Finite Group Databasebeta

← #12021953

Subgroups — #12021953

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C211yesmaximal, characteristic
2C2×#65276C211yesmaximal, characteristic
3C2×#65262C211yesmaximal, characteristic, complemented
4C2×#65217C211yesmaximal, characteristic, complemented
5C2×C4×#685C211yesmaximal, characteristic
6C5×C4⋊#95C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10600221C212yesmaximal
9#10600221C212yesmaximal
10#10600197C212yesmaximal, complemented
11#10600194C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×#685C2211yescharacteristic
17C22×#685C2211yescharacteristic
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×#683C2212yes—
23C22×#683C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2212yes—
26C2×#4038—24no—
27C2×#4038—24no—
28C2×#4038C418yescomplemented
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C2×#3963C2212yes—
38#65276—24no—
39#65262—24no—
40C4×#685—24no—
41#65217—24no—
42#13951—51nomaximal, Sylow
43C24×D5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2312yes—
53C23×Dic5C2311yescharacteristic
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5C2×C414yes—
59C22×C4×D5D414yes—
60C22×C4×D5Q814yes—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—22no—
66C2×C5×C4⋊C4C2×C414yes—
67C2×C42×C5—22no—
68C2×C42×C5—22no—
69C2×C42×C5—22no—
70C2×#685—22no—
71C2×#685—22no—
72C2×#685—22no—
73C2×#685—22no—
74C2×#685—24no—
75C2×#685—24no—
76C2×#685—22no—
77C2×#685—22no—
78C2×#685—24no—
79C2×#685—42no—
80C2×#685—42no—
81C2×#685C2×C418yes—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5—22no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5C2×C414yes—
86C2×C4⋊Dic5D414yes—
87C2×C4⋊Dic5D414yes—
88C2×#683—24no—
89C2×#683—24no—
90C2×#683—24no—
91C2×#683—24no—
92C2×#683—42no—
93C2×#683—42no—
94C2×C4×Dic5—24no—
95C2×C4×Dic5—24no—
96C2×C4×Dic5—22no—
97C2×C4×Dic5—22no—
98C2×C4×Dic5—22no—
99C2×C4×Dic5C2×C418yes—
100#4038—232no—
101C5×#95—24no—
102C5×#95—42no—
103#3963—24no—
104#3963—22no—
105#3963—22no—
106#3963—24no—
107#3963—24no—
108#3963—24no—
109#3963—42no—
110C22×#117—51no—
111C2×#389—51no—
112C2×#389—51no—
113C2×#380—51no—
114C2×C4×C22⋊C4—51no—
115#1439—52no—
116#1439—52no—
117C4⋊#95—52no—
118C4⋊#95—51no—
119C4⋊#95D511yescharacteristic, complemented
120#1434—52no—
121C24×C5C2411yescharacteristic
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×D5—21no—
133C23×D5—21no—
134C23×D5C22×C412yes—
135C23×D5C2×D412yes—
136C23×D5C2×Q812yes—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—22no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5C22×C414yes—
163C22×C4×C5C22×C412yes—
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×D412yes—
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2×Q812yes—
168C22×C4×C5#4112yes—
169C22×C4×C5#4112yes—
170C22×C4×C5#4112yes—
171C22×C4×C5#4112yes—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5C22×C414yes—
200C22×Dic5C22×C412yes—
201C22×Dic5C2×D414yes—
202C22×Dic5C2×D414yes—
203C22×Dic5C2×D412yes—
204C22×Dic5C2×Q812yes—
205C22×Dic5#4112yes—
206C22×Dic5#4112yes—
207C2×C4×D5—28no—
208C2×C4×D5—28no—
209C2×C4×D5—28no—
210C2×C4×D5—28no—
211C2×C4×D5—28no—
212C2×C4×D5—28no—
213C2×C4×D5C4⋊C4116yescomplemented
214C5×C4⋊C4—28no—
215C5×C4⋊C4—44no—
216C42×C5—44no—
217#685—28no—
218#685—28no—
219#685—216no—
220#685—48no—
221C4⋊Dic5—44no—
222C4⋊Dic5C22⋊C4116yescomplemented
223#683—48no—
224#683—48no—
225C4×Dic5—216no—
226C4×Dic5—44no—
227C24×C4—51no—
228C2×#117—58no—
229C2×#117—104no—
