Finite Group Databasebeta

← #12022136

Subgroups — #12022136

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×#65276C211yesmaximal, characteristic
2C2×#65276C211yesmaximal, characteristic
3C2×#65274C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5C2×C4×#685C211yesmaximal, characteristic
6C5×C4⋊#95C211yesmaximal, characteristic, complemented
7#10602328C211yesmaximal, characteristic, complemented
8#10600220C212yesmaximal
9#10600208C212yesmaximal, complemented
10#10600201C212yesmaximal
11#10600195C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×#685C2211yescharacteristic
17C22×#685C2212yes—
18C22×#685C2211yescharacteristic
19C22×#685C2212yes—
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2212yes—
23C22×C4×Dic5C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C2×C5×#95C2212yes—
26C2×C5×#95C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35#65276—24no—
36#65276C418yescomplemented
37#65274—24no—
38C4⋊C4×Dic5—24no—
39C4×#685—24no—
40#13973—51nomaximal, Sylow
41C24×D5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C22×C4×D5—22no—
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5C2×C414yes—
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⋊C4D414yes—
65C2×C42×C5—22no—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×#685—22no—
69C2×#685—22no—
70C2×#685—22no—
71C2×#685—22no—
72C2×#685—22no—
73C2×#685—24no—
74C2×#685—24no—
75C2×#685—42no—
76C2×#685—42no—
77C2×#685—42no—
78C2×#685C2×C418yes—
79C2×#685Q814yes—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5—22no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—24no—
86C2×C4⋊Dic5—42no—
87C2×C4⋊Dic5—42no—
88C2×C4⋊Dic5C2×C414yes—
89C2×C4×Dic5—22no—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—24no—
92C2×C4×Dic5—24no—
93C2×C4×Dic5—42no—
94C2×C4×Dic5D414yes—
95C5×#95—42no—
96C5×#95—42no—
97#3963—24no—
98#3963—24no—
99#3963—24no—
100#3963—22no—
101#3963—22no—
102#3963—24no—
103#3963—42no—
104#3963C2×C418yes—
105C2×#389—51no—
106C2×#380—51no—
107C2×#380—51no—
108C2×C4×C4⋊C4—51no—
109C2×C4×C22⋊C4—51no—
110#1442—52no—
111#1439—52no—
112#1437—52no—
113C4⋊#95—51no—
114C4⋊#95D511yescharacteristic, complemented
115#1434—52no—
116C24×C5C2411yescharacteristic
117C23×D5—21no—
118C23×D5—21no—
119C23×D5—21no—
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×D5C22×C412yes—
130C23×D5C2×Q812yes—
131C23×D5#4112yes—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—22no—
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—22no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
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—21no—
156C22×C4×C5C22×C414yes—
157C22×C4×C5C22×C412yes—
158C22×C4×C5C2×D414yes—
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×Q812yes—
162C22×C4×C5#4112yes—
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—22no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—22no—
180C22×Dic5—21no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5C22×C412yes—
197C22×Dic5C22×C414yes—
198C22×Dic5C2×D412yes—
199C22×Dic5C2×D412yes—
200C22×Dic5C2×Q812yes—
201C22×Dic5#4112yes—
202C2×C4×D5—28no—
203C2×C4×D5—28no—
204C2×C4×D5—28no—
205C2×C4×D5—44no—
206C2×C4×D5—44no—
207C2×C4×D5—44no—
208C2×C4×D5—44no—
209C5×C4⋊C4—28no—
210C5×C4⋊C4—28no—
211C42×C5—44no—
212#685—28no—
213#685—28no—
214#685—48no—
215#685—48no—
216C4⋊Dic5—28no—
217C4⋊Dic5—48no—
218C4⋊Dic5—44no—
219C4×Dic5—28no—
220C4×Dic5—48no—
221C24×C4—51no—
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—52no—
