—
381C23×C4—51no—
382C23×C4—52no—
383C23×C4C2×Dic514yes—
384C23×C4C22×D512yes—
385C23×C4C22×D512yes—
386C23×C4C22×D511yescharacteristic
387C23×C4C22×D511yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—54no—
393C2×C4⋊C4—102no—
394C2×C4⋊C4—102no—
395C2×C4⋊C4—104no—
396C2×C4⋊C4—102no—
397C2×C4⋊C4—102no—
398C2×C4⋊C4—102no—
399C2×C4⋊C4—202no—
400C2×C4⋊C4—202no—
401C2×C4⋊C4C2×Dic514yes—
402C2×C4⋊C4C2×Dic514yes—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—54no—
406C2×C22⋊C4—102no—
407C2×C22⋊C4—102no—
408C2×C22⋊C4—102no—
409C2×C22⋊C4—102no—
410C2×C22⋊C4—102no—
411C2×C22⋊C4—104no—
412C2×C22⋊C4—104no—
413C2×C22⋊C4—202no—
414C2×C22⋊C4C2×Dic518yes—
415C2×C42—54no—
416C2×C42—102no—
417C2×C42—102no—
418C2×C42—104no—
419C2×C42—104no—
420C2×C42—102no—
421C2×C42—102no—
422C2×C42—102no—
423C2×C42—202no—
424#95—102no—
425#95—102no—
426#95—104no—
427#95—104no—
428#95—104no—
429#95—104no—
430#95—202no—
431#95—202no—
432#95—202no—
433#95C2×Dic518yes—
434C22×C5—24no—
435C22×C5—24no—
436C22×C5—24no—
437C22×C5—42no—
438C22×C5—42no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5C2×#11711yescharacteristic
450C22×C5C2×C4×D411yescharacteristic
451C22×C5C2×C4×D411yescharacteristic
452C22×C5C2×C4×Q811yescharacteristic
453C22×C5C4×#4111yescharacteristic
454C22×C5#51811yescharacteristic
455C22×C5#52011yescharacteristic
456C22×C5C2×#12111yescharacteristic
457C22×C5C2×C22⋊Q811yescharacteristic
458C22×C5C2×#12311yescharacteristic
459C22×C5#52511yescharacteristic
460C22×C5C2×#12411yescharacteristic
461C22×C5C2×#12611yescharacteristic
462C22×C5#52911yescharacteristic
463C22×C5#53311yescharacteristic
464C22×C5#53511yescharacteristic
465C22×C5#53711yescharacteristic
466C22×C5#54011yescharacteristic
467C22×C5#54211yescharacteristic
468C22×C5#54611yescharacteristic
469C22×C5#54611yescharacteristic
470C22×C5D4×Q811yescharacteristic
471C22×C5#55011yescharacteristic
472C22×C5#55211yescharacteristic
473C22×C5#55211yescharacteristic
474C22×C5#55211yescharacteristic
475C22×C5#55311yescharacteristic
476C22×C5#55311yescharacteristic
477C22×C5#55311yescharacteristic
478C22×C5#55411yescharacteristic
479C22×C5#55411yescharacteristic
480C22×C5#55411yescharacteristic
481C22×C5#55511yescharacteristic
482C22×C5#55511yescharacteristic
483C22×C5#55511yescharacteristic
484C4×C5—44no—
485C4×C5—44no—
486C4×C5—42no—
487C4×C5#38818yes—
488Dic5—24no—
489Dic5—42no—
490Dic5—42no—
491Dic5—42no—
492Dic5—44no—
493Dic5—82no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24Q8×D512yes—
507C24#71312yes—
508C24C22×Dic512yes—
509C24C23×D511yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—52no—
536C22×C4—52no—
537C22×C4—52no—
538C22×C4—54no—
539C22×C4—52no—
540C22×C4—52no—
541C22×C4—52no—
542C22×C4—101no—
543C22×C4—101no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—102no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—102no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—102no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—101no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—102no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4#70912yes—
578C22×C4#70912yes—
579C22×C4D4×D512yes—
580C22×C4D4×D512yes—
581C22×C4#71112yes—
582C22×C4#71112yes—
583C22×C4C22×Dic512yes—
584C22×C4C22×Dic514yes—
585C22×C4C22×Dic514yes—
586C22×C4C22×Dic512yes—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—108no—
590C4⋊C4—208no—
591C4⋊C4—204no—
592C22⋊C4—48no—
593C22⋊C4—108no—
594C22⋊C4—108no—
595C22⋊C4—208no—
596C42—108no—
597C42—208no—
598C42—204no—
599C2×C5—44no—
600C2×C5C2×#38811yescharacteristic
601C2×C5C4×C22⋊Q811yescharacteristic
602C2×C5#232411yescharacteristic
603C2×C5#234511yescharacteristic
604C2×C5#234611yescharacteristic
605C2×C5#236011yescharacteristic
606C2×C5#236311yescharacteristic
607C2×C5#241411yescharacteristic
608C2×C5#241711yescharacteristic
609C2×C5#242011yescharacteristic
610C2×C5#242311yescharacteristic