230C2×#117—104no—
231C22×C4⋊C4—51no—
232C22×C4⋊C4—51no—
233C22×C4⋊C4—52no—
234C22×C4⋊C4—52no—
235C22×C4⋊C4C2×D511yescharacteristic
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C22⋊C4—52no—
238C22×C22⋊C4—51no—
239C22×C22⋊C4—51no—
240C22×C22⋊C4—52no—
241C22×C42—52no—
242C22×C42—51no—
243C22×C42C2×D511yescharacteristic
244#389—104no—
245#389—104no—
246#380—104no—
247C4×C22⋊C4—104no—
248C2×#95—51no—
249C2×#95—52no—
250C2×#95—52no—
251C2×#95—52no—
252C2×#95—52no—
253C2×#95—51no—
254C2×#95—52no—
255C2×#95C2×D512yes—
256C2×#95C2×D512yes—
257C23×C5C23×C411yescharacteristic
258C23×C5C22×D411yescharacteristic
259C23×C5C22×D411yescharacteristic
260C23×C5C22×D411yescharacteristic
261C23×C5C22×Q811yescharacteristic
262C23×C5C2×#4111yescharacteristic
263C23×C5C2×#4111yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5C2×#4111yescharacteristic
266C23×C5C2×#4111yescharacteristic
267C23×C5C2×#4111yescharacteristic
268C23×C5H(5,𝔽2)11yescharacteristic
269C23×C5H(5,𝔽2)11yescharacteristic
270C23×C52−1+411yescharacteristic
271C23×C52−1+411yescharacteristic
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—22no—
288C22×D5—22no—
289C22×D5—22no—
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×D5—41no—
304C22×D5—41no—
305C22×D5—41no—
306C22×D5C2×C4⋊C414yes—
307C2×C4×C5—24no—
308C2×C4×C5—24no—
309C2×C4×C5—24no—
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—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
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—41no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5C2×C22⋊C414yes—
336C2×C4×C5C2×C4⋊C414yes—
337C2×C4×C5#11714yes—
338C2×C4×C5#12114yes—
339C2×C4×C5#12114yes—
340C2×C4×C5C22⋊Q814yes—
341C2×C4×C5C22⋊Q814yes—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—24no—
345C2×Dic5—24no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—24no—
351C2×Dic5—24no—
352C2×Dic5—24no—
353C2×Dic5—24no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—41no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5—41no—
366C2×Dic5—41no—
367C2×Dic5—41no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5C2×C22⋊C418yes—
376C2×Dic5C2×C4⋊C414yes—
377C4×D5—232no—
378C25—51no—
379C23×C4—52no—
380C23×C4—51no—
381C23×C4—54no—
382C23×C4—54no—
383C23×C4—54no—
384C23×C4—51no—
385C23×C4—51no—
386C23×C4—52no—
387C23×C4—102no—
388C23×C4—102no—
389C23×C4—102no—
390C23×C4—102no—
391C23×C4C22×D512yes—
392C23×C4C22×D512yes—
393C23×C4C22×D511yescharacteristic
394C23×C4C22×D511yescharacteristic
395C23×C4C22×D511yescharacteristic
396#117—1032no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—54no—
403C2×C4⋊C4—54no—
404C2×C4⋊C4—54no—
405C2×C4⋊C4—104no—
406C2×C4⋊C4—104no—
407C2×C4⋊C4—104no—
408C2×C4⋊C4—102no—
409C2×C4⋊C4—102no—
410C2×C4⋊C4—102no—
411C2×C4⋊C4—104no—
412C2×C4⋊C4—202no—
413C2×C4⋊C4—202no—
414C2×C4⋊C4C4×D514yes—
415C2×C22⋊C4—58no—
416C2×C22⋊C4—104no—
417C2×C22⋊C4—104no—
418C2×C22⋊C4—102no—
419C2×C22⋊C4—102no—
420C2×C22⋊C4—102no—
421C2×C22⋊C4—102no—
422C2×C22⋊C4—102no—
423C2×C22⋊C4—102no—
424C2×C22⋊C4—104no—
425C2×C22⋊C4—202no—
426C2×C22⋊C4—202no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—58no—
431C2×C42—104no—
432C2×C42—104no—
433C2×C42—102no—
434C2×C42—102no—
435C2×C42—102no—
436#95—24no—
437#95—42no—
438#95—102no—
439#95—102no—
440#95—104no—
441#95—104no—
442#95—104no—
443#95—104no—
444#95—202no—
445C22×C5C22×C22⋊C411yescharacteristic
446C22×C5C22×C4⋊C411yescharacteristic
447C22×C5C2×#11711yescharacteristic
448C22×C5C4×#4111yescharacteristic