229C22×C22⋊C4—51no—
230C22×C22⋊C4—52no—
231C22×C42—51no—
232C22×C42—52no—
233C22×C42C2×D511yescharacteristic
234#389—104no—
235#380—58no—
236#380—104no—
237C4×C4⋊C4—104no—
238C4×C22⋊C4—104no—
239C2×#95—52no—
240C2×#95—51no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95—51no—
246C2×#95—52no—
247C2×#95C2×D512yes—
248C2×#95C2×D512yes—
249C23×C5C23×C411yescharacteristic
250C23×C5C22×D411yescharacteristic
251C23×C5C22×D411yescharacteristic
252C23×C5C22×Q811yescharacteristic
253C23×C5C2×#4111yescharacteristic
254C23×C5C2×#4111yescharacteristic
255C23×C5C2×#4111yescharacteristic
256C23×C5C2×#4111yescharacteristic
257C23×C5C2×#4111yescharacteristic
258C23×C5C2×#4111yescharacteristic
259C23×C5C2×#4111yescharacteristic
260C23×C5H(5,𝔽2)11yescharacteristic
261C23×C5H(5,𝔽2)11yescharacteristic
262C23×C5H(5,𝔽2)11yescharacteristic
263C23×C52−1+411yescharacteristic
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—22no—
267C22×D5—22no—
268C22×D5—22no—
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—41no—
283C22×D5—41no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
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×D5C4×Q814yes—
299C2×C4×C5—24no—
300C2×C4×C5—24no—
301C2×C4×C5—24no—
302C2×C4×C5—22no—
303C2×C4×C5—24no—
304C2×C4×C5—22no—
305C2×C4×C5—24no—
306C2×C4×C5—24no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—42no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—42no—
327C2×C4×C5#11714yes—
328C2×C4×C5C4×D414yes—
329C2×C4×C5C4×D414yes—
330C2×C4×C5#12114yes—
331C2×C4×C5#12314yes—
332C2×C4×C5#12414yes—
333C2×C4×C5#12614yes—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—22no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—24no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—24no—
345C2×Dic5—24no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—41no—
350C2×Dic5—41no—
351C2×Dic5—41no—
352C2×Dic5—41no—
353C2×Dic5—42no—
354C2×Dic5—41no—
355C2×Dic5—42no—
356C2×Dic5—41no—
357C2×Dic5—42no—
358C2×Dic5—41no—
359C2×Dic5—41no—
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×Dic5C22⋊Q814yes—
369C4×D5—416no—
370C25—51no—
371C23×C4—51no—
372C23×C4—51no—
373C23×C4—52no—
374C23×C4—51no—
375C23×C4—54no—
376C23×C4—52no—
377C23×C4—102no—
378C23×C4—102no—
379C23×C4—102no—
380C23×C4—102no—
381C23×C4—102no—
382C23×C4—102no—
383C23×C4C22×D512yes—
384C23×C4C22×D512yes—
385C23×C4C22×D511yescharacteristic
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⋊C4C4×D514yes—
402C2×C4⋊C4D2014yes—
403C2×C22⋊C4—54no—
404C2×C22⋊C4—58no—
405C2×C22⋊C4—102no—
406C2×C22⋊C4—102no—
407C2×C22⋊C4—102no—
408C2×C22⋊C4—102no—
409C2×C22⋊C4—102no—
410C2×C22⋊C4—104no—
411C2×C22⋊C4—104no—
412C2×C22⋊C4—202no—
413C2×C22⋊C4—202no—
414C2×C22⋊C4—202no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—54no—
419C2×C42—102no—
420C2×C42—102no—
421C2×C42—104no—
422C2×C42—104no—
423C2×C42—202no—
424#95—42no—
425#95—42no—
426#95—58no—
427#95—102no—
428#95—102no—
429#95—104no—
430#95—104no—
431#95—104no—
432#95—104no—
433#95—202no—
434C22×C5C2×#11711yescharacteristic
435C22×C5C2×C4×D411yescharacteristic
436C22×C5C2×C4×D411yescharacteristic
437C22×C5C2×C4×Q811yescharacteristic
438C22×C5C4×#4111yescharacteristic
439C22×C5#51811yescharacteristic
440C22×C5#52011yescharacteristic
441C22×C5C2×#12111yescharacteristic
442C22×C5C2×C22⋊Q811yescharacteristic
443C22×C5C2×#12311yescharacteristic
444C22×C5#52511yescharacteristic
445C22×C5C2×#12411yescharacteristic
446C22×C5C2×#12611yescharacteristic