611C2×C5#249511yescharacteristic
612C2×C5#249711yescharacteristic
613C2×C5#256211yescharacteristic
614C2×C5#256311yescharacteristic
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23Q8×Dic514yes—
650C23C2×#70911yescharacteristic
651C23C2×#70911yescharacteristic
652C23C2×D4×D511yescharacteristic
653C23C2×D4×D511yescharacteristic
654C23C2×#71111yescharacteristic
655C23C2×#71111yescharacteristic
656C23#414411yescharacteristic
657C23#414411yescharacteristic
658C23C2×Q8×D511yescharacteristic
659C23C2×#71311yescharacteristic
660C23D5×#4111yescharacteristic
661C23D5×#4111yescharacteristic
662C23#414911yescharacteristic
663C23#415011yescharacteristic
664C23C23×Dic511yescharacteristic
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—416no—
687C2×C4—54no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—104no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—104no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—104no—
705C2×C4—102no—
706C2×C4—201no—
707C2×C4—201no—
708C2×C4—202no—
709C2×C4—201no—
710C2×C4—201no—
711C2×C4—202no—
712C2×C4—201no—
713C2×C4—201no—
714C2×C4—201no—
715C2×C4—201no—
716C2×C4—201no—
717C2×C4—201no—
718C2×C4—202no—
719C2×C4—202no—
720C2×C4—201no—
721C2×C4—201no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4#402514yes—
730C2×C4#402914yes—
731C2×C4#403014yes—
732C2×C4#403114yes—
733C2×C4#407214yes—
734C2×C4D4×Dic514yes—
735C2×C4D4×Dic514yes—
736C5#1397311yescharacteristic, complemented, Sylow
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#402511yescharacteristic
753C22C2×#402911yescharacteristic
754C22C2×#403011yescharacteristic
755C22C2×#403111yescharacteristic
756C22#6584511yescharacteristic
757C22#6584511yescharacteristic
758C22#6584811yescharacteristic
759C22#6584811yescharacteristic
760C22#6586311yescharacteristic
761C22#6586311yescharacteristic
762C22#6586611yescharacteristic
763C22#6586611yescharacteristic
764C22#6593311yescharacteristic
765C22#6593711yescharacteristic
766C22#6594111yescharacteristic
767C22#6594211yescharacteristic
768C22#6594611yescharacteristic
769C22#6594811yescharacteristic
770C22#6595011yescharacteristic
771C22#6595311yescharacteristic
772C22#6595611yescharacteristic
773C22#6595811yescharacteristic
774C22D5×C22⋊Q811yescharacteristic
775C22#6596111yescharacteristic
776C22#6596411yescharacteristic
777C22#6596611yescharacteristic
778C22#6596911yescharacteristic
779C22#6597611yescharacteristic
780C22C2×#407211yescharacteristic
781C22C2×D4×Dic511yescharacteristic
782C22C2×D4×Dic511yescharacteristic
783C22#6613211yescharacteristic
784C22C2×Q8×Dic511yescharacteristic
785C22#41×Dic511yescharacteristic
786C22#6616111yescharacteristic
787C4—42no—
788C4—44no—
789C4—44no—
790C4—104no—
791C4—204no—
792C4—202no—
793C4—202no—
794C4—202no—
795C4—402no—
796C4#6524018yes—
797C2—44no—
798C2#1060561911yescharacteristic
799C2#1060562211yescharacteristic
800C2#1060562511yescharacteristic
801C2#1060565111yescharacteristic
802C2#1060565511yescharacteristic
803C2#1060567211yescharacteristic
804C2#1060567311yescharacteristic
805C2#1060575011yescharacteristic
806C2C2×#6524011yescharacteristic
807C2#1061389111yescharacteristic
808C2#1061397011yescharacteristic
809C2#1061436411yescharacteristic
810C2#1061436811yescharacteristic
811C2Dic5×C22⋊Q811yescharacteristic
812C2#1061447811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#380C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#380D5
hypocenterC5#13973
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#65274C2semidirect
5. C2×C4⋊C4×Dic5C2semidirect
6. #10602356C2semidirect
7. #10602356C2semidirect
10. #10600205C2semidirect
11. #10600194C2semidirect
25. C5×#380C4semidirect
236. #380Dic5semidirect
736. C5#13973semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3802
C2×#655012
C2×C4×C22⋊Dic52
C2×#652742
C2×C4⋊C4×Dic52
#106023562
#106023392
#106023382
#106002052
#106001942
#139735