449C22×C5C4×#4111yescharacteristic
450C22×C5#52011yescharacteristic
451C22×C5#52011yescharacteristic
452C22×C5C2×#12111yescharacteristic
453C22×C5C2×#12111yescharacteristic
454C22×C5C2×C22⋊Q811yescharacteristic
455C22×C5C2×C22⋊Q811yescharacteristic
456C22×C5#52511yescharacteristic
457C22×C5#52511yescharacteristic
458C22×C5#53311yescharacteristic
459C22×C5#53311yescharacteristic
460C22×C5#53511yescharacteristic
461C22×C5#53611yescharacteristic
462C22×C5#54411yescharacteristic
463C22×C5#54411yescharacteristic
464C22×C5#54611yescharacteristic
465C22×C5#54611yescharacteristic
466C22×C5#54711yescharacteristic
467C22×C5#54711yescharacteristic
468C22×C5#54811yescharacteristic
469C22×C5#54811yescharacteristic
470C22×C5#55011yescharacteristic
471C22×C5#55011yescharacteristic
472C22×C5#55211yescharacteristic
473C22×C5#55211yescharacteristic
474C22×C5#55311yescharacteristic
475C22×C5#55311yescharacteristic
476C22×C5#55511yescharacteristic
477C22×C5#55511yescharacteristic
478C22×C5#55611yescharacteristic
479C22×C5#55611yescharacteristic
480C2×D5—24no—
481C2×D5—24no—
482C2×D5—24no—
483C2×D5—42no—
484C2×D5—42no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5—42no—
489C2×D5—42no—
490C2×D5—42no—
491C2×D5—42no—
492C2×D5—42no—
493C2×D5—42no—
494C2×D5—42no—
495C4×C5—44no—
496C4×C5—42no—
497C4×C5—42no—
498C4×C5—82no—
499C4×C5#38018yes—
500Dic5—28no—
501Dic5—24no—
502Dic5—42no—
503Dic5—42no—
504Dic5—82no—
505C24—52no—
506C24—52no—
507C24—52no—
508C24—101no—
509C24—101no—
510C24—101no—
511C24—101no—
512C24—101no—
513C24—101no—
514C24—101no—
515C24—101no—
516C24—101no—
517C24—101no—
518C24—101no—
519C24—101no—
520C24C23×D511yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—52no—
547C22×C4—54no—
548C22×C4—52no—
549C22×C4—54no—
550C22×C4—54no—
551C22×C4—52no—
552C22×C4—516no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—108no—
564C22×C4—108no—
565C22×C4—108no—
566C22×C4—108no—
567C22×C4—108no—
568C22×C4—108no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4C2×C4×D514yes—
589C22×C4C2×C4×D512yes—
590C22×C4#70912yes—
591C22×C4#70912yes—
592C22×C4D4×D512yes—
593C22×C4D4×D512yes—
594C22×C4D4×D512yes—
595C22×C4#71112yes—
596C22×C4Q8×D512yes—
597C22×C4#71312yes—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—516no—
601C4⋊C4—208no—
602C4⋊C4—208no—
603C4⋊C4—204no—
604C22⋊C4—1016no—
605C22⋊C4—108no—
606C22⋊C4—108no—
607C22⋊C4—208no—
608C42—44no—
609C42—1016no—
610C42—204no—
611C2×C5C2×#38011yescharacteristic
612C2×C5#229611yescharacteristic
613C2×C5#231711yescharacteristic
614C2×C5#233911yescharacteristic
615C2×C5#234111yescharacteristic
616C2×C5#234611yescharacteristic
617C2×C5#234711yescharacteristic
618C2×C5#241411yescharacteristic
619C2×C5#241411yescharacteristic
620C2×C5#241511yescharacteristic
621C2×C5#241511yescharacteristic
622C2×C5#243911yescharacteristic
623C2×C5#243911yescharacteristic
624C2×C5#244111yescharacteristic
625C2×C5#244111yescharacteristic
626D5—44no—
627C23—54no—
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—102no—
643C23—102no—
644C23—102no—
645C23—102no—
646C23—201no—
647C23—201no—
648C23—201no—
649C23—201no—
650C23—201no—
651C23—201no—
652C23—201no—
653C23—201no—
654C23—201no—
655C23—201no—
656C23—201no—
657C23—201no—
658C23—201no—
659C23—201no—
660C23—201no—
661C23—201no—
662C23C22×C4×D511yescharacteristic
663C23C2×#70911yescharacteristic
664C23C2×#70911yescharacteristic
665C23C2×D4×D511yescharacteristic
666C23C2×D4×D511yescharacteristic
667C23C2×D4×D511yescharacteristic