447C22×C5#52911yescharacteristic
448C22×C5#53311yescharacteristic
449C22×C5#53511yescharacteristic
450C22×C5#53711yescharacteristic
451C22×C5#54011yescharacteristic
452C22×C5#54211yescharacteristic
453C22×C5#54611yescharacteristic
454C22×C5#54611yescharacteristic
455C22×C5D4×Q811yescharacteristic
456C22×C5#55011yescharacteristic
457C22×C5#55211yescharacteristic
458C22×C5#55211yescharacteristic
459C22×C5#55211yescharacteristic
460C22×C5#55311yescharacteristic
461C22×C5#55311yescharacteristic
462C22×C5#55311yescharacteristic
463C22×C5#55411yescharacteristic
464C22×C5#55411yescharacteristic
465C22×C5#55411yescharacteristic
466C22×C5#55511yescharacteristic
467C22×C5#55511yescharacteristic
468C22×C5#55511yescharacteristic
469C2×D5—24no—
470C2×D5—24no—
471C2×D5—24no—
472C2×D5—42no—
473C2×D5—42no—
474C2×D5—42no—
475C2×D5—42no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—42no—
479C2×D5—42no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C4×C5—42no—
485C4×C5—42no—
486C4×C5—44no—
487C4×C5—44no—
488C4×C5#38818yes—
489Dic5—24no—
490Dic5—44no—
491Dic5—42no—
492Dic5—42no—
493Dic5—82no—
494C24—52no—
495C24—52no—
496C24—52no—
497C24—101no—
498C24—101no—
499C24—101no—
500C24—101no—
501C24—101no—
502C24—101no—
503C24—101no—
504C24—101no—
505C24—101no—
506C24—101no—
507C24—101no—
508C24—101no—
509C24C23×D511yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
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—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—52no—
535C22×C4—52no—
536C22×C4—52no—
537C22×C4—52no—
538C22×C4—54no—
539C22×C4—52no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—102no—
547C22×C4—102no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—102no—
553C22×C4—101no—
554C22×C4—102no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—102no—
559C22×C4—101no—
560C22×C4—102no—
561C22×C4—101no—
562C22×C4—108no—
563C22×C4—108no—
564C22×C4—108no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—204no—
573C22×C4—204no—
574C22×C4—204no—
575C22×C4—204no—
576C22×C4C2×C4×D514yes—
577C22×C4C2×C4×D512yes—
578C22×C4C2×D2014yes—
579C22×C4C2×D2012yes—
580C22×C4#70912yes—
581C22×C4D4×D512yes—
582C22×C4#71112yes—
583C22×C4#71112yes—
584C22×C4Q8×D512yes—
585C22×C4#71312yes—
586C22×C4#71312yes—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—108no—
590C4⋊C4—208no—
591C4⋊C4—204no—
592C22⋊C4—108no—
593C22⋊C4—108no—
594C22⋊C4—208no—
595C22⋊C4—208no—
596C42—44no—
597C42—108no—
598C42—208no—
599C2×C5C2×#38811yescharacteristic
600C2×C5C4×C22⋊Q811yescharacteristic
601C2×C5#232411yescharacteristic
602C2×C5#234511yescharacteristic
603C2×C5#234611yescharacteristic
604C2×C5#236011yescharacteristic
605C2×C5#236311yescharacteristic
606C2×C5#241411yescharacteristic
607C2×C5#241711yescharacteristic
608C2×C5#242011yescharacteristic
609C2×C5#242311yescharacteristic
610C2×C5#249511yescharacteristic
611C2×C5#249711yescharacteristic
612C2×C5#256211yescharacteristic
613C2×C5#256311yescharacteristic
614D5—44no—
615C23—54no—
616C23—102no—
617C23—102no—
618C23—102no—
619C23—102no—
620C23—102no—
621C23—102no—
622C23—102no—
623C23—102no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—201no—
635C23—201no—
636C23—201no—
637C23—201no—
638C23—201no—
639C23—201no—
640C23—201no—
641C23—201no—
642C23—201no—
643C23—201no—
644C23—201no—
645C23—201no—
646C23—201no—
647C23—201no—
648C23—201no—
649C23—201no—
650C23C22×C4×D511yescharacteristic
651C23C22×D2011yescharacteristic
652C23C2×#70911yescharacteristic