668C23C2×#71111yescharacteristic
669C23#414411yescharacteristic
670C23C2×Q8×D511yescharacteristic
671C23C2×#71311yescharacteristic
672C23#414711yescharacteristic
673C23D5×#4111yescharacteristic
674C23D5×#4111yescharacteristic
675C23#414911yescharacteristic
676C23#415011yescharacteristic
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—58no—
706C2×C4—54no—
707C2×C4—104no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—104no—
715C2×C4—104no—
716C2×C4—104no—
717C2×C4—104no—
718C2×C4—104no—
719C2×C4—1032no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—201no—
727C2×C4—201no—
728C2×C4—201no—
729C2×C4—201no—
730C2×C4—201no—
731C2×C4—201no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—202no—
735C2×C4—202no—
736C2×C4—202no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4#401814yes—
742C2×C4D5×C22⋊C414yes—
743C2×C4#403014yes—
744C2×C4#403014yes—
745C2×C4D5×C4⋊C414yes—
746C2×C4#404214yes—
747C2×C4#404214yes—
748C5#1395111yescharacteristic, complemented, Sylow
749C22—104no—
750C22—104no—
751C22—104no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—202no—
762C22—202no—
763C22—202no—
764C22C2×#401811yescharacteristic
765C22C2×D5×C22⋊C411yescharacteristic
766C22C2×#403011yescharacteristic
767C22C2×#403011yescharacteristic
768C22C2×D5×C4⋊C411yescharacteristic
769C22C2×#404211yescharacteristic
770C22C2×#404211yescharacteristic
771C22#6584711yescharacteristic
772C22#6584811yescharacteristic
773C22#6586611yescharacteristic
774C22#6586711yescharacteristic
775C22C4×#71111yescharacteristic
776C22#6588011yescharacteristic
777C22#6589211yescharacteristic
778C22#6589711yescharacteristic
779C22C4×#71311yescharacteristic
780C22#6590811yescharacteristic
781C22#6591511yescharacteristic
782C22#6591811yescharacteristic
783C22#6593211yescharacteristic
784C22#6593311yescharacteristic
785C22#6594011yescharacteristic
786C22#6594111yescharacteristic
787C22#6596111yescharacteristic
788C22#6596211yescharacteristic
789C22#6596411yescharacteristic
790C22#6596511yescharacteristic
791C22#6601011yescharacteristic
792C22#6601111yescharacteristic
793C22#6602211yescharacteristic
794C22#6602311yescharacteristic
795C22#6605211yescharacteristic
796C22#6606011yescharacteristic
797C22#6606211yescharacteristic
798C22#6606311yescharacteristic
799C4—44no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—104no—
804C4—108no—
805C4—202no—
806C4—202no—
807C4—402no—
808C4#6495618yes—
809C2—204no—
810C2C2×#6495611yescharacteristic
811C2#1060536411yescharacteristic
812C2#1060536511yescharacteristic
813C2#1060575011yescharacteristic
814C2#1060575111yescharacteristic
815C2#1060589311yescharacteristic
816C2#1060605811yescharacteristic
817C2#1060769411yescharacteristic
818C2#1060769911yescharacteristic
819C2#1060795411yescharacteristic
820C2#1060795511yescharacteristic
821C2#1060803211yescharacteristic
822C2#1060816911yescharacteristic
823C2#1060834411yescharacteristic
824C2#1060835111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13951
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#65262C2semidirect
4. C2×#65217C2semidirect
6. C5×C4⋊#95C2semidirect
7. #10602356C2semidirect
10. #10600197C2semidirect
11. #10600194C2semidirect
28. C2×#4038C4semidirect
119. C4⋊#95D5semidirect
213. C2×C4×D5C4⋊C4semidirect
222. C4⋊Dic5C22⋊C4semidirect
748. C5#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#40382
C2×#652762
C2×#652622
C2×#652172
C2×C4×#6852
C5×C4⋊#952
#106023562
#106002212
#106001972
#106001942
#139515