653C23C2×D4×D511yescharacteristic
654C23C2×#71111yescharacteristic
655C23C2×#71111yescharacteristic
656C23#414411yescharacteristic
657C23#414411yescharacteristic
658C23C2×Q8×D511yescharacteristic
659C23C2×#71311yescharacteristic
660C23C2×#71311yescharacteristic
661C23D5×#4111yescharacteristic
662C23D5×#4111yescharacteristic
663C23#414911yescharacteristic
664C23#415011yescharacteristic
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—54no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—104no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—104no—
706C2×C4—104no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—201no—
710C2×C4—201no—
711C2×C4—201no—
712C2×C4—201no—
713C2×C4—201no—
714C2×C4—202no—
715C2×C4—202no—
716C2×C4—202no—
717C2×C4—201no—
718C2×C4—202no—
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×C4C4×D2014yes—
730C2×C4#402714yes—
731C2×C4#403114yes—
732C2×C4#403214yes—
733C2×C4#403814yes—
734C2×C4#404114yes—
735C2×C4#404414yes—
736C5#1397311yescharacteristic, complemented, Sylow
737C22—104no—
738C22—104no—
739C22—104no—
740C22—202no—
741C22—202no—
742C22—202no—
743C22—202no—
744C22—202no—
745C22—202no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22C2×C4×D2011yescharacteristic
753C22C2×#402711yescharacteristic
754C22C2×#403111yescharacteristic
755C22C2×#403211yescharacteristic
756C22C2×#403811yescharacteristic
757C22C2×#404111yescharacteristic
758C22#6584511yescharacteristic
759C22C2×#404411yescharacteristic
760C22#6584811yescharacteristic
761C22#6586311yescharacteristic
762C22#6586611yescharacteristic
763C22#6587911yescharacteristic
764C22#6588011yescharacteristic
765C22#6588811yescharacteristic
766C22#6588811yescharacteristic
767C22C4×Q8×D511yescharacteristic
768C22C4×#71311yescharacteristic
769C22Q8×D2011yescharacteristic
770C22#6591111yescharacteristic
771C22#6594111yescharacteristic
772C22#6594211yescharacteristic
773C22#6594811yescharacteristic
774C22#6595011yescharacteristic
775C22D5×C22⋊Q811yescharacteristic
776C22#6596111yescharacteristic
777C22#6596911yescharacteristic
778C22#6597611yescharacteristic
779C22#6601411yescharacteristic
780C22#6601611yescharacteristic
781C22#6602811yescharacteristic
782C22#6602911yescharacteristic
783C22#6605311yescharacteristic
784C22#6606211yescharacteristic
785C22#6606411yescharacteristic
786C22#6606811yescharacteristic
787C4—44no—
788C4—44no—
789C4—42no—
790C4—42no—
791C4—104no—
792C4—202no—
793C4—204no—
794C4—202no—
795C4—402no—
796C4#6495918yes—
797C2—204no—
798C2C2×#6495911yescharacteristic
799C2#1060538011yescharacteristic
800C2#1060550411yescharacteristic
801C2#1060567211yescharacteristic
802C2#1060567311yescharacteristic
803C2#1060596611yescharacteristic
804C2#1060609611yescharacteristic
805C2#1060771011yescharacteristic
806C2#1060793211yescharacteristic
807C2#1060794011yescharacteristic
808C2#1060794311yescharacteristic
809C2#1060816111yescharacteristic
810C2#1060817111yescharacteristic
811C2#1060821011yescharacteristic
812C2#1060835411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13973
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#65274C2semidirect
4. C2×C4⋊C4×Dic5C2semidirect
6. C5×C4⋊#95C2semidirect
7. #10602328C2semidirect
9. #10600208C2semidirect
11. #10600195C2semidirect
36. #65276C4semidirect
114. C4⋊#95D5semidirect
736. C5#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#652762
C2×#652742
C2×C4⋊C4×Dic52
C2×C4×#6852
C5×C4⋊#952
#106023282
#106002202
#106002082
#106002012
#106001952
#